Properties

Label 5077.2.a.c.1.4
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 1.4
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68288 q^{2} +3.14006 q^{3} +5.19783 q^{4} +4.08506 q^{5} -8.42439 q^{6} -2.34598 q^{7} -8.57939 q^{8} +6.85996 q^{9} +O(q^{10})\) \(q-2.68288 q^{2} +3.14006 q^{3} +5.19783 q^{4} +4.08506 q^{5} -8.42439 q^{6} -2.34598 q^{7} -8.57939 q^{8} +6.85996 q^{9} -10.9597 q^{10} +1.39341 q^{11} +16.3215 q^{12} +2.23756 q^{13} +6.29397 q^{14} +12.8273 q^{15} +12.6218 q^{16} -2.46873 q^{17} -18.4044 q^{18} -2.12049 q^{19} +21.2334 q^{20} -7.36651 q^{21} -3.73833 q^{22} +1.69194 q^{23} -26.9398 q^{24} +11.6877 q^{25} -6.00310 q^{26} +12.1205 q^{27} -12.1940 q^{28} +3.37309 q^{29} -34.4141 q^{30} +1.22846 q^{31} -16.7039 q^{32} +4.37537 q^{33} +6.62330 q^{34} -9.58346 q^{35} +35.6569 q^{36} +3.30712 q^{37} +5.68900 q^{38} +7.02607 q^{39} -35.0473 q^{40} +8.05246 q^{41} +19.7634 q^{42} +10.9608 q^{43} +7.24268 q^{44} +28.0233 q^{45} -4.53926 q^{46} +5.87362 q^{47} +39.6331 q^{48} -1.49638 q^{49} -31.3566 q^{50} -7.75196 q^{51} +11.6305 q^{52} -8.03095 q^{53} -32.5178 q^{54} +5.69214 q^{55} +20.1271 q^{56} -6.65845 q^{57} -9.04958 q^{58} -14.8996 q^{59} +66.6742 q^{60} -4.83726 q^{61} -3.29582 q^{62} -16.0933 q^{63} +19.5710 q^{64} +9.14056 q^{65} -11.7386 q^{66} +0.756524 q^{67} -12.8320 q^{68} +5.31278 q^{69} +25.7112 q^{70} +8.63596 q^{71} -58.8543 q^{72} -1.98826 q^{73} -8.87259 q^{74} +36.7000 q^{75} -11.0219 q^{76} -3.26890 q^{77} -18.8501 q^{78} -16.1028 q^{79} +51.5607 q^{80} +17.4792 q^{81} -21.6038 q^{82} +5.37002 q^{83} -38.2899 q^{84} -10.0849 q^{85} -29.4066 q^{86} +10.5917 q^{87} -11.9546 q^{88} +0.688158 q^{89} -75.1832 q^{90} -5.24927 q^{91} +8.79440 q^{92} +3.85745 q^{93} -15.7582 q^{94} -8.66230 q^{95} -52.4512 q^{96} -15.9906 q^{97} +4.01461 q^{98} +9.55871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68288 −1.89708 −0.948540 0.316656i \(-0.897440\pi\)
−0.948540 + 0.316656i \(0.897440\pi\)
\(3\) 3.14006 1.81291 0.906457 0.422299i \(-0.138777\pi\)
0.906457 + 0.422299i \(0.138777\pi\)
\(4\) 5.19783 2.59892
\(5\) 4.08506 1.82689 0.913446 0.406959i \(-0.133411\pi\)
0.913446 + 0.406959i \(0.133411\pi\)
\(6\) −8.42439 −3.43924
\(7\) −2.34598 −0.886697 −0.443348 0.896349i \(-0.646210\pi\)
−0.443348 + 0.896349i \(0.646210\pi\)
\(8\) −8.57939 −3.03327
\(9\) 6.85996 2.28665
\(10\) −10.9597 −3.46576
\(11\) 1.39341 0.420127 0.210064 0.977688i \(-0.432633\pi\)
0.210064 + 0.977688i \(0.432633\pi\)
\(12\) 16.3215 4.71161
\(13\) 2.23756 0.620588 0.310294 0.950641i \(-0.399573\pi\)
0.310294 + 0.950641i \(0.399573\pi\)
\(14\) 6.29397 1.68214
\(15\) 12.8273 3.31200
\(16\) 12.6218 3.15544
\(17\) −2.46873 −0.598755 −0.299378 0.954135i \(-0.596779\pi\)
−0.299378 + 0.954135i \(0.596779\pi\)
\(18\) −18.4044 −4.33797
\(19\) −2.12049 −0.486473 −0.243236 0.969967i \(-0.578209\pi\)
−0.243236 + 0.969967i \(0.578209\pi\)
\(20\) 21.2334 4.74794
\(21\) −7.36651 −1.60750
\(22\) −3.73833 −0.797016
\(23\) 1.69194 0.352793 0.176397 0.984319i \(-0.443556\pi\)
0.176397 + 0.984319i \(0.443556\pi\)
\(24\) −26.9398 −5.49906
\(25\) 11.6877 2.33754
\(26\) −6.00310 −1.17731
\(27\) 12.1205 2.33259
\(28\) −12.1940 −2.30445
\(29\) 3.37309 0.626366 0.313183 0.949693i \(-0.398605\pi\)
0.313183 + 0.949693i \(0.398605\pi\)
\(30\) −34.4141 −6.28313
\(31\) 1.22846 0.220639 0.110319 0.993896i \(-0.464813\pi\)
0.110319 + 0.993896i \(0.464813\pi\)
\(32\) −16.7039 −2.95286
\(33\) 4.37537 0.761655
\(34\) 6.62330 1.13589
\(35\) −9.58346 −1.61990
\(36\) 35.6569 5.94282
\(37\) 3.30712 0.543687 0.271843 0.962342i \(-0.412367\pi\)
0.271843 + 0.962342i \(0.412367\pi\)
\(38\) 5.68900 0.922878
\(39\) 7.02607 1.12507
\(40\) −35.0473 −5.54146
\(41\) 8.05246 1.25758 0.628791 0.777574i \(-0.283550\pi\)
0.628791 + 0.777574i \(0.283550\pi\)
\(42\) 19.7634 3.04956
\(43\) 10.9608 1.67151 0.835756 0.549101i \(-0.185030\pi\)
0.835756 + 0.549101i \(0.185030\pi\)
\(44\) 7.24268 1.09188
\(45\) 28.0233 4.17747
\(46\) −4.53926 −0.669277
\(47\) 5.87362 0.856756 0.428378 0.903600i \(-0.359085\pi\)
0.428378 + 0.903600i \(0.359085\pi\)
\(48\) 39.6331 5.72055
\(49\) −1.49638 −0.213769
\(50\) −31.3566 −4.43450
\(51\) −7.75196 −1.08549
\(52\) 11.6305 1.61285
\(53\) −8.03095 −1.10314 −0.551568 0.834130i \(-0.685970\pi\)
−0.551568 + 0.834130i \(0.685970\pi\)
\(54\) −32.5178 −4.42512
\(55\) 5.69214 0.767528
\(56\) 20.1271 2.68959
\(57\) −6.65845 −0.881933
\(58\) −9.04958 −1.18827
\(59\) −14.8996 −1.93977 −0.969883 0.243571i \(-0.921681\pi\)
−0.969883 + 0.243571i \(0.921681\pi\)
\(60\) 66.6742 8.60760
\(61\) −4.83726 −0.619347 −0.309674 0.950843i \(-0.600220\pi\)
−0.309674 + 0.950843i \(0.600220\pi\)
\(62\) −3.29582 −0.418569
\(63\) −16.0933 −2.02757
\(64\) 19.5710 2.44637
\(65\) 9.14056 1.13375
\(66\) −11.7386 −1.44492
\(67\) 0.756524 0.0924241 0.0462121 0.998932i \(-0.485285\pi\)
0.0462121 + 0.998932i \(0.485285\pi\)
\(68\) −12.8320 −1.55611
\(69\) 5.31278 0.639583
\(70\) 25.7112 3.07308
