Properties

Label 8041.2.a.g.1.12
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.12129 q^{2} +1.35005 q^{3} +2.49986 q^{4} -1.60395 q^{5} -2.86383 q^{6} -4.53308 q^{7} -1.06034 q^{8} -1.17738 q^{9} +O(q^{10})\) \(q-2.12129 q^{2} +1.35005 q^{3} +2.49986 q^{4} -1.60395 q^{5} -2.86383 q^{6} -4.53308 q^{7} -1.06034 q^{8} -1.17738 q^{9} +3.40244 q^{10} -1.00000 q^{11} +3.37492 q^{12} +0.894770 q^{13} +9.61596 q^{14} -2.16540 q^{15} -2.75042 q^{16} +1.00000 q^{17} +2.49755 q^{18} +5.74568 q^{19} -4.00965 q^{20} -6.11986 q^{21} +2.12129 q^{22} -5.62341 q^{23} -1.43151 q^{24} -2.42735 q^{25} -1.89806 q^{26} -5.63965 q^{27} -11.3321 q^{28} -3.02816 q^{29} +4.59344 q^{30} +6.20713 q^{31} +7.95513 q^{32} -1.35005 q^{33} -2.12129 q^{34} +7.27082 q^{35} -2.94328 q^{36} +6.17491 q^{37} -12.1882 q^{38} +1.20798 q^{39} +1.70074 q^{40} +11.3513 q^{41} +12.9820 q^{42} +1.00000 q^{43} -2.49986 q^{44} +1.88845 q^{45} +11.9289 q^{46} +3.38378 q^{47} -3.71320 q^{48} +13.5488 q^{49} +5.14910 q^{50} +1.35005 q^{51} +2.23680 q^{52} +3.66404 q^{53} +11.9633 q^{54} +1.60395 q^{55} +4.80662 q^{56} +7.75693 q^{57} +6.42359 q^{58} -8.84019 q^{59} -5.41320 q^{60} -10.1961 q^{61} -13.1671 q^{62} +5.33714 q^{63} -11.3743 q^{64} -1.43516 q^{65} +2.86383 q^{66} +2.85720 q^{67} +2.49986 q^{68} -7.59185 q^{69} -15.4235 q^{70} +0.715674 q^{71} +1.24843 q^{72} +9.17039 q^{73} -13.0988 q^{74} -3.27703 q^{75} +14.3634 q^{76} +4.53308 q^{77} -2.56247 q^{78} -15.9552 q^{79} +4.41154 q^{80} -4.08165 q^{81} -24.0793 q^{82} -12.3232 q^{83} -15.2988 q^{84} -1.60395 q^{85} -2.12129 q^{86} -4.08815 q^{87} +1.06034 q^{88} +6.18834 q^{89} -4.00595 q^{90} -4.05606 q^{91} -14.0577 q^{92} +8.37991 q^{93} -7.17797 q^{94} -9.21577 q^{95} +10.7398 q^{96} +18.0060 q^{97} -28.7409 q^{98} +1.17738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12129 −1.49998 −0.749988 0.661451i \(-0.769941\pi\)
−0.749988 + 0.661451i \(0.769941\pi\)
\(3\) 1.35005 0.779449 0.389725 0.920931i \(-0.372570\pi\)
0.389725 + 0.920931i \(0.372570\pi\)
\(4\) 2.49986 1.24993
\(5\) −1.60395 −0.717308 −0.358654 0.933471i \(-0.616764\pi\)
−0.358654 + 0.933471i \(0.616764\pi\)
\(6\) −2.86383 −1.16916
\(7\) −4.53308 −1.71334 −0.856671 0.515863i \(-0.827471\pi\)
−0.856671 + 0.515863i \(0.827471\pi\)
\(8\) −1.06034 −0.374888
\(9\) −1.17738 −0.392459
\(10\) 3.40244 1.07594
\(11\) −1.00000 −0.301511
\(12\) 3.37492 0.974257
\(13\) 0.894770 0.248164 0.124082 0.992272i \(-0.460401\pi\)
0.124082 + 0.992272i \(0.460401\pi\)
\(14\) 9.61596 2.56997
\(15\) −2.16540 −0.559105
\(16\) −2.75042 −0.687606
\(17\) 1.00000 0.242536
\(18\) 2.49755 0.588679
\(19\) 5.74568 1.31815 0.659074 0.752078i \(-0.270948\pi\)
0.659074 + 0.752078i \(0.270948\pi\)
\(20\) −4.00965 −0.896584
\(21\) −6.11986 −1.33546
\(22\) 2.12129 0.452260
\(23\) −5.62341 −1.17256 −0.586281 0.810108i \(-0.699408\pi\)
−0.586281 + 0.810108i \(0.699408\pi\)
\(24\) −1.43151 −0.292206
\(25\) −2.42735 −0.485470
\(26\) −1.89806 −0.372241
\(27\) −5.63965 −1.08535
\(28\) −11.3321 −2.14156
\(29\) −3.02816 −0.562314 −0.281157 0.959662i \(-0.590718\pi\)
−0.281157 + 0.959662i \(0.590718\pi\)
\(30\) 4.59344 0.838644
\(31\) 6.20713 1.11483 0.557417 0.830233i \(-0.311793\pi\)
0.557417 + 0.830233i \(0.311793\pi\)
\(32\) 7.95513 1.40628
\(33\) −1.35005 −0.235013
\(34\) −2.12129 −0.363798
\(35\) 7.27082 1.22899
\(36\) −2.94328 −0.490546
\(37\) 6.17491 1.01515 0.507575 0.861608i \(-0.330542\pi\)
0.507575 + 0.861608i \(0.330542\pi\)
\(38\) −12.1882 −1.97719
\(39\) 1.20798 0.193432
\(40\) 1.70074 0.268910
\(41\) 11.3513 1.77277 0.886387 0.462946i \(-0.153208\pi\)
0.886387 + 0.462946i \(0.153208\pi\)
\(42\) 12.9820 2.00316
\(43\) 1.00000 0.152499
\(44\) −2.49986 −0.376868
\(45\) 1.88845 0.281514
\(46\) 11.9289 1.75881
\(47\) 3.38378 0.493575 0.246788 0.969070i \(-0.420625\pi\)
0.246788 + 0.969070i \(0.420625\pi\)
\(48\) −3.71320 −0.535954
\(49\) 13.5488 1.93554
\(50\) 5.14910 0.728193
\(51\) 1.35005 0.189044
\(52\) 2.23680 0.310188
\(53\) 3.66404 0.503294 0.251647 0.967819i \(-0.419028\pi\)
0.251647 + 0.967819i \(0.419028\pi\)
\(54\) 11.9633 1.62800
\(55\) 1.60395 0.216276
\(56\) 4.80662 0.642312
\(57\) 7.75693 1.02743
\(58\) 6.42359 0.843458
\(59\) −8.84019 −1.15089 −0.575447 0.817839i \(-0.695172\pi\)
−0.575447 + 0.817839i \(0.695172\pi\)
\(60\) −5.41320 −0.698842
\(61\) −10.1961 −1.30548 −0.652739 0.757583i \(-0.726380\pi\)
−0.652739 + 0.757583i \(0.726380\pi\)
\(62\) −13.1671 −1.67222
\(63\) 5.33714 0.672416
\(64\) −11.3743 −1.42178
\(65\) −1.43516 −0.178010
\(66\) 2.86383 0.352514
\(67\) 2.85720 0.349063 0.174532 0.984652i \(-0.444159\pi\)
0.174532 + 0.984652i \(0.444159\pi\)
\(68\) 2.49986 0.303152
\(69\) −7.59185 −0.913952
\(70\) −15.4235 −1.84346
\(71\) 0.715674 0.0849349 0.0424675 0.999098i \(-0.486478\pi\)
0.0424675 + 0.999098i \(0.486478\pi\)
\(72\) 1.24843 0.147128
\(73\) 9.17039 1.07331 0.536657 0.843801i \(-0.319687\pi\)
0.536657 + 0.843801i \(0.319687\pi\)
\(74\) −13.0988 −1.52270
\(75\) −3.27703 −0.378399
