Properties

Label 5077.2.a.c.1.12
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

Related objects

Downloads

Learn more about

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 1.12
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.49199 q^{2} +1.36067 q^{3} +4.21003 q^{4} -1.81458 q^{5} -3.39077 q^{6} +0.512290 q^{7} -5.50738 q^{8} -1.14858 q^{9} +O(q^{10})\) \(q-2.49199 q^{2} +1.36067 q^{3} +4.21003 q^{4} -1.81458 q^{5} -3.39077 q^{6} +0.512290 q^{7} -5.50738 q^{8} -1.14858 q^{9} +4.52191 q^{10} -3.00840 q^{11} +5.72845 q^{12} -2.35946 q^{13} -1.27662 q^{14} -2.46903 q^{15} +5.30430 q^{16} +3.40058 q^{17} +2.86227 q^{18} -3.31296 q^{19} -7.63942 q^{20} +0.697056 q^{21} +7.49692 q^{22} -4.63075 q^{23} -7.49372 q^{24} -1.70732 q^{25} +5.87976 q^{26} -5.64484 q^{27} +2.15676 q^{28} +4.84984 q^{29} +6.15281 q^{30} -7.08465 q^{31} -2.20351 q^{32} -4.09343 q^{33} -8.47423 q^{34} -0.929588 q^{35} -4.83558 q^{36} -3.49372 q^{37} +8.25588 q^{38} -3.21044 q^{39} +9.99356 q^{40} +9.86767 q^{41} -1.73706 q^{42} +2.36986 q^{43} -12.6655 q^{44} +2.08419 q^{45} +11.5398 q^{46} +10.7109 q^{47} +7.21739 q^{48} -6.73756 q^{49} +4.25462 q^{50} +4.62706 q^{51} -9.93341 q^{52} -6.73596 q^{53} +14.0669 q^{54} +5.45897 q^{55} -2.82138 q^{56} -4.50784 q^{57} -12.0858 q^{58} -3.76947 q^{59} -10.3947 q^{60} -5.85227 q^{61} +17.6549 q^{62} -0.588408 q^{63} -5.11746 q^{64} +4.28142 q^{65} +10.2008 q^{66} -7.69235 q^{67} +14.3166 q^{68} -6.30091 q^{69} +2.31653 q^{70} +0.317430 q^{71} +6.32570 q^{72} +1.09624 q^{73} +8.70633 q^{74} -2.32309 q^{75} -13.9477 q^{76} -1.54117 q^{77} +8.00040 q^{78} +10.2566 q^{79} -9.62505 q^{80} -4.23500 q^{81} -24.5902 q^{82} -0.399742 q^{83} +2.93463 q^{84} -6.17062 q^{85} -5.90568 q^{86} +6.59902 q^{87} +16.5684 q^{88} +15.2571 q^{89} -5.19380 q^{90} -1.20873 q^{91} -19.4956 q^{92} -9.63985 q^{93} -26.6915 q^{94} +6.01162 q^{95} -2.99825 q^{96} +11.2814 q^{97} +16.7900 q^{98} +3.45541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49199 −1.76211 −0.881053 0.473018i \(-0.843165\pi\)
−0.881053 + 0.473018i \(0.843165\pi\)
\(3\) 1.36067 0.785582 0.392791 0.919628i \(-0.371510\pi\)
0.392791 + 0.919628i \(0.371510\pi\)
\(4\) 4.21003 2.10502
\(5\) −1.81458 −0.811503 −0.405751 0.913983i \(-0.632990\pi\)
−0.405751 + 0.913983i \(0.632990\pi\)
\(6\) −3.39077 −1.38428
\(7\) 0.512290 0.193627 0.0968136 0.995303i \(-0.469135\pi\)
0.0968136 + 0.995303i \(0.469135\pi\)
\(8\) −5.50738 −1.94715
\(9\) −1.14858 −0.382862
\(10\) 4.52191 1.42995
\(11\) −3.00840 −0.907067 −0.453534 0.891239i \(-0.649837\pi\)
−0.453534 + 0.891239i \(0.649837\pi\)
\(12\) 5.72845 1.65366
\(13\) −2.35946 −0.654397 −0.327198 0.944956i \(-0.606105\pi\)
−0.327198 + 0.944956i \(0.606105\pi\)
\(14\) −1.27662 −0.341192
\(15\) −2.46903 −0.637502
\(16\) 5.30430 1.32608
\(17\) 3.40058 0.824763 0.412381 0.911011i \(-0.364697\pi\)
0.412381 + 0.911011i \(0.364697\pi\)
\(18\) 2.86227 0.674643
\(19\) −3.31296 −0.760046 −0.380023 0.924977i \(-0.624084\pi\)
−0.380023 + 0.924977i \(0.624084\pi\)
\(20\) −7.63942 −1.70823
\(21\) 0.697056 0.152110
\(22\) 7.49692 1.59835
\(23\) −4.63075 −0.965578 −0.482789 0.875737i \(-0.660376\pi\)
−0.482789 + 0.875737i \(0.660376\pi\)
\(24\) −7.49372 −1.52965
\(25\) −1.70732 −0.341463
\(26\) 5.87976 1.15312
\(27\) −5.64484 −1.08635
\(28\) 2.15676 0.407588
\(29\) 4.84984 0.900593 0.450297 0.892879i \(-0.351318\pi\)
0.450297 + 0.892879i \(0.351318\pi\)
\(30\) 6.15281 1.12335
\(31\) −7.08465 −1.27244 −0.636220 0.771508i \(-0.719503\pi\)
−0.636220 + 0.771508i \(0.719503\pi\)
\(32\) −2.20351 −0.389530
\(33\) −4.09343 −0.712575
\(34\) −8.47423 −1.45332
\(35\) −0.929588 −0.157129
\(36\) −4.83558 −0.805930
\(37\) −3.49372 −0.574364 −0.287182 0.957876i \(-0.592718\pi\)
−0.287182 + 0.957876i \(0.592718\pi\)
\(38\) 8.25588 1.33928
\(39\) −3.21044 −0.514082
\(40\) 9.99356 1.58012
\(41\) 9.86767 1.54107 0.770535 0.637397i \(-0.219989\pi\)
0.770535 + 0.637397i \(0.219989\pi\)
\(42\) −1.73706 −0.268034
\(43\) 2.36986 0.361401 0.180700 0.983538i \(-0.442164\pi\)
0.180700 + 0.983538i \(0.442164\pi\)
\(44\) −12.6655 −1.90939
\(45\) 2.08419 0.310693
\(46\) 11.5398 1.70145
\(47\) 10.7109 1.56234 0.781172 0.624316i \(-0.214622\pi\)
0.781172 + 0.624316i \(0.214622\pi\)
\(48\) 7.21739 1.04174
\(49\) −6.73756 −0.962508
\(50\) 4.25462 0.601694
\(51\) 4.62706 0.647918
\(52\) −9.93341 −1.37752
\(53\) −6.73596 −0.925256 −0.462628 0.886553i \(-0.653093\pi\)
−0.462628 + 0.886553i \(0.653093\pi\)
\(54\) 14.0669 1.91426
\(55\) 5.45897 0.736088
\(56\) −2.82138 −0.377022
\(57\) −4.50784 −0.597078
\(58\) −12.0858 −1.58694
\(59\) −3.76947 −0.490743 −0.245372 0.969429i \(-0.578910\pi\)
−0.245372 + 0.969429i \(0.578910\pi\)
\(60\) −10.3947 −1.34195
\(61\) −5.85227 −0.749307 −0.374653 0.927165i \(-0.622238\pi\)
−0.374653 + 0.927165i \(0.622238\pi\)
\(62\) 17.6549 2.24217
\(63\) −0.588408 −0.0741325
\(64\) −5.11746 −0.639682
\(65\) 4.28142 0.531045
\(66\) 10.2008 1.25563
\(67\) −7.69235 −0.939770 −0.469885 0.882728i \(-0.655705\pi\)
