Properties

Label 619.2.a.b.1.18
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 1.18
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.993756 q^{2} +2.38151 q^{3} -1.01245 q^{4} +2.26626 q^{5} +2.36664 q^{6} +3.26853 q^{7} -2.99364 q^{8} +2.67158 q^{9} +O(q^{10})\) \(q+0.993756 q^{2} +2.38151 q^{3} -1.01245 q^{4} +2.26626 q^{5} +2.36664 q^{6} +3.26853 q^{7} -2.99364 q^{8} +2.67158 q^{9} +2.25211 q^{10} -3.48891 q^{11} -2.41115 q^{12} -0.0423457 q^{13} +3.24812 q^{14} +5.39712 q^{15} -0.950051 q^{16} +0.559856 q^{17} +2.65490 q^{18} +1.62574 q^{19} -2.29447 q^{20} +7.78402 q^{21} -3.46712 q^{22} +4.81952 q^{23} -7.12938 q^{24} +0.135941 q^{25} -0.0420813 q^{26} -0.782128 q^{27} -3.30921 q^{28} -6.07768 q^{29} +5.36342 q^{30} -6.33396 q^{31} +5.04316 q^{32} -8.30887 q^{33} +0.556360 q^{34} +7.40733 q^{35} -2.70484 q^{36} -9.01381 q^{37} +1.61558 q^{38} -0.100847 q^{39} -6.78437 q^{40} +7.61121 q^{41} +7.73542 q^{42} -1.05671 q^{43} +3.53234 q^{44} +6.05451 q^{45} +4.78942 q^{46} +2.17333 q^{47} -2.26255 q^{48} +3.68326 q^{49} +0.135092 q^{50} +1.33330 q^{51} +0.0428728 q^{52} +4.67404 q^{53} -0.777245 q^{54} -7.90678 q^{55} -9.78479 q^{56} +3.87170 q^{57} -6.03973 q^{58} -6.68730 q^{59} -5.46431 q^{60} +8.79056 q^{61} -6.29442 q^{62} +8.73214 q^{63} +6.91177 q^{64} -0.0959664 q^{65} -8.25699 q^{66} +15.4972 q^{67} -0.566825 q^{68} +11.4777 q^{69} +7.36108 q^{70} -4.11028 q^{71} -7.99776 q^{72} -6.53747 q^{73} -8.95753 q^{74} +0.323744 q^{75} -1.64597 q^{76} -11.4036 q^{77} -0.100217 q^{78} -12.7015 q^{79} -2.15306 q^{80} -9.87739 q^{81} +7.56369 q^{82} -6.39009 q^{83} -7.88092 q^{84} +1.26878 q^{85} -1.05011 q^{86} -14.4741 q^{87} +10.4445 q^{88} +10.4798 q^{89} +6.01670 q^{90} -0.138408 q^{91} -4.87951 q^{92} -15.0844 q^{93} +2.15976 q^{94} +3.68434 q^{95} +12.0103 q^{96} +2.73737 q^{97} +3.66026 q^{98} -9.32091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.993756 0.702692 0.351346 0.936246i \(-0.385724\pi\)
0.351346 + 0.936246i \(0.385724\pi\)
\(3\) 2.38151 1.37496 0.687482 0.726201i \(-0.258716\pi\)
0.687482 + 0.726201i \(0.258716\pi\)
\(4\) −1.01245 −0.506224
\(5\) 2.26626 1.01350 0.506751 0.862092i \(-0.330846\pi\)
0.506751 + 0.862092i \(0.330846\pi\)
\(6\) 2.36664 0.966176
\(7\) 3.26853 1.23539 0.617693 0.786419i \(-0.288067\pi\)
0.617693 + 0.786419i \(0.288067\pi\)
\(8\) −2.99364 −1.05841
\(9\) 2.67158 0.890528
\(10\) 2.25211 0.712180
\(11\) −3.48891 −1.05195 −0.525973 0.850501i \(-0.676299\pi\)
−0.525973 + 0.850501i \(0.676299\pi\)
\(12\) −2.41115 −0.696040
\(13\) −0.0423457 −0.0117446 −0.00587229 0.999983i \(-0.501869\pi\)
−0.00587229 + 0.999983i \(0.501869\pi\)
\(14\) 3.24812 0.868096
\(15\) 5.39712 1.39353
\(16\) −0.950051 −0.237513
\(17\) 0.559856 0.135785 0.0678925 0.997693i \(-0.478373\pi\)