\(76\) 14.3634 1.64759
\(77\) 4.53308 0.516592
\(78\) −2.56247 −0.290143
\(79\) −15.9552 −1.79510 −0.897550 0.440912i \(-0.854655\pi\)
−0.897550 + 0.440912i \(0.854655\pi\)
\(80\) 4.41154 0.493225
\(81\) −4.08165 −0.453517
\(82\) −24.0793 −2.65912
\(83\) −12.3232 −1.35265 −0.676325 0.736603i \(-0.736429\pi\)
−0.676325 + 0.736603i \(0.736429\pi\)
\(84\) −15.2988 −1.66923
\(85\) −1.60395 −0.173973
\(86\) −2.12129 −0.228744
\(87\) −4.08815 −0.438295
\(88\) 1.06034 0.113033
\(89\) 6.18834 0.655963 0.327982 0.944684i \(-0.393632\pi\)
0.327982 + 0.944684i \(0.393632\pi\)
\(90\) −4.00595 −0.422264
\(91\) −4.05606 −0.425191
\(92\) −14.0577 −1.46562
\(93\) 8.37991 0.868956
\(94\) −7.17797 −0.740351
\(95\) −9.21577 −0.945518
\(96\) 10.7398 1.09612
\(97\) 18.0060 1.82823 0.914114 0.405457i \(-0.132888\pi\)
0.914114 + 0.405457i \(0.132888\pi\)
\(98\) −28.7409 −2.90327
\(99\) 1.17738 0.118331
\(100\) −6.06803 −0.606803
\(101\) 10.1588 1.01084 0.505421 0.862873i \(-0.331337\pi\)
0.505421 + 0.862873i \(0.331337\pi\)
\(102\) −2.86383 −0.283562
\(103\) 11.8307 1.16571 0.582857 0.812575i \(-0.301935\pi\)
0.582857 + 0.812575i \(0.301935\pi\)
\(104\) −0.948764 −0.0930340
\(105\) 9.81594 0.957938
\(106\) −7.77248 −0.754930
\(107\) 7.66772 0.741267 0.370633 0.928779i \(-0.379141\pi\)
0.370633 + 0.928779i \(0.379141\pi\)
\(108\) −14.0983 −1.35661
\(109\) 1.24366 0.119121 0.0595607 0.998225i \(-0.481030\pi\)
0.0595607 + 0.998225i \(0.481030\pi\)
\(110\) −3.40244 −0.324409
\(111\) 8.33641 0.791257
\(112\) 12.4679 1.17810
\(113\) 3.81585 0.358965 0.179483 0.983761i \(-0.442558\pi\)
0.179483 + 0.983761i \(0.442558\pi\)
\(114\) −16.4547 −1.54112
\(115\) 9.01965 0.841087
\(116\) −7.56996 −0.702853
\(117\) −1.05348 −0.0973944
\(118\) 18.7526 1.72632
\(119\) −4.53308 −0.415546
\(120\) 2.29607 0.209602
\(121\) 1.00000 0.0909091
\(122\) 21.6289 1.95819
\(123\) 15.3248 1.38179
\(124\) 15.5170 1.39346
\(125\) 11.9131 1.06554
\(126\) −11.3216 −1.00861
\(127\) −14.8361 −1.31649 −0.658243 0.752805i \(-0.728700\pi\)
−0.658243 + 0.752805i \(0.728700\pi\)
\(128\) 8.21782 0.726359
\(129\) 1.35005 0.118865
\(130\) 3.04440 0.267011
\(131\) 7.44224 0.650231 0.325116 0.945674i \(-0.394597\pi\)
0.325116 + 0.945674i \(0.394597\pi\)
\(132\) −3.37492 −0.293749
\(133\) −26.0456 −2.25844
\(134\) −6.06095 −0.523586
\(135\) 9.04571 0.778531
\(136\) −1.06034 −0.0909238
\(137\) −21.9270 −1.87335 −0.936675 0.350201i \(-0.886113\pi\)
−0.936675 + 0.350201i \(0.886113\pi\)
\(138\) 16.1045 1.37091
\(139\) 7.16231 0.607499 0.303750 0.952752i \(-0.401761\pi\)
0.303750 + 0.952752i \(0.401761\pi\)
\(140\) 18.1760 1.53615
\(141\) 4.56826 0.384717
\(142\) −1.51815 −0.127400
\(143\) −0.894770 −0.0748244
\(144\) 3.23828 0.269857
\(145\) 4.85701 0.403352
\(146\) −19.4530 −1.60994
\(147\) 18.2915 1.50866
\(148\) 15.4364 1.26886
\(149\) 8.18872 0.670846 0.335423 0.942068i \(-0.391121\pi\)
0.335423 + 0.942068i \(0.391121\pi\)
\(150\) 6.95153 0.567590
\(151\) −18.1026 −1.47317 −0.736584 0.676347i \(-0.763562\pi\)
−0.736584 + 0.676347i \(0.763562\pi\)
\(152\) −6.09240 −0.494159
\(153\) −1.17738 −0.0951853
\(154\) −9.61596 −0.774876
\(155\) −9.95592 −0.799679
\(156\) 3.01978 0.241776
\(157\) 17.1521 1.36889 0.684444 0.729065i \(-0.260045\pi\)
0.684444 + 0.729065i \(0.260045\pi\)
\(158\) 33.8456 2.69261
\(159\) 4.94662 0.392292
\(160\) −12.7596 −1.00874
\(161\) 25.4913 2.00900
\(162\) 8.65836 0.680265
\(163\) 0.737702 0.0577813 0.0288906 0.999583i \(-0.490803\pi\)
0.0288906 + 0.999583i \(0.490803\pi\)
\(164\) 28.3766 2.21584
\(165\) 2.16540 0.168576
\(166\) 26.1411 2.02894
\(167\) 4.70137 0.363803 0.181901 0.983317i \(-0.441775\pi\)
0.181901 + 0.983317i \(0.441775\pi\)
\(168\) 6.48916 0.500650
\(169\) −12.1994 −0.938414
\(170\) 3.40244 0.260955
\(171\) −6.76483 −0.517319
\(172\) 2.49986 0.190612
\(173\) −17.7514 −1.34962 −0.674809 0.737993i \(-0.735774\pi\)
−0.674809 + 0.737993i \(0.735774\pi\)
\(174\) 8.67214 0.657433
\(175\) 11.0034 0.831776
\(176\) 2.75042 0.207321
\(177\) −11.9347 −0.897064
\(178\) −13.1273 −0.983929
\(179\) 4.16077 0.310991 0.155495 0.987837i \(-0.450303\pi\)
0.155495 + 0.987837i \(0.450303\pi\)
\(180\) 4.72086 0.351872
\(181\) 17.0430 1.26680 0.633399 0.773826i \(-0.281659\pi\)
0.633399 + 0.773826i \(0.281659\pi\)
\(182\) 8.60407 0.637776
\(183\) −13.7652 −1.01755
\(184\) 5.96275 0.439580
\(185\) −9.90424 −0.728174
\(186\) −17.7762 −1.30341
\(187\) −1.00000 −0.0731272
\(188\) 8.45898 0.616934
\(189\) 25.5650 1.85958
\(190\) 19.5493 1.41825
\(191\) 9.68610 0.700861 0.350431 0.936589i \(-0.386035\pi\)
0.350431 + 0.936589i \(0.386035\pi\)
\(192\) −15.3558 −1.10821
\(193\) 6.74611 0.485596 0.242798 0.970077i \(-0.421935\pi\)
0.242798 + 0.970077i \(0.421935\pi\)
\(194\) −38.1958 −2.74230
\(195\) −1.93754 −0.138750
\(196\) 33.8701 2.41929
\(197\) −7.49347 −0.533888 −0.266944 0.963712i \(-0.586014\pi\)
−0.266944 + 0.963712i \(0.586014\pi\)
\(198\) −2.49755 −0.177493
\(199\) −16.1205 −1.14275 −0.571375 0.820689i \(-0.693590\pi\)
−0.571375 + 0.820689i \(0.693590\pi\)