−0.469885 + 0.882728i \(0.655705\pi\)
\(68\) 14.3166 1.73614
\(69\) −6.30091 −0.758541
\(70\) 2.31653 0.276878
\(71\) 0.317430 0.0376720 0.0188360 0.999823i \(-0.494004\pi\)
0.0188360 + 0.999823i \(0.494004\pi\)
\(72\) 6.32570 0.745491
\(73\) 1.09624 0.128305 0.0641526 0.997940i \(-0.479566\pi\)
0.0641526 + 0.997940i \(0.479566\pi\)
\(74\) 8.70633 1.01209
\(75\) −2.32309 −0.268247
\(76\) −13.9477 −1.59991
\(77\) −1.54117 −0.175633
\(78\) 8.00040 0.905867
\(79\) 10.2566 1.15396 0.576978 0.816759i \(-0.304232\pi\)
0.576978 + 0.816759i \(0.304232\pi\)
\(80\) −9.62505 −1.07611
\(81\) −4.23500 −0.470555
\(82\) −24.5902 −2.71553
\(83\) −0.399742 −0.0438774 −0.0219387 0.999759i \(-0.506984\pi\)
−0.0219387 + 0.999759i \(0.506984\pi\)
\(84\) 2.93463 0.320194
\(85\) −6.17062 −0.669297
\(86\) −5.90568 −0.636826
\(87\) 6.59902 0.707489
\(88\) 16.5684 1.76620
\(89\) 15.2571 1.61725 0.808625 0.588324i \(-0.200212\pi\)
0.808625 + 0.588324i \(0.200212\pi\)
\(90\) −5.19380 −0.547474
\(91\) −1.20873 −0.126709
\(92\) −19.4956 −2.03256
\(93\) −9.63985 −0.999606
\(94\) −26.6915 −2.75302
\(95\) 6.01162 0.616779
\(96\) −2.99825 −0.306008
\(97\) 11.2814 1.14545 0.572724 0.819748i \(-0.305887\pi\)
0.572724 + 0.819748i \(0.305887\pi\)
\(98\) 16.7900 1.69604
\(99\) 3.45541 0.347281
\(100\) −7.18785 −0.718785
\(101\) 6.46082 0.642876 0.321438 0.946931i \(-0.395834\pi\)
0.321438 + 0.946931i \(0.395834\pi\)
\(102\) −11.5306 −1.14170
\(103\) −8.13531 −0.801596 −0.400798 0.916166i \(-0.631267\pi\)
−0.400798 + 0.916166i \(0.631267\pi\)
\(104\) 12.9945 1.27421
\(105\) −1.26486 −0.123438
\(106\) 16.7860 1.63040
\(107\) 10.4304 1.00834 0.504171 0.863604i \(-0.331798\pi\)
0.504171 + 0.863604i \(0.331798\pi\)
\(108\) −23.7650 −2.28678
\(109\) −3.74534 −0.358739 −0.179369 0.983782i \(-0.557406\pi\)
−0.179369 + 0.983782i \(0.557406\pi\)
\(110\) −13.6037 −1.29706
\(111\) −4.75379 −0.451210
\(112\) 2.71734 0.256764
\(113\) −15.2430 −1.43394 −0.716969 0.697105i \(-0.754471\pi\)
−0.716969 + 0.697105i \(0.754471\pi\)
\(114\) 11.2335 1.05211
\(115\) 8.40285 0.783569
\(116\) 20.4180 1.89576
\(117\) 2.71004 0.250543
\(118\) 9.39349 0.864741
\(119\) 1.74208 0.159697
\(120\) 13.5979 1.24131
\(121\) −1.94952 −0.177229
\(122\) 14.5838 1.32036
\(123\) 13.4266 1.21064
\(124\) −29.8266 −2.67851
\(125\) 12.1709 1.08860
\(126\) 1.46631 0.130629
\(127\) −22.0317 −1.95500 −0.977501 0.210932i \(-0.932350\pi\)
−0.977501 + 0.210932i \(0.932350\pi\)
\(128\) 17.1597 1.51672
\(129\) 3.22459 0.283910
\(130\) −10.6693 −0.935757
\(131\) 8.36085 0.730491 0.365246 0.930911i \(-0.380985\pi\)
0.365246 + 0.930911i \(0.380985\pi\)
\(132\) −17.2335 −1.49998
\(133\) −1.69720 −0.147166
\(134\) 19.1693 1.65597
\(135\) 10.2430 0.881577
\(136\) −18.7283 −1.60594
\(137\) −5.51957 −0.471568 −0.235784 0.971805i \(-0.575766\pi\)
−0.235784 + 0.971805i \(0.575766\pi\)
\(138\) 15.7018 1.33663
\(139\) 13.7119 1.16303 0.581514 0.813537i \(-0.302461\pi\)
0.581514 + 0.813537i \(0.302461\pi\)
\(140\) −3.91359 −0.330759
\(141\) 14.5740 1.22735
\(142\) −0.791033 −0.0663820
\(143\) 7.09821 0.593582
\(144\) −6.09244 −0.507703
\(145\) −8.80040 −0.730834
\(146\) −2.73182 −0.226087
\(147\) −9.16758 −0.756129
\(148\) −14.7087 −1.20905
\(149\) −3.14875 −0.257956 −0.128978 0.991647i \(-0.541170\pi\)
−0.128978 + 0.991647i \(0.541170\pi\)
\(150\) 5.78912 0.472680
\(151\) 20.9607 1.70575 0.852877 0.522112i \(-0.174856\pi\)
0.852877 + 0.522112i \(0.174856\pi\)
\(152\) 18.2458 1.47993
\(153\) −3.90586 −0.315770
\(154\) 3.84059 0.309484
\(155\) 12.8556 1.03259
\(156\) −13.5161 −1.08215
\(157\) 6.51309 0.519801 0.259901 0.965635i \(-0.416310\pi\)
0.259901 + 0.965635i \(0.416310\pi\)
\(158\) −25.5594 −2.03339
\(159\) −9.16541 −0.726864
\(160\) 3.99844 0.316105
\(161\) −2.37229 −0.186962
\(162\) 10.5536 0.829168
\(163\) 11.4678 0.898224 0.449112 0.893475i \(-0.351740\pi\)
0.449112 + 0.893475i \(0.351740\pi\)
\(164\) 41.5432 3.24398
\(165\) 7.42784 0.578257
\(166\) 0.996154 0.0773165
\(167\) −7.28721 −0.563901 −0.281951 0.959429i \(-0.590981\pi\)
−0.281951 + 0.959429i \(0.590981\pi\)
\(168\) −3.83895 −0.296182
\(169\) −7.43294 −0.571765
\(170\) 15.3771 1.17937
\(171\) 3.80522 0.290992
\(172\) 9.97719 0.760754
\(173\) 3.74482 0.284714 0.142357 0.989815i \(-0.454532\pi\)
0.142357 + 0.989815i \(0.454532\pi\)
\(174\) −16.4447 −1.24667
\(175\) −0.874640 −0.0661166
\(176\) −15.9575 −1.20284
\(177\) −5.12899 −0.385519
\(178\) −38.0206 −2.84977
\(179\) −7.78663 −0.582000 −0.291000 0.956723i \(-0.593988\pi\)
−0.291000 + 0.956723i \(0.593988\pi\)
\(180\) 8.77452 0.654014
\(181\) 21.5800 1.60403 0.802014 0.597306i \(-0.203762\pi\)
0.802014 + 0.597306i \(0.203762\pi\)
\(182\) 3.01214 0.223275
\(183\) −7.96299 −0.588641
\(184\) 25.5033 1.88013
\(185\) 6.33962 0.466098
\(186\) 24.0224 1.76141
\(187\) −10.2303 −0.748115
\(188\) 45.0932 3.28876
\(189\) −2.89179 −0.210347
\(190\) −14.9809 −1.08683
\(191\) 26.0340 1.88375 0.941876 0.335960i \(-0.109061\pi\)
0.941876 + 0.335960i \(0.109061\pi\)
\(192\) −6.96315 −0.502522
\(193\) 11.0302 0.793971 0.396985 0.917825i \(-0.370056\pi\)
