Properties

Label 619.2.a.b.1.13
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.192901 q^{2} -3.10998 q^{3} -1.96279 q^{4} +2.33409 q^{5} +0.599918 q^{6} -3.05253 q^{7} +0.764427 q^{8} +6.67195 q^{9} +O(q^{10})\) \(q-0.192901 q^{2} -3.10998 q^{3} -1.96279 q^{4} +2.33409 q^{5} +0.599918 q^{6} -3.05253 q^{7} +0.764427 q^{8} +6.67195 q^{9} -0.450249 q^{10} -6.12235 q^{11} +6.10423 q^{12} -5.12075 q^{13} +0.588836 q^{14} -7.25897 q^{15} +3.77812 q^{16} -0.896358 q^{17} -1.28703 q^{18} +2.17256 q^{19} -4.58133 q^{20} +9.49328 q^{21} +1.18101 q^{22} +4.34757 q^{23} -2.37735 q^{24} +0.447982 q^{25} +0.987800 q^{26} -11.4197 q^{27} +5.99147 q^{28} +3.04370 q^{29} +1.40026 q^{30} +2.83568 q^{31} -2.25766 q^{32} +19.0404 q^{33} +0.172909 q^{34} -7.12488 q^{35} -13.0956 q^{36} +6.95323 q^{37} -0.419089 q^{38} +15.9254 q^{39} +1.78424 q^{40} +3.82879 q^{41} -1.83127 q^{42} +12.6249 q^{43} +12.0169 q^{44} +15.5729 q^{45} -0.838652 q^{46} -11.9938 q^{47} -11.7499 q^{48} +2.31792 q^{49} -0.0864163 q^{50} +2.78765 q^{51} +10.0510 q^{52} -2.38334 q^{53} +2.20287 q^{54} -14.2901 q^{55} -2.33343 q^{56} -6.75661 q^{57} -0.587133 q^{58} +7.29784 q^{59} +14.2478 q^{60} +13.8005 q^{61} -0.547006 q^{62} -20.3663 q^{63} -7.12073 q^{64} -11.9523 q^{65} -3.67291 q^{66} +2.68532 q^{67} +1.75936 q^{68} -13.5208 q^{69} +1.37440 q^{70} +6.53661 q^{71} +5.10022 q^{72} -11.2484 q^{73} -1.34129 q^{74} -1.39321 q^{75} -4.26428 q^{76} +18.6887 q^{77} -3.07203 q^{78} -9.47425 q^{79} +8.81848 q^{80} +15.4990 q^{81} -0.738579 q^{82} +2.39915 q^{83} -18.6333 q^{84} -2.09218 q^{85} -2.43535 q^{86} -9.46583 q^{87} -4.68009 q^{88} -5.93380 q^{89} -3.00404 q^{90} +15.6312 q^{91} -8.53336 q^{92} -8.81889 q^{93} +2.31363 q^{94} +5.07095 q^{95} +7.02126 q^{96} +9.10352 q^{97} -0.447130 q^{98} -40.8480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.192901 −0.136402 −0.0682009 0.997672i \(-0.521726\pi\)
−0.0682009 + 0.997672i \(0.521726\pi\)
\(3\) −3.10998 −1.79555 −0.897773 0.440459i \(-0.854816\pi\)
−0.897773 + 0.440459i \(0.854816\pi\)
\(4\) −1.96279 −0.981395
\(5\) 2.33409 1.04384 0.521919 0.852995i \(-0.325216\pi\)
0.521919 + 0.852995i \(0.325216\pi\)
\(6\) 0.599918 0.244916
\(7\) −3.05253 −1.15375 −0.576873 0.816834i \(-0.695727\pi\)
−0.576873 + 0.816834i \(0.695727\pi\)
\(8\) 0.764427 0.270266
\(9\) 6.67195 2.22398
\(10\) −0.450249 −0.142381
\(11\) −6.12235 −1.84596 −0.922980 0.384849i \(-0.874254\pi\)
−0.922980 + 0.384849i \(0.874254\pi\)
\(12\) 6.10423 1.76214
\(13\) −5.12075 −1.42024 −0.710121 0.704080i \(-0.751360\pi\)
−0.710121 + 0.704080i \(0.751360\pi\)
\(14\) 0.588836 0.157373
\(15\) −7.25897 −1.87426
\(16\) 3.77812 0.944530
\(17\) −0.896358 −0.217399 −0.108699 0.994075i \(-0.534669\pi\)
−0.108699 + 0.994075i \(0.534669\pi\)
\(18\) −1.28703 −0.303355
\(19\) 2.17256 0.498419 0.249210 0.968450i \(-0.419829\pi\)
0.249210 + 0.968450i \(0.419829\pi\)
\(20\) −4.58133 −1.02442
\(21\) 9.49328 2.07160
\(22\) 1.18101 0.251792
\(23\) 4.34757 0.906531 0.453265 0.891376i \(-0.350259\pi\)
0.453265 + 0.891376i \(0.350259\pi\)
\(24\) −2.37735 −0.485274
\(25\) 0.447982 0.0895964
\(26\) 0.987800 0.193723
\(27\) −11.4197 −2.19771
\(28\) 5.99147 1.13228
\(29\) 3.04370 0.565201 0.282600 0.959238i \(-0.408803\pi\)
0.282600 + 0.959238i \(0.408803\pi\)
\(30\) 1.40026 0.255652
\(31\) 2.83568 0.509303 0.254651 0.967033i \(-0.418039\pi\)
0.254651 + 0.967033i \(0.418039\pi\)
\(32\) −2.25766 −0.399101
\(33\) 19.0404 3.31450
\(34\) 0.172909 0.0296536
\(35\) −7.12488 −1.20432
\(36\) −13.0956 −2.18260
\(37\) 6.95323 1.14310 0.571552 0.820566i \(-0.306342\pi\)
0.571552 + 0.820566i \(0.306342\pi\)
\(38\) −0.419089 −0.0679853
\(39\) 15.9254 2.55011
\(40\) 1.78424 0.282113
\(41\) 3.82879 0.597957 0.298978 0.954260i \(-0.403354\pi\)
0.298978 + 0.954260i \(0.403354\pi\)
\(42\) −1.83127 −0.282571
\(43\) 12.6249 1.92528 0.962638 0.270793i \(-0.0872858\pi\)
0.962638 + 0.270793i \(0.0872858\pi\)
\(44\) 12.0169 1.81161
\(45\) 15.5729 2.32148
\(46\) −0.838652 −0.123652
\(47\) −11.9938 −1.74948 −0.874741 0.484591i \(-0.838968\pi\)
−0.874741 + 0.484591i \(0.838968\pi\)
\(48\) −11.7499 −1.69595
\(49\) 2.31792 0.331132
\(50\) −0.0864163 −0.0122211
\(51\) 2.78765 0.390349
\(52\) 10.0510 1.39382
\(53\) −2.38334 −0.327376 −0.163688 0.986512i \(-0.552339\pi\)
−0.163688 + 0.986512i \(0.552339\pi\)
\(54\) 2.20287 0.299772
\(55\) −14.2901 −1.92688
\(56\) −2.33343 −0.311818
\(57\) −6.75661 −0.894934
\(58\) −0.587133 −0.0770944
\(59\) 7.29784 0.950098 0.475049 0.879959i \(-0.342430\pi\)
0.475049 + 0.879959i \(0.342430\pi\)
\(60\) 14.2478 1.83939
\(61\) 13.8005 1.76697 0.883484 0.468462i \(-0.155192\pi\)
0.883484 + 0.468462i \(0.155192\pi\)
\(62\) −0.547006 −0.0694698
\(63\) −20.3663 −2.56591
\(64\) −7.12073 −0.890092
\(65\) −11.9523 −1.48250
\(66\) −3.67291 −0.452104
\(67\) 2.68532 0.328064 0.164032 0.986455i \(-0.447550\pi\)
0.164032 + 0.986455i \(0.447550\pi\)
\(68\) 1.75936 0.213354
\(69\) −13.5208 −1.62772
\(70\) 1.37440 0.164272
\(71\) 6.53661 0.775753 0.387877 0.921711i \(-0.373209\pi\)