\(200\) 2.57383 0.181997
\(201\) 3.85736 0.272077
\(202\) −21.5498 −1.51624
\(203\) 13.7269 0.963437
\(204\) 3.37492 0.236292
\(205\) −18.2069 −1.27162
\(206\) −25.0963 −1.74854
\(207\) 6.62087 0.460182
\(208\) −2.46100 −0.170639
\(209\) −5.74568 −0.397437
\(210\) −20.8224 −1.43688
\(211\) −19.7117 −1.35701 −0.678504 0.734597i \(-0.737371\pi\)
−0.678504 + 0.734597i \(0.737371\pi\)
\(212\) 9.15958 0.629082
\(213\) 0.966193 0.0662025
\(214\) −16.2654 −1.11188
\(215\) −1.60395 −0.109388
\(216\) 5.97997 0.406885
\(217\) −28.1374 −1.91009
\(218\) −2.63817 −0.178679
\(219\) 12.3804 0.836593
\(220\) 4.00965 0.270330
\(221\) 0.894770 0.0601887
\(222\) −17.6839 −1.18687
\(223\) 12.4905 0.836428 0.418214 0.908348i \(-0.362656\pi\)
0.418214 + 0.908348i \(0.362656\pi\)
\(224\) −36.0612 −2.40944
\(225\) 2.85790 0.190527
\(226\) −8.09452 −0.538440
\(227\) −11.3312 −0.752081 −0.376041 0.926603i \(-0.622715\pi\)
−0.376041 + 0.926603i \(0.622715\pi\)
\(228\) 19.3912 1.28421
\(229\) 0.800643 0.0529080 0.0264540 0.999650i \(-0.491578\pi\)
0.0264540 + 0.999650i \(0.491578\pi\)
\(230\) −19.1333 −1.26161
\(231\) 6.11986 0.402657
\(232\) 3.21089 0.210805
\(233\) −0.607229 −0.0397809 −0.0198904 0.999802i \(-0.506332\pi\)
−0.0198904 + 0.999802i \(0.506332\pi\)
\(234\) 2.23474 0.146089
\(235\) −5.42741 −0.354045
\(236\) −22.0992 −1.43854
\(237\) −21.5403 −1.39919
\(238\) 9.61596 0.623310
\(239\) −11.4642 −0.741556 −0.370778 0.928722i \(-0.620909\pi\)
−0.370778 + 0.928722i \(0.620909\pi\)
\(240\) 5.95578 0.384444
\(241\) −11.3964 −0.734105 −0.367053 0.930200i \(-0.619633\pi\)
−0.367053 + 0.930200i \(0.619633\pi\)
\(242\) −2.12129 −0.136361
\(243\) 11.4085 0.731858
\(244\) −25.4888 −1.63175
\(245\) −21.7316 −1.38838
\(246\) −32.5082 −2.07265
\(247\) 5.14106 0.327118
\(248\) −6.58170 −0.417938
\(249\) −16.6369 −1.05432
\(250\) −25.2711 −1.59828
\(251\) −14.0964 −0.889757 −0.444879 0.895591i \(-0.646753\pi\)
−0.444879 + 0.895591i \(0.646753\pi\)
\(252\) 13.3421 0.840473
\(253\) 5.62341 0.353541
\(254\) 31.4715 1.97470
\(255\) −2.16540 −0.135603
\(256\) 5.31617 0.332260
\(257\) −24.3319 −1.51778 −0.758890 0.651219i \(-0.774258\pi\)
−0.758890 + 0.651219i \(0.774258\pi\)
\(258\) −2.86383 −0.178295
\(259\) −27.9913 −1.73930
\(260\) −3.58771 −0.222500
\(261\) 3.56528 0.220685
\(262\) −15.7871 −0.975332
\(263\) 8.06694 0.497429 0.248714 0.968577i \(-0.419992\pi\)
0.248714 + 0.968577i \(0.419992\pi\)
\(264\) 1.43151 0.0881036
\(265\) −5.87693 −0.361017
\(266\) 55.2502 3.38761
\(267\) 8.35455 0.511290
\(268\) 7.14261 0.436304
\(269\) −5.22515 −0.318583 −0.159292 0.987232i \(-0.550921\pi\)
−0.159292 + 0.987232i \(0.550921\pi\)
\(270\) −19.1885 −1.16778
\(271\) −16.8716 −1.02488 −0.512438 0.858724i \(-0.671258\pi\)
−0.512438 + 0.858724i \(0.671258\pi\)
\(272\) −2.75042 −0.166769
\(273\) −5.47587 −0.331414
\(274\) 46.5134 2.80998
\(275\) 2.42735 0.146375
\(276\) −18.9786 −1.14238
\(277\) 21.8995 1.31581 0.657905 0.753101i \(-0.271443\pi\)
0.657905 + 0.753101i \(0.271443\pi\)
\(278\) −15.1933 −0.911235
\(279\) −7.30813 −0.437526
\(280\) −7.70958 −0.460735
\(281\) 9.16234 0.546579 0.273290 0.961932i \(-0.411888\pi\)
0.273290 + 0.961932i \(0.411888\pi\)
\(282\) −9.69059 −0.577066
\(283\) −2.28900 −0.136067 −0.0680336 0.997683i \(-0.521673\pi\)
−0.0680336 + 0.997683i \(0.521673\pi\)
\(284\) 1.78909 0.106163
\(285\) −12.4417 −0.736983
\(286\) 1.89806 0.112235
\(287\) −51.4563 −3.03737
\(288\) −9.36618 −0.551908
\(289\) 1.00000 0.0588235
\(290\) −10.3031 −0.605019
\(291\) 24.3089 1.42501
\(292\) 22.9247 1.34157
\(293\) −21.8462 −1.27627 −0.638134 0.769925i \(-0.720293\pi\)
−0.638134 + 0.769925i \(0.720293\pi\)
\(294\) −38.8015 −2.26295
\(295\) 14.1792 0.825546
\(296\) −6.54753 −0.380568
\(297\) 5.63965 0.327246
\(298\) −17.3706 −1.00625
\(299\) −5.03165 −0.290988
\(300\) −8.19212 −0.472972
\(301\) −4.53308 −0.261282
\(302\) 38.4008 2.20972
\(303\) 13.7149 0.787900
\(304\) −15.8030 −0.906367
\(305\) 16.3540 0.936429
\(306\) 2.49755 0.142776
\(307\) −27.0810 −1.54559 −0.772797 0.634653i \(-0.781143\pi\)
−0.772797 + 0.634653i \(0.781143\pi\)
\(308\) 11.3321 0.645704
\(309\) 15.9720 0.908614
\(310\) 21.1194 1.19950
\(311\) −1.20649 −0.0684139 −0.0342069 0.999415i \(-0.510891\pi\)
−0.0342069 + 0.999415i \(0.510891\pi\)
\(312\) −1.28087 −0.0725153
\(313\) 9.18903 0.519395 0.259697 0.965690i \(-0.416377\pi\)
0.259697 + 0.965690i \(0.416377\pi\)
\(314\) −36.3846 −2.05330
\(315\) −8.56050 −0.482329
\(316\) −39.8858 −2.24375
\(317\) 4.75104 0.266845 0.133422 0.991059i \(-0.457403\pi\)
0.133422 + 0.991059i \(0.457403\pi\)
\(318\) −10.4932 −0.588429
\(319\) 3.02816 0.169544
\(320\) 18.2437 1.01986
\(321\) 10.3518 0.577780
\(322\) −54.0744 −3.01345
\(323\) 5.74568 0.319698
\(324\) −10.2036 −0.566864
\(325\) −2.17192 −0.120476
\(326\) −1.56488 −0.0866706
\(327\) 1.67900 0.0928491
\(328\) −12.0363 −0.664592
\(329\) −15.3389 −0.845663
\(330\) −4.59344 −0.252861
\(331\) 27.1099 1.49009 0.745047 0.667012i \(-0.232427\pi\)