\(71\) 8.63596 1.02490 0.512450 0.858717i \(-0.328738\pi\)
0.512450 + 0.858717i \(0.328738\pi\)
\(72\) −58.8543 −6.93604
\(73\) −1.98826 −0.232708 −0.116354 0.993208i \(-0.537121\pi\)
−0.116354 + 0.993208i \(0.537121\pi\)
\(74\) −8.87259 −1.03142
\(75\) 36.7000 4.23775
\(76\) −11.0219 −1.26430
\(77\) −3.26890 −0.372526
\(78\) −18.8501 −2.13435
\(79\) −16.1028 −1.81170 −0.905852 0.423594i \(-0.860768\pi\)
−0.905852 + 0.423594i \(0.860768\pi\)
\(80\) 51.5607 5.76466
\(81\) 17.4792 1.94213
\(82\) −21.6038 −2.38574
\(83\) 5.37002 0.589436 0.294718 0.955584i \(-0.404774\pi\)
0.294718 + 0.955584i \(0.404774\pi\)
\(84\) −38.2899 −4.17777
\(85\) −10.0849 −1.09386
\(86\) −29.4066 −3.17099
\(87\) 10.5917 1.13555
\(88\) −11.9546 −1.27436
\(89\) 0.688158 0.0729446 0.0364723 0.999335i \(-0.488388\pi\)
0.0364723 + 0.999335i \(0.488388\pi\)
\(90\) −75.1832 −7.92500
\(91\) −5.24927 −0.550273
\(92\) 8.79440 0.916879
\(93\) 3.85745 0.399998
\(94\) −15.7582 −1.62534
\(95\) −8.66230 −0.888734
\(96\) −52.4512 −5.35328
\(97\) −15.9906 −1.62360 −0.811799 0.583937i \(-0.801512\pi\)
−0.811799 + 0.583937i \(0.801512\pi\)
\(98\) 4.01461 0.405537
\(99\) 9.55871 0.960686
\(100\) 60.7506 6.07506
\(101\) −17.6389 −1.75514 −0.877568 0.479452i \(-0.840835\pi\)
−0.877568 + 0.479452i \(0.840835\pi\)
\(102\) 20.7976 2.05926
\(103\) 0.857510 0.0844929 0.0422465 0.999107i \(-0.486549\pi\)
0.0422465 + 0.999107i \(0.486549\pi\)
\(104\) −19.1969 −1.88241
\(105\) −30.0926 −2.93674
\(106\) 21.5460 2.09274
\(107\) −18.3807 −1.77693 −0.888467 0.458941i \(-0.848229\pi\)
−0.888467 + 0.458941i \(0.848229\pi\)
\(108\) 63.0003 6.06221
\(109\) 4.42303 0.423650 0.211825 0.977308i \(-0.432059\pi\)
0.211825 + 0.977308i \(0.432059\pi\)
\(110\) −15.2713 −1.45606
\(111\) 10.3845 0.985657
\(112\) −29.6104 −2.79792
\(113\) −9.98876 −0.939664 −0.469832 0.882756i \(-0.655685\pi\)
−0.469832 + 0.882756i \(0.655685\pi\)
\(114\) 17.8638 1.67310
\(115\) 6.91165 0.644515
\(116\) 17.5327 1.62787
\(117\) 15.3496 1.41907
\(118\) 39.9739 3.67989
\(119\) 5.79159 0.530914
\(120\) −110.050 −10.0462
\(121\) −9.05842 −0.823493
\(122\) 12.9778 1.17495
\(123\) 25.2852 2.27989
\(124\) 6.38534 0.573421
\(125\) 27.3196 2.44354
\(126\) 43.1764 3.84646
\(127\) 11.1459 0.989037 0.494519 0.869167i \(-0.335344\pi\)
0.494519 + 0.869167i \(0.335344\pi\)
\(128\) −19.0987 −1.68810
\(129\) 34.4177 3.03031
\(130\) −24.5230 −2.15081
\(131\) 8.90629 0.778146 0.389073 0.921207i \(-0.372795\pi\)
0.389073 + 0.921207i \(0.372795\pi\)
\(132\) 22.7424 1.97948
\(133\) 4.97461 0.431354
\(134\) −2.02966 −0.175336
\(135\) 49.5130 4.26140
\(136\) 21.1802 1.81619
\(137\) 19.2386 1.64367 0.821834 0.569727i \(-0.192951\pi\)
0.821834 + 0.569727i \(0.192951\pi\)
\(138\) −14.2535 −1.21334
\(139\) −13.2315 −1.12228 −0.561142 0.827720i \(-0.689638\pi\)
−0.561142 + 0.827720i \(0.689638\pi\)
\(140\) −49.8132 −4.20998
\(141\) 18.4435 1.55322
\(142\) −23.1692 −1.94432
\(143\) 3.11783 0.260726
\(144\) 86.5849 7.21541
\(145\) 13.7792 1.14430
\(146\) 5.33426 0.441466
\(147\) −4.69873 −0.387545
\(148\) 17.1898 1.41300
\(149\) −20.4829 −1.67803 −0.839013 0.544112i \(-0.816867\pi\)
−0.839013 + 0.544112i \(0.816867\pi\)
\(150\) −98.4616 −8.03936
\(151\) 22.0250 1.79237 0.896183 0.443684i \(-0.146329\pi\)
0.896183 + 0.443684i \(0.146329\pi\)
\(152\) 18.1925 1.47560
\(153\) −16.9354 −1.36915
\(154\) 8.77005 0.706711
\(155\) 5.01834 0.403083
\(156\) 36.5203 2.92397
\(157\) −6.47884 −0.517068 −0.258534 0.966002i \(-0.583239\pi\)
−0.258534 + 0.966002i \(0.583239\pi\)
\(158\) 43.2018 3.43695
\(159\) −25.2176 −1.99989
\(160\) −68.2364 −5.39456
\(161\) −3.96925 −0.312820
\(162\) −46.8946 −3.68439
\(163\) 15.9531 1.24954 0.624771 0.780808i \(-0.285192\pi\)
0.624771 + 0.780808i \(0.285192\pi\)
\(164\) 41.8553 3.26835
\(165\) 17.8736 1.39146
\(166\) −14.4071 −1.11821
\(167\) 18.2471 1.41200 0.706001 0.708210i \(-0.250497\pi\)
0.706001 + 0.708210i \(0.250497\pi\)
\(168\) 63.2001 4.87600
\(169\) −7.99332 −0.614871
\(170\) 27.0566 2.07514
\(171\) −14.5465 −1.11240
\(172\) 56.9726 4.34412
\(173\) 0.507915 0.0386161 0.0193080 0.999814i \(-0.493854\pi\)
0.0193080 + 0.999814i \(0.493854\pi\)
\(174\) −28.4162 −2.15423
\(175\) −27.4191 −2.07269
\(176\) 17.5873 1.32569
\(177\) −46.7857 −3.51663
\(178\) −1.84624 −0.138382
\(179\) 3.07179 0.229596 0.114798 0.993389i \(-0.463378\pi\)
0.114798 + 0.993389i \(0.463378\pi\)
\(180\) 145.661 10.8569
\(181\) 11.0963 0.824782 0.412391 0.911007i \(-0.364694\pi\)
0.412391 + 0.911007i \(0.364694\pi\)
\(182\) 14.0831 1.04391
\(183\) −15.1893 −1.12282
\(184\) −14.5158 −1.07012
\(185\) 13.5098 0.993257
\(186\) −10.3491 −0.758829
\(187\) −3.43994 −0.251554
\(188\) 30.5301 2.22664
\(189\) −28.4345 −2.06830
\(190\) 23.2399 1.68600
\(191\) −5.38597 −0.389715 −0.194858 0.980832i \(-0.562424\pi\)
−0.194858 + 0.980832i \(0.562424\pi\)
\(192\) 61.4540 4.43506
\(193\) −9.10502 −0.655394 −0.327697 0.944783i \(-0.606272\pi\)
−0.327697 + 0.944783i \(0.606272\pi\)
\(194\) 42.9008 3.08010