0.387877 + 0.921711i \(0.373209\pi\)
\(72\) 5.10022 0.601066
\(73\) −11.2484 −1.31653 −0.658263 0.752788i \(-0.728709\pi\)
−0.658263 + 0.752788i \(0.728709\pi\)
\(74\) −1.34129 −0.155921
\(75\) −1.39321 −0.160874
\(76\) −4.26428 −0.489146
\(77\) 18.6887 2.12977
\(78\) −3.07203 −0.347839
\(79\) −9.47425 −1.06594 −0.532968 0.846135i \(-0.678923\pi\)
−0.532968 + 0.846135i \(0.678923\pi\)
\(80\) 8.81848 0.985936
\(81\) 15.4990 1.72211
\(82\) −0.738579 −0.0815624
\(83\) 2.39915 0.263341 0.131670 0.991294i \(-0.457966\pi\)
0.131670 + 0.991294i \(0.457966\pi\)
\(84\) −18.6333 −2.03306
\(85\) −2.09218 −0.226929
\(86\) −2.43535 −0.262611
\(87\) −9.46583 −1.01484
\(88\) −4.68009 −0.498900
\(89\) −5.93380 −0.628981 −0.314491 0.949261i \(-0.601834\pi\)
−0.314491 + 0.949261i \(0.601834\pi\)
\(90\) −3.00404 −0.316653
\(91\) 15.6312 1.63860
\(92\) −8.53336 −0.889665
\(93\) −8.81889 −0.914476
\(94\) 2.31363 0.238632
\(95\) 5.07095 0.520269
\(96\) 7.02126 0.716604
\(97\) 9.10352 0.924323 0.462161 0.886796i \(-0.347074\pi\)
0.462161 + 0.886796i \(0.347074\pi\)
\(98\) −0.447130 −0.0451670
\(99\) −40.8480 −4.10538
\(100\) −0.879295 −0.0879295
\(101\) 5.90918 0.587985 0.293993 0.955808i \(-0.405016\pi\)
0.293993 + 0.955808i \(0.405016\pi\)
\(102\) −0.537741 −0.0532443
\(103\) −0.766934 −0.0755682 −0.0377841 0.999286i \(-0.512030\pi\)
−0.0377841 + 0.999286i \(0.512030\pi\)
\(104\) −3.91444 −0.383843
\(105\) 22.1582 2.16242
\(106\) 0.459749 0.0446547
\(107\) −4.51674 −0.436650 −0.218325 0.975876i \(-0.570059\pi\)
−0.218325 + 0.975876i \(0.570059\pi\)
\(108\) 22.4144 2.15683
\(109\) 0.114687 0.0109850 0.00549251 0.999985i \(-0.498252\pi\)
0.00549251 + 0.999985i \(0.498252\pi\)
\(110\) 2.75658 0.262830
\(111\) −21.6244 −2.05249
\(112\) −11.5328 −1.08975
\(113\) −10.3205 −0.970869 −0.485434 0.874273i \(-0.661339\pi\)
−0.485434 + 0.874273i \(0.661339\pi\)
\(114\) 1.30336 0.122071
\(115\) 10.1476 0.946271
\(116\) −5.97414 −0.554685
\(117\) −34.1654 −3.15859
\(118\) −1.40776 −0.129595
\(119\) 2.73616 0.250823
\(120\) −5.54895 −0.506547
\(121\) 26.4832 2.40757
\(122\) −2.66212 −0.241017
\(123\) −11.9074 −1.07366
\(124\) −5.56584 −0.499827
\(125\) −10.6248 −0.950313
\(126\) 3.92868 0.349995
\(127\) −10.9177 −0.968791 −0.484396 0.874849i \(-0.660960\pi\)
−0.484396 + 0.874849i \(0.660960\pi\)
\(128\) 5.88891 0.520511
\(129\) −39.2630 −3.45692
\(130\) 2.30561 0.202216
\(131\) 14.4727 1.26449 0.632243 0.774770i \(-0.282134\pi\)
0.632243 + 0.774770i \(0.282134\pi\)
\(132\) −37.3722 −3.25284
\(133\) −6.63180 −0.575050
\(134\) −0.518002 −0.0447486
\(135\) −26.6545 −2.29406
\(136\) −0.685200 −0.0587554
\(137\) 4.72791 0.403932 0.201966 0.979393i \(-0.435267\pi\)
0.201966 + 0.979393i \(0.435267\pi\)
\(138\) 2.60819 0.222024
\(139\) 2.38264 0.202093 0.101047 0.994882i \(-0.467781\pi\)
0.101047 + 0.994882i \(0.467781\pi\)
\(140\) 13.9846 1.18192
\(141\) 37.3006 3.14127
\(142\) −1.26092 −0.105814
\(143\) 31.3511 2.62171
\(144\) 25.2074 2.10062
\(145\) 7.10427 0.589978
\(146\) 2.16983 0.179577
\(147\) −7.20869 −0.594562
\(148\) −13.6477 −1.12184
\(149\) 17.1483 1.40485 0.702424 0.711759i \(-0.252101\pi\)
0.702424 + 0.711759i \(0.252101\pi\)
\(150\) 0.268753 0.0219436
\(151\) −22.6841 −1.84601 −0.923003 0.384792i \(-0.874273\pi\)
−0.923003 + 0.384792i \(0.874273\pi\)
\(152\) 1.66076 0.134706
\(153\) −5.98045 −0.483491
\(154\) −3.60506 −0.290504
\(155\) 6.61873 0.531629
\(156\) −31.2582 −2.50266
\(157\) 15.4343 1.23179 0.615894 0.787829i \(-0.288795\pi\)
0.615894 + 0.787829i \(0.288795\pi\)
\(158\) 1.82759 0.145396
\(159\) 7.41212 0.587819
\(160\) −5.26958 −0.416597
\(161\) −13.2711 −1.04591
\(162\) −2.98978 −0.234899
\(163\) −18.6812 −1.46322 −0.731612 0.681721i \(-0.761232\pi\)
−0.731612 + 0.681721i \(0.761232\pi\)
\(164\) −7.51511 −0.586832
\(165\) 44.4420 3.45980
\(166\) −0.462799 −0.0359202
\(167\) 10.0226 0.775573 0.387787 0.921749i \(-0.373240\pi\)
0.387787 + 0.921749i \(0.373240\pi\)
\(168\) 7.25692 0.559884
\(169\) 13.2221 1.01709
\(170\) 0.403584 0.0309535
\(171\) 14.4952 1.10848
\(172\) −24.7800 −1.88945
\(173\) 5.44221 0.413764 0.206882 0.978366i \(-0.433668\pi\)
0.206882 + 0.978366i \(0.433668\pi\)
\(174\) 1.82597 0.138426
\(175\) −1.36748 −0.103372
\(176\) −23.1310 −1.74356
\(177\) −22.6961 −1.70594
\(178\) 1.14464 0.0857942
\(179\) 15.8771 1.18671 0.593354 0.804942i \(-0.297804\pi\)
0.593354 + 0.804942i \(0.297804\pi\)
\(180\) −30.5664 −2.27828
\(181\) 2.92930 0.217733 0.108866 0.994056i \(-0.465278\pi\)
0.108866 + 0.994056i \(0.465278\pi\)
\(182\) −3.01529 −0.223508
\(183\) −42.9191 −3.17267
\(184\) 3.32340 0.245004
\(185\) 16.2295 1.19321
\(186\) 1.70117 0.124736
\(187\) 5.48782 0.401309
\(188\) 23.5414 1.71693
\(189\) 34.8588 2.53561
\(190\) −0.978193 −0.0709656
\(191\) 19.6763 1.42373 0.711863 0.702318i \(-0.247852\pi\)
0.711863 + 0.702318i \(0.247852\pi\)
\(192\) 22.1453 1.59820
\(193\) 12.8235 0.923059 0.461529 0.887125i \(-0.347301\pi\)
0.461529 + 0.887125i \(0.347301\pi\)
\(194\) −1.75608 −0.126079