0.396985 + 0.917825i \(0.370056\pi\)
\(194\) −28.1131 −2.01840
\(195\) 5.82559 0.417179
\(196\) −28.3653 −2.02610
\(197\) 9.89003 0.704635 0.352318 0.935880i \(-0.385394\pi\)
0.352318 + 0.935880i \(0.385394\pi\)
\(198\) −8.61085 −0.611946
\(199\) −10.2461 −0.726325 −0.363163 0.931726i \(-0.618303\pi\)
−0.363163 + 0.931726i \(0.618303\pi\)
\(200\) 9.40284 0.664882
\(201\) −10.4667 −0.738266
\(202\) −16.1003 −1.13281
\(203\) 2.48452 0.174379
\(204\) 19.4801 1.36388
\(205\) −17.9056 −1.25058
\(206\) 20.2731 1.41250
\(207\) 5.31881 0.369683
\(208\) −12.5153 −0.867779
\(209\) 9.96673 0.689413
\(210\) 3.15202 0.217510
\(211\) 22.8926 1.57599 0.787995 0.615682i \(-0.211119\pi\)
0.787995 + 0.615682i \(0.211119\pi\)
\(212\) −28.3586 −1.94768
\(213\) 0.431916 0.0295944
\(214\) −25.9924 −1.77680
\(215\) −4.30029 −0.293278
\(216\) 31.0883 2.11529
\(217\) −3.62939 −0.246379
\(218\) 9.33337 0.632135
\(219\) 1.49162 0.100794
\(220\) 22.9824 1.54948
\(221\) −8.02355 −0.539722
\(222\) 11.8464 0.795079
\(223\) 25.1335 1.68306 0.841531 0.540209i \(-0.181655\pi\)
0.841531 + 0.540209i \(0.181655\pi\)
\(224\) −1.12884 −0.0754236
\(225\) 1.96100 0.130733
\(226\) 37.9854 2.52675
\(227\) −5.65346 −0.375233 −0.187617 0.982242i \(-0.560076\pi\)
−0.187617 + 0.982242i \(0.560076\pi\)
\(228\) −18.9782 −1.25686
\(229\) −6.61196 −0.436930 −0.218465 0.975845i \(-0.570105\pi\)
−0.218465 + 0.975845i \(0.570105\pi\)
\(230\) −20.9398 −1.38073
\(231\) −2.09702 −0.137974
\(232\) −26.7099 −1.75359
\(233\) 8.63136 0.565459 0.282729 0.959200i \(-0.408760\pi\)
0.282729 + 0.959200i \(0.408760\pi\)
\(234\) −6.75341 −0.441484
\(235\) −19.4357 −1.26785
\(236\) −15.8696 −1.03302
\(237\) 13.9558 0.906527
\(238\) −4.34126 −0.281402
\(239\) 18.0615 1.16830 0.584151 0.811645i \(-0.301428\pi\)
0.584151 + 0.811645i \(0.301428\pi\)
\(240\) −13.0965 −0.845375
\(241\) −18.8189 −1.21223 −0.606115 0.795377i \(-0.707273\pi\)
−0.606115 + 0.795377i \(0.707273\pi\)
\(242\) 4.85818 0.312296
\(243\) 11.1721 0.716691
\(244\) −24.6382 −1.57730
\(245\) 12.2258 0.781078
\(246\) −33.4590 −2.13327
\(247\) 7.81681 0.497372
\(248\) 39.0179 2.47764
\(249\) −0.543916 −0.0344693
\(250\) −30.3299 −1.91823
\(251\) −20.7115 −1.30730 −0.653650 0.756797i \(-0.726763\pi\)
−0.653650 + 0.756797i \(0.726763\pi\)
\(252\) −2.47722 −0.156050
\(253\) 13.9312 0.875845
\(254\) 54.9030 3.44492
\(255\) −8.39615 −0.525788
\(256\) −32.5269 −2.03293
\(257\) −6.51829 −0.406600 −0.203300 0.979116i \(-0.565167\pi\)
−0.203300 + 0.979116i \(0.565167\pi\)
\(258\) −8.03567 −0.500279
\(259\) −1.78980 −0.111213
\(260\) 18.0249 1.11786
\(261\) −5.57046 −0.344803
\(262\) −20.8352 −1.28720
\(263\) −1.37161 −0.0845770 −0.0422885 0.999105i \(-0.513465\pi\)
−0.0422885 + 0.999105i \(0.513465\pi\)
\(264\) 22.5441 1.38749
\(265\) 12.2229 0.750848
\(266\) 4.22940 0.259321
\(267\) 20.7598 1.27048
\(268\) −32.3850 −1.97823
\(269\) −25.6805 −1.56577 −0.782883 0.622170i \(-0.786251\pi\)
−0.782883 + 0.622170i \(0.786251\pi\)
\(270\) −25.5255 −1.55343
\(271\) −30.7191 −1.86605 −0.933026 0.359810i \(-0.882842\pi\)
−0.933026 + 0.359810i \(0.882842\pi\)
\(272\) 18.0377 1.09370
\(273\) −1.64468 −0.0995403
\(274\) 13.7547 0.830953
\(275\) 5.13629 0.309730
\(276\) −26.5270 −1.59674
\(277\) −15.9672 −0.959375 −0.479687 0.877439i \(-0.659250\pi\)
−0.479687 + 0.877439i \(0.659250\pi\)
\(278\) −34.1699 −2.04938
\(279\) 8.13732 0.487169
\(280\) 5.11960 0.305954
\(281\) −29.8097 −1.77830 −0.889149 0.457618i \(-0.848703\pi\)
−0.889149 + 0.457618i \(0.848703\pi\)
\(282\) −36.3182 −2.16272
\(283\) 22.5367 1.33967 0.669834 0.742511i \(-0.266365\pi\)
0.669834 + 0.742511i \(0.266365\pi\)
\(284\) 1.33639 0.0793001
\(285\) 8.17982 0.484531
\(286\) −17.6887 −1.04595
\(287\) 5.05510 0.298393
\(288\) 2.53092 0.149136
\(289\) −5.43603 −0.319766
\(290\) 21.9305 1.28781
\(291\) 15.3502 0.899843
\(292\) 4.61521 0.270085
\(293\) −7.60079 −0.444043 −0.222021 0.975042i \(-0.571265\pi\)
−0.222021 + 0.975042i \(0.571265\pi\)
\(294\) 22.8455 1.33238
\(295\) 6.83999 0.398239
\(296\) 19.2413 1.11838
\(297\) 16.9820 0.985393
\(298\) 7.84667 0.454545
\(299\) 10.9261 0.631871
\(300\) −9.78028 −0.564665
\(301\) 1.21406 0.0699770
\(302\) −52.2338 −3.00572
\(303\) 8.79103 0.505031
\(304\) −17.5730 −1.00788
\(305\) 10.6194 0.608064
\(306\) 9.73338 0.556420
\(307\) 25.1769 1.43692 0.718460 0.695568i \(-0.244847\pi\)
0.718460 + 0.695568i \(0.244847\pi\)
\(308\) −6.48839 −0.369710
\(309\) −11.0694 −0.629719
\(310\) −32.0361 −1.81953
\(311\) −11.5492 −0.654892 −0.327446 0.944870i \(-0.606188\pi\)
−0.327446 + 0.944870i \(0.606188\pi\)
\(312\) 17.6811 1.00100
\(313\) −0.629683 −0.0355918 −0.0177959 0.999842i \(-0.505665\pi\)
−0.0177959 + 0.999842i \(0.505665\pi\)
\(314\) −16.2306 −0.915945
\(315\) 1.06771 0.0601587
\(316\) 43.1806 2.42910
\(317\) 9.76090 0.548227 0.274113 0.961697i \(-0.411616\pi\)
0.274113 + 0.961697i \(0.411616\pi\)
\(318\) 22.8401 1.28081
\(319\) −14.5903 −0.816899
\(320\) 9.28601 0.519104
\(321\) 14.1923 0.792134
\(322\) 5.91172 0.329447