0.745047 + 0.667012i \(0.232427\pi\)
\(332\) −30.8063 −1.69072
\(333\) −7.27020 −0.398404
\(334\) −9.97295 −0.545696
\(335\) −4.58281 −0.250386
\(336\) 16.8322 0.918272
\(337\) −11.5539 −0.629380 −0.314690 0.949195i \(-0.601901\pi\)
−0.314690 + 0.949195i \(0.601901\pi\)
\(338\) 25.8784 1.40760
\(339\) 5.15158 0.279795
\(340\) −4.00965 −0.217454
\(341\) −6.20713 −0.336135
\(342\) 14.3501 0.775967
\(343\) −29.6862 −1.60290
\(344\) −1.06034 −0.0571699
\(345\) 12.1769 0.655585
\(346\) 37.6559 2.02439
\(347\) 22.9132 1.23004 0.615022 0.788510i \(-0.289147\pi\)
0.615022 + 0.788510i \(0.289147\pi\)
\(348\) −10.2198 −0.547838
\(349\) −26.0383 −1.39380 −0.696898 0.717170i \(-0.745437\pi\)
−0.696898 + 0.717170i \(0.745437\pi\)
\(350\) −23.3413 −1.24764
\(351\) −5.04619 −0.269346
\(352\) −7.95513 −0.424010
\(353\) −0.901560 −0.0479852 −0.0239926 0.999712i \(-0.507638\pi\)
−0.0239926 + 0.999712i \(0.507638\pi\)
\(354\) 25.3168 1.34558
\(355\) −1.14790 −0.0609245
\(356\) 15.4700 0.819908
\(357\) −6.11986 −0.323897
\(358\) −8.82619 −0.466479
\(359\) −17.8974 −0.944588 −0.472294 0.881441i \(-0.656574\pi\)
−0.472294 + 0.881441i \(0.656574\pi\)
\(360\) −2.00241 −0.105536
\(361\) 14.0128 0.737516
\(362\) −36.1531 −1.90017
\(363\) 1.35005 0.0708590
\(364\) −10.1396 −0.531458
\(365\) −14.7088 −0.769896
\(366\) 29.2000 1.52631
\(367\) 35.5802 1.85727 0.928635 0.370995i \(-0.120983\pi\)
0.928635 + 0.370995i \(0.120983\pi\)
\(368\) 15.4667 0.806260
\(369\) −13.3647 −0.695741
\(370\) 21.0097 1.09224
\(371\) −16.6094 −0.862315
\(372\) 20.9486 1.08613
\(373\) 35.2062 1.82291 0.911455 0.411401i \(-0.134960\pi\)
0.911455 + 0.411401i \(0.134960\pi\)
\(374\) 2.12129 0.109689
\(375\) 16.0832 0.830533
\(376\) −3.58797 −0.185036
\(377\) −2.70950 −0.139546
\(378\) −54.2306 −2.78932
\(379\) 18.9428 0.973026 0.486513 0.873673i \(-0.338269\pi\)
0.486513 + 0.873673i \(0.338269\pi\)
\(380\) −23.0381 −1.18183
\(381\) −20.0293 −1.02613
\(382\) −20.5470 −1.05128
\(383\) −4.24810 −0.217068 −0.108534 0.994093i \(-0.534616\pi\)
−0.108534 + 0.994093i \(0.534616\pi\)
\(384\) 11.0944 0.566160
\(385\) −7.27082 −0.370555
\(386\) −14.3104 −0.728382
\(387\) −1.17738 −0.0598494
\(388\) 45.0124 2.28516
\(389\) −28.5944 −1.44979 −0.724897 0.688857i \(-0.758113\pi\)
−0.724897 + 0.688857i \(0.758113\pi\)
\(390\) 4.11007 0.208122
\(391\) −5.62341 −0.284388
\(392\) −14.3664 −0.725612
\(393\) 10.0474 0.506822
\(394\) 15.8958 0.800819
\(395\) 25.5913 1.28764
\(396\) 2.94328 0.147905
\(397\) −21.7445 −1.09133 −0.545664 0.838004i \(-0.683722\pi\)
−0.545664 + 0.838004i \(0.683722\pi\)
\(398\) 34.1961 1.71410
\(399\) −35.1627 −1.76034
\(400\) 6.67624 0.333812
\(401\) −20.6726 −1.03234 −0.516169 0.856487i \(-0.672643\pi\)
−0.516169 + 0.856487i \(0.672643\pi\)
\(402\) −8.18256 −0.408109
\(403\) 5.55395 0.276662
\(404\) 25.3957 1.26348
\(405\) 6.54676 0.325311
\(406\) −29.1186 −1.44513
\(407\) −6.17491 −0.306079
\(408\) −1.43151 −0.0708705
\(409\) −14.9278 −0.738131 −0.369066 0.929403i \(-0.620322\pi\)
−0.369066 + 0.929403i \(0.620322\pi\)
\(410\) 38.6220 1.90741
\(411\) −29.6024 −1.46018
\(412\) 29.5751 1.45706
\(413\) 40.0733 1.97188
\(414\) −14.0448 −0.690262
\(415\) 19.7658 0.970267
\(416\) 7.11801 0.348989
\(417\) 9.66945 0.473515
\(418\) 12.1882 0.596146
\(419\) −20.0504 −0.979528 −0.489764 0.871855i \(-0.662917\pi\)
−0.489764 + 0.871855i \(0.662917\pi\)
\(420\) 24.5385 1.19735
\(421\) −26.6335 −1.29804 −0.649018 0.760773i \(-0.724820\pi\)
−0.649018 + 0.760773i \(0.724820\pi\)
\(422\) 41.8141 2.03548
\(423\) −3.98399 −0.193708
\(424\) −3.88514 −0.188679
\(425\) −2.42735 −0.117744
\(426\) −2.04957 −0.0993021
\(427\) 46.2197 2.23673
\(428\) 19.1682 0.926531
\(429\) −1.20798 −0.0583218
\(430\) 3.40244 0.164080
\(431\) −38.6023 −1.85941 −0.929704 0.368307i \(-0.879937\pi\)
−0.929704 + 0.368307i \(0.879937\pi\)
\(432\) 15.5114 0.746294
\(433\) 15.3579 0.738056 0.369028 0.929418i \(-0.379691\pi\)
0.369028 + 0.929418i \(0.379691\pi\)
\(434\) 59.6875 2.86509
\(435\) 6.55718 0.314393
\(436\) 3.10898 0.148893
\(437\) −32.3103 −1.54561
\(438\) −26.2625 −1.25487
\(439\) 17.0823 0.815292 0.407646 0.913140i \(-0.366350\pi\)
0.407646 + 0.913140i \(0.366350\pi\)
\(440\) −1.70074 −0.0810795
\(441\) −15.9520 −0.759620
\(442\) −1.89806 −0.0902817
\(443\) 0.699711 0.0332443 0.0166221 0.999862i \(-0.494709\pi\)
0.0166221 + 0.999862i \(0.494709\pi\)
\(444\) 20.8399 0.989016
\(445\) −9.92578 −0.470527
\(446\) −26.4960 −1.25462
\(447\) 11.0552 0.522891
\(448\) 51.5604 2.43600
\(449\) 20.5926 0.971827 0.485913 0.874007i \(-0.338487\pi\)
0.485913 + 0.874007i \(0.338487\pi\)
\(450\) −6.06244 −0.285786
\(451\) −11.3513 −0.534511
\(452\) 9.53910 0.448681
\(453\) −24.4393 −1.14826
\(454\) 24.0368 1.12810
\(455\) 6.50571 0.304992
\(456\) −8.22501 −0.385172
\(457\) 7.34008 0.343354 0.171677 0.985153i \(-0.445081\pi\)
0.171677 + 0.985153i \(0.445081\pi\)
\(458\) −1.69839 −0.0793608
\(459\) −5.63965 −0.263236
\(460\) 22.5479 1.05130
\(461\) −22.4511 −1.04565 −0.522827 0.852439i \(-0.675122\pi\)