\(195\) 37.1714 2.66190
\(196\) −4.54960 −0.324971
\(197\) 8.15721 0.581177 0.290589 0.956848i \(-0.406149\pi\)
0.290589 + 0.956848i \(0.406149\pi\)
\(198\) 7.87963 0.559981
\(199\) 1.48857 0.105522 0.0527611 0.998607i \(-0.483198\pi\)
0.0527611 + 0.998607i \(0.483198\pi\)
\(200\) 0.342450 0.0242149
\(201\) −8.35129 −0.589054
\(202\) −1.13989 −0.0802023
\(203\) −9.29098 −0.652099
\(204\) −5.47157 −0.383087
\(205\) 8.93675 0.624170
\(206\) 0.147942 0.0103076
\(207\) 29.0068 2.01611
\(208\) −19.3468 −1.34146
\(209\) −13.3012 −0.920062
\(210\) −4.27434 −0.294958
\(211\) 9.10315 0.626687 0.313343 0.949640i \(-0.398551\pi\)
0.313343 + 0.949640i \(0.398551\pi\)
\(212\) 4.67799 0.321285
\(213\) −20.3287 −1.39290
\(214\) 0.871285 0.0595598
\(215\) 29.4676 2.00967
\(216\) −8.72950 −0.593967
\(217\) −8.65598 −0.587606
\(218\) −0.0221233 −0.00149838
\(219\) 34.9823 2.36388
\(220\) 28.0485 1.89103
\(221\) 4.59003 0.308759
\(222\) 4.17137 0.279964
\(223\) 8.18333 0.547996 0.273998 0.961730i \(-0.411654\pi\)
0.273998 + 0.961730i \(0.411654\pi\)
\(224\) 6.89156 0.460462
\(225\) 2.98891 0.199261
\(226\) 1.99083 0.132428
\(227\) −5.86743 −0.389435 −0.194717 0.980859i \(-0.562379\pi\)
−0.194717 + 0.980859i \(0.562379\pi\)
\(228\) 13.2618 0.878284
\(229\) −21.6773 −1.43248 −0.716240 0.697854i \(-0.754138\pi\)
−0.716240 + 0.697854i \(0.754138\pi\)
\(230\) −1.95749 −0.129073
\(231\) −58.1212 −3.82410
\(232\) 2.32669 0.152754
\(233\) −4.03046 −0.264044 −0.132022 0.991247i \(-0.542147\pi\)
−0.132022 + 0.991247i \(0.542147\pi\)
\(234\) 6.59055 0.430838
\(235\) −27.9947 −1.82617
\(236\) −14.3241 −0.932421
\(237\) 29.4647 1.91394
\(238\) −0.527808 −0.0342127
\(239\) 12.9688 0.838882 0.419441 0.907783i \(-0.362226\pi\)
0.419441 + 0.907783i \(0.362226\pi\)
\(240\) −27.4252 −1.77029
\(241\) −25.7754 −1.66034 −0.830170 0.557511i \(-0.811756\pi\)
−0.830170 + 0.557511i \(0.811756\pi\)
\(242\) −5.10865 −0.328396
\(243\) −13.9426 −0.894418
\(244\) −27.0874 −1.73409
\(245\) 5.41025 0.345648
\(246\) 2.29696 0.146449
\(247\) −11.1251 −0.707876
\(248\) 2.16767 0.137647
\(249\) −7.46130 −0.472841
\(250\) 2.04954 0.129624
\(251\) −17.4975 −1.10443 −0.552217 0.833701i \(-0.686218\pi\)
−0.552217 + 0.833701i \(0.686218\pi\)
\(252\) 39.9747 2.51817
\(253\) −26.6174 −1.67342
\(254\) 2.10604 0.132145
\(255\) 6.50663 0.407461
\(256\) 13.1055 0.819093
\(257\) −14.9171 −0.930503 −0.465251 0.885179i \(-0.654036\pi\)
−0.465251 + 0.885179i \(0.654036\pi\)
\(258\) 7.57389 0.471530
\(259\) −21.2249 −1.31885
\(260\) 23.4599 1.45492
\(261\) 20.3074 1.25700
\(262\) −2.79180 −0.172478
\(263\) 6.59081 0.406407 0.203203 0.979137i \(-0.434865\pi\)
0.203203 + 0.979137i \(0.434865\pi\)
\(264\) 14.5550 0.895797
\(265\) −5.56292 −0.341728
\(266\) 1.27928 0.0784378
\(267\) 18.4540 1.12936
\(268\) −5.27072 −0.321961
\(269\) −29.7208 −1.81211 −0.906056 0.423158i \(-0.860922\pi\)
−0.906056 + 0.423158i \(0.860922\pi\)
\(270\) 5.14169 0.312913
\(271\) 17.7722 1.07959 0.539793 0.841798i \(-0.318502\pi\)
0.539793 + 0.841798i \(0.318502\pi\)
\(272\) −3.38655 −0.205340
\(273\) −48.6128 −2.94218
\(274\) −0.912019 −0.0550971
\(275\) −2.74271 −0.165391
\(276\) 26.5385 1.59743
\(277\) −24.3785 −1.46476 −0.732382 0.680894i \(-0.761591\pi\)
−0.732382 + 0.680894i \(0.761591\pi\)
\(278\) −0.459615 −0.0275659
\(279\) 18.9195 1.13268
\(280\) −5.44645 −0.325488
\(281\) 29.5644 1.76366 0.881831 0.471566i \(-0.156311\pi\)
0.881831 + 0.471566i \(0.156311\pi\)
\(282\) −7.19532 −0.428475
\(283\) −1.10776 −0.0658495 −0.0329248 0.999458i \(-0.510482\pi\)
−0.0329248 + 0.999458i \(0.510482\pi\)
\(284\) −12.8300 −0.761320
\(285\) −15.7705 −0.934166
\(286\) −6.04766 −0.357606
\(287\) −11.6875 −0.689891
\(288\) −15.0630 −0.887594
\(289\) −16.1965 −0.952738
\(290\) −1.37042 −0.0804740
\(291\) −28.3117 −1.65966
\(292\) 22.0783 1.29203
\(293\) 11.5075 0.672278 0.336139 0.941812i \(-0.390879\pi\)
0.336139 + 0.941812i \(0.390879\pi\)
\(294\) 1.39056 0.0810994
\(295\) 17.0338 0.991747
\(296\) 5.31524 0.308942
\(297\) 69.9152 4.05689
\(298\) −3.30794 −0.191624
\(299\) −22.2628 −1.28749
\(300\) 2.73458 0.157881
\(301\) −38.5378 −2.22128
\(302\) 4.37579 0.251799
\(303\) −18.3774 −1.05575
\(304\) 8.20819 0.470772
\(305\) 32.2115 1.84443
\(306\) 1.15364 0.0659490
\(307\) 6.14683 0.350818 0.175409 0.984496i \(-0.443875\pi\)
0.175409 + 0.984496i \(0.443875\pi\)
\(308\) −36.6819 −2.09014
\(309\) 2.38514 0.135686
\(310\) −1.27676 −0.0725152
\(311\) 13.4926 0.765094 0.382547 0.923936i \(-0.375047\pi\)
0.382547 + 0.923936i \(0.375047\pi\)
\(312\) 12.1738 0.689207
\(313\) −12.0457 −0.680865 −0.340433 0.940269i \(-0.610574\pi\)
−0.340433 + 0.940269i \(0.610574\pi\)
\(314\) −2.97729 −0.168018
\(315\) −47.5368 −2.67840
\(316\) 18.5960 1.04610
\(317\) 7.50974 0.421789 0.210895 0.977509i \(-0.432362\pi\)
0.210895 + 0.977509i \(0.432362\pi\)
\(318\) −1.42981 −0.0801796
\(319\) −18.6346 −1.04334
\(320\) −16.6204 −0.929111
\(321\) 14.0470 0.784025
\(322\) 2.56001 0.142664
\(323\) −1.94739 −0.108356
\(324\) −30.4213 −1.69007