\(195\) 28.7019 2.05539
\(196\) −7.77795 −0.555568
\(197\) −6.85379 −0.488312 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(198\) −25.6448 −1.82250
\(199\) −3.58336 −0.254018 −0.127009 0.991902i \(-0.540538\pi\)
−0.127009 + 0.991902i \(0.540538\pi\)
\(200\) −100.273 −7.09038
\(201\) 2.37553 0.167557
\(202\) 47.3230 3.32964
\(203\) −7.91319 −0.555397
\(204\) −40.2934 −2.82110
\(205\) 32.8948 2.29747
\(206\) −2.30059 −0.160290
\(207\) 11.6066 0.806716
\(208\) 28.2420 1.95823
\(209\) −2.95470 −0.204381
\(210\) 80.7348 5.57123
\(211\) −4.81467 −0.331456 −0.165728 0.986172i \(-0.552997\pi\)
−0.165728 + 0.986172i \(0.552997\pi\)
\(212\) −41.7435 −2.86696
\(213\) 27.1174 1.85806
\(214\) 49.3133 3.37099
\(215\) 44.7756 3.05367
\(216\) −103.987 −7.07539
\(217\) −2.88195 −0.195639
\(218\) −11.8665 −0.803698
\(219\) −6.24325 −0.421880
\(220\) 29.5868 1.99474
\(221\) −5.52394 −0.371580
\(222\) −27.8604 −1.86987
\(223\) 6.08564 0.407524 0.203762 0.979020i \(-0.434683\pi\)
0.203762 + 0.979020i \(0.434683\pi\)
\(224\) 39.1870 2.61829
\(225\) 80.1771 5.34514
\(226\) 26.7986 1.78262
\(227\) 21.7568 1.44405 0.722026 0.691866i \(-0.243211\pi\)
0.722026 + 0.691866i \(0.243211\pi\)
\(228\) −34.6095 −2.29207
\(229\) −8.06476 −0.532934 −0.266467 0.963844i \(-0.585856\pi\)
−0.266467 + 0.963844i \(0.585856\pi\)
\(230\) −18.5431 −1.22270
\(231\) −10.2645 −0.675357
\(232\) −28.9390 −1.89994
\(233\) 1.97368 0.129300 0.0646500 0.997908i \(-0.479407\pi\)
0.0646500 + 0.997908i \(0.479407\pi\)
\(234\) −41.1811 −2.69209
\(235\) 23.9941 1.56520
\(236\) −77.4457 −5.04129
\(237\) −50.5637 −3.28446
\(238\) −15.5381 −1.00719
\(239\) 23.9967 1.55221 0.776107 0.630601i \(-0.217191\pi\)
0.776107 + 0.630601i \(0.217191\pi\)
\(240\) 161.904 10.4508
\(241\) 8.29668 0.534436 0.267218 0.963636i \(-0.413896\pi\)
0.267218 + 0.963636i \(0.413896\pi\)
\(242\) 24.3026 1.56223
\(243\) 18.5242 1.18833
\(244\) −25.1432 −1.60963
\(245\) −6.11281 −0.390533
\(246\) −67.8371 −4.32513
\(247\) −4.74472 −0.301899
\(248\) −10.5395 −0.669256
\(249\) 16.8622 1.06860
\(250\) −73.2951 −4.63559
\(251\) −24.8412 −1.56796 −0.783982 0.620784i \(-0.786814\pi\)
−0.783982 + 0.620784i \(0.786814\pi\)
\(252\) −83.6504 −5.26948
\(253\) 2.35755 0.148218
\(254\) −29.9030 −1.87628
\(255\) −31.6672 −1.98308
\(256\) 12.0976 0.756098
\(257\) 24.1772 1.50813 0.754065 0.656800i \(-0.228090\pi\)
0.754065 + 0.656800i \(0.228090\pi\)
\(258\) −92.3384 −5.74874
\(259\) −7.75842 −0.482085
\(260\) 47.5111 2.94651
\(261\) 23.1393 1.43228
\(262\) −23.8945 −1.47621
\(263\) 14.5678 0.898291 0.449145 0.893459i \(-0.351729\pi\)
0.449145 + 0.893459i \(0.351729\pi\)
\(264\) −37.5380 −2.31030
\(265\) −32.8069 −2.01531
\(266\) −13.3463 −0.818313
\(267\) 2.16086 0.132242
\(268\) 3.93228 0.240202
\(269\) 15.2469 0.929619 0.464810 0.885411i \(-0.346123\pi\)
0.464810 + 0.885411i \(0.346123\pi\)
\(270\) −132.837 −8.08421
\(271\) −25.1895 −1.53015 −0.765075 0.643941i \(-0.777298\pi\)
−0.765075 + 0.643941i \(0.777298\pi\)
\(272\) −31.1598 −1.88934
\(273\) −16.4830 −0.997597
\(274\) −51.6149 −3.11817
\(275\) 16.2857 0.982064
\(276\) 27.6149 1.66222
\(277\) −19.0153 −1.14252 −0.571261 0.820769i \(-0.693546\pi\)
−0.571261 + 0.820769i \(0.693546\pi\)
\(278\) 35.4986 2.12906
\(279\) 8.42721 0.504524
\(280\) 82.2202 4.91359
\(281\) 29.4643 1.75769 0.878847 0.477104i \(-0.158313\pi\)
0.878847 + 0.477104i \(0.158313\pi\)
\(282\) −49.4817 −2.94659
\(283\) 21.4121 1.27281 0.636407 0.771353i \(-0.280420\pi\)
0.636407 + 0.771353i \(0.280420\pi\)
\(284\) 44.8883 2.66363
\(285\) −27.2001 −1.61120
\(286\) −8.36475 −0.494618
\(287\) −18.8909 −1.11509
\(288\) −114.588 −6.75218
\(289\) −10.9054 −0.641492
\(290\) −36.9680 −2.17084
\(291\) −50.2114 −2.94344
\(292\) −10.3346 −0.604789
\(293\) −5.48018 −0.320155 −0.160078 0.987104i \(-0.551174\pi\)
−0.160078 + 0.987104i \(0.551174\pi\)
\(294\) 12.6061 0.735204
\(295\) −60.8658 −3.54374
\(296\) −28.3730 −1.64915
\(297\) 16.8888 0.979986
\(298\) 54.9531 3.18335
\(299\) 3.78581 0.218939
\(300\) 190.760 11.0136
\(301\) −25.7139 −1.48212
\(302\) −59.0903 −3.40026
\(303\) −55.3872 −3.18191
\(304\) −26.7643 −1.53504
\(305\) −19.7605 −1.13148
\(306\) 45.4356 2.59738
\(307\) 17.3622 0.990913 0.495457 0.868633i \(-0.335001\pi\)
0.495457 + 0.868633i \(0.335001\pi\)
\(308\) −16.9912 −0.968162
\(309\) 2.69263 0.153178
\(310\) −13.4636 −0.764681
\(311\) −10.4238 −0.591082 −0.295541 0.955330i \(-0.595500\pi\)
−0.295541 + 0.955330i \(0.595500\pi\)
\(312\) −60.2794 −3.41265
\(313\) 17.4205 0.984664 0.492332 0.870407i \(-0.336145\pi\)
0.492332 + 0.870407i \(0.336145\pi\)
\(314\) 17.3819 0.980920
\(315\) −65.7422 −3.70415
\(316\) −83.6995 −4.70847
\(317\) 1.73958 0.0977047 0.0488524 0.998806i \(-0.484444\pi\)
0.0488524 + 0.998806i \(0.484444\pi\)
\(318\) 67.6558 3.79395
\(319\) 4.70008 0.263154
\(320\) 79.9486 4.46926
\(321\) −57.7166 −3.22143
\(322\) 10.6490 0.593446
\(323\) 5.23491 0.291278
\(324\) 90.8540 5.04744
\(325\) 26.1519 1.45065
\(326\) −42.8002 −2.37048