0.0678925 + 0.997693i \(0.478373\pi\)
\(18\) 2.65490 0.625766
\(19\) 1.62574 0.372969 0.186485 0.982458i \(-0.440291\pi\)
0.186485 + 0.982458i \(0.440291\pi\)
\(20\) −2.29447 −0.513060
\(21\) 7.78402 1.69861
\(22\) −3.46712 −0.739193
\(23\) 4.81952 1.00494 0.502469 0.864595i \(-0.332425\pi\)
0.502469 + 0.864595i \(0.332425\pi\)
\(24\) −7.12938 −1.45528
\(25\) 0.135941 0.0271882
\(26\) −0.0420813 −0.00825282
\(27\) −0.782128 −0.150521
\(28\) −3.30921 −0.625383
\(29\) −6.07768 −1.12860 −0.564299 0.825571i \(-0.690853\pi\)
−0.564299 + 0.825571i \(0.690853\pi\)
\(30\) 5.36342 0.979223
\(31\) −6.33396 −1.13761 −0.568807 0.822471i \(-0.692595\pi\)
−0.568807 + 0.822471i \(0.692595\pi\)
\(32\) 5.04316 0.891513
\(33\) −8.30887 −1.44639
\(34\) 0.556360 0.0954150
\(35\) 7.40733 1.25207
\(36\) −2.70484 −0.450807
\(37\) −9.01381 −1.48186 −0.740931 0.671581i \(-0.765615\pi\)
−0.740931 + 0.671581i \(0.765615\pi\)
\(38\) 1.61558 0.262082
\(39\) −0.100847 −0.0161484
\(40\) −6.78437 −1.07270
\(41\) 7.61121 1.18867 0.594336 0.804217i \(-0.297415\pi\)
0.594336 + 0.804217i \(0.297415\pi\)
\(42\) 7.73542 1.19360
\(43\) −1.05671 −0.161146 −0.0805732 0.996749i \(-0.525675\pi\)
−0.0805732 + 0.996749i \(0.525675\pi\)
\(44\) 3.53234 0.532520
\(45\) 6.05451 0.902552
\(46\) 4.78942 0.706162
\(47\) 2.17333 0.317013 0.158506 0.987358i \(-0.449332\pi\)
0.158506 + 0.987358i \(0.449332\pi\)
\(48\) −2.26255 −0.326572
\(49\) 3.68326 0.526180
\(50\) 0.135092 0.0191049
\(51\) 1.33330 0.186700
\(52\) 0.0428728 0.00594539
\(53\) 4.67404 0.642029 0.321014 0.947074i \(-0.395976\pi\)
0.321014 + 0.947074i \(0.395976\pi\)
\(54\) −0.777245 −0.105770
\(55\) −7.90678 −1.06615
\(56\) −9.78479 −1.30755
\(57\) 3.87170 0.512820
\(58\) −6.03973 −0.793056
\(59\) −6.68730 −0.870612 −0.435306 0.900283i \(-0.643360\pi\)
−0.435306 + 0.900283i \(0.643360\pi\)
\(60\) −5.46431 −0.705439
\(61\) 8.79056 1.12552 0.562758 0.826622i \(-0.309740\pi\)
0.562758 + 0.826622i \(0.309740\pi\)
\(62\) −6.29442 −0.799392
\(63\) 8.73214 1.10015
\(64\) 6.91177 0.863972
\(65\) −0.0959664 −0.0119032
\(66\) −8.25699 −1.01636
\(67\) 15.4972 1.89329 0.946643 0.322285i \(-0.104451\pi\)
0.946643 + 0.322285i \(0.104451\pi\)
\(68\) −0.566825 −0.0687377
\(69\) 11.4777 1.38175
\(70\) 7.36108 0.879818
\(71\) −4.11028 −0.487800 −0.243900 0.969800i \(-0.578427\pi\)
−0.243900 + 0.969800i \(0.578427\pi\)
\(72\) −7.99776 −0.942545
\(73\) −6.53747 −0.765153 −0.382577 0.923924i \(-0.624963\pi\)
−0.382577 + 0.923924i \(0.624963\pi\)
\(74\) −8.95753 −1.04129
\(75\) 0.323744 0.0373828
\(76\) −1.64597 −0.188806
\(77\) −11.4036 −1.29956
\(78\) −0.100217 −0.0113473
\(79\) −12.7015 −1.42903 −0.714516 0.699619i \(-0.753353\pi\)
−0.714516 + 0.699619i \(0.753353\pi\)
\(80\) −2.15306 −0.240720