\(325\) −2.29401 −0.127249
\(326\) 3.60363 0.199586
\(327\) −0.356674 −0.0197241
\(328\) 2.92683 0.161607
\(329\) 36.6115 2.01846
\(330\) −8.57291 −0.471923
\(331\) 33.9328 1.86512 0.932558 0.361021i \(-0.117572\pi\)
0.932558 + 0.361021i \(0.117572\pi\)
\(332\) −4.70903 −0.258441
\(333\) 46.3916 2.54224
\(334\) −1.93338 −0.105790
\(335\) 6.26779 0.342446
\(336\) 35.8668 1.95669
\(337\) 26.2816 1.43165 0.715826 0.698279i \(-0.246050\pi\)
0.715826 + 0.698279i \(0.246050\pi\)
\(338\) −2.55056 −0.138732
\(339\) 32.0964 1.74324
\(340\) 4.10651 0.222707
\(341\) −17.3610 −0.940152
\(342\) −2.79614 −0.151198
\(343\) 14.2922 0.771704
\(344\) 9.65080 0.520336
\(345\) −31.5589 −1.69907
\(346\) −1.04981 −0.0564381
\(347\) 24.6552 1.32356 0.661780 0.749698i \(-0.269801\pi\)
0.661780 + 0.749698i \(0.269801\pi\)
\(348\) 18.5794 0.995962
\(349\) −5.96668 −0.319389 −0.159695 0.987166i \(-0.551051\pi\)
−0.159695 + 0.987166i \(0.551051\pi\)
\(350\) 0.263788 0.0141001
\(351\) 58.4773 3.12129
\(352\) 13.8222 0.736725
\(353\) −17.6586 −0.939870 −0.469935 0.882701i \(-0.655723\pi\)
−0.469935 + 0.882701i \(0.655723\pi\)
\(354\) 4.37811 0.232694
\(355\) 15.2571 0.809760
\(356\) 11.6468 0.617279
\(357\) −8.50938 −0.450364
\(358\) −3.06270 −0.161869
\(359\) 25.7625 1.35969 0.679847 0.733354i \(-0.262046\pi\)
0.679847 + 0.733354i \(0.262046\pi\)
\(360\) 11.9044 0.627415
\(361\) −14.2800 −0.751578
\(362\) −0.565065 −0.0296991
\(363\) −82.3622 −4.32289
\(364\) −30.6808 −1.60811
\(365\) −26.2548 −1.37424
\(366\) 8.27914 0.432758
\(367\) −3.26236 −0.170294 −0.0851468 0.996368i \(-0.527136\pi\)
−0.0851468 + 0.996368i \(0.527136\pi\)
\(368\) 16.4256 0.856246
\(369\) 25.5455 1.32985
\(370\) −3.13069 −0.162757
\(371\) 7.27520 0.377710
\(372\) 17.3096 0.897462
\(373\) −10.0770 −0.521767 −0.260883 0.965370i \(-0.584014\pi\)
−0.260883 + 0.965370i \(0.584014\pi\)
\(374\) −1.05861 −0.0547393
\(375\) 33.0429 1.70633
\(376\) −9.16842 −0.472825
\(377\) −15.5860 −0.802722
\(378\) −6.72431 −0.345861
\(379\) 21.4912 1.10393 0.551965 0.833867i \(-0.313878\pi\)
0.551965 + 0.833867i \(0.313878\pi\)
\(380\) −9.95321 −0.510589
\(381\) 33.9538 1.73951
\(382\) −3.79558 −0.194199
\(383\) 19.5424 0.998568 0.499284 0.866438i \(-0.333596\pi\)
0.499284 + 0.866438i \(0.333596\pi\)
\(384\) −18.3144 −0.934602
\(385\) 43.6210 2.22313
\(386\) −2.47368 −0.125907
\(387\) 84.2325 4.28178
\(388\) −17.8683 −0.907125
\(389\) −32.9546 −1.67086 −0.835432 0.549593i \(-0.814783\pi\)
−0.835432 + 0.549593i \(0.814783\pi\)
\(390\) −7.17041 −0.363088
\(391\) −3.89698 −0.197079
\(392\) 1.77188 0.0894936
\(393\) −45.0098 −2.27044
\(394\) −1.57354 −0.0792736
\(395\) −22.1138 −1.11266
\(396\) 80.1760 4.02900
\(397\) 12.0311 0.603822 0.301911 0.953336i \(-0.402375\pi\)
0.301911 + 0.953336i \(0.402375\pi\)
\(398\) −0.287148 −0.0143934
\(399\) 20.6247 1.03253
\(400\) 1.69253 0.0846265
\(401\) 19.1683 0.957219 0.478610 0.878028i \(-0.341141\pi\)
0.478610 + 0.878028i \(0.341141\pi\)
\(402\) 1.61097 0.0803481
\(403\) −14.5208 −0.723333
\(404\) −11.5985 −0.577046
\(405\) 36.1761 1.79761
\(406\) 1.79224 0.0889474
\(407\) −42.5701 −2.11012
\(408\) 2.13096 0.105498
\(409\) −3.17142 −0.156817 −0.0784084 0.996921i \(-0.524984\pi\)
−0.0784084 + 0.996921i \(0.524984\pi\)
\(410\) −1.72391 −0.0851379
\(411\) −14.7037 −0.725278
\(412\) 1.50533 0.0741622
\(413\) −22.2769 −1.09617
\(414\) −5.59544 −0.275001
\(415\) 5.59984 0.274885
\(416\) 11.5609 0.566820
\(417\) −7.40996 −0.362867
\(418\) 2.56581 0.125498
\(419\) 30.6433 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(420\) −43.4919 −2.12219
\(421\) 30.8789 1.50495 0.752474 0.658622i \(-0.228861\pi\)
0.752474 + 0.658622i \(0.228861\pi\)
\(422\) −1.75601 −0.0854812
\(423\) −80.0223 −3.89082
\(424\) −1.82189 −0.0884786
\(425\) −0.401552 −0.0194782
\(426\) 3.92143 0.189994
\(427\) −42.1263 −2.03863
\(428\) 8.86541 0.428526
\(429\) −97.5010 −4.70739
\(430\) −5.68434 −0.274123
\(431\) 14.4654 0.696774 0.348387 0.937351i \(-0.386730\pi\)
0.348387 + 0.937351i \(0.386730\pi\)
\(432\) −43.1448 −2.07581
\(433\) 7.59106 0.364803 0.182402 0.983224i \(-0.441613\pi\)
0.182402 + 0.983224i \(0.441613\pi\)
\(434\) 1.66975 0.0801506
\(435\) −22.0941 −1.05933
\(436\) −0.225107 −0.0107806
\(437\) 9.44535 0.451832
\(438\) −6.74812 −0.322438
\(439\) −24.1038 −1.15041 −0.575206 0.818009i \(-0.695078\pi\)
−0.575206 + 0.818009i \(0.695078\pi\)
\(440\) −10.9238 −0.520770
\(441\) 15.4651 0.736432
\(442\) −0.885422 −0.0421152
\(443\) −19.9951 −0.949996 −0.474998 0.879987i \(-0.657551\pi\)
−0.474998 + 0.879987i \(0.657551\pi\)
\(444\) 42.4441 2.01431
\(445\) −13.8500 −0.656554
\(446\) −1.57857 −0.0747477
\(447\) −53.3309 −2.52247
\(448\) 21.7362 1.02694
\(449\) 14.0576 0.663417 0.331709 0.943382i \(-0.392375\pi\)
0.331709 + 0.943382i \(0.392375\pi\)
\(450\) −0.576565 −0.0271795
\(451\) −23.4412 −1.10380
\(452\) 20.2569 0.952805
\(453\) 70.5470 3.31459
\(454\) 1.13183 0.0531196
\(455\) 36.4847 1.71043
\(456\) −5.16493 −0.241870
\(457\) −2.92697 −0.136918 −0.0684590 0.997654i \(-0.521808\pi\)