\(323\) −11.2660 −0.626858
\(324\) −17.8295 −0.990526
\(325\) 4.02835 0.223453
\(326\) −28.5776 −1.58277
\(327\) −5.09616 −0.281819
\(328\) −54.3450 −3.00070
\(329\) 5.48708 0.302512
\(330\) −18.5101 −1.01895
\(331\) 35.6830 1.96132 0.980659 0.195725i \(-0.0627060\pi\)
0.980659 + 0.195725i \(0.0627060\pi\)
\(332\) −1.68293 −0.0923625
\(333\) 4.01283 0.219902
\(334\) 18.1597 0.993654
\(335\) 13.9583 0.762626
\(336\) 3.69739 0.201709
\(337\) −13.6237 −0.742131 −0.371066 0.928607i \(-0.621008\pi\)
−0.371066 + 0.928607i \(0.621008\pi\)
\(338\) 18.5228 1.00751
\(339\) −20.7406 −1.12648
\(340\) −25.9785 −1.40888
\(341\) 21.3135 1.15419
\(342\) −9.48258 −0.512759
\(343\) −7.03761 −0.379995
\(344\) −13.0517 −0.703703
\(345\) 11.4335 0.615558
\(346\) −9.33207 −0.501695
\(347\) 28.1710 1.51230 0.756151 0.654398i \(-0.227078\pi\)
0.756151 + 0.654398i \(0.227078\pi\)
\(348\) 27.7821 1.48928
\(349\) 9.89154 0.529482 0.264741 0.964320i \(-0.414714\pi\)
0.264741 + 0.964320i \(0.414714\pi\)
\(350\) 2.17960 0.116504
\(351\) 13.3188 0.710904
\(352\) 6.62906 0.353330
\(353\) 9.05771 0.482093 0.241047 0.970514i \(-0.422509\pi\)
0.241047 + 0.970514i \(0.422509\pi\)
\(354\) 12.7814 0.679325
\(355\) −0.576001 −0.0305709
\(356\) 64.2329 3.40434
\(357\) 2.37040 0.125455
\(358\) 19.4042 1.02555
\(359\) −0.380069 −0.0200593 −0.0100296 0.999950i \(-0.503193\pi\)
−0.0100296 + 0.999950i \(0.503193\pi\)
\(360\) −11.4785 −0.604968
\(361\) −8.02427 −0.422330
\(362\) −53.7772 −2.82646
\(363\) −2.65264 −0.139228
\(364\) −5.08878 −0.266725
\(365\) −1.98921 −0.104120
\(366\) 19.8437 1.03725
\(367\) −20.5074 −1.07048 −0.535238 0.844701i \(-0.679778\pi\)
−0.535238 + 0.844701i \(0.679778\pi\)
\(368\) −24.5629 −1.28043
\(369\) −11.3339 −0.590017
\(370\) −15.7983 −0.821314
\(371\) −3.45076 −0.179155
\(372\) −40.5841 −2.10419
\(373\) 28.9303 1.49796 0.748978 0.662595i \(-0.230545\pi\)
0.748978 + 0.662595i \(0.230545\pi\)
\(374\) 25.4939 1.31826
\(375\) 16.5606 0.855185
\(376\) −58.9890 −3.04212
\(377\) −11.4430 −0.589345
\(378\) 7.20633 0.370654
\(379\) −1.87085 −0.0960993 −0.0480497 0.998845i \(-0.515301\pi\)
−0.0480497 + 0.998845i \(0.515301\pi\)
\(380\) 25.3091 1.29833
\(381\) −29.9779 −1.53581
\(382\) −64.8765 −3.31937
\(383\) −12.8186 −0.655002 −0.327501 0.944851i \(-0.606206\pi\)
−0.327501 + 0.944851i \(0.606206\pi\)
\(384\) 23.3486 1.19151
\(385\) 2.79658 0.142527
\(386\) −27.4872 −1.39906
\(387\) −2.72199 −0.138366
\(388\) 47.4949 2.41119
\(389\) −11.9404 −0.605405 −0.302702 0.953085i \(-0.597889\pi\)
−0.302702 + 0.953085i \(0.597889\pi\)
\(390\) −14.5173 −0.735114
\(391\) −15.7473 −0.796373
\(392\) 37.1063 1.87415
\(393\) 11.3763 0.573860
\(394\) −24.6459 −1.24164
\(395\) −18.6114 −0.936439
\(396\) 14.5474 0.731033
\(397\) −5.56832 −0.279466 −0.139733 0.990189i \(-0.544624\pi\)
−0.139733 + 0.990189i \(0.544624\pi\)
\(398\) 25.5332 1.27986
\(399\) −2.30932 −0.115611
\(400\) −9.05612 −0.452806
\(401\) 20.2629 1.01188 0.505941 0.862568i \(-0.331145\pi\)
0.505941 + 0.862568i \(0.331145\pi\)
\(402\) 26.0830 1.30090
\(403\) 16.7160 0.832681
\(404\) 27.2003 1.35326
\(405\) 7.68472 0.381857
\(406\) −6.19142 −0.307275
\(407\) 10.5105 0.520987
\(408\) −25.4830 −1.26160
\(409\) −24.1456 −1.19392 −0.596962 0.802269i \(-0.703626\pi\)
−0.596962 + 0.802269i \(0.703626\pi\)
\(410\) 44.6207 2.20366
\(411\) −7.51029 −0.370455
\(412\) −34.2499 −1.68737
\(413\) −1.93106 −0.0950213
\(414\) −13.2544 −0.651420
\(415\) 0.725362 0.0356066
\(416\) 5.19911 0.254907
\(417\) 18.6573 0.913653
\(418\) −24.8370 −1.21482
\(419\) 8.70428 0.425232 0.212616 0.977136i \(-0.431802\pi\)
0.212616 + 0.977136i \(0.431802\pi\)
\(420\) −5.32510 −0.259838
\(421\) 22.1647 1.08024 0.540122 0.841587i \(-0.318378\pi\)
0.540122 + 0.841587i \(0.318378\pi\)
\(422\) −57.0482 −2.77706
\(423\) −12.3024 −0.598162
\(424\) 37.0975 1.80162
\(425\) −5.80587 −0.281626
\(426\) −1.07633 −0.0521485
\(427\) −2.99806 −0.145086
\(428\) 43.9122 2.12257
\(429\) 9.65830 0.466307
\(430\) 10.7163 0.516786
\(431\) −33.2190 −1.60010 −0.800052 0.599931i \(-0.795195\pi\)
−0.800052 + 0.599931i \(0.795195\pi\)
\(432\) −29.9419 −1.44058
\(433\) −23.0968 −1.10996 −0.554980 0.831864i \(-0.687274\pi\)
−0.554980 + 0.831864i \(0.687274\pi\)
\(434\) 9.04442 0.434146
\(435\) −11.9744 −0.574130
\(436\) −15.7680 −0.755151
\(437\) 15.3415 0.733884
\(438\) −3.71710 −0.177610
\(439\) −28.0195 −1.33730 −0.668650 0.743578i \(-0.733127\pi\)
−0.668650 + 0.743578i \(0.733127\pi\)
\(440\) −30.0647 −1.43328
\(441\) 7.73866 0.368508
\(442\) 19.9946 0.951047
\(443\) −7.63730 −0.362859 −0.181430 0.983404i \(-0.558072\pi\)
−0.181430 + 0.983404i \(0.558072\pi\)
\(444\) −20.0136 −0.949804
\(445\) −27.6852 −1.31240
\(446\) −62.6325 −2.96573
\(447\) −4.28440 −0.202645
\(448\) −2.62162 −0.123860
\(449\) 21.8958 1.03333 0.516664 0.856188i \(-0.327174\pi\)
0.516664 + 0.856188i \(0.327174\pi\)
\(450\) −4.88679 −0.230366
\(451\) −29.6859 −1.39786
\(452\) −64.1734 −3.01846
\(453\) 28.5205 1.34001
\(454\) 14.0884 0.661201
\(455\) 2.19333 0.102825