\(81\) −9.87739 −1.09749
\(82\) 7.56369 0.835270
\(83\) −6.39009 −0.701404 −0.350702 0.936487i \(-0.614057\pi\)
−0.350702 + 0.936487i \(0.614057\pi\)
\(84\) −7.88092 −0.859879
\(85\) 1.26878 0.137619
\(86\) −1.05011 −0.113236
\(87\) −14.4741 −1.55178
\(88\) 10.4445 1.11339
\(89\) 10.4798 1.11086 0.555430 0.831563i \(-0.312554\pi\)
0.555430 + 0.831563i \(0.312554\pi\)
\(90\) 6.01670 0.634216
\(91\) −0.138408 −0.0145091
\(92\) −4.87951 −0.508724
\(93\) −15.0844 −1.56418
\(94\) 2.15976 0.222762
\(95\) 3.68434 0.378005
\(96\) 12.0103 1.22580
\(97\) 2.73737 0.277938 0.138969 0.990297i \(-0.455621\pi\)
0.138969 + 0.990297i \(0.455621\pi\)
\(98\) 3.66026 0.369742
\(99\) −9.32091 −0.936787
\(100\) −0.137633 −0.0137633
\(101\) −2.53899 −0.252639 −0.126320 0.991990i \(-0.540317\pi\)
−0.126320 + 0.991990i \(0.540317\pi\)
\(102\) 1.32498 0.131192
\(103\) 4.72956 0.466017 0.233008 0.972475i \(-0.425143\pi\)
0.233008 + 0.972475i \(0.425143\pi\)
\(104\) 0.126768 0.0124306
\(105\) 17.6406 1.72155
\(106\) 4.64486 0.451148
\(107\) −1.10752 −0.107068 −0.0535338 0.998566i \(-0.517048\pi\)
−0.0535338 + 0.998566i \(0.517048\pi\)
\(108\) 0.791864 0.0761972
\(109\) −11.8815 −1.13804 −0.569021 0.822323i \(-0.692678\pi\)
−0.569021 + 0.822323i \(0.692678\pi\)
\(110\) −7.85741 −0.749175
\(111\) −21.4665 −2.03751
\(112\) −3.10527 −0.293420
\(113\) −8.27758 −0.778689 −0.389345 0.921092i \(-0.627298\pi\)
−0.389345 + 0.921092i \(0.627298\pi\)
\(114\) 3.84753 0.360354
\(115\) 10.9223 1.01851
\(116\) 6.15334 0.571323
\(117\) −0.113130 −0.0104589
\(118\) −6.64554 −0.611772
\(119\) 1.82990 0.167747
\(120\) −16.1570 −1.47493
\(121\) 1.17248 0.106589
\(122\) 8.73568 0.790891
\(123\) 18.1262 1.63438
\(124\) 6.41281 0.575888
\(125\) −11.0232 −0.985948
\(126\) 8.67762 0.773063
\(127\) −9.64782 −0.856106 −0.428053 0.903754i \(-0.640800\pi\)
−0.428053 + 0.903754i \(0.640800\pi\)
\(128\) −3.21770 −0.284407
\(129\) −2.51656 −0.221571
\(130\) −0.0953672 −0.00836426
\(131\) 15.5141 1.35547 0.677735 0.735306i \(-0.262961\pi\)
0.677735 + 0.735306i \(0.262961\pi\)
\(132\) 8.41230 0.732197
\(133\) 5.31376 0.460761
\(134\) 15.4004 1.33040
\(135\) −1.77251 −0.152553
\(136\) −1.67601 −0.143716
\(137\) 0.728793 0.0622650 0.0311325 0.999515i \(-0.490089\pi\)
0.0311325 + 0.999515i \(0.490089\pi\)
\(138\) 11.4061 0.970948
\(139\) −12.4402 −1.05516 −0.527581 0.849505i \(-0.676901\pi\)
−0.527581 + 0.849505i \(0.676901\pi\)
\(140\) −7.49954 −0.633827
\(141\) 5.17580 0.435881
\(142\) −4.08461 −0.342773
\(143\) 0.147740 0.0123547
\(144\) −2.53814 −0.211512
\(145\) −13.7736 −1.14384
\(146\) −6.49665 −0.537667
\(147\) 8.77171 0.723479
\(148\) 9.12602 0.750154
\(149\) 3.71652 0.304470 0.152235 0.988344i \(-0.451353\pi\)
0.152235 + 0.988344i \(0.451353\pi\)
\(150\) 0.321723 0.0262686