−0.0684590 + 0.997654i \(0.521808\pi\)
\(458\) 4.18159 0.195393
\(459\) 10.2361 0.477780
\(460\) −19.9176 −0.928665
\(461\) 18.7341 0.872533 0.436267 0.899817i \(-0.356300\pi\)
0.436267 + 0.899817i \(0.356300\pi\)
\(462\) 11.2117 0.521614
\(463\) −5.40895 −0.251375 −0.125688 0.992070i \(-0.540114\pi\)
−0.125688 + 0.992070i \(0.540114\pi\)
\(464\) 11.4995 0.533849
\(465\) −20.5841 −0.954564
\(466\) 0.777481 0.0360161
\(467\) −20.4289 −0.945337 −0.472668 0.881240i \(-0.656709\pi\)
−0.472668 + 0.881240i \(0.656709\pi\)
\(468\) 67.0595 3.09982
\(469\) −8.19702 −0.378503
\(470\) 5.40022 0.249093
\(471\) −48.0001 −2.21173
\(472\) 5.57866 0.256779
\(473\) −77.2940 −3.55398
\(474\) −5.68377 −0.261064
\(475\) 0.973268 0.0446566
\(476\) −5.37050 −0.246156
\(477\) −15.9015 −0.728079
\(478\) −2.50170 −0.114425
\(479\) −3.83097 −0.175041 −0.0875207 0.996163i \(-0.527894\pi\)
−0.0875207 + 0.996163i \(0.527894\pi\)
\(480\) 16.3883 0.748018
\(481\) −35.6058 −1.62348
\(482\) 4.97211 0.226473
\(483\) 41.2727 1.87797
\(484\) −51.9810 −2.36277
\(485\) 21.2485 0.964843
\(486\) 2.68954 0.122000
\(487\) 23.6208 1.07036 0.535179 0.844738i \(-0.320244\pi\)
0.535179 + 0.844738i \(0.320244\pi\)
\(488\) 10.5494 0.477551
\(489\) 58.0981 2.62728
\(490\) −1.04364 −0.0471470
\(491\) −0.0396717 −0.00179036 −0.000895180 1.00000i \(-0.500285\pi\)
−0.000895180 1.00000i \(0.500285\pi\)
\(492\) 23.3718 1.05368
\(493\) −2.72824 −0.122874
\(494\) 2.14605 0.0965555
\(495\) −95.3430 −4.28535
\(496\) 10.7135 0.481052
\(497\) −19.9532 −0.895023
\(498\) 1.43929 0.0644963
\(499\) 22.3479 1.00043 0.500215 0.865901i \(-0.333254\pi\)
0.500215 + 0.865901i \(0.333254\pi\)
\(500\) 20.8543 0.932632
\(501\) −31.1701 −1.39258
\(502\) 3.37529 0.150647
\(503\) 3.65604 0.163015 0.0815074 0.996673i \(-0.474027\pi\)
0.0815074 + 0.996673i \(0.474027\pi\)
\(504\) −15.5685 −0.693478
\(505\) 13.7926 0.613761
\(506\) 5.13452 0.228257
\(507\) −41.1205 −1.82622
\(508\) 21.4292 0.950766
\(509\) −33.3734 −1.47925 −0.739625 0.673019i \(-0.764997\pi\)
−0.739625 + 0.673019i \(0.764997\pi\)
\(510\) −1.25514 −0.0555784
\(511\) 34.3361 1.51894
\(512\) −14.3059 −0.632237
\(513\) −24.8099 −1.09538
\(514\) 2.87753 0.126922
\(515\) −1.79009 −0.0788809
\(516\) 77.0651 3.39260
\(517\) 73.4305 3.22947
\(518\) 4.09431 0.179894
\(519\) −16.9251 −0.742932
\(520\) −9.13667 −0.400669
\(521\) 26.9294 1.17980 0.589900 0.807476i \(-0.299167\pi\)
0.589900 + 0.807476i \(0.299167\pi\)
\(522\) −3.91732 −0.171457
\(523\) 6.84563 0.299338 0.149669 0.988736i \(-0.452179\pi\)
0.149669 + 0.988736i \(0.452179\pi\)
\(524\) −28.4069 −1.24096
\(525\) 4.25282 0.185608
\(526\) −1.27138 −0.0554346
\(527\) −2.54178 −0.110722
\(528\) 71.9368 3.13065
\(529\) −4.09864 −0.178202
\(530\) 1.07310 0.0466123
\(531\) 48.6908 2.11300
\(532\) 13.0168 0.564351
\(533\) −19.6063 −0.849243
\(534\) −3.55979 −0.154047
\(535\) −10.5425 −0.455792
\(536\) 2.05273 0.0886646
\(537\) −49.3773 −2.13079
\(538\) 5.73319 0.247175
\(539\) −14.1911 −0.611256
\(540\) 52.3172 2.25137
\(541\) 39.0545 1.67908 0.839542 0.543295i \(-0.182824\pi\)
0.839542 + 0.543295i \(0.182824\pi\)
\(542\) −3.42829 −0.147258
\(543\) −9.11004 −0.390949
\(544\) 2.02367 0.0867641
\(545\) 0.267690 0.0114666
\(546\) 9.37746 0.401318
\(547\) 38.4058 1.64211 0.821057 0.570846i \(-0.193385\pi\)
0.821057 + 0.570846i \(0.193385\pi\)
\(548\) −9.27988 −0.396417
\(549\) 92.0759 3.92970
\(550\) 0.529071 0.0225597
\(551\) 6.61262 0.281707
\(552\) −10.3357 −0.439916
\(553\) 28.9204 1.22982
\(554\) 4.70265 0.199796
\(555\) −50.4733 −2.14247
\(556\) −4.67662 −0.198333
\(557\) 17.6576 0.748177 0.374088 0.927393i \(-0.377956\pi\)
0.374088 + 0.927393i \(0.377956\pi\)
\(558\) −3.64959 −0.154500
\(559\) −64.6489 −2.73436
\(560\) −26.9186 −1.13752
\(561\) −17.0670 −0.720569
\(562\) −5.70300 −0.240567
\(563\) 15.6668 0.660277 0.330138 0.943933i \(-0.392905\pi\)
0.330138 + 0.943933i \(0.392905\pi\)
\(564\) −73.2131 −3.08283
\(565\) −24.0889 −1.01343
\(566\) 0.213688 0.00898199
\(567\) −47.3112 −1.98688
\(568\) 4.99676 0.209660
\(569\) 32.7556 1.37319 0.686593 0.727042i \(-0.259105\pi\)
0.686593 + 0.727042i \(0.259105\pi\)
\(570\) 3.04216 0.127422
\(571\) −0.652610 −0.0273109 −0.0136554 0.999907i \(-0.504347\pi\)
−0.0136554 + 0.999907i \(0.504347\pi\)
\(572\) −61.5355 −2.57293
\(573\) −61.1928 −2.55636
\(574\) 2.25453 0.0941023
\(575\) 1.94763 0.0812220
\(576\) −47.5091 −1.97955
\(577\) −2.79694 −0.116438 −0.0582191 0.998304i \(-0.518542\pi\)
−0.0582191 + 0.998304i \(0.518542\pi\)
\(578\) 3.12433 0.129955
\(579\) −39.8809 −1.65739
\(580\) −13.9442 −0.579001
\(581\) −7.32347 −0.303829
\(582\) 5.46137 0.226381
\(583\) 14.5916 0.604324
\(584\) −8.59859 −0.355812
\(585\) −79.7451 −3.29706
\(586\) −2.21982 −0.0916999
\(587\) −3.42878 −0.141521 −0.0707604 0.997493i \(-0.522543\pi\)
−0.0707604 + 0.997493i \(0.522543\pi\)
\(588\) 14.1491 0.583500
\(589\) 6.16068 0.253846
\(590\) −3.28585 −0.135276
\(591\) −25.3687 −1.04353
\(592\) 26.2701 1.07970