−0.522827 + 0.852439i \(0.675122\pi\)
\(462\) −12.9820 −0.603976
\(463\) −32.2725 −1.49983 −0.749915 0.661534i \(-0.769906\pi\)
−0.749915 + 0.661534i \(0.769906\pi\)
\(464\) 8.32871 0.386651
\(465\) −13.4409 −0.623309
\(466\) 1.28811 0.0596704
\(467\) 1.93299 0.0894482 0.0447241 0.998999i \(-0.485759\pi\)
0.0447241 + 0.998999i \(0.485759\pi\)
\(468\) −2.63355 −0.121736
\(469\) −12.9519 −0.598065
\(470\) 11.5131 0.531060
\(471\) 23.1561 1.06698
\(472\) 9.37365 0.431457
\(473\) −1.00000 −0.0459800
\(474\) 45.6931 2.09875
\(475\) −13.9468 −0.639921
\(476\) −11.3321 −0.519404
\(477\) −4.31395 −0.197522
\(478\) 24.3188 1.11232
\(479\) −30.1508 −1.37763 −0.688813 0.724939i \(-0.741868\pi\)
−0.688813 + 0.724939i \(0.741868\pi\)
\(480\) −17.2261 −0.786258
\(481\) 5.52512 0.251924
\(482\) 24.1750 1.10114
\(483\) 34.4145 1.56591
\(484\) 2.49986 0.113630
\(485\) −28.8806 −1.31140
\(486\) −24.2008 −1.09777
\(487\) 21.3503 0.967473 0.483736 0.875214i \(-0.339279\pi\)
0.483736 + 0.875214i \(0.339279\pi\)
\(488\) 10.8114 0.489408
\(489\) 0.995932 0.0450376
\(490\) 46.0989 2.08253
\(491\) 4.90253 0.221248 0.110624 0.993862i \(-0.464715\pi\)
0.110624 + 0.993862i \(0.464715\pi\)
\(492\) 38.3097 1.72714
\(493\) −3.02816 −0.136381
\(494\) −10.9057 −0.490669
\(495\) −1.88845 −0.0848796
\(496\) −17.0722 −0.766566
\(497\) −3.24421 −0.145523
\(498\) 35.2917 1.58146
\(499\) 25.7276 1.15172 0.575862 0.817547i \(-0.304666\pi\)
0.575862 + 0.817547i \(0.304666\pi\)
\(500\) 29.7810 1.33185
\(501\) 6.34706 0.283566
\(502\) 29.9025 1.33462
\(503\) 2.70094 0.120429 0.0602144 0.998185i \(-0.480822\pi\)
0.0602144 + 0.998185i \(0.480822\pi\)
\(504\) −5.65921 −0.252081
\(505\) −16.2943 −0.725085
\(506\) −11.9289 −0.530302
\(507\) −16.4697 −0.731446
\(508\) −37.0880 −1.64552
\(509\) −40.2878 −1.78572 −0.892862 0.450331i \(-0.851306\pi\)
−0.892862 + 0.450331i \(0.851306\pi\)
\(510\) 4.59344 0.203401
\(511\) −41.5701 −1.83895
\(512\) −27.7128 −1.22474
\(513\) −32.4036 −1.43065
\(514\) 51.6149 2.27663
\(515\) −18.9758 −0.836175
\(516\) 3.37492 0.148573
\(517\) −3.38378 −0.148819
\(518\) 59.3777 2.60891
\(519\) −23.9653 −1.05196
\(520\) 1.52177 0.0667340
\(521\) −37.5481 −1.64501 −0.822506 0.568756i \(-0.807425\pi\)
−0.822506 + 0.568756i \(0.807425\pi\)
\(522\) −7.56298 −0.331023
\(523\) 10.6478 0.465597 0.232799 0.972525i \(-0.425212\pi\)
0.232799 + 0.972525i \(0.425212\pi\)
\(524\) 18.6045 0.812743
\(525\) 14.8550 0.648327
\(526\) −17.1123 −0.746131
\(527\) 6.20713 0.270387
\(528\) 3.71320 0.161596
\(529\) 8.62269 0.374900
\(530\) 12.4667 0.541517
\(531\) 10.4082 0.451679
\(532\) −65.1103 −2.82289
\(533\) 10.1568 0.439939
\(534\) −17.7224 −0.766923
\(535\) −12.2986 −0.531716
\(536\) −3.02962 −0.130860
\(537\) 5.61723 0.242401
\(538\) 11.0840 0.477867
\(539\) −13.5488 −0.583588
\(540\) 22.6130 0.973108
\(541\) 9.70174 0.417110 0.208555 0.978011i \(-0.433124\pi\)
0.208555 + 0.978011i \(0.433124\pi\)
\(542\) 35.7895 1.53729
\(543\) 23.0089 0.987404
\(544\) 7.95513 0.341073
\(545\) −1.99477 −0.0854467
\(546\) 11.6159 0.497114
\(547\) −14.2489 −0.609241 −0.304620 0.952474i \(-0.598530\pi\)
−0.304620 + 0.952474i \(0.598530\pi\)
\(548\) −54.8144 −2.34155
\(549\) 12.0047 0.512346
\(550\) −5.14910 −0.219559
\(551\) −17.3988 −0.741214
\(552\) 8.04998 0.342630
\(553\) 72.3262 3.07562
\(554\) −46.4550 −1.97368
\(555\) −13.3712 −0.567575
\(556\) 17.9048 0.759331
\(557\) −4.01900 −0.170291 −0.0851453 0.996369i \(-0.527135\pi\)
−0.0851453 + 0.996369i \(0.527135\pi\)
\(558\) 15.5026 0.656279
\(559\) 0.894770 0.0378447
\(560\) −19.9978 −0.845063
\(561\) −1.35005 −0.0569990
\(562\) −19.4360 −0.819856
\(563\) 24.5602 1.03509 0.517544 0.855657i \(-0.326846\pi\)
0.517544 + 0.855657i \(0.326846\pi\)
\(564\) 11.4200 0.480869
\(565\) −6.12044 −0.257489
\(566\) 4.85564 0.204098
\(567\) 18.5024 0.777030
\(568\) −0.758861 −0.0318411
\(569\) −8.81938 −0.369728 −0.184864 0.982764i \(-0.559184\pi\)
−0.184864 + 0.982764i \(0.559184\pi\)
\(570\) 26.3924 1.10546
\(571\) −36.1769 −1.51396 −0.756978 0.653440i \(-0.773325\pi\)
−0.756978 + 0.653440i \(0.773325\pi\)
\(572\) −2.23680 −0.0935252
\(573\) 13.0767 0.546286
\(574\) 109.153 4.55598
\(575\) 13.6500 0.569243
\(576\) 13.3918 0.557991
\(577\) −4.71121 −0.196130 −0.0980652 0.995180i \(-0.531265\pi\)
−0.0980652 + 0.995180i \(0.531265\pi\)
\(578\) −2.12129 −0.0882339
\(579\) 9.10756 0.378497
\(580\) 12.1418 0.504162
\(581\) 55.8622 2.31755
\(582\) −51.5661 −2.13748
\(583\) −3.66404 −0.151749
\(584\) −9.72377 −0.402373
\(585\) 1.68973 0.0698617
\(586\) 46.3420 1.91437
\(587\) 23.8581 0.984729 0.492364 0.870389i \(-0.336133\pi\)
0.492364 + 0.870389i \(0.336133\pi\)
\(588\) 45.7261 1.88571
\(589\) 35.6642 1.46952
\(590\) −30.0782 −1.23830
\(591\) −10.1165 −0.416138
\(592\) −16.9836 −0.698022
\(593\) 36.8701 1.51408 0.757038 0.653371i \(-0.226646\pi\)
0.757038 + 0.653371i \(0.226646\pi\)
\(594\) −11.9633 −0.490861
\(595\) 7.27082 0.298075
\(596\) 20.4707 0.838511
\(597\) −21.7634 −0.890715