\(327\) 13.8886 0.768040
\(328\) −69.0852 −3.81459
\(329\) −13.7794 −0.759683
\(330\) −47.9528 −2.63971
\(331\) 6.76687 0.371941 0.185970 0.982555i \(-0.440457\pi\)
0.185970 + 0.982555i \(0.440457\pi\)
\(332\) 27.9125 1.53190
\(333\) 22.6867 1.24322
\(334\) −48.9547 −2.67868
\(335\) 3.09044 0.168849
\(336\) −92.9784 −5.07239
\(337\) −4.69744 −0.255886 −0.127943 0.991782i \(-0.540837\pi\)
−0.127943 + 0.991782i \(0.540837\pi\)
\(338\) 21.4451 1.16646
\(339\) −31.3653 −1.70353
\(340\) −52.4196 −2.84285
\(341\) 1.71175 0.0926963
\(342\) 39.0263 2.11030
\(343\) 19.9323 1.07624
\(344\) −94.0372 −5.07015
\(345\) 21.7030 1.16845
\(346\) −1.36267 −0.0732578
\(347\) −7.21120 −0.387117 −0.193559 0.981089i \(-0.562003\pi\)
−0.193559 + 0.981089i \(0.562003\pi\)
\(348\) 55.0538 2.95119
\(349\) −11.4099 −0.610759 −0.305380 0.952231i \(-0.598783\pi\)
−0.305380 + 0.952231i \(0.598783\pi\)
\(350\) 73.5620 3.93205
\(351\) 27.1204 1.44758
\(352\) −23.2753 −1.24058
\(353\) −18.1380 −0.965389 −0.482694 0.875789i \(-0.660342\pi\)
−0.482694 + 0.875789i \(0.660342\pi\)
\(354\) 125.520 6.67133
\(355\) 35.2784 1.87238
\(356\) 3.57693 0.189577
\(357\) 18.1859 0.962502
\(358\) −8.24123 −0.435563
\(359\) 25.7648 1.35981 0.679907 0.733298i \(-0.262020\pi\)
0.679907 + 0.733298i \(0.262020\pi\)
\(360\) −240.423 −12.6714
\(361\) −14.5035 −0.763344
\(362\) −29.7700 −1.56468
\(363\) −28.4440 −1.49292
\(364\) −27.2848 −1.43011
\(365\) −8.12215 −0.425133
\(366\) 40.7509 2.13008
\(367\) −15.0475 −0.785471 −0.392735 0.919651i \(-0.628471\pi\)
−0.392735 + 0.919651i \(0.628471\pi\)
\(368\) 21.3552 1.11322
\(369\) 55.2396 2.87566
\(370\) −36.2450 −1.88429
\(371\) 18.8404 0.978147
\(372\) 20.0503 1.03956
\(373\) 18.6590 0.966128 0.483064 0.875585i \(-0.339524\pi\)
0.483064 + 0.875585i \(0.339524\pi\)
\(374\) 9.22894 0.477217
\(375\) 85.7851 4.42992
\(376\) −50.3921 −2.59877
\(377\) 7.54749 0.388715
\(378\) 76.2862 3.92374
\(379\) −10.7844 −0.553959 −0.276980 0.960876i \(-0.589333\pi\)
−0.276980 + 0.960876i \(0.589333\pi\)
\(380\) −45.0252 −2.30974
\(381\) 34.9987 1.79304
\(382\) 14.4499 0.739321
\(383\) −18.9502 −0.968310 −0.484155 0.874982i \(-0.660873\pi\)
−0.484155 + 0.874982i \(0.660873\pi\)
\(384\) −59.9711 −3.06039
\(385\) −13.3536 −0.680564
\(386\) 24.4277 1.24333
\(387\) 75.1909 3.82217
\(388\) −83.1164 −4.21959
\(389\) 15.4821 0.784973 0.392486 0.919758i \(-0.371615\pi\)
0.392486 + 0.919758i \(0.371615\pi\)
\(390\) −77.0037 −3.89923
\(391\) −4.17694 −0.211237
\(392\) 12.8381 0.648420
\(393\) 27.9663 1.41071
\(394\) 18.3879 0.926368
\(395\) −65.7808 −3.30979
\(396\) 49.6845 2.49674
\(397\) −27.2082 −1.36554 −0.682770 0.730634i \(-0.739225\pi\)
−0.682770 + 0.730634i \(0.739225\pi\)
\(398\) 9.61371 0.481892
\(399\) 15.6206 0.782007
\(400\) 147.519 7.37597
\(401\) 7.41100 0.370088 0.185044 0.982730i \(-0.440757\pi\)
0.185044 + 0.982730i \(0.440757\pi\)
\(402\) −6.37325 −0.317869
\(403\) 2.74876 0.136926
\(404\) −91.6840 −4.56145
\(405\) 71.4036 3.54807
\(406\) 21.2301 1.05363
\(407\) 4.60815 0.228418
\(408\) 66.5071 3.29259
\(409\) 4.92746 0.243647 0.121824 0.992552i \(-0.461126\pi\)
0.121824 + 0.992552i \(0.461126\pi\)
\(410\) −88.2526 −4.35848
\(411\) 60.4105 2.97983
\(412\) 4.45719 0.219590
\(413\) 34.9542 1.71998
\(414\) −31.1391 −1.53040
\(415\) 21.9368 1.07684
\(416\) −37.3760 −1.83251
\(417\) −41.5478 −2.03460
\(418\) 7.92708 0.387726
\(419\) 20.1264 0.983237 0.491619 0.870811i \(-0.336405\pi\)
0.491619 + 0.870811i \(0.336405\pi\)
\(420\) −156.416 −7.63233
\(421\) −25.9634 −1.26538 −0.632689 0.774406i \(-0.718049\pi\)
−0.632689 + 0.774406i \(0.718049\pi\)
\(422\) 12.9172 0.628798
\(423\) 40.2928 1.95910
\(424\) 68.9006 3.34611
\(425\) −28.8538 −1.39961
\(426\) −72.7527 −3.52488
\(427\) 11.3481 0.549173
\(428\) −95.5400 −4.61810
\(429\) 9.79016 0.472674
\(430\) −120.128 −5.79306
\(431\) −16.5683 −0.798065 −0.399032 0.916937i \(-0.630654\pi\)
−0.399032 + 0.916937i \(0.630654\pi\)
\(432\) 152.982 7.36037
\(433\) −11.9747 −0.575466 −0.287733 0.957711i \(-0.592901\pi\)
−0.287733 + 0.957711i \(0.592901\pi\)
\(434\) 7.73191 0.371144
\(435\) 43.2676 2.07452
\(436\) 22.9902 1.10103
\(437\) −3.58773 −0.171624
\(438\) 16.7499 0.800340
\(439\) −32.2304 −1.53828 −0.769138 0.639083i \(-0.779314\pi\)
−0.769138 + 0.639083i \(0.779314\pi\)
\(440\) −48.8351 −2.32812
\(441\) −10.2651 −0.488816
\(442\) 14.8200 0.704918
\(443\) 23.0127 1.09336 0.546682 0.837340i \(-0.315891\pi\)
0.546682 + 0.837340i \(0.315891\pi\)
\(444\) 53.9771 2.56164
\(445\) 2.81117 0.133262
\(446\) −16.3270 −0.773106
\(447\) −64.3175 −3.04211
\(448\) −45.9131 −2.16919
\(449\) 7.33176 0.346007 0.173003 0.984921i \(-0.444653\pi\)
0.173003 + 0.984921i \(0.444653\pi\)
\(450\) −215.105 −10.1402
\(451\) 11.2203 0.528345
\(452\) −51.9199 −2.44211
\(453\) 69.1597 3.24940
\(454\) −58.3709 −2.73948
\(455\) −21.4436 −1.00529
\(456\) 57.1254 2.67514
\(457\) 2.97162 0.139006 0.0695032 0.997582i \(-0.477859\pi\)
0.0695032 + 0.997582i \(0.477859\pi\)