\(593\) −28.3718 −1.16509 −0.582545 0.812798i \(-0.697943\pi\)
−0.582545 + 0.812798i \(0.697943\pi\)
\(594\) −13.4867 −0.553367
\(595\) 6.38644 0.261819
\(596\) −33.6586 −1.37871
\(597\) −4.62943 −0.189470
\(598\) 4.29453 0.175616
\(599\) −46.1714 −1.88651 −0.943256 0.332067i \(-0.892254\pi\)
−0.943256 + 0.332067i \(0.892254\pi\)
\(600\) −1.06501 −0.0434789
\(601\) 2.63498 0.107483 0.0537416 0.998555i \(-0.482885\pi\)
0.0537416 + 0.998555i \(0.482885\pi\)
\(602\) 7.43399 0.302987
\(603\) 17.9163 0.729609
\(604\) 44.5241 1.81166
\(605\) 61.8143 2.51311
\(606\) 3.54502 0.144007
\(607\) −28.4421 −1.15443 −0.577215 0.816592i \(-0.695860\pi\)
−0.577215 + 0.816592i \(0.695860\pi\)
\(608\) −4.90490 −0.198920
\(609\) 28.8947 1.17087
\(610\) −6.21364 −0.251583
\(611\) 61.4175 2.48469
\(612\) 11.7384 0.474495
\(613\) 7.10940 0.287146 0.143573 0.989640i \(-0.454141\pi\)
0.143573 + 0.989640i \(0.454141\pi\)
\(614\) −1.18573 −0.0478522
\(615\) −27.7931 −1.12072
\(616\) 14.2861 0.575604
\(617\) 13.9339 0.560959 0.280479 0.959860i \(-0.409507\pi\)
0.280479 + 0.959860i \(0.409507\pi\)
\(618\) −0.460097 −0.0185078
\(619\) 1.00000 0.0401934
\(620\) −12.9912 −0.521738
\(621\) −49.6478 −1.99230
\(622\) −2.60274 −0.104360
\(623\) 18.1131 0.725685
\(624\) 60.1681 2.40865
\(625\) −27.0392 −1.08157
\(626\) 2.32364 0.0928712
\(627\) 41.3663 1.65201
\(628\) −30.2942 −1.20887
\(629\) −6.23258 −0.248509
\(630\) 9.16991 0.365338
\(631\) −33.1836 −1.32102 −0.660509 0.750818i \(-0.729660\pi\)
−0.660509 + 0.750818i \(0.729660\pi\)
\(632\) −7.24237 −0.288086
\(633\) −28.3106 −1.12524
\(634\) −1.44864 −0.0575328
\(635\) −25.4830 −1.01126
\(636\) −14.5484 −0.576882
\(637\) −11.8695 −0.470287
\(638\) 3.59464 0.142313
\(639\) 43.6119 1.72526
\(640\) 13.7453 0.543329
\(641\) 8.15248 0.322003 0.161002 0.986954i \(-0.448528\pi\)
0.161002 + 0.986954i \(0.448528\pi\)
\(642\) −2.70968 −0.106942
\(643\) 8.80607 0.347277 0.173639 0.984809i \(-0.444448\pi\)
0.173639 + 0.984809i \(0.444448\pi\)
\(644\) 26.0483 1.02645
\(645\) −91.6435 −3.60846
\(646\) 0.375654 0.0147799
\(647\) −10.8997 −0.428510 −0.214255 0.976778i \(-0.568732\pi\)
−0.214255 + 0.976778i \(0.568732\pi\)
\(648\) 11.8479 0.465428
\(649\) −44.6799 −1.75384
\(650\) 0.442517 0.0173569
\(651\) 26.9199 1.05507
\(652\) 36.6672 1.43600
\(653\) 47.3004 1.85101 0.925505 0.378736i \(-0.123641\pi\)
0.925505 + 0.378736i \(0.123641\pi\)
\(654\) 0.0688028 0.00269040
\(655\) 33.7806 1.31992
\(656\) 14.4656 0.564788
\(657\) −75.0488 −2.92793
\(658\) −7.06241 −0.275321
\(659\) 13.1863 0.513666 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(660\) −87.2302 −3.39543
\(661\) 24.8215 0.965445 0.482723 0.875773i \(-0.339648\pi\)
0.482723 + 0.875773i \(0.339648\pi\)
\(662\) −6.54568 −0.254405
\(663\) −14.2749 −0.554390
\(664\) 1.83398 0.0711720
\(665\) −15.4792 −0.600258
\(666\) −8.94899 −0.346766
\(667\) 13.2327 0.512372
\(668\) −19.6723 −0.761143
\(669\) −25.4500 −0.983952
\(670\) −1.20906 −0.0467102
\(671\) −84.4913 −3.26175
\(672\) −21.4326 −0.826780
\(673\) 34.6977 1.33750 0.668749 0.743488i \(-0.266830\pi\)
0.668749 + 0.743488i \(0.266830\pi\)
\(674\) −5.06976 −0.195280
\(675\) −5.11581 −0.196907
\(676\) −25.9522 −0.998163
\(677\) −30.7289 −1.18101 −0.590504 0.807035i \(-0.701071\pi\)
−0.590504 + 0.807035i \(0.701071\pi\)
\(678\) −6.19144 −0.237781
\(679\) −27.7888 −1.06643
\(680\) −1.59932 −0.0613311
\(681\) 18.2476 0.699248
\(682\) 3.34896 0.128238
\(683\) −5.04846 −0.193174 −0.0965870 0.995325i \(-0.530793\pi\)
−0.0965870 + 0.995325i \(0.530793\pi\)
\(684\) −28.4510 −1.08785
\(685\) 11.0354 0.421640
\(686\) −2.75698 −0.105262
\(687\) 67.4160 2.57208
\(688\) 47.6983 1.81848
\(689\) 12.2045 0.464954
\(690\) 6.08774 0.231756
\(691\) −12.3140 −0.468448 −0.234224 0.972183i \(-0.575255\pi\)
−0.234224 + 0.972183i \(0.575255\pi\)
\(692\) −10.6819 −0.406066
\(693\) 124.690 4.73657
\(694\) −4.75602 −0.180536
\(695\) 5.56131 0.210952
\(696\) −7.23594 −0.274277
\(697\) −3.43197 −0.129995
\(698\) 1.15098 0.0435652
\(699\) 12.5346 0.474103
\(700\) 2.68407 0.101448
\(701\) −2.74300 −0.103602 −0.0518008 0.998657i \(-0.516496\pi\)
−0.0518008 + 0.998657i \(0.516496\pi\)
\(702\) −11.2803 −0.425749
\(703\) 15.1063 0.569745
\(704\) 43.5957 1.64307
\(705\) 87.0629 3.27898
\(706\) 3.40636 0.128200
\(707\) −18.0379 −0.678386
\(708\) 44.5477 1.67420
\(709\) −36.1836 −1.35890 −0.679452 0.733720i \(-0.737782\pi\)
−0.679452 + 0.733720i \(0.737782\pi\)
\(710\) −2.94310 −0.110453
\(711\) −63.2117 −2.37062
\(712\) −4.53596 −0.169992
\(713\) 12.3283 0.461699
\(714\) 1.64147 0.0614305
\(715\) 73.1763 2.73664
\(716\) −31.1633 −1.16463
\(717\) −40.3327 −1.50625
\(718\) −4.96963 −0.185465
\(719\) −7.81506 −0.291453 −0.145726 0.989325i \(-0.546552\pi\)
−0.145726 + 0.989325i \(0.546552\pi\)
\(720\) 58.8364 2.19270
\(721\) 2.34109 0.0871866
\(722\) 2.75463 0.102517
\(723\) 80.1608 2.98121
\(724\) −5.74959 −0.213682
\(725\) 1.36352 0.0506400
\(726\) 15.8878 0.589650
\(727\) −4.62432 −0.171507 −0.0857534 0.996316i \(-0.527330\pi\)
−0.0857534 + 0.996316i \(0.527330\pi\)