\(598\) 10.6736 0.436475
\(599\) −3.24023 −0.132392 −0.0661962 0.997807i \(-0.521086\pi\)
−0.0661962 + 0.997807i \(0.521086\pi\)
\(600\) 3.47478 0.141857
\(601\) 19.1314 0.780386 0.390193 0.920733i \(-0.372408\pi\)
0.390193 + 0.920733i \(0.372408\pi\)
\(602\) 9.61596 0.391917
\(603\) −3.36401 −0.136993
\(604\) −45.2539 −1.84135
\(605\) −1.60395 −0.0652098
\(606\) −29.0932 −1.18183
\(607\) −20.9200 −0.849117 −0.424558 0.905401i \(-0.639571\pi\)
−0.424558 + 0.905401i \(0.639571\pi\)
\(608\) 45.7076 1.85369
\(609\) 18.5319 0.750950
\(610\) −34.6916 −1.40462
\(611\) 3.02771 0.122488
\(612\) −2.94328 −0.118975
\(613\) −34.5619 −1.39594 −0.697971 0.716126i \(-0.745913\pi\)
−0.697971 + 0.716126i \(0.745913\pi\)
\(614\) 57.4466 2.31835
\(615\) −24.5801 −0.991166
\(616\) −4.80662 −0.193664
\(617\) −19.9308 −0.802384 −0.401192 0.915994i \(-0.631404\pi\)
−0.401192 + 0.915994i \(0.631404\pi\)
\(618\) −33.8812 −1.36290
\(619\) 30.8898 1.24157 0.620784 0.783982i \(-0.286815\pi\)
0.620784 + 0.783982i \(0.286815\pi\)
\(620\) −24.8884 −0.999542
\(621\) 31.7140 1.27264
\(622\) 2.55931 0.102619
\(623\) −28.0522 −1.12389
\(624\) −3.32246 −0.133005
\(625\) −6.97123 −0.278849
\(626\) −19.4926 −0.779080
\(627\) −7.75693 −0.309782
\(628\) 42.8779 1.71101
\(629\) 6.17491 0.246210
\(630\) 18.1593 0.723483
\(631\) 8.18195 0.325718 0.162859 0.986649i \(-0.447928\pi\)
0.162859 + 0.986649i \(0.447928\pi\)
\(632\) 16.9180 0.672962
\(633\) −26.6117 −1.05772
\(634\) −10.0783 −0.400261
\(635\) 23.7963 0.944326
\(636\) 12.3658 0.490338
\(637\) 12.1230 0.480332
\(638\) −6.42359 −0.254312
\(639\) −0.842619 −0.0333335
\(640\) −13.1810 −0.521023
\(641\) 45.0270 1.77846 0.889229 0.457462i \(-0.151241\pi\)
0.889229 + 0.457462i \(0.151241\pi\)
\(642\) −21.9591 −0.866656
\(643\) 3.21875 0.126935 0.0634675 0.997984i \(-0.479784\pi\)
0.0634675 + 0.997984i \(0.479784\pi\)
\(644\) 63.7247 2.51111
\(645\) −2.16540 −0.0852627
\(646\) −12.1882 −0.479539
\(647\) −29.7823 −1.17086 −0.585432 0.810721i \(-0.699075\pi\)
−0.585432 + 0.810721i \(0.699075\pi\)
\(648\) 4.32796 0.170018
\(649\) 8.84019 0.347008
\(650\) 4.60726 0.180712
\(651\) −37.9868 −1.48882
\(652\) 1.84415 0.0722226
\(653\) 16.2837 0.637232 0.318616 0.947884i \(-0.396782\pi\)
0.318616 + 0.947884i \(0.396782\pi\)
\(654\) −3.56165 −0.139271
\(655\) −11.9370 −0.466416
\(656\) −31.2208 −1.21897
\(657\) −10.7970 −0.421231
\(658\) 32.5383 1.26848
\(659\) −1.47647 −0.0575149 −0.0287575 0.999586i \(-0.509155\pi\)
−0.0287575 + 0.999586i \(0.509155\pi\)
\(660\) 5.41320 0.210709
\(661\) 29.7457 1.15697 0.578487 0.815692i \(-0.303643\pi\)
0.578487 + 0.815692i \(0.303643\pi\)
\(662\) −57.5078 −2.23511
\(663\) 1.20798 0.0469141
\(664\) 13.0669 0.507093
\(665\) 41.7758 1.62000
\(666\) 15.4222 0.597597
\(667\) 17.0285 0.659348
\(668\) 11.7528 0.454728
\(669\) 16.8628 0.651953
\(670\) 9.72146 0.375573
\(671\) 10.1961 0.393616
\(672\) −48.6843 −1.87804
\(673\) 6.11258 0.235623 0.117811 0.993036i \(-0.462412\pi\)
0.117811 + 0.993036i \(0.462412\pi\)
\(674\) 24.5091 0.944055
\(675\) 13.6894 0.526905
\(676\) −30.4967 −1.17295
\(677\) −40.0929 −1.54090 −0.770448 0.637503i \(-0.779968\pi\)
−0.770448 + 0.637503i \(0.779968\pi\)
\(678\) −10.9280 −0.419686
\(679\) −81.6224 −3.13238
\(680\) 1.70074 0.0652203
\(681\) −15.2977 −0.586209
\(682\) 13.1671 0.504195
\(683\) 24.9039 0.952921 0.476461 0.879196i \(-0.341919\pi\)
0.476461 + 0.879196i \(0.341919\pi\)
\(684\) −16.9111 −0.646613
\(685\) 35.1698 1.34377
\(686\) 62.9729 2.40431
\(687\) 1.08091 0.0412391
\(688\) −2.75042 −0.104859
\(689\) 3.27847 0.124900
\(690\) −25.8308 −0.983362
\(691\) 16.5740 0.630504 0.315252 0.949008i \(-0.397911\pi\)
0.315252 + 0.949008i \(0.397911\pi\)
\(692\) −44.3761 −1.68693
\(693\) −5.33714 −0.202741
\(694\) −48.6054 −1.84504
\(695\) −11.4880 −0.435764
\(696\) 4.33484 0.164312
\(697\) 11.3513 0.429961
\(698\) 55.2346 2.09066
\(699\) −0.819787 −0.0310072
\(700\) 27.5068 1.03966
\(701\) −11.7750 −0.444737 −0.222369 0.974963i \(-0.571379\pi\)
−0.222369 + 0.974963i \(0.571379\pi\)
\(702\) 10.7044 0.404012
\(703\) 35.4790 1.33812
\(704\) 11.3743 0.428684
\(705\) −7.32725 −0.275960
\(706\) 1.91247 0.0719766
\(707\) −46.0508 −1.73192
\(708\) −29.8350 −1.12127
\(709\) 30.7825 1.15606 0.578031 0.816015i \(-0.303821\pi\)
0.578031 + 0.816015i \(0.303821\pi\)
\(710\) 2.43504 0.0913853
\(711\) 18.7853 0.704503
\(712\) −6.56177 −0.245913
\(713\) −34.9052 −1.30721
\(714\) 12.9820 0.485838
\(715\) 1.43516 0.0536721
\(716\) 10.4013 0.388716
\(717\) −15.4772 −0.578005
\(718\) 37.9655 1.41686
\(719\) 6.01929 0.224482 0.112241 0.993681i \(-0.464197\pi\)
0.112241 + 0.993681i \(0.464197\pi\)
\(720\) −5.19404 −0.193571
\(721\) −53.6295 −1.99727
\(722\) −29.7252 −1.10626
\(723\) −15.3856 −0.572198
\(724\) 42.6051 1.58341
\(725\) 7.35039 0.272987
\(726\) −2.86383 −0.106287
\(727\) −42.3690 −1.57138 −0.785690 0.618621i \(-0.787692\pi\)
−0.785690 + 0.618621i \(0.787692\pi\)
\(728\) 4.30082 0.159399
\(729\) 27.6470 1.02396