\(456\) 24.8264 1.16260
\(457\) 22.8014 1.06661 0.533303 0.845924i \(-0.320950\pi\)
0.533303 + 0.845924i \(0.320950\pi\)
\(458\) 16.4770 0.769917
\(459\) −19.1958 −0.895981
\(460\) 35.3762 1.64943
\(461\) 12.6269 0.588095 0.294048 0.955791i \(-0.404998\pi\)
0.294048 + 0.955791i \(0.404998\pi\)
\(462\) 5.22577 0.243125
\(463\) 32.7446 1.52177 0.760886 0.648885i \(-0.224764\pi\)
0.760886 + 0.648885i \(0.224764\pi\)
\(464\) 25.7250 1.19425
\(465\) 17.4922 0.811183
\(466\) −21.5093 −0.996398
\(467\) −21.1605 −0.979189 −0.489595 0.871950i \(-0.662855\pi\)
−0.489595 + 0.871950i \(0.662855\pi\)
\(468\) 11.4094 0.527398
\(469\) −3.94071 −0.181965
\(470\) 48.4337 2.23408
\(471\) 8.86215 0.408346
\(472\) 20.7599 0.955552
\(473\) −7.12950 −0.327815
\(474\) −34.7778 −1.59740
\(475\) 5.65628 0.259528
\(476\) 7.33423 0.336164
\(477\) 7.73683 0.354245
\(478\) −45.0092 −2.05867
\(479\) −25.1452 −1.14891 −0.574457 0.818534i \(-0.694787\pi\)
−0.574457 + 0.818534i \(0.694787\pi\)
\(480\) 5.44055 0.248326
\(481\) 8.24330 0.375862
\(482\) 46.8965 2.13608
\(483\) −3.22789 −0.146874
\(484\) −8.20752 −0.373069
\(485\) −20.4709 −0.929535
\(486\) −27.8408 −1.26289
\(487\) 40.5311 1.83664 0.918321 0.395838i \(-0.129546\pi\)
0.918321 + 0.395838i \(0.129546\pi\)
\(488\) 32.2307 1.45902
\(489\) 15.6038 0.705628
\(490\) −30.4666 −1.37634
\(491\) 4.51990 0.203980 0.101990 0.994785i \(-0.467479\pi\)
0.101990 + 0.994785i \(0.467479\pi\)
\(492\) 56.5265 2.54841
\(493\) 16.4923 0.742776
\(494\) −19.4794 −0.876421
\(495\) −6.27009 −0.281820
\(496\) −37.5791 −1.68735
\(497\) 0.162616 0.00729433
\(498\) 1.35543 0.0607385
\(499\) 36.1623 1.61885 0.809423 0.587226i \(-0.199780\pi\)
0.809423 + 0.587226i \(0.199780\pi\)
\(500\) 51.2400 2.29152
\(501\) −9.91547 −0.442991
\(502\) 51.6130 2.30360
\(503\) −26.9054 −1.19965 −0.599826 0.800131i \(-0.704763\pi\)
−0.599826 + 0.800131i \(0.704763\pi\)
\(504\) 3.24059 0.144347
\(505\) −11.7236 −0.521695
\(506\) −34.7164 −1.54333
\(507\) −10.1138 −0.449168
\(508\) −92.7543 −4.11531
\(509\) 3.48536 0.154486 0.0772429 0.997012i \(-0.475388\pi\)
0.0772429 + 0.997012i \(0.475388\pi\)
\(510\) 20.9232 0.926493
\(511\) 0.561593 0.0248434
\(512\) 46.7375 2.06553
\(513\) 18.7012 0.825676
\(514\) 16.2435 0.716472
\(515\) 14.7621 0.650497
\(516\) 13.5756 0.597634
\(517\) −32.2227 −1.41715
\(518\) 4.46016 0.195968
\(519\) 5.09546 0.223666
\(520\) −23.5794 −1.03403
\(521\) −11.8954 −0.521145 −0.260573 0.965454i \(-0.583911\pi\)
−0.260573 + 0.965454i \(0.583911\pi\)
\(522\) 13.8815 0.607578
\(523\) 21.5635 0.942907 0.471453 0.881891i \(-0.343730\pi\)
0.471453 + 0.881891i \(0.343730\pi\)
\(524\) 35.1995 1.53770
\(525\) −1.19009 −0.0519400
\(526\) 3.41804 0.149034
\(527\) −24.0919 −1.04946
\(528\) −21.7128 −0.944929
\(529\) −1.55615 −0.0676585
\(530\) −30.4594 −1.32307
\(531\) 4.32956 0.187887
\(532\) −7.14525 −0.309786
\(533\) −23.2824 −1.00847
\(534\) −51.7334 −2.23872
\(535\) −18.9267 −0.818272
\(536\) 42.3647 1.82988
\(537\) −10.5950 −0.457208
\(538\) 63.9955 2.75904
\(539\) 20.2693 0.873060
\(540\) 43.1233 1.85573
\(541\) 36.8686 1.58510 0.792552 0.609804i \(-0.208752\pi\)
0.792552 + 0.609804i \(0.208752\pi\)
\(542\) 76.5517 3.28818
\(543\) 29.3632 1.26009
\(544\) −7.49324 −0.321270
\(545\) 6.79621 0.291117
\(546\) 4.09852 0.175401
\(547\) 6.52774 0.279106 0.139553 0.990215i \(-0.455433\pi\)
0.139553 + 0.990215i \(0.455433\pi\)
\(548\) −23.2376 −0.992659
\(549\) 6.72183 0.286881
\(550\) −12.7996 −0.545777
\(551\) −16.0674 −0.684492
\(552\) 34.7015 1.47700
\(553\) 5.25435 0.223437
\(554\) 39.7901 1.69052
\(555\) 8.62611 0.366158
\(556\) 57.7275 2.44819
\(557\) 35.5163 1.50487 0.752437 0.658664i \(-0.228878\pi\)
0.752437 + 0.658664i \(0.228878\pi\)
\(558\) −20.2781 −0.858442
\(559\) −5.59160 −0.236499
\(560\) −4.93081 −0.208365
\(561\) −13.9201 −0.587706
\(562\) 74.2856 3.13355
\(563\) 36.6482 1.54454 0.772269 0.635296i \(-0.219122\pi\)
0.772269 + 0.635296i \(0.219122\pi\)
\(564\) 61.3568 2.58359
\(565\) 27.6595 1.16364
\(566\) −56.1613 −2.36064
\(567\) −2.16955 −0.0911124
\(568\) −1.74821 −0.0733532
\(569\) −7.17768 −0.300904 −0.150452 0.988617i \(-0.548073\pi\)
−0.150452 + 0.988617i \(0.548073\pi\)
\(570\) −20.3840 −0.853794
\(571\) 2.26544 0.0948058 0.0474029 0.998876i \(-0.484906\pi\)
0.0474029 + 0.998876i \(0.484906\pi\)
\(572\) 29.8837 1.24950
\(573\) 35.4236 1.47984
\(574\) −12.5973 −0.525801
\(575\) 7.90616 0.329710
\(576\) 5.87783 0.244910
\(577\) −13.4283 −0.559029 −0.279515 0.960141i \(-0.590174\pi\)
−0.279515 + 0.960141i \(0.590174\pi\)
\(578\) 13.5465 0.563462
\(579\) 15.0084 0.623729
\(580\) −37.0500 −1.53842
\(581\) −0.204784 −0.00849586
\(582\) −38.2525 −1.58562
\(583\) 20.2645 0.839270
\(584\) −6.03742 −0.249830
\(585\) −4.91758 −0.203317
\(586\) 18.9411 0.782450
\(587\) 27.4001 1.13092 0.565462 0.824774i \(-0.308698\pi\)
0.565462 + 0.824774i \(0.308698\pi\)
\(588\) −38.5958 −1.59166
\(589\) 23.4712 0.967113
\(590\) −17.0452 −0.701740
\(591\) 13.4570 0.553549
\(592\) −18.5317 −0.761650