\(728\) 11.9489 0.442857
\(729\) −3.13594 −0.116146
\(730\) 5.06459 0.187449
\(731\) −11.3164 −0.418552
\(732\) 84.2411 3.11364
\(733\) 6.95390 0.256848 0.128424 0.991719i \(-0.459008\pi\)
0.128424 + 0.991719i \(0.459008\pi\)
\(734\) 0.629312 0.0232283
\(735\) −16.8257 −0.620626
\(736\) −9.81533 −0.361798
\(737\) −16.4405 −0.605594
\(738\) −4.92776 −0.181393
\(739\) −11.7768 −0.433218 −0.216609 0.976258i \(-0.569500\pi\)
−0.216609 + 0.976258i \(0.569500\pi\)
\(740\) −31.8550 −1.17101
\(741\) 34.5989 1.27102
\(742\) −1.40340 −0.0515203
\(743\) 4.75069 0.174286 0.0871430 0.996196i \(-0.472226\pi\)
0.0871430 + 0.996196i \(0.472226\pi\)
\(744\) −6.74140 −0.247152
\(745\) 40.0258 1.46643
\(746\) 1.94386 0.0711699
\(747\) 16.0070 0.585666
\(748\) −10.7714 −0.393843
\(749\) 13.7875 0.503784
\(750\) −6.37403 −0.232746
\(751\) −34.8760 −1.27264 −0.636321 0.771425i \(-0.719545\pi\)
−0.636321 + 0.771425i \(0.719545\pi\)
\(752\) −45.3142 −1.65244
\(753\) 54.4168 1.98306
\(754\) 3.00657 0.109493
\(755\) −52.9468 −1.92693
\(756\) −68.4205 −2.48843
\(757\) −42.2809 −1.53672 −0.768362 0.640016i \(-0.778928\pi\)
−0.768362 + 0.640016i \(0.778928\pi\)
\(758\) −4.14569 −0.150578
\(759\) 82.7793 3.00470
\(760\) 3.87637 0.140611
\(761\) 28.6763 1.03952 0.519758 0.854313i \(-0.326022\pi\)
0.519758 + 0.854313i \(0.326022\pi\)
\(762\) −6.54974 −0.237272
\(763\) −0.350085 −0.0126739
\(764\) −38.6204 −1.39724
\(765\) −13.9589 −0.504686
\(766\) −3.76975 −0.136206
\(767\) −37.3704 −1.34937
\(768\) −40.7577 −1.47072
\(769\) 13.3613 0.481821 0.240910 0.970547i \(-0.422554\pi\)
0.240910 + 0.970547i \(0.422554\pi\)
\(770\) −8.41455 −0.303239
\(771\) 46.3918 1.67076
\(772\) −25.1699 −0.905885
\(773\) −35.3199 −1.27037 −0.635185 0.772360i \(-0.719076\pi\)
−0.635185 + 0.772360i \(0.719076\pi\)
\(774\) −16.2486 −0.584042
\(775\) 1.27033 0.0456317
\(776\) 6.95898 0.249813
\(777\) 66.0090 2.36806
\(778\) 6.35698 0.227909
\(779\) 8.31828 0.298033
\(780\) −72.9596 −2.61237
\(781\) −40.0195 −1.43201
\(782\) 0.751732 0.0268819
\(783\) −34.7580 −1.24215
\(784\) 8.75739 0.312764
\(785\) 36.0250 1.28579
\(786\) 8.68244 0.309692
\(787\) 38.6584 1.37802 0.689011 0.724751i \(-0.258045\pi\)
0.689011 + 0.724751i \(0.258045\pi\)
\(788\) −16.0109 −0.570364
\(789\) −20.4973 −0.729722
\(790\) 4.26577 0.151769
\(791\) 31.5035 1.12014
\(792\) −31.2253 −1.10954
\(793\) −70.6687 −2.50952
\(794\) −2.32081 −0.0823624
\(795\) 17.3006 0.613588
\(796\) −2.92176 −0.103559
\(797\) 7.09882 0.251453 0.125727 0.992065i \(-0.459874\pi\)
0.125727 + 0.992065i \(0.459874\pi\)
\(798\) −3.97853 −0.140839
\(799\) 10.7508 0.380335
\(800\) −1.01139 −0.0357581
\(801\) −39.5900 −1.39884
\(802\) −3.69759 −0.130566
\(803\) 68.8667 2.43025
\(804\) 16.3918 0.578095
\(805\) −30.9759 −1.09176
\(806\) 2.80108 0.0986639
\(807\) 92.4311 3.25373
\(808\) 4.51714 0.158912
\(809\) 29.9032 1.05134 0.525671 0.850688i \(-0.323814\pi\)
0.525671 + 0.850688i \(0.323814\pi\)
\(810\) −6.97842 −0.245197
\(811\) −5.52383 −0.193968 −0.0969839 0.995286i \(-0.530920\pi\)
−0.0969839 + 0.995286i \(0.530920\pi\)
\(812\) 18.2362 0.639966
\(813\) −55.2712 −1.93845
\(814\) 8.21183 0.287825
\(815\) −43.6036 −1.52737
\(816\) 10.5321 0.368697
\(817\) 27.4283 0.959594
\(818\) 0.611772 0.0213901
\(819\) 104.291 3.64422
\(820\) −17.5410 −0.612557
\(821\) 16.1777 0.564607 0.282304 0.959325i \(-0.408901\pi\)
0.282304 + 0.959325i \(0.408901\pi\)
\(822\) 2.83636 0.0989293
\(823\) 4.49097 0.156545 0.0782727 0.996932i \(-0.475060\pi\)
0.0782727 + 0.996932i \(0.475060\pi\)
\(824\) −0.586265 −0.0204235
\(825\) 8.52975 0.296968
\(826\) 4.29723 0.149520
\(827\) 21.2785 0.739927 0.369964 0.929046i \(-0.379370\pi\)
0.369964 + 0.929046i \(0.379370\pi\)
\(828\) −56.9341 −1.97860
\(829\) 10.1423 0.352258 0.176129 0.984367i \(-0.443642\pi\)
0.176129 + 0.984367i \(0.443642\pi\)
\(830\) −1.08022 −0.0374948
\(831\) 75.8166 2.63005
\(832\) 36.4635 1.26415
\(833\) −2.07769 −0.0719877
\(834\) 1.42939 0.0494957
\(835\) 23.3937 0.809572
\(836\) 26.1074 0.902943
\(837\) −32.3825 −1.11930
\(838\) −5.91112 −0.204196
\(839\) 8.67984 0.299661 0.149831 0.988712i \(-0.452127\pi\)
0.149831 + 0.988712i \(0.452127\pi\)
\(840\) 16.9383 0.584428
\(841\) −19.7359 −0.680548
\(842\) −5.95659 −0.205277
\(843\) −91.9444 −3.16673
\(844\) −17.8676 −0.615027
\(845\) 30.8616 1.06167
\(846\) 15.4364 0.530714
\(847\) −80.8408 −2.77772
\(848\) −9.00453 −0.309217
\(849\) 3.44511 0.118236
\(850\) 0.0774600 0.00265686
\(851\) 30.2296 1.03626
\(852\) 39.9010 1.36698
\(853\) −26.9142 −0.921523 −0.460762 0.887524i \(-0.652424\pi\)
−0.460762 + 0.887524i \(0.652424\pi\)
\(854\) 8.12621 0.278073
\(855\) 33.8331 1.15707
\(856\) −3.45272 −0.118012
\(857\) 15.1059 0.516006 0.258003 0.966144i \(-0.416935\pi\)
0.258003 + 0.966144i \(0.416935\pi\)
\(858\) 18.8081 0.642097
\(859\) −18.2394 −0.622322 −0.311161 0.950357i \(-0.600718\pi\)
−0.311161 + 0.950357i \(0.600718\pi\)
\(860\) −57.8387 −1.97228
\(861\) 36.3478 1.23873
\(862\) −2.79039 −0.0950412