\(151\) −9.93395 −0.808413 −0.404207 0.914668i \(-0.632452\pi\)
−0.404207 + 0.914668i \(0.632452\pi\)
\(152\) −4.86687 −0.394755
\(153\) 1.49570 0.120920
\(154\) −11.3324 −0.913190
\(155\) −14.3544 −1.15297
\(156\) 0.102102 0.00817470
\(157\) 21.8988 1.74772 0.873859 0.486180i \(-0.161610\pi\)
0.873859 + 0.486180i \(0.161610\pi\)
\(158\) −12.6222 −1.00417
\(159\) 11.1313 0.882767
\(160\) 11.4291 0.903551
\(161\) 15.7527 1.24149
\(162\) −9.81572 −0.771196
\(163\) 16.5248 1.29433 0.647163 0.762352i \(-0.275955\pi\)
0.647163 + 0.762352i \(0.275955\pi\)
\(164\) −7.70596 −0.601735
\(165\) −18.8301 −1.46592
\(166\) −6.35019 −0.492871
\(167\) 18.4365 1.42666 0.713330 0.700829i \(-0.247186\pi\)
0.713330 + 0.700829i \(0.247186\pi\)
\(168\) −23.3026 −1.79783
\(169\) −12.9982 −0.999862
\(170\) 1.26086 0.0967034
\(171\) 4.34329 0.332139
\(172\) 1.06986 0.0815762
\(173\) 4.62720 0.351799 0.175900 0.984408i \(-0.443717\pi\)
0.175900 + 0.984408i \(0.443717\pi\)
\(174\) −14.3837 −1.09042
\(175\) 0.444326 0.0335879
\(176\) 3.31464 0.249850
\(177\) −15.9259 −1.19706
\(178\) 10.4144 0.780592
\(179\) 8.34650 0.623847 0.311924 0.950107i \(-0.399027\pi\)
0.311924 + 0.950107i \(0.399027\pi\)
\(180\) −6.12987 −0.456894
\(181\) 13.3973 0.995813 0.497907 0.867231i \(-0.334102\pi\)
0.497907 + 0.867231i \(0.334102\pi\)
\(182\) −0.137544 −0.0101954
\(183\) 20.9348 1.54755
\(184\) −14.4279 −1.06364
\(185\) −20.4277 −1.50187
\(186\) −14.9902 −1.09914
\(187\) −1.95329 −0.142838
\(188\) −2.20038 −0.160480
\(189\) −2.55641 −0.185951
\(190\) 3.66134 0.265621
\(191\) −6.08952 −0.440622 −0.220311 0.975430i \(-0.570707\pi\)
−0.220311 + 0.975430i \(0.570707\pi\)
\(192\) 16.4604 1.18793
\(193\) −7.50218 −0.540019 −0.270009 0.962858i \(-0.587027\pi\)
−0.270009 + 0.962858i \(0.587027\pi\)
\(194\) 2.72028 0.195305
\(195\) −0.228545 −0.0163664
\(196\) −3.72911 −0.266365
\(197\) 8.24651 0.587540 0.293770 0.955876i \(-0.405090\pi\)
0.293770 + 0.955876i \(0.405090\pi\)
\(198\) −9.26271 −0.658272
\(199\) 8.50919 0.603200 0.301600 0.953435i \(-0.402479\pi\)
0.301600 + 0.953435i \(0.402479\pi\)
\(200\) −0.406958 −0.0287763
\(201\) 36.9067 2.60320
\(202\) −2.52314 −0.177528
\(203\) −19.8651 −1.39425
\(204\) −1.34990 −0.0945119
\(205\) 17.2490 1.20472
\(206\) 4.70002 0.327466
\(207\) 12.8757 0.894925
\(208\) 0.0402306 0.00278949
\(209\) −5.67204 −0.392343
\(210\) 17.5305 1.20972
\(211\) −5.91072 −0.406910 −0.203455 0.979084i \(-0.565217\pi\)
−0.203455 + 0.979084i \(0.565217\pi\)
\(212\) −4.73223 −0.325011
\(213\) −9.78866 −0.670708
\(214\) −1.10060 −0.0752356
\(215\) −2.39478 −0.163322
\(216\) 2.34141 0.159313
\(217\) −20.7027 −1.40539
\(218\) −11.8073 −0.799693
\(219\) −15.5690 −1.05206
\(220\) 8.00521 0.539711
\(221\) −0.0237075 −0.00159474
\(222\) −21.3324 −1.43174