\(730\) 31.2017 1.15483
\(731\) 1.00000 0.0369863
\(732\) −34.4111 −1.27187
\(733\) 11.1677 0.412487 0.206243 0.978501i \(-0.433876\pi\)
0.206243 + 0.978501i \(0.433876\pi\)
\(734\) −75.4757 −2.78586
\(735\) −29.3386 −1.08217
\(736\) −44.7349 −1.64895
\(737\) −2.85720 −0.105246
\(738\) 28.3505 1.04359
\(739\) 27.3680 1.00675 0.503374 0.864069i \(-0.332092\pi\)
0.503374 + 0.864069i \(0.332092\pi\)
\(740\) −24.7592 −0.910167
\(741\) 6.94066 0.254972
\(742\) 35.2332 1.29345
\(743\) −35.1915 −1.29105 −0.645525 0.763739i \(-0.723361\pi\)
−0.645525 + 0.763739i \(0.723361\pi\)
\(744\) −8.88559 −0.325762
\(745\) −13.1343 −0.481203
\(746\) −74.6825 −2.73432
\(747\) 14.5091 0.530860
\(748\) −2.49986 −0.0914039
\(749\) −34.7584 −1.27004
\(750\) −34.1171 −1.24578
\(751\) −17.4790 −0.637819 −0.318910 0.947785i \(-0.603317\pi\)
−0.318910 + 0.947785i \(0.603317\pi\)
\(752\) −9.30683 −0.339385
\(753\) −19.0308 −0.693521
\(754\) 5.74763 0.209316
\(755\) 29.0356 1.05671
\(756\) 63.9088 2.32434
\(757\) −37.1050 −1.34860 −0.674302 0.738456i \(-0.735555\pi\)
−0.674302 + 0.738456i \(0.735555\pi\)
\(758\) −40.1831 −1.45952
\(759\) 7.59185 0.275567
\(760\) 9.77189 0.354464
\(761\) −22.6338 −0.820476 −0.410238 0.911978i \(-0.634554\pi\)
−0.410238 + 0.911978i \(0.634554\pi\)
\(762\) 42.4880 1.53918
\(763\) −5.63762 −0.204096
\(764\) 24.2139 0.876027
\(765\) 1.88845 0.0682771
\(766\) 9.01144 0.325596
\(767\) −7.90994 −0.285611
\(768\) 7.17707 0.258980
\(769\) 12.5856 0.453848 0.226924 0.973912i \(-0.427133\pi\)
0.226924 + 0.973912i \(0.427133\pi\)
\(770\) 15.4235 0.555824
\(771\) −32.8491 −1.18303
\(772\) 16.8643 0.606960
\(773\) 16.3638 0.588566 0.294283 0.955718i \(-0.404919\pi\)
0.294283 + 0.955718i \(0.404919\pi\)
\(774\) 2.49755 0.0897727
\(775\) −15.0669 −0.541218
\(776\) −19.0925 −0.685382
\(777\) −37.7896 −1.35569
\(778\) 60.6570 2.17466
\(779\) 65.2208 2.33678
\(780\) −4.84357 −0.173428
\(781\) −0.715674 −0.0256088
\(782\) 11.9289 0.426575
\(783\) 17.0777 0.610308
\(784\) −37.2649 −1.33089
\(785\) −27.5111 −0.981914
\(786\) −21.3133 −0.760222
\(787\) 1.59031 0.0566884 0.0283442 0.999598i \(-0.490977\pi\)
0.0283442 + 0.999598i \(0.490977\pi\)
\(788\) −18.7326 −0.667322
\(789\) 10.8907 0.387720
\(790\) −54.2865 −1.93143
\(791\) −17.2976 −0.615031
\(792\) −1.24843 −0.0443609
\(793\) −9.12317 −0.323973
\(794\) 46.1264 1.63697
\(795\) −7.93412 −0.281394
\(796\) −40.2989 −1.42836
\(797\) −23.4033 −0.828987 −0.414494 0.910052i \(-0.636041\pi\)
−0.414494 + 0.910052i \(0.636041\pi\)
\(798\) 74.5903 2.64047
\(799\) 3.38378 0.119710
\(800\) −19.3099 −0.682707
\(801\) −7.28601 −0.257439
\(802\) 43.8525 1.54848
\(803\) −9.17039 −0.323616
\(804\) 9.64285 0.340077
\(805\) −40.8868 −1.44107
\(806\) −11.7815 −0.414987
\(807\) −7.05419 −0.248319
\(808\) −10.7719 −0.378953
\(809\) 34.6676 1.21885 0.609424 0.792844i \(-0.291401\pi\)
0.609424 + 0.792844i \(0.291401\pi\)
\(810\) −13.8876 −0.487959
\(811\) −25.8975 −0.909384 −0.454692 0.890649i \(-0.650251\pi\)
−0.454692 + 0.890649i \(0.650251\pi\)
\(812\) 34.3152 1.20423
\(813\) −22.7774 −0.798839
\(814\) 13.0988 0.459111
\(815\) −1.18324 −0.0414470
\(816\) −3.71320 −0.129988
\(817\) 5.74568 0.201016
\(818\) 31.6661 1.10718
\(819\) 4.77551 0.166870
\(820\) −45.5146 −1.58944
\(821\) 47.8939 1.67151 0.835755 0.549103i \(-0.185030\pi\)
0.835755 + 0.549103i \(0.185030\pi\)
\(822\) 62.7953 2.19024
\(823\) −21.5145 −0.749949 −0.374975 0.927035i \(-0.622349\pi\)
−0.374975 + 0.927035i \(0.622349\pi\)
\(824\) −12.5446 −0.437012
\(825\) 3.27703 0.114092
\(826\) −85.0069 −2.95777
\(827\) −50.8283 −1.76747 −0.883737 0.467983i \(-0.844981\pi\)
−0.883737 + 0.467983i \(0.844981\pi\)
\(828\) 16.5512 0.575195
\(829\) −1.79519 −0.0623494 −0.0311747 0.999514i \(-0.509925\pi\)
−0.0311747 + 0.999514i \(0.509925\pi\)
\(830\) −41.9290 −1.45538
\(831\) 29.5653 1.02561
\(832\) −10.1773 −0.352836
\(833\) 13.5488 0.469438
\(834\) −20.5117 −0.710261
\(835\) −7.54075 −0.260958
\(836\) −14.3634 −0.496768
\(837\) −35.0060 −1.20999
\(838\) 42.5328 1.46927
\(839\) −52.1184 −1.79933 −0.899664 0.436582i \(-0.856189\pi\)
−0.899664 + 0.436582i \(0.856189\pi\)
\(840\) −10.4083 −0.359120
\(841\) −19.8303 −0.683803
\(842\) 56.4972 1.94702
\(843\) 12.3696 0.426031
\(844\) −49.2764 −1.69616
\(845\) 19.5672 0.673132
\(846\) 8.45118 0.290558
\(847\) −4.53308 −0.155758
\(848\) −10.0777 −0.346068
\(849\) −3.09026 −0.106057
\(850\) 5.14910 0.176613
\(851\) −34.7240 −1.19032
\(852\) 2.41535 0.0827484
\(853\) −14.2140 −0.486678 −0.243339 0.969941i \(-0.578243\pi\)
−0.243339 + 0.969941i \(0.578243\pi\)
\(854\) −98.0453 −3.35504
\(855\) 10.8504 0.371077
\(856\) −8.13042 −0.277892
\(857\) −8.13322 −0.277825 −0.138913 0.990305i \(-0.544361\pi\)
−0.138913 + 0.990305i \(0.544361\pi\)
\(858\) 2.56247 0.0874814
\(859\) 14.3524 0.489698 0.244849 0.969561i \(-0.421262\pi\)
0.244849 + 0.969561i \(0.421262\pi\)
\(860\) −4.00965 −0.136728
\(861\) −69.4683 −2.36747
\(862\) 81.8866 2.78907
\(863\) 55.1946 1.87885 0.939423 0.342760i \(-0.111362\pi\)