\(458\) 21.6368 1.01102
\(459\) −29.9223 −1.39665
\(460\) 35.9256 1.67504
\(461\) 42.9331 1.99959 0.999796 0.0201759i \(-0.00642263\pi\)
0.999796 + 0.0201759i \(0.00642263\pi\)
\(462\) 27.5385 1.28121
\(463\) 24.1708 1.12331 0.561656 0.827371i \(-0.310164\pi\)
0.561656 + 0.827371i \(0.310164\pi\)
\(464\) 42.5744 1.97646
\(465\) 15.7579 0.730754
\(466\) −5.29514 −0.245293
\(467\) 1.86550 0.0863251 0.0431626 0.999068i \(-0.486257\pi\)
0.0431626 + 0.999068i \(0.486257\pi\)
\(468\) 79.7845 3.68804
\(469\) −1.77479 −0.0819521
\(470\) −64.3732 −2.96931
\(471\) −20.3439 −0.937399
\(472\) 127.830 5.88384
\(473\) 15.2729 0.702248
\(474\) 135.656 6.23089
\(475\) −24.7836 −1.13715
\(476\) 30.1037 1.37980
\(477\) −55.0920 −2.52249
\(478\) −64.3801 −2.94468
\(479\) −24.9493 −1.13996 −0.569982 0.821657i \(-0.693050\pi\)
−0.569982 + 0.821657i \(0.693050\pi\)
\(480\) −214.266 −9.77987
\(481\) 7.39987 0.337405
\(482\) −22.2590 −1.01387
\(483\) −12.4637 −0.567116
\(484\) −47.0841 −2.14019
\(485\) −65.3224 −2.96614
\(486\) −49.6982 −2.25435
\(487\) −22.3404 −1.01234 −0.506169 0.862434i \(-0.668939\pi\)
−0.506169 + 0.862434i \(0.668939\pi\)
\(488\) 41.5007 1.87865
\(489\) 50.0936 2.26531
\(490\) 16.3999 0.740873
\(491\) 32.0212 1.44510 0.722549 0.691320i \(-0.242970\pi\)
0.722549 + 0.691320i \(0.242970\pi\)
\(492\) 131.428 5.92524
\(493\) −8.32724 −0.375040
\(494\) 12.7295 0.572727
\(495\) 39.0479 1.75507
\(496\) 15.5054 0.696213
\(497\) −20.2598 −0.908776
\(498\) −45.2392 −2.02722
\(499\) 18.4458 0.825745 0.412873 0.910789i \(-0.364525\pi\)
0.412873 + 0.910789i \(0.364525\pi\)
\(500\) 142.003 6.35055
\(501\) 57.2969 2.55984
\(502\) 66.6459 2.97455
\(503\) 20.3309 0.906509 0.453255 0.891381i \(-0.350263\pi\)
0.453255 + 0.891381i \(0.350263\pi\)
\(504\) 138.071 6.15017
\(505\) −72.0559 −3.20645
\(506\) −6.32502 −0.281182
\(507\) −25.0995 −1.11471
\(508\) 57.9344 2.57042
\(509\) −6.64088 −0.294352 −0.147176 0.989110i \(-0.547018\pi\)
−0.147176 + 0.989110i \(0.547018\pi\)
\(510\) 84.9592 3.76206
\(511\) 4.66442 0.206342
\(512\) 5.74116 0.253726
\(513\) −25.7014 −1.13474
\(514\) −64.8644 −2.86105
\(515\) 3.50298 0.154360
\(516\) 178.897 7.87551
\(517\) 8.18434 0.359947
\(518\) 20.8149 0.914554
\(519\) 1.59488 0.0700076
\(520\) −78.4204 −3.43896
\(521\) 7.09924 0.311024 0.155512 0.987834i \(-0.450297\pi\)
0.155512 + 0.987834i \(0.450297\pi\)
\(522\) −62.0798 −2.71716
\(523\) −12.2593 −0.536063 −0.268032 0.963410i \(-0.586373\pi\)
−0.268032 + 0.963410i \(0.586373\pi\)
\(524\) 46.2934 2.02234
\(525\) −86.0975 −3.75760
\(526\) −39.0837 −1.70413
\(527\) −3.03275 −0.132108
\(528\) 55.2250 2.40336
\(529\) −20.1374 −0.875537
\(530\) 88.0168 3.82321
\(531\) −102.211 −4.43557
\(532\) 25.8572 1.12105
\(533\) 18.0179 0.780441
\(534\) −5.79731 −0.250874
\(535\) −75.0864 −3.24627
\(536\) −6.49051 −0.280347
\(537\) 9.64560 0.416238
\(538\) −40.9055 −1.76356
\(539\) −2.08507 −0.0898103
\(540\) 257.360 11.0750
\(541\) −30.9395 −1.33019 −0.665097 0.746757i \(-0.731610\pi\)
−0.665097 + 0.746757i \(0.731610\pi\)
\(542\) 67.5802 2.90282
\(543\) 34.8430 1.49526
\(544\) 41.2375 1.76804
\(545\) 18.0683 0.773963
\(546\) 44.2219 1.89252
\(547\) 7.41581 0.317077 0.158539 0.987353i \(-0.449322\pi\)
0.158539 + 0.987353i \(0.449322\pi\)
\(548\) 99.9992 4.27175
\(549\) −33.1834 −1.41623
\(550\) −43.6925 −1.86305
\(551\) −7.15258 −0.304710
\(552\) −45.5804 −1.94003
\(553\) 37.7768 1.60643
\(554\) 51.0158 2.16746
\(555\) 42.4214 1.80069
\(556\) −68.7752 −2.91672
\(557\) −29.1192 −1.23382 −0.616909 0.787034i \(-0.711616\pi\)
−0.616909 + 0.787034i \(0.711616\pi\)
\(558\) −22.6092 −0.957123
\(559\) 24.5255 1.03732
\(560\) −120.960 −5.11150
\(561\) −10.8016 −0.456045
\(562\) −79.0491 −3.33449
\(563\) 25.0408 1.05534 0.527672 0.849449i \(-0.323065\pi\)
0.527672 + 0.849449i \(0.323065\pi\)
\(564\) 95.8663 4.03670
\(565\) −40.8047 −1.71666
\(566\) −57.4459 −2.41463
\(567\) −41.0059 −1.72208
\(568\) −74.0913 −3.10880
\(569\) 29.4750 1.23566 0.617828 0.786313i \(-0.288013\pi\)
0.617828 + 0.786313i \(0.288013\pi\)
\(570\) 72.9746 3.05657
\(571\) −44.7250 −1.87168 −0.935842 0.352421i \(-0.885359\pi\)
−0.935842 + 0.352421i \(0.885359\pi\)
\(572\) 16.2059 0.677605
\(573\) −16.9123 −0.706520
\(574\) 50.6820 2.11542
\(575\) 19.7748 0.824667
\(576\) 134.256 5.59401
\(577\) −16.3536 −0.680811 −0.340406 0.940279i \(-0.610564\pi\)
−0.340406 + 0.940279i \(0.610564\pi\)
\(578\) 29.2578 1.21696
\(579\) −28.5903 −1.18817
\(580\) 71.6222 2.97395
\(581\) −12.5980 −0.522651
\(582\) 134.711 5.58395
\(583\) −11.1904 −0.463458
\(584\) 17.0580 0.705867
\(585\) 62.7039 2.59249
\(586\) 14.7026 0.607361
\(587\) 11.1077 0.458466 0.229233 0.973372i \(-0.426378\pi\)
0.229233 + 0.973372i \(0.426378\pi\)
\(588\) −24.4232 −1.00720
\(589\) −2.60494 −0.107335
\(590\) 163.296 6.72277
\(591\) −21.5213 −0.885268
\(592\) 41.7417 1.71557
\(593\) 15.5637 0.639124 0.319562 0.947565i \(-0.396464\pi\)
0.319562 + 0.947565i \(0.396464\pi\)
\(594\) −45.3105 −1.85911