\(593\) −13.0818 −0.537206 −0.268603 0.963251i \(-0.586562\pi\)
−0.268603 + 0.963251i \(0.586562\pi\)
\(594\) −42.3189 −1.73637
\(595\) −3.16114 −0.129594
\(596\) −13.2563 −0.543001
\(597\) −13.9415 −0.570588
\(598\) −27.2277 −1.11342
\(599\) 23.5557 0.962459 0.481230 0.876595i \(-0.340190\pi\)
0.481230 + 0.876595i \(0.340190\pi\)
\(600\) 12.7941 0.522319
\(601\) 14.3441 0.585108 0.292554 0.956249i \(-0.405495\pi\)
0.292554 + 0.956249i \(0.405495\pi\)
\(602\) −3.02542 −0.123307
\(603\) 8.83531 0.359802
\(604\) 88.2450 3.59064
\(605\) 3.53754 0.143822
\(606\) −21.9072 −0.889918
\(607\) −13.9269 −0.565274 −0.282637 0.959227i \(-0.591209\pi\)
−0.282637 + 0.959227i \(0.591209\pi\)
\(608\) 7.30016 0.296061
\(609\) 3.38061 0.136989
\(610\) −26.4634 −1.07147
\(611\) −25.2719 −1.02239
\(612\) −16.4438 −0.664701
\(613\) 18.6322 0.752549 0.376275 0.926508i \(-0.377205\pi\)
0.376275 + 0.926508i \(0.377205\pi\)
\(614\) −62.7406 −2.53200
\(615\) −24.3636 −0.982435
\(616\) 8.48783 0.341984
\(617\) 42.3108 1.70337 0.851685 0.524054i \(-0.175581\pi\)
0.851685 + 0.524054i \(0.175581\pi\)
\(618\) 27.5850 1.10963
\(619\) −17.1210 −0.688150 −0.344075 0.938942i \(-0.611808\pi\)
−0.344075 + 0.938942i \(0.611808\pi\)
\(620\) 54.1226 2.17362
\(621\) 26.1399 1.04896
\(622\) 28.7804 1.15399
\(623\) 7.81606 0.313144
\(624\) −17.0291 −0.681712
\(625\) −13.5485 −0.541940
\(626\) 1.56917 0.0627165
\(627\) 13.5614 0.541590
\(628\) 27.4203 1.09419
\(629\) −11.8807 −0.473714
\(630\) −2.66073 −0.106006
\(631\) −16.8010 −0.668839 −0.334420 0.942424i \(-0.608540\pi\)
−0.334420 + 0.942424i \(0.608540\pi\)
\(632\) −56.4870 −2.24693
\(633\) 31.1492 1.23807
\(634\) −24.3241 −0.966033
\(635\) 39.9783 1.58649
\(636\) −38.5866 −1.53006
\(637\) 15.8970 0.629863
\(638\) 36.3589 1.43946
\(639\) −0.364595 −0.0144232
\(640\) −31.1376 −1.23082
\(641\) 38.1190 1.50561 0.752805 0.658244i \(-0.228700\pi\)
0.752805 + 0.658244i \(0.228700\pi\)
\(642\) −35.3670 −1.39582
\(643\) 24.9236 0.982891 0.491445 0.870908i \(-0.336469\pi\)
0.491445 + 0.870908i \(0.336469\pi\)
\(644\) −9.98740 −0.393559
\(645\) −5.85127 −0.230393
\(646\) 28.0748 1.10459
\(647\) 30.6660 1.20561 0.602803 0.797890i \(-0.294050\pi\)
0.602803 + 0.797890i \(0.294050\pi\)
\(648\) 23.3238 0.916244
\(649\) 11.3401 0.445137
\(650\) −10.0386 −0.393747
\(651\) −4.93839 −0.193551
\(652\) 48.2796 1.89078
\(653\) −41.6499 −1.62988 −0.814942 0.579542i \(-0.803231\pi\)
−0.814942 + 0.579542i \(0.803231\pi\)
\(654\) 12.6996 0.496594
\(655\) −15.1714 −0.592796
\(656\) 52.3411 2.04358
\(657\) −1.25913 −0.0491232
\(658\) −13.6738 −0.533059
\(659\) −3.44756 −0.134298 −0.0671488 0.997743i \(-0.521390\pi\)
−0.0671488 + 0.997743i \(0.521390\pi\)
\(660\) 31.2715 1.21724
\(661\) −5.20211 −0.202339 −0.101169 0.994869i \(-0.532258\pi\)
−0.101169 + 0.994869i \(0.532258\pi\)
\(662\) −88.9219 −3.45605
\(663\) −10.9174 −0.423996
\(664\) 2.20153 0.0854360
\(665\) 3.07969 0.119425
\(666\) −9.99996 −0.387490
\(667\) −22.4584 −0.869593
\(668\) −30.6794 −1.18702
\(669\) 34.1983 1.32218
\(670\) −34.7841 −1.34383
\(671\) 17.6060 0.679672
\(672\) −1.53597 −0.0592514
\(673\) 2.62727 0.101274 0.0506369 0.998717i \(-0.483875\pi\)
0.0506369 + 0.998717i \(0.483875\pi\)
\(674\) 33.9502 1.30771
\(675\) 9.63753 0.370949
\(676\) −31.2929 −1.20357
\(677\) 25.1463 0.966452 0.483226 0.875496i \(-0.339465\pi\)
0.483226 + 0.875496i \(0.339465\pi\)
\(678\) 51.6855 1.98497
\(679\) 5.77932 0.221790
\(680\) 33.9839 1.30322
\(681\) −7.69248 −0.294777
\(682\) −53.1130 −2.03380
\(683\) −29.8515 −1.14224 −0.571119 0.820867i \(-0.693490\pi\)
−0.571119 + 0.820867i \(0.693490\pi\)
\(684\) 16.0201 0.612544
\(685\) 10.0157 0.382679
\(686\) 17.5377 0.669592
\(687\) −8.99667 −0.343244
\(688\) 12.5705 0.479244
\(689\) 15.8933 0.605485
\(690\) −28.4922 −1.08468
\(691\) −33.7003 −1.28202 −0.641010 0.767532i \(-0.721484\pi\)
−0.641010 + 0.767532i \(0.721484\pi\)
\(692\) 15.7658 0.599327
\(693\) 1.77017 0.0672431
\(694\) −70.2021 −2.66483
\(695\) −24.8813 −0.943800
\(696\) −36.3433 −1.37759
\(697\) 33.5558 1.27102
\(698\) −24.6496 −0.933003
\(699\) 11.7444 0.444214
\(700\) −3.68226 −0.139176
\(701\) 4.91523 0.185646 0.0928228 0.995683i \(-0.470411\pi\)
0.0928228 + 0.995683i \(0.470411\pi\)
\(702\) −33.1903 −1.25269
\(703\) 11.5746 0.436543
\(704\) 15.3954 0.580235
\(705\) −26.4455 −0.995997
\(706\) −22.5718 −0.849499
\(707\) 3.30981 0.124478
\(708\) −21.5932 −0.811523
\(709\) 37.5864 1.41159 0.705793 0.708418i \(-0.250591\pi\)
0.705793 + 0.708418i \(0.250591\pi\)
\(710\) 1.43539 0.0538692
\(711\) −11.7806 −0.441806
\(712\) −84.0267 −3.14904
\(713\) 32.8072 1.22864
\(714\) −5.90701 −0.221064
\(715\) −12.8802 −0.481694
\(716\) −32.7819 −1.22512
\(717\) 24.5757 0.917797
\(718\) 0.947130 0.0353466
\(719\) 29.5220 1.10098 0.550492 0.834841i \(-0.314440\pi\)
0.550492 + 0.834841i \(0.314440\pi\)
\(720\) 11.0552 0.412003
\(721\) −4.16763 −0.155211
\(722\) 19.9964 0.744190
\(723\) −25.6062 −0.952306
\(724\) 90.8524 3.37650
\(725\) −8.28021 −0.307519
\(726\) 6.61037 0.245334