0.939423 + 0.342760i \(0.111362\pi\)
\(864\) −44.8641 −1.52631
\(865\) 28.4724 0.968091
\(866\) −32.5786 −1.10707
\(867\) 1.35005 0.0458500
\(868\) −70.3395 −2.38748
\(869\) 15.9552 0.541243
\(870\) −13.9097 −0.471582
\(871\) 2.55654 0.0866251
\(872\) −1.31871 −0.0446572
\(873\) −21.1998 −0.717505
\(874\) 68.5394 2.31838
\(875\) −54.0029 −1.82563
\(876\) 30.9494 1.04568
\(877\) 53.2848 1.79930 0.899650 0.436611i \(-0.143822\pi\)
0.899650 + 0.436611i \(0.143822\pi\)
\(878\) −36.2364 −1.22292
\(879\) −29.4933 −0.994786
\(880\) −4.41154 −0.148713
\(881\) −9.74148 −0.328199 −0.164099 0.986444i \(-0.552472\pi\)
−0.164099 + 0.986444i \(0.552472\pi\)
\(882\) 33.8388 1.13941
\(883\) −1.20413 −0.0405222 −0.0202611 0.999795i \(-0.506450\pi\)
−0.0202611 + 0.999795i \(0.506450\pi\)
\(884\) 2.23680 0.0752317
\(885\) 19.1426 0.643471
\(886\) −1.48429 −0.0498656
\(887\) −27.4999 −0.923356 −0.461678 0.887048i \(-0.652752\pi\)
−0.461678 + 0.887048i \(0.652752\pi\)
\(888\) −8.83947 −0.296633
\(889\) 67.2530 2.25559
\(890\) 21.0554 0.705780
\(891\) 4.08165 0.136741
\(892\) 31.2246 1.04548
\(893\) 19.4421 0.650606
\(894\) −23.4512 −0.784324
\(895\) −6.67366 −0.223076
\(896\) −37.2520 −1.24450
\(897\) −6.79296 −0.226810
\(898\) −43.6829 −1.45772
\(899\) −18.7962 −0.626887
\(900\) 7.14436 0.238145
\(901\) 3.66404 0.122067
\(902\) 24.0793 0.801754
\(903\) −6.11986 −0.203656
\(904\) −4.04612 −0.134572
\(905\) −27.3361 −0.908683
\(906\) 51.8428 1.72236
\(907\) 5.75278 0.191018 0.0955089 0.995429i \(-0.469552\pi\)
0.0955089 + 0.995429i \(0.469552\pi\)
\(908\) −28.3265 −0.940049
\(909\) −11.9608 −0.396714
\(910\) −13.8005 −0.457482
\(911\) −25.8306 −0.855806 −0.427903 0.903825i \(-0.640748\pi\)
−0.427903 + 0.903825i \(0.640748\pi\)
\(912\) −21.3348 −0.706467
\(913\) 12.3232 0.407840
\(914\) −15.5704 −0.515023
\(915\) 22.0787 0.729899
\(916\) 2.00150 0.0661313
\(917\) −33.7362 −1.11407
\(918\) 11.9633 0.394848
\(919\) 59.1823 1.95224 0.976122 0.217224i \(-0.0697003\pi\)
0.976122 + 0.217224i \(0.0697003\pi\)
\(920\) −9.56394 −0.315314
\(921\) −36.5606 −1.20471
\(922\) 47.6253 1.56846
\(923\) 0.640364 0.0210778
\(924\) 15.2988 0.503293
\(925\) −14.9887 −0.492824
\(926\) 68.4592 2.24971
\(927\) −13.9292 −0.457495
\(928\) −24.0894 −0.790772
\(929\) 53.6562 1.76040 0.880201 0.474602i \(-0.157408\pi\)
0.880201 + 0.474602i \(0.157408\pi\)
\(930\) 28.5121 0.934949
\(931\) 77.8469 2.55133
\(932\) −1.51799 −0.0497233
\(933\) −1.62882 −0.0533251
\(934\) −4.10043 −0.134170
\(935\) 1.60395 0.0524547
\(936\) 1.11705 0.0365120
\(937\) 21.5314 0.703401 0.351701 0.936113i \(-0.385604\pi\)
0.351701 + 0.936113i \(0.385604\pi\)
\(938\) 27.4748 0.897083
\(939\) 12.4056 0.404842
\(940\) −13.5678 −0.442532
\(941\) −7.49397 −0.244296 −0.122148 0.992512i \(-0.538978\pi\)
−0.122148 + 0.992512i \(0.538978\pi\)
\(942\) −49.1208 −1.60044
\(943\) −63.8329 −2.07869
\(944\) 24.3143 0.791362
\(945\) −41.0049 −1.33389
\(946\) 2.12129 0.0689690
\(947\) −61.1766 −1.98797 −0.993987 0.109500i \(-0.965075\pi\)
−0.993987 + 0.109500i \(0.965075\pi\)
\(948\) −53.8476 −1.74889
\(949\) 8.20539 0.266358
\(950\) 29.5851 0.959867
\(951\) 6.41411 0.207992
\(952\) 4.80662 0.155784
\(953\) −34.1480 −1.10616 −0.553082 0.833127i \(-0.686548\pi\)
−0.553082 + 0.833127i \(0.686548\pi\)
\(954\) 9.15113 0.296279
\(955\) −15.5360 −0.502733
\(956\) −28.6588 −0.926892
\(957\) 4.08815 0.132151
\(958\) 63.9585 2.06641
\(959\) 99.3967 3.20969
\(960\) 24.6299 0.794925
\(961\) 7.52848 0.242854
\(962\) −11.7204 −0.377880
\(963\) −9.02780 −0.290917
\(964\) −28.4893 −0.917580
\(965\) −10.8204 −0.348321
\(966\) −73.0030 −2.34883
\(967\) −21.5863 −0.694169 −0.347084 0.937834i \(-0.612828\pi\)
−0.347084 + 0.937834i \(0.612828\pi\)
\(968\) −1.06034 −0.0340808
\(969\) 7.75693 0.249188
\(970\) 61.2641 1.96707
\(971\) −21.9094 −0.703106 −0.351553 0.936168i \(-0.614346\pi\)
−0.351553 + 0.936168i \(0.614346\pi\)
\(972\) 28.5197 0.914770
\(973\) −32.4673 −1.04085
\(974\) −45.2900 −1.45119
\(975\) −2.93219 −0.0939052
\(976\) 28.0436 0.897654
\(977\) 6.59345 0.210943 0.105472 0.994422i \(-0.466365\pi\)
0.105472 + 0.994422i \(0.466365\pi\)
\(978\) −2.11266 −0.0675553
\(979\) −6.18834 −0.197780
\(980\) −54.3258 −1.73537
\(981\) −1.46426 −0.0467503
\(982\) −10.3997 −0.331867
\(983\) −17.2978 −0.551713 −0.275857 0.961199i \(-0.588962\pi\)
−0.275857 + 0.961199i \(0.588962\pi\)
\(984\) −16.2495 −0.518016
\(985\) 12.0191 0.382962
\(986\) 6.42359 0.204569
\(987\) −20.7083 −0.659152
\(988\) 12.8519 0.408874
\(989\) −5.62341 −0.178814
\(990\) 4.00595 0.127317
\(991\) 34.2575 1.08823 0.544113 0.839012i \(-0.316866\pi\)
0.544113 + 0.839012i \(0.316866\pi\)
\(992\) 49.3785 1.56777
\(993\) 36.5996 1.16145
\(994\) 6.88189 0.218280
\(995\) 25.8564 0.819703
\(996\) −41.5900 −1.31783
\(997\) 8.48372 0.268682 0.134341 0.990935i \(-0.457108\pi\)
0.134341 + 0.990935i \(0.457108\pi\)
\(998\) −54.5756 −1.72756
\(999\) −34.8243 −1.10179
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 \(a_p\))