\(595\) 23.6590 0.969924
\(596\) −106.467 −4.36104
\(597\) −11.2520 −0.460512
\(598\) −10.1569 −0.415345
\(599\) −1.52371 −0.0622571 −0.0311285 0.999515i \(-0.509910\pi\)
−0.0311285 + 0.999515i \(0.509910\pi\)
\(600\) −314.864 −12.8543
\(601\) −47.8890 −1.95343 −0.976717 0.214533i \(-0.931177\pi\)
−0.976717 + 0.214533i \(0.931177\pi\)
\(602\) 68.9872 2.81171
\(603\) 5.18973 0.211342
\(604\) 114.482 4.65821
\(605\) −37.0042 −1.50443
\(606\) 148.597 6.03634
\(607\) −12.9136 −0.524146 −0.262073 0.965048i \(-0.584406\pi\)
−0.262073 + 0.965048i \(0.584406\pi\)
\(608\) 35.4204 1.43649
\(609\) −24.8479 −1.00689
\(610\) 53.0149 2.14651
\(611\) 13.1426 0.531692
\(612\) −88.0274 −3.55830
\(613\) 36.6839 1.48165 0.740825 0.671698i \(-0.234435\pi\)
0.740825 + 0.671698i \(0.234435\pi\)
\(614\) −46.5807 −1.87984
\(615\) 103.291 4.16511
\(616\) 28.0451 1.12997
\(617\) 12.3003 0.495193 0.247596 0.968863i \(-0.420359\pi\)
0.247596 + 0.968863i \(0.420359\pi\)
\(618\) −7.22400 −0.290592
\(619\) −24.4238 −0.981676 −0.490838 0.871251i \(-0.663309\pi\)
−0.490838 + 0.871251i \(0.663309\pi\)
\(620\) 26.0845 1.04758
\(621\) 20.5071 0.822923
\(622\) 27.9659 1.12133
\(623\) −1.61440 −0.0646798
\(624\) 88.6815 3.55010
\(625\) 53.1636 2.12654
\(626\) −46.7370 −1.86799
\(627\) −9.27791 −0.370524
\(628\) −33.6759 −1.34382
\(629\) −8.16438 −0.325535
\(630\) 176.378 7.02707
\(631\) −42.2361 −1.68139 −0.840695 0.541508i \(-0.817853\pi\)
−0.840695 + 0.541508i \(0.817853\pi\)
\(632\) 138.152 5.49539
\(633\) −15.1183 −0.600900
\(634\) −4.66709 −0.185354
\(635\) 45.5316 1.80687
\(636\) −131.077 −5.19754
\(637\) −3.34825 −0.132662
\(638\) −12.6097 −0.499224
\(639\) 59.2424 2.34359
\(640\) −78.0194 −3.08399
\(641\) −20.3293 −0.802959 −0.401479 0.915868i \(-0.631504\pi\)
−0.401479 + 0.915868i \(0.631504\pi\)
\(642\) 154.847 6.11131
\(643\) 2.29951 0.0906840 0.0453420 0.998972i \(-0.485562\pi\)
0.0453420 + 0.998972i \(0.485562\pi\)
\(644\) −20.6315 −0.812994
\(645\) 140.598 5.53604
\(646\) −14.0446 −0.552578
\(647\) 19.1508 0.752896 0.376448 0.926438i \(-0.377145\pi\)
0.376448 + 0.926438i \(0.377145\pi\)
\(648\) −149.961 −5.89102
\(649\) −20.7612 −0.814949
\(650\) −70.1624 −2.75199
\(651\) −9.04949 −0.354677
\(652\) 82.9215 3.24745
\(653\) −35.2735 −1.38036 −0.690180 0.723638i \(-0.742469\pi\)
−0.690180 + 0.723638i \(0.742469\pi\)
\(654\) −37.2614 −1.45703
\(655\) 36.3827 1.42159
\(656\) 101.636 3.96823
\(657\) −13.6394 −0.532123
\(658\) 36.9684 1.44118
\(659\) 26.2409 1.02220 0.511099 0.859522i \(-0.329238\pi\)
0.511099 + 0.859522i \(0.329238\pi\)
\(660\) 92.9042 3.61629
\(661\) −32.3847 −1.25962 −0.629810 0.776749i \(-0.716867\pi\)
−0.629810 + 0.776749i \(0.716867\pi\)
\(662\) −18.1547 −0.705602
\(663\) −17.3455 −0.673643
\(664\) −46.0715 −1.78792
\(665\) 20.3216 0.788037
\(666\) −60.8656 −2.35850
\(667\) 5.70705 0.220978
\(668\) 94.8453 3.66968
\(669\) 19.1092 0.738806
\(670\) −8.29128 −0.320320
\(671\) −6.74026 −0.260205
\(672\) 123.050 4.74674
\(673\) −30.2726 −1.16692 −0.583461 0.812141i \(-0.698302\pi\)
−0.583461 + 0.812141i \(0.698302\pi\)
\(674\) 12.6027 0.485436
\(675\) 141.661 5.45252
\(676\) −41.5479 −1.59800
\(677\) −29.7403 −1.14301 −0.571506 0.820598i \(-0.693641\pi\)
−0.571506 + 0.820598i \(0.693641\pi\)
\(678\) 84.1492 3.23173
\(679\) 37.5136 1.43964
\(680\) 86.5223 3.31798
\(681\) 68.3177 2.61794
\(682\) −4.59241 −0.175852
\(683\) 10.6268 0.406624 0.203312 0.979114i \(-0.434829\pi\)
0.203312 + 0.979114i \(0.434829\pi\)
\(684\) −75.6100 −2.89102
\(685\) 78.5910 3.00281
\(686\) −53.4760 −2.04172
\(687\) −25.3238 −0.966164
\(688\) 138.345 5.27436
\(689\) −17.9697 −0.684592
\(690\) −58.2265 −2.21664
\(691\) −27.7002 −1.05377 −0.526883 0.849938i \(-0.676639\pi\)
−0.526883 + 0.849938i \(0.676639\pi\)
\(692\) 2.64006 0.100360
\(693\) −22.4245 −0.851837
\(694\) 19.3468 0.734393
\(695\) −54.0515 −2.05029
\(696\) −90.8702 −3.44442
\(697\) −19.8794 −0.752984
\(698\) 30.6114 1.15866
\(699\) 6.19747 0.234410
\(700\) −142.520 −5.38674
\(701\) −49.8467 −1.88268 −0.941341 0.337456i \(-0.890434\pi\)
−0.941341 + 0.337456i \(0.890434\pi\)
\(702\) −72.7606 −2.74617
\(703\) −7.01269 −0.264489
\(704\) 27.2703 1.02779
\(705\) 75.3428 2.83757
\(706\) 48.6620 1.83142
\(707\) 41.3805 1.55627
\(708\) −243.184 −9.13942
\(709\) −0.681840 −0.0256070 −0.0128035 0.999918i \(-0.504076\pi\)
−0.0128035 + 0.999918i \(0.504076\pi\)
\(710\) −94.6476 −3.55206
\(711\) −110.464 −4.14274
\(712\) −5.90398 −0.221261
\(713\) 2.07848 0.0778397
\(714\) −48.7906 −1.82594
\(715\) 12.7365 0.476318
\(716\) 15.9666 0.596701
\(717\) 75.3509 2.81403
\(718\) −69.1238 −2.57968
\(719\) −30.1854 −1.12572 −0.562862 0.826551i \(-0.690300\pi\)
−0.562862 + 0.826551i \(0.690300\pi\)
\(720\) 353.704 13.1818
\(721\) −2.01170 −0.0749196
\(722\) 38.9112 1.44813
\(723\) 26.0521 0.968886
\(724\) 57.6767 2.14354
\(725\) 39.4236 1.46415
\(726\) 76.3117 2.83219
\(727\) 21.6399 0.802578 0.401289 0.915951i \(-0.368562\pi\)
0.401289 + 0.915951i \(0.368562\pi\)