\(727\) 14.0981 0.522868 0.261434 0.965221i \(-0.415805\pi\)
0.261434 + 0.965221i \(0.415805\pi\)
\(728\) 6.65693 0.246722
\(729\) 27.9065 1.03357
\(730\) 4.95710 0.183471
\(731\) 8.05891 0.298070
\(732\) −33.5244 −1.23910
\(733\) −45.4599 −1.67910 −0.839551 0.543282i \(-0.817182\pi\)
−0.839551 + 0.543282i \(0.817182\pi\)
\(734\) 51.1042 1.88629
\(735\) 16.6353 0.613601
\(736\) 10.2039 0.376122
\(737\) 23.1417 0.852435
\(738\) 28.2439 1.03967
\(739\) −8.32747 −0.306331 −0.153166 0.988201i \(-0.548947\pi\)
−0.153166 + 0.988201i \(0.548947\pi\)
\(740\) 26.6900 0.981144
\(741\) 10.6361 0.390726
\(742\) 8.59928 0.315690
\(743\) 22.1916 0.814130 0.407065 0.913399i \(-0.366552\pi\)
0.407065 + 0.913399i \(0.366552\pi\)
\(744\) 53.0903 1.94639
\(745\) 5.71365 0.209332
\(746\) −72.0942 −2.63956
\(747\) 0.459137 0.0167990
\(748\) −43.0700 −1.57479
\(749\) 5.34337 0.195242
\(750\) −41.2689 −1.50693
\(751\) 3.98537 0.145428 0.0727141 0.997353i \(-0.476834\pi\)
0.0727141 + 0.997353i \(0.476834\pi\)
\(752\) 56.8138 2.07179
\(753\) −28.1815 −1.02699
\(754\) 28.5159 1.03849
\(755\) −38.0347 −1.38422
\(756\) −12.1745 −0.442784
\(757\) 16.1230 0.586002 0.293001 0.956112i \(-0.405346\pi\)
0.293001 + 0.956112i \(0.405346\pi\)
\(758\) 4.66216 0.169337
\(759\) 18.9557 0.688047
\(760\) −33.1083 −1.20096
\(761\) 52.0191 1.88569 0.942845 0.333231i \(-0.108139\pi\)
0.942845 + 0.333231i \(0.108139\pi\)
\(762\) 74.7047 2.70626
\(763\) −1.91870 −0.0694616
\(764\) 109.604 3.96533
\(765\) 7.08748 0.256248
\(766\) 31.9440 1.15418
\(767\) 8.89392 0.321141
\(768\) −44.2583 −1.59704
\(769\) 3.18271 0.114771 0.0573857 0.998352i \(-0.481724\pi\)
0.0573857 + 0.998352i \(0.481724\pi\)
\(770\) −6.96905 −0.251147
\(771\) −8.86923 −0.319417
\(772\) 46.4375 1.67132
\(773\) 43.2851 1.55686 0.778428 0.627734i \(-0.216017\pi\)
0.778428 + 0.627734i \(0.216017\pi\)
\(774\) 6.78318 0.243816
\(775\) 12.0957 0.434492
\(776\) −62.1308 −2.23036
\(777\) −2.43532 −0.0873665
\(778\) 29.7555 1.06679
\(779\) −32.6912 −1.17128
\(780\) 24.5259 0.878168
\(781\) −0.954957 −0.0341710
\(782\) 39.2421 1.40329
\(783\) −27.3766 −0.978360
\(784\) −35.7380 −1.27636
\(785\) −11.8185 −0.421820
\(786\) −28.3498 −1.01120
\(787\) 42.2240 1.50512 0.752562 0.658522i \(-0.228818\pi\)
0.752562 + 0.658522i \(0.228818\pi\)
\(788\) 41.6373 1.48327
\(789\) −1.86630 −0.0664421
\(790\) 46.3794 1.65010
\(791\) −7.80882 −0.277650
\(792\) −19.0302 −0.676210
\(793\) 13.8082 0.490344
\(794\) 13.8762 0.492448
\(795\) 16.6313 0.589852
\(796\) −43.1363 −1.52893
\(797\) 22.7388 0.805449 0.402725 0.915321i \(-0.368063\pi\)
0.402725 + 0.915321i \(0.368063\pi\)
\(798\) 5.75481 0.203718
\(799\) 36.4233 1.28856
\(800\) 3.76210 0.133010
\(801\) −17.5241 −0.619183
\(802\) −50.4951 −1.78304
\(803\) −3.29793 −0.116382
\(804\) −44.0652 −1.55406
\(805\) 4.30469 0.151720
\(806\) −41.6561 −1.46727
\(807\) −34.9426 −1.23004
\(808\) −35.5822 −1.25178
\(809\) −0.0868030 −0.00305183 −0.00152591 0.999999i \(-0.500486\pi\)
−0.00152591 + 0.999999i \(0.500486\pi\)
\(810\) −19.1503 −0.672872
\(811\) −31.4066 −1.10283 −0.551417 0.834230i \(-0.685913\pi\)
−0.551417 + 0.834230i \(0.685913\pi\)
\(812\) 10.4599 0.367071
\(813\) −41.7984 −1.46594
\(814\) −26.1921 −0.918034
\(815\) −20.8091 −0.728911
\(816\) 24.5433 0.859188
\(817\) −7.85127 −0.274681
\(818\) 60.1708 2.10382
\(819\) 1.38833 0.0485120
\(820\) −75.3833 −2.63250
\(821\) −6.67996 −0.233132 −0.116566 0.993183i \(-0.537189\pi\)
−0.116566 + 0.993183i \(0.537189\pi\)
\(822\) 18.7156 0.652782
\(823\) 29.6088 1.03210 0.516050 0.856559i \(-0.327402\pi\)
0.516050 + 0.856559i \(0.327402\pi\)
\(824\) 44.8043 1.56083
\(825\) 6.98879 0.243318
\(826\) 4.81219 0.167437
\(827\) −43.5090 −1.51296 −0.756479 0.654018i \(-0.773082\pi\)
−0.756479 + 0.654018i \(0.773082\pi\)
\(828\) 22.3924 0.778188
\(829\) 27.0151 0.938272 0.469136 0.883126i \(-0.344565\pi\)
0.469136 + 0.883126i \(0.344565\pi\)
\(830\) −1.80760 −0.0627426
\(831\) −21.7260 −0.753667
\(832\) 12.0744 0.418606
\(833\) −22.9116 −0.793841
\(834\) −46.4939 −1.60995
\(835\) 13.2232 0.457608
\(836\) 41.9602 1.45122
\(837\) 39.9917 1.38232
\(838\) −21.6910 −0.749303
\(839\) −17.6099 −0.607960 −0.303980 0.952678i \(-0.598316\pi\)
−0.303980 + 0.952678i \(0.598316\pi\)
\(840\) 6.96607 0.240352
\(841\) −5.47903 −0.188932
\(842\) −55.2344 −1.90350
\(843\) −40.5611 −1.39700
\(844\) 96.3785 3.31748
\(845\) 13.4876 0.463989
\(846\) 30.6574 1.05402
\(847\) −0.998717 −0.0343163
\(848\) −35.7296 −1.22696
\(849\) 30.6650 1.05242
\(850\) 14.4682 0.496255
\(851\) 16.1785 0.554594
\(852\) 1.81838 0.0622967
\(853\) −11.5200 −0.394438 −0.197219 0.980359i \(-0.563191\pi\)
−0.197219 + 0.980359i \(0.563191\pi\)
\(854\) 7.47114 0.255657
\(855\) −6.90486 −0.236141
\(856\) −57.4440 −1.96340
\(857\) 42.6810 1.45795 0.728977 0.684538i \(-0.239996\pi\)
0.728977 + 0.684538i \(0.239996\pi\)
\(858\) −24.0684 −0.821682
\(859\) 5.37251 0.183308 0.0916539 0.995791i \(-0.470785\pi\)
0.0916539 + 0.995791i \(0.470785\pi\)
\(860\) −18.1044 −0.617354
\(861\) 6.87831 0.234412
\(862\) 82.7816 2.81955