\(223\) −10.2228 −0.684567 −0.342283 0.939597i \(-0.611200\pi\)
−0.342283 + 0.939597i \(0.611200\pi\)
\(224\) 16.4837 1.10136
\(225\) 0.363177 0.0242118
\(226\) −8.22590 −0.547179
\(227\) 25.7805 1.71111 0.855555 0.517713i \(-0.173216\pi\)
0.855555 + 0.517713i \(0.173216\pi\)
\(228\) −3.91990 −0.259602
\(229\) 3.62202 0.239350 0.119675 0.992813i \(-0.461815\pi\)
0.119675 + 0.992813i \(0.461815\pi\)
\(230\) 10.8541 0.715697
\(231\) −27.1577 −1.78685
\(232\) 18.1944 1.19452
\(233\) −8.02271 −0.525585 −0.262792 0.964852i \(-0.584643\pi\)
−0.262792 + 0.964852i \(0.584643\pi\)
\(234\) −0.112424 −0.00734937
\(235\) 4.92533 0.321293
\(236\) 6.77054 0.440725
\(237\) −30.2488 −1.96487
\(238\) 1.81848 0.117874
\(239\) −17.3902 −1.12488 −0.562438 0.826839i \(-0.690136\pi\)
−0.562438 + 0.826839i \(0.690136\pi\)
\(240\) −5.12754 −0.330981
\(241\) 10.2145 0.657974 0.328987 0.944334i \(-0.393293\pi\)
0.328987 + 0.944334i \(0.393293\pi\)
\(242\) 1.16516 0.0748995
\(243\) −21.1767 −1.35849
\(244\) −8.89999 −0.569764
\(245\) 8.34723 0.533285
\(246\) 18.0130 1.14847
\(247\) −0.0688429 −0.00438037
\(248\) 18.9616 1.20406
\(249\) −15.2181 −0.964405
\(250\) −10.9544 −0.692817
\(251\) 8.85928 0.559193 0.279596 0.960118i \(-0.409799\pi\)
0.279596 + 0.960118i \(0.409799\pi\)
\(252\) −8.84084 −0.556921
\(253\) −16.8148 −1.05714
\(254\) −9.58758 −0.601578
\(255\) 3.02161 0.189221
\(256\) −17.0212 −1.06382
\(257\) 29.5926 1.84594 0.922968 0.384877i \(-0.125756\pi\)
0.922968 + 0.384877i \(0.125756\pi\)
\(258\) −2.50085 −0.155696
\(259\) −29.4619 −1.83067
\(260\) 0.0971611 0.00602567
\(261\) −16.2370 −1.00505
\(262\) 15.4172 0.952478
\(263\) 13.1829 0.812893 0.406446 0.913675i \(-0.366768\pi\)
0.406446 + 0.913675i \(0.366768\pi\)
\(264\) 24.8737 1.53087
\(265\) 10.5926 0.650698
\(266\) 5.28058 0.323773
\(267\) 24.9578 1.52739
\(268\) −15.6901 −0.958427
\(269\) 6.16528 0.375904 0.187952 0.982178i \(-0.439815\pi\)
0.187952 + 0.982178i \(0.439815\pi\)
\(270\) −1.76144 −0.107198
\(271\) −7.42818 −0.451230 −0.225615 0.974217i \(-0.572439\pi\)
−0.225615 + 0.974217i \(0.572439\pi\)
\(272\) −0.531892 −0.0322507
\(273\) −0.329620 −0.0199495
\(274\) 0.724242 0.0437531
\(275\) −0.474285 −0.0286005
\(276\) −11.6206 −0.699478
\(277\) 28.4319 1.70831 0.854155 0.520019i \(-0.174075\pi\)
0.854155 + 0.520019i \(0.174075\pi\)
\(278\) −12.3625 −0.741454
\(279\) −16.9217 −1.01308
\(280\) −22.1749 −1.32520
\(281\) −1.93121 −0.115206 −0.0576031 0.998340i \(-0.518346\pi\)
−0.0576031 + 0.998340i \(0.518346\pi\)
\(282\) 5.14349 0.306290
\(283\) −4.39718 −0.261385 −0.130693 0.991423i \(-0.541720\pi\)
−0.130693 + 0.991423i \(0.541720\pi\)
\(284\) 4.16144 0.246936
\(285\) 8.77429 0.519744
\(286\) 0.146818 0.00868152
\(287\) 24.8774 1.46847
\(288\) 13.4732 0.793917