\(728\) 45.0355 1.66913
\(729\) 5.72944 0.212201
\(730\) 21.7907 0.806511
\(731\) −27.0594 −1.00083
\(732\) −78.9512 −2.91812
\(733\) −36.5735 −1.35087 −0.675436 0.737419i \(-0.736044\pi\)
−0.675436 + 0.737419i \(0.736044\pi\)
\(734\) 40.3705 1.49010
\(735\) −19.1946 −0.708003
\(736\) −28.2619 −1.04175
\(737\) 1.05414 0.0388299
\(738\) −148.201 −5.45535
\(739\) 44.4501 1.63513 0.817563 0.575840i \(-0.195325\pi\)
0.817563 + 0.575840i \(0.195325\pi\)
\(740\) 70.2214 2.58139
\(741\) −14.8987 −0.547317
\(742\) −50.5466 −1.85562
\(743\) −36.9598 −1.35592 −0.677961 0.735098i \(-0.737136\pi\)
−0.677961 + 0.735098i \(0.737136\pi\)
\(744\) −33.0945 −1.21330
\(745\) −83.6738 −3.06557
\(746\) −50.0599 −1.83282
\(747\) 36.8382 1.34784
\(748\) −17.8802 −0.653766
\(749\) 43.1208 1.57560
\(750\) −230.151 −8.40392
\(751\) 40.1748 1.46600 0.733001 0.680228i \(-0.238119\pi\)
0.733001 + 0.680228i \(0.238119\pi\)
\(752\) 74.1356 2.70345
\(753\) −78.0028 −2.84258
\(754\) −20.2490 −0.737424
\(755\) 89.9732 3.27446
\(756\) −147.797 −5.37534
\(757\) 6.34713 0.230690 0.115345 0.993325i \(-0.463203\pi\)
0.115345 + 0.993325i \(0.463203\pi\)
\(758\) 28.9333 1.05091
\(759\) 7.40285 0.268706
\(760\) 74.3172 2.69577
\(761\) −40.8153 −1.47955 −0.739776 0.672853i \(-0.765069\pi\)
−0.739776 + 0.672853i \(0.765069\pi\)
\(762\) −93.8973 −3.40154
\(763\) −10.3763 −0.375649
\(764\) −27.9954 −1.01284
\(765\) −69.1821 −2.50128
\(766\) 50.8410 1.83696
\(767\) −33.3388 −1.20380
\(768\) 37.9871 1.37074
\(769\) −8.82122 −0.318101 −0.159051 0.987270i \(-0.550843\pi\)
−0.159051 + 0.987270i \(0.550843\pi\)
\(770\) 35.8262 1.29109
\(771\) 75.9177 2.73411
\(772\) −47.3263 −1.70331
\(773\) 25.5803 0.920061 0.460030 0.887903i \(-0.347838\pi\)
0.460030 + 0.887903i \(0.347838\pi\)
\(774\) −201.728 −7.25097
\(775\) 14.3579 0.515751
\(776\) 137.189 4.92481
\(777\) −24.3619 −0.873978
\(778\) −41.5365 −1.48916
\(779\) −17.0751 −0.611780
\(780\) 149.188 5.34177
\(781\) 12.0334 0.430589
\(782\) 11.2062 0.400733
\(783\) 40.8835 1.46106
\(784\) −18.8870 −0.674536
\(785\) −26.4664 −0.944628
\(786\) −75.0301 −2.67623
\(787\) 3.40230 0.121279 0.0606395 0.998160i \(-0.480686\pi\)
0.0606395 + 0.998160i \(0.480686\pi\)
\(788\) −35.6248 −1.26908
\(789\) 45.7438 1.62852
\(790\) 176.482 6.27894
\(791\) 23.4334 0.833197
\(792\) −82.0078 −2.91402
\(793\) −10.8237 −0.384359
\(794\) 72.9962 2.59054
\(795\) −103.015 −3.65358
\(796\) −18.6257 −0.660170
\(797\) −9.20586 −0.326088 −0.163044 0.986619i \(-0.552131\pi\)
−0.163044 + 0.986619i \(0.552131\pi\)
\(798\) −41.9081 −1.48353
\(799\) −14.5004 −0.512987
\(800\) −195.230 −6.90243
\(801\) 4.72074 0.166799
\(802\) −19.8828 −0.702086
\(803\) −2.77045 −0.0977671
\(804\) 12.3476 0.435466
\(805\) −16.2146 −0.571489
\(806\) −7.37459 −0.259759
\(807\) 47.8761 1.68532
\(808\) 151.331 5.32380
\(809\) 50.7471 1.78417 0.892087 0.451864i \(-0.149241\pi\)
0.892087 + 0.451864i \(0.149241\pi\)
\(810\) −191.567 −6.73098
\(811\) 21.4834 0.754384 0.377192 0.926135i \(-0.376890\pi\)
0.377192 + 0.926135i \(0.376890\pi\)
\(812\) −41.1314 −1.44343
\(813\) −79.0964 −2.77403
\(814\) −12.3631 −0.433327
\(815\) 65.1693 2.28278
\(816\) −97.8435 −3.42521
\(817\) −23.2423 −0.813145
\(818\) −13.2198 −0.462218
\(819\) −36.0098 −1.25828
\(820\) 170.981 5.97093
\(821\) −4.59681 −0.160430 −0.0802149 0.996778i \(-0.525561\pi\)
−0.0802149 + 0.996778i \(0.525561\pi\)
\(822\) −162.074 −5.65297
\(823\) −4.84527 −0.168895 −0.0844477 0.996428i \(-0.526913\pi\)
−0.0844477 + 0.996428i \(0.526913\pi\)
\(824\) −7.35691 −0.256290
\(825\) 51.1380 1.78040
\(826\) −93.7778 −3.26295
\(827\) 16.9875 0.590712 0.295356 0.955387i \(-0.404562\pi\)
0.295356 + 0.955387i \(0.404562\pi\)
\(828\) 60.3292 2.09659
\(829\) −8.10719 −0.281574 −0.140787 0.990040i \(-0.544963\pi\)
−0.140787 + 0.990040i \(0.544963\pi\)
\(830\) −58.8539 −2.04285
\(831\) −59.7093 −2.07129
\(832\) 43.7913 1.51819
\(833\) 3.69417 0.127995
\(834\) 111.468 3.85981
\(835\) 74.5404 2.57958
\(836\) −15.3580 −0.531168
\(837\) 14.8896 0.514660
\(838\) −53.9966 −1.86528
\(839\) 51.6351 1.78264 0.891320 0.453374i \(-0.149780\pi\)
0.891320 + 0.453374i \(0.149780\pi\)
\(840\) 258.176 8.90792
\(841\) −17.6223 −0.607665
\(842\) 69.6566 2.40052
\(843\) 92.5197 3.18655
\(844\) −25.0258 −0.861425
\(845\) −32.6532 −1.12330
\(846\) −108.101 −3.71658
\(847\) 21.2509 0.730188
\(848\) −101.365 −3.48088
\(849\) 67.2351 2.30750
\(850\) 77.4111 2.65518
\(851\) 5.59543 0.191809
\(852\) 140.952 4.82893
\(853\) 50.8386 1.74068 0.870340 0.492452i \(-0.163899\pi\)
0.870340 + 0.492452i \(0.163899\pi\)
\(854\) −30.4456 −1.04183
\(855\) −59.4231 −2.03223
\(856\) 157.696 5.38992
\(857\) −30.7979 −1.05204 −0.526018 0.850473i \(-0.676316\pi\)
−0.526018 + 0.850473i \(0.676316\pi\)
\(858\) −26.2658 −0.896700
\(859\) −6.25880 −0.213548 −0.106774 0.994283i \(-0.534052\pi\)
−0.106774 + 0.994283i \(0.534052\pi\)
\(860\) 232.736 7.93624
\(861\) −59.3185 −2.02157
\(862\) 44.4506 1.51399