\(863\) −39.3149 −1.33830 −0.669148 0.743129i \(-0.733341\pi\)
−0.669148 + 0.743129i \(0.733341\pi\)
\(864\) 12.4385 0.423166
\(865\) −6.79526 −0.231046
\(866\) 57.5570 1.95587
\(867\) −7.39663 −0.251203
\(868\) −15.2799 −0.518632
\(869\) −30.8560 −1.04672
\(870\) 29.8402 1.01168
\(871\) 18.1498 0.614982
\(872\) 20.6270 0.698519
\(873\) −12.9576 −0.438548
\(874\) −38.2309 −1.29318
\(875\) 6.23504 0.210783
\(876\) 6.27976 0.212173
\(877\) 11.6510 0.393426 0.196713 0.980461i \(-0.436973\pi\)
0.196713 + 0.980461i \(0.436973\pi\)
\(878\) 69.8245 2.35646
\(879\) −10.3421 −0.348832
\(880\) 28.9560 0.976108
\(881\) −46.9121 −1.58051 −0.790255 0.612778i \(-0.790052\pi\)
−0.790255 + 0.612778i \(0.790052\pi\)
\(882\) −19.2847 −0.649349
\(883\) −37.5313 −1.26303 −0.631514 0.775364i \(-0.717566\pi\)
−0.631514 + 0.775364i \(0.717566\pi\)
\(884\) −33.7794 −1.13612
\(885\) 9.30695 0.312850
\(886\) 19.0321 0.639396
\(887\) −51.6675 −1.73482 −0.867412 0.497590i \(-0.834218\pi\)
−0.867412 + 0.497590i \(0.834218\pi\)
\(888\) 26.1809 0.878575
\(889\) −11.2866 −0.378542
\(890\) 68.9913 2.31259
\(891\) 12.7406 0.426825
\(892\) 105.813 3.54287
\(893\) −35.4848 −1.18745
\(894\) 10.6767 0.357083
\(895\) 14.1294 0.472295
\(896\) 8.79073 0.293678
\(897\) 14.8668 0.496387
\(898\) −54.5643 −1.82083
\(899\) −34.3594 −1.14595
\(900\) 8.25586 0.275195
\(901\) −22.9062 −0.763117
\(902\) 73.9771 2.46317
\(903\) 1.65193 0.0549726
\(904\) 83.9489 2.79210
\(905\) −39.1585 −1.30167
\(906\) −71.0728 −2.36124
\(907\) 21.0701 0.699620 0.349810 0.936821i \(-0.386246\pi\)
0.349810 + 0.936821i \(0.386246\pi\)
\(908\) −23.8013 −0.789872
\(909\) −7.42080 −0.246132
\(910\) −5.46576 −0.181188
\(911\) −11.3971 −0.377602 −0.188801 0.982015i \(-0.560460\pi\)
−0.188801 + 0.982015i \(0.560460\pi\)
\(912\) −23.9109 −0.791770
\(913\) 1.20258 0.0397997
\(914\) −56.8210 −1.87947
\(915\) 14.4495 0.477684
\(916\) −27.8365 −0.919745
\(917\) 4.28318 0.141443
\(918\) 47.8357 1.57881
\(919\) 19.0341 0.627878 0.313939 0.949443i \(-0.398351\pi\)
0.313939 + 0.949443i \(0.398351\pi\)
\(920\) −46.2777 −1.52573
\(921\) 34.2573 1.12882
\(922\) −31.4663 −1.03629
\(923\) −0.748964 −0.0246524
\(924\) −8.82854 −0.290438
\(925\) 5.96489 0.196124
\(926\) −81.5994 −2.68152
\(927\) 9.34409 0.306900
\(928\) −10.6867 −0.350808
\(929\) 11.1706 0.366495 0.183248 0.983067i \(-0.441339\pi\)
0.183248 + 0.983067i \(0.441339\pi\)
\(930\) −43.5905 −1.42939
\(931\) 22.3213 0.731551
\(932\) 36.3383 1.19030
\(933\) −15.7145 −0.514471
\(934\) 52.7317 1.72543
\(935\) 18.5637 0.607098
\(936\) −14.9252 −0.487847
\(937\) 11.5626 0.377734 0.188867 0.982003i \(-0.439518\pi\)
0.188867 + 0.982003i \(0.439518\pi\)
\(938\) 9.82022 0.320642
\(939\) −0.856789 −0.0279603
\(940\) −81.8250 −2.66884
\(941\) −27.9240 −0.910296 −0.455148 0.890416i \(-0.650414\pi\)
−0.455148 + 0.890416i \(0.650414\pi\)
\(942\) −22.0844 −0.719549
\(943\) −45.6947 −1.48802
\(944\) −19.9944 −0.650762
\(945\) 5.24738 0.170697
\(946\) 17.7667 0.577644
\(947\) −17.2983 −0.562120 −0.281060 0.959690i \(-0.590686\pi\)
−0.281060 + 0.959690i \(0.590686\pi\)
\(948\) 58.7544 1.90825
\(949\) −2.58654 −0.0839626
\(950\) −14.0954 −0.457315
\(951\) 13.2813 0.430677
\(952\) −9.59432 −0.310954
\(953\) 35.6175 1.15376 0.576882 0.816827i \(-0.304269\pi\)
0.576882 + 0.816827i \(0.304269\pi\)
\(954\) −19.2801 −0.624217
\(955\) −47.2406 −1.52867
\(956\) 76.0395 2.45929
\(957\) −19.8525 −0.641741
\(958\) 62.6617 2.02451
\(959\) −2.82762 −0.0913085
\(960\) 12.6352 0.407798
\(961\) 19.1922 0.619104
\(962\) −20.5422 −0.662309
\(963\) −11.9802 −0.386055
\(964\) −79.2281 −2.55176
\(965\) −20.0151 −0.644309
\(966\) 8.04388 0.258808
\(967\) 47.5952 1.53056 0.765279 0.643699i \(-0.222601\pi\)
0.765279 + 0.643699i \(0.222601\pi\)
\(968\) 10.7367 0.345092
\(969\) −15.3293 −0.492448
\(970\) 51.0133 1.63794
\(971\) 25.0675 0.804454 0.402227 0.915540i \(-0.368236\pi\)
0.402227 + 0.915540i \(0.368236\pi\)
\(972\) 47.0349 1.50865
\(973\) 7.02446 0.225194
\(974\) −101.003 −3.23636
\(975\) 5.48124 0.175540
\(976\) −31.0422 −0.993637
\(977\) −19.4337 −0.621738 −0.310869 0.950453i \(-0.600620\pi\)
−0.310869 + 0.950453i \(0.600620\pi\)
\(978\) −38.8846 −1.24339
\(979\) −45.8995 −1.46695
\(980\) 51.4710 1.64418
\(981\) 4.30184 0.137347
\(982\) −11.2635 −0.359434
\(983\) −42.7531 −1.36361 −0.681805 0.731534i \(-0.738805\pi\)
−0.681805 + 0.731534i \(0.738805\pi\)
\(984\) −73.9455 −2.35730
\(985\) −17.9462 −0.571814
\(986\) −41.0987 −1.30885
\(987\) 7.46609 0.237648
\(988\) 32.9090 1.04698
\(989\) −10.9742 −0.348961
\(990\) 15.6250 0.496596
\(991\) −37.6302 −1.19536 −0.597681 0.801734i \(-0.703911\pi\)
−0.597681 + 0.801734i \(0.703911\pi\)
\(992\) 15.6111 0.495654
\(993\) 48.5528 1.54077
\(994\) −0.405238 −0.0128534
\(995\) 18.5923 0.589415
\(996\) −2.28990 −0.0725583
\(997\) −23.7150 −0.751060 −0.375530 0.926810i \(-0.622539\pi\)
−0.375530 + 0.926810i \(0.622539\pi\)
\(998\) −90.1162 −2.85258
\(999\) 19.7215 0.623961
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 \(a_p\))