\(863\) 18.5997 0.633140 0.316570 0.948569i \(-0.397469\pi\)
0.316570 + 0.948569i \(0.397469\pi\)
\(864\) 25.7817 0.877111
\(865\) 12.7026 0.431902
\(866\) −1.46433 −0.0497598
\(867\) 50.3708 1.71068
\(868\) 16.9899 0.576674
\(869\) 58.0047 1.96767
\(870\) 4.26198 0.144495
\(871\) −13.7509 −0.465931
\(872\) 0.0876699 0.00296888
\(873\) 60.7382 2.05568
\(874\) −1.82202 −0.0616308
\(875\) 32.4326 1.09642
\(876\) −68.6628 −2.31990
\(877\) 45.0998 1.52291 0.761456 0.648216i \(-0.224485\pi\)
0.761456 + 0.648216i \(0.224485\pi\)
\(878\) 4.64965 0.156918
\(879\) −35.7882 −1.20710
\(880\) −53.9898 −1.82000
\(881\) 6.30846 0.212537 0.106269 0.994337i \(-0.466110\pi\)
0.106269 + 0.994337i \(0.466110\pi\)
\(882\) −2.98323 −0.100451
\(883\) −28.9146 −0.973052 −0.486526 0.873666i \(-0.661736\pi\)
−0.486526 + 0.873666i \(0.661736\pi\)
\(884\) −9.00926 −0.303014
\(885\) −52.9748 −1.78073
\(886\) 3.85708 0.129581
\(887\) −16.0395 −0.538552 −0.269276 0.963063i \(-0.586784\pi\)
−0.269276 + 0.963063i \(0.586784\pi\)
\(888\) −16.5303 −0.554719
\(889\) 33.3266 1.11774
\(890\) 2.67169 0.0895552
\(891\) −94.8905 −3.17895
\(892\) −16.0622 −0.537801
\(893\) −26.0573 −0.871975
\(894\) 10.2876 0.344069
\(895\) 37.0585 1.23873
\(896\) −17.9761 −0.600538
\(897\) 69.2369 2.31175
\(898\) −2.71172 −0.0904913
\(899\) 8.63095 0.287858
\(900\) −5.86661 −0.195554
\(901\) 2.13632 0.0711712
\(902\) 4.52184 0.150561
\(903\) 119.852 3.98841
\(904\) −7.88925 −0.262393
\(905\) 6.83724 0.227278
\(906\) −13.6086 −0.452116
\(907\) −27.7263 −0.920637 −0.460318 0.887754i \(-0.652265\pi\)
−0.460318 + 0.887754i \(0.652265\pi\)
\(908\) 11.5165 0.382189
\(909\) 39.4257 1.30767
\(910\) −7.03795 −0.233306
\(911\) 37.3050 1.23597 0.617985 0.786190i \(-0.287949\pi\)
0.617985 + 0.786190i \(0.287949\pi\)
\(912\) −25.5273 −0.845292
\(913\) −14.6884 −0.486117
\(914\) 0.564616 0.0186759
\(915\) −100.177 −3.31175
\(916\) 42.5481 1.40583
\(917\) −44.1783 −1.45890
\(918\) −1.97456 −0.0651701
\(919\) −43.8040 −1.44496 −0.722481 0.691391i \(-0.756998\pi\)
−0.722481 + 0.691391i \(0.756998\pi\)
\(920\) 7.75712 0.255745
\(921\) −19.1165 −0.629910
\(922\) −3.61383 −0.119015
\(923\) −33.4724 −1.10176
\(924\) 114.080 3.75295
\(925\) 3.11492 0.102418
\(926\) 1.04339 0.0342880
\(927\) −5.11694 −0.168062
\(928\) −6.87163 −0.225572
\(929\) −33.8061 −1.10914 −0.554572 0.832136i \(-0.687118\pi\)
−0.554572 + 0.832136i \(0.687118\pi\)
\(930\) 3.97070 0.130204
\(931\) 5.03583 0.165043
\(932\) 7.91094 0.259132
\(933\) −41.9616 −1.37376
\(934\) 3.94076 0.128946
\(935\) 12.8091 0.418902
\(936\) −26.1169 −0.853659
\(937\) 2.84293 0.0928745 0.0464373 0.998921i \(-0.485213\pi\)
0.0464373 + 0.998921i \(0.485213\pi\)
\(938\) 1.58122 0.0516285
\(939\) 37.4619 1.22252
\(940\) 54.9477 1.79220
\(941\) 48.3307 1.57554 0.787769 0.615971i \(-0.211236\pi\)
0.787769 + 0.615971i \(0.211236\pi\)
\(942\) 9.25929 0.301684
\(943\) 16.6459 0.542066
\(944\) 27.5721 0.897396
\(945\) 81.3637 2.64676
\(946\) 14.9101 0.484769
\(947\) 0.860898 0.0279754 0.0139877 0.999902i \(-0.495547\pi\)
0.0139877 + 0.999902i \(0.495547\pi\)
\(948\) −57.8329 −1.87833
\(949\) 57.6003 1.86979
\(950\) −0.187745 −0.00609124
\(951\) −23.3551 −0.757342
\(952\) 2.09159 0.0677889
\(953\) 49.7730 1.61230 0.806152 0.591708i \(-0.201546\pi\)
0.806152 + 0.591708i \(0.201546\pi\)
\(954\) 3.06742 0.0993113
\(955\) 45.9262 1.48614
\(956\) −25.4550 −0.823275
\(957\) 57.9532 1.87336
\(958\) 0.738999 0.0238760
\(959\) −14.4321 −0.466036
\(960\) 51.6892 1.66826
\(961\) −22.9589 −0.740611
\(962\) 6.86840 0.221446
\(963\) −30.1355 −0.971102
\(964\) 50.5917 1.62945
\(965\) 29.9313 0.963523
\(966\) −7.96156 −0.256159
\(967\) −22.4175 −0.720900 −0.360450 0.932779i \(-0.617377\pi\)
−0.360450 + 0.932779i \(0.617377\pi\)
\(968\) 20.2445 0.650682
\(969\) 6.05634 0.194558
\(970\) −4.09885 −0.131606
\(971\) 19.3501 0.620974 0.310487 0.950578i \(-0.399508\pi\)
0.310487 + 0.950578i \(0.399508\pi\)
\(972\) 27.3664 0.877777
\(973\) −7.27308 −0.233164
\(974\) −4.55647 −0.145999
\(975\) 7.13430 0.228481
\(976\) 52.1398 1.66895
\(977\) −40.6152 −1.29940 −0.649698 0.760193i \(-0.725105\pi\)
−0.649698 + 0.760193i \(0.725105\pi\)
\(978\) −11.2072 −0.358366
\(979\) 36.3288 1.16107
\(980\) −10.6192 −0.339217
\(981\) 0.765186 0.0244305
\(982\) 0.00765273 0.000244208 0
\(983\) 29.6287 0.945009 0.472504 0.881328i \(-0.343350\pi\)
0.472504 + 0.881328i \(0.343350\pi\)
\(984\) −9.10237 −0.290173
\(985\) 19.0397 0.606654
\(986\) 0.526282 0.0167602
\(987\) −113.861 −3.62423
\(988\) 21.8363 0.694705
\(989\) 54.8875 1.74532
\(990\) 18.3918 0.584529
\(991\) 25.0134 0.794577 0.397288 0.917694i \(-0.369951\pi\)
0.397288 + 0.917694i \(0.369951\pi\)
\(992\) −6.40199 −0.203263
\(993\) −105.530 −3.34890
\(994\) 3.84900 0.122083
\(995\) 3.47447 0.110148
\(996\) 14.6450 0.464043
\(997\) −4.99363 −0.158150 −0.0790749 0.996869i \(-0.525197\pi\)
−0.0790749 + 0.996869i \(0.525197\pi\)
\(998\) −4.31094 −0.136460
\(999\) −79.4035 −2.51222
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 \(a_p\))