\(863\) 21.5658 0.734108 0.367054 0.930200i \(-0.380366\pi\)
0.367054 + 0.930200i \(0.380366\pi\)
\(864\) −202.460 −6.88783
\(865\) 2.07486 0.0705475
\(866\) 32.1265 1.09170
\(867\) −34.2435 −1.16297
\(868\) −14.9799 −0.508450
\(869\) −22.4377 −0.761147
\(870\) −116.082 −3.93554
\(871\) 1.69277 0.0573573
\(872\) −37.9469 −1.28504
\(873\) −109.695 −3.71261
\(874\) 9.62543 0.325585
\(875\) −64.0912 −2.16668
\(876\) −32.4514 −1.09643
\(877\) 32.6558 1.10271 0.551355 0.834271i \(-0.314111\pi\)
0.551355 + 0.834271i \(0.314111\pi\)
\(878\) 86.4703 2.91823
\(879\) −17.2081 −0.580414
\(880\) 71.8449 2.42189
\(881\) −47.7673 −1.60932 −0.804661 0.593734i \(-0.797653\pi\)
−0.804661 + 0.593734i \(0.797653\pi\)
\(882\) 27.5401 0.927323
\(883\) −39.5477 −1.33089 −0.665443 0.746449i \(-0.731757\pi\)
−0.665443 + 0.746449i \(0.731757\pi\)
\(884\) −28.7125 −0.965705
\(885\) −191.122 −6.42450
\(886\) −61.7401 −2.07420
\(887\) 2.15065 0.0722119 0.0361059 0.999348i \(-0.488505\pi\)
0.0361059 + 0.999348i \(0.488505\pi\)
\(888\) −89.0929 −2.98976
\(889\) −26.1480 −0.876976
\(890\) −7.54201 −0.252809
\(891\) 24.3556 0.815944
\(892\) 31.6321 1.05912
\(893\) −12.4549 −0.416788
\(894\) 172.556 5.77114
\(895\) 12.5484 0.419448
\(896\) 44.8052 1.49684
\(897\) 11.8877 0.396917
\(898\) −19.6702 −0.656403
\(899\) 4.14371 0.138201
\(900\) 416.747 13.8916
\(901\) 19.8263 0.660508
\(902\) −30.1028 −1.00231
\(903\) −80.7431 −2.68696
\(904\) 85.6974 2.85025
\(905\) 45.3290 1.50679
\(906\) −185.547 −6.16438
\(907\) 39.8616 1.32358 0.661792 0.749688i \(-0.269796\pi\)
0.661792 + 0.749688i \(0.269796\pi\)
\(908\) 113.088 3.75297
\(909\) −121.002 −4.01339
\(910\) 57.5305 1.90712
\(911\) −5.80320 −0.192268 −0.0961342 0.995368i \(-0.530648\pi\)
−0.0961342 + 0.995368i \(0.530648\pi\)
\(912\) −84.0414 −2.78289
\(913\) 7.48262 0.247638
\(914\) −7.97249 −0.263706
\(915\) −62.0490 −2.05128
\(916\) −41.9192 −1.38505
\(917\) −20.8940 −0.689980
\(918\) 80.2778 2.64956
\(919\) 7.30300 0.240904 0.120452 0.992719i \(-0.461566\pi\)
0.120452 + 0.992719i \(0.461566\pi\)
\(920\) −59.2977 −1.95499
\(921\) 54.5183 1.79644
\(922\) −115.184 −3.79339
\(923\) 19.3235 0.636041
\(924\) −53.3533 −1.75519
\(925\) 38.6525 1.27089
\(926\) −64.8473 −2.13101
\(927\) 5.88248 0.193206
\(928\) −56.3437 −1.84957
\(929\) 16.5241 0.542138 0.271069 0.962560i \(-0.412623\pi\)
0.271069 + 0.962560i \(0.412623\pi\)
\(930\) −42.2765 −1.38630
\(931\) 3.17306 0.103993
\(932\) 10.2588 0.336040
\(933\) −32.7315 −1.07158
\(934\) −5.00491 −0.163766
\(935\) −14.0524 −0.459561
\(936\) −131.690 −4.30442
\(937\) −35.2346 −1.15107 −0.575533 0.817779i \(-0.695205\pi\)
−0.575533 + 0.817779i \(0.695205\pi\)
\(938\) 4.76154 0.155470
\(939\) 54.7013 1.78511
\(940\) 124.717 4.06783
\(941\) 9.58947 0.312608 0.156304 0.987709i \(-0.450042\pi\)
0.156304 + 0.987709i \(0.450042\pi\)
\(942\) 54.5803 1.77832
\(943\) 13.6242 0.443666
\(944\) −188.060 −6.12082
\(945\) −116.156 −3.77857
\(946\) −40.9753 −1.33222
\(947\) −16.7846 −0.545427 −0.272713 0.962095i \(-0.587921\pi\)
−0.272713 + 0.962095i \(0.587921\pi\)
\(948\) −262.821 −8.53604
\(949\) −4.44885 −0.144416
\(950\) 66.4913 2.15726
\(951\) 5.46239 0.177130
\(952\) −49.6883 −1.61041
\(953\) −39.2131 −1.27024 −0.635119 0.772414i \(-0.719049\pi\)
−0.635119 + 0.772414i \(0.719049\pi\)
\(954\) 147.805 4.78537
\(955\) −22.0020 −0.711968
\(956\) 124.731 4.03407
\(957\) 14.7585 0.477075
\(958\) 66.9359 2.16260
\(959\) −45.1335 −1.45744
\(960\) 251.043 8.10238
\(961\) −29.4909 −0.951319
\(962\) −19.8530 −0.640085
\(963\) −126.091 −4.06323
\(964\) 43.1247 1.38895
\(965\) −37.1945 −1.19733
\(966\) 33.4385 1.07587
\(967\) −54.2512 −1.74460 −0.872300 0.488972i \(-0.837372\pi\)
−0.872300 + 0.488972i \(0.837372\pi\)
\(968\) 77.7157 2.49788
\(969\) 16.4379 0.528062
\(970\) 175.252 5.62701
\(971\) −1.88461 −0.0604799 −0.0302399 0.999543i \(-0.509627\pi\)
−0.0302399 + 0.999543i \(0.509627\pi\)
\(972\) 96.2856 3.08836
\(973\) 31.0409 0.995125
\(974\) 59.9365 1.92049
\(975\) 82.1185 2.62990
\(976\) −61.0548 −1.95432
\(977\) −39.8840 −1.27600 −0.638001 0.770036i \(-0.720238\pi\)
−0.638001 + 0.770036i \(0.720238\pi\)
\(978\) −134.395 −4.29748
\(979\) 0.958883 0.0306460
\(980\) −31.7734 −1.01496
\(981\) 30.3419 0.968741
\(982\) −85.9090 −2.74147
\(983\) −25.8008 −0.822919 −0.411460 0.911428i \(-0.634981\pi\)
−0.411460 + 0.911428i \(0.634981\pi\)
\(984\) −216.931 −6.91552
\(985\) −27.9981 −0.892095
\(986\) 22.3410 0.711482
\(987\) −43.2681 −1.37724
\(988\) −24.6622 −0.784610
\(989\) 18.5450 0.589698
\(990\) −104.761 −3.32951
\(991\) 30.3481 0.964039 0.482020 0.876160i \(-0.339903\pi\)
0.482020 + 0.876160i \(0.339903\pi\)
\(992\) −20.5201 −0.651515
\(993\) 21.2484 0.674296
\(994\) 54.3545 1.72402
\(995\) −14.6382 −0.464063
\(996\) 87.6467 2.77719
\(997\) −39.4036 −1.24793 −0.623963 0.781454i \(-0.714478\pi\)
−0.623963 + 0.781454i \(0.714478\pi\)
\(998\) −49.4877 −1.56651
\(999\) 40.0839 1.26820
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 \(a_p\))