\(289\) −16.6866 −0.981562
\(290\) −13.6876 −0.803765
\(291\) 6.51908 0.382155
\(292\) 6.61885 0.387339
\(293\) 28.4616 1.66274 0.831371 0.555717i \(-0.187556\pi\)
0.831371 + 0.555717i \(0.187556\pi\)
\(294\) 8.71695 0.508383
\(295\) −15.1552 −0.882368
\(296\) 26.9841 1.56842
\(297\) 2.72877 0.158339
\(298\) 3.69332 0.213948
\(299\) −0.204086 −0.0118026
\(300\) −0.327774 −0.0189241
\(301\) −3.45388 −0.199078
\(302\) −9.87192 −0.568065
\(303\) −6.04664 −0.347370
\(304\) −1.54453 −0.0885850
\(305\) 19.9217 1.14071
\(306\) 1.48636 0.0849697
\(307\) 31.7094 1.80975 0.904874 0.425679i \(-0.139965\pi\)
0.904874 + 0.425679i \(0.139965\pi\)
\(308\) 11.5455 0.657868
\(309\) 11.2635 0.640757
\(310\) −14.2648 −0.810186
\(311\) −17.5426 −0.994748 −0.497374 0.867536i \(-0.665702\pi\)
−0.497374 + 0.867536i \(0.665702\pi\)
\(312\) 0.301898 0.0170916
\(313\) 24.0671 1.36035 0.680175 0.733049i \(-0.261904\pi\)
0.680175 + 0.733049i \(0.261904\pi\)
\(314\) 21.7621 1.22811
\(315\) 19.7893 1.11500
\(316\) 12.8596 0.723411
\(317\) 30.3259 1.70327 0.851636 0.524134i \(-0.175611\pi\)
0.851636 + 0.524134i \(0.175611\pi\)
\(318\) 11.0618 0.620313
\(319\) 21.2045 1.18722
\(320\) 15.6639 0.875638
\(321\) −2.63756 −0.147214
\(322\) 15.6544 0.872383
\(323\) 0.910178 0.0506436
\(324\) 10.0004 0.555575
\(325\) −0.00575651 −0.000319314 0
\(326\) 16.4217 0.909512
\(327\) −28.2959 −1.56477
\(328\) −22.7852 −1.25810
\(329\) 7.10358 0.391633
\(330\) −18.7125 −1.03009
\(331\) −14.1141 −0.775783 −0.387892 0.921705i \(-0.626797\pi\)
−0.387892 + 0.921705i \(0.626797\pi\)
\(332\) 6.46964 0.355067
\(333\) −24.0811 −1.31964
\(334\) 18.3214 1.00250
\(335\) 35.1207 1.91885
\(336\) −7.39522 −0.403442
\(337\) 33.3303 1.81562 0.907810 0.419382i \(-0.137753\pi\)
0.907810 + 0.419382i \(0.137753\pi\)
\(338\) −12.9170 −0.702595
\(339\) −19.7131 −1.07067
\(340\) −1.28457 −0.0696658
\(341\) 22.0986 1.19671
\(342\) 4.31617 0.233392
\(343\) −10.8409 −0.585351
\(344\) 3.16340 0.170559
\(345\) 26.0115 1.40041
\(346\) 4.59830 0.247206
\(347\) −1.57665 −0.0846392 −0.0423196 0.999104i \(-0.513475\pi\)
−0.0423196 + 0.999104i \(0.513475\pi\)
\(348\) 14.6542 0.785549
\(349\) −5.53888 −0.296490 −0.148245 0.988951i \(-0.547362\pi\)
−0.148245 + 0.988951i \(0.547362\pi\)
\(350\) 0.441552 0.0236019
\(351\) 0.0331198 0.00176780
\(352\) −17.5951 −0.937823
\(353\) −11.6547 −0.620317 −0.310158 0.950685i \(-0.600382\pi\)
−0.310158 + 0.950685i \(0.600382\pi\)
\(354\) −15.8264 −0.841165
\(355\) −9.31496 −0.494387
\(356\) −10.6103 −0.562344
\(357\) 4.35793 0.230646
\(358\) 8.29439 0.438372
\(359\) 19.8234 1.04624 0.523120 0.852259i \(-0.324768\pi\)
0.523120 + 0.852259i \(0.324768\pi\)
\(360\) −18.1250 −0.955272
\(361\) −16.3570 −0.860894
\(362\) 13.3137 0.699750
\(363\) 2.79228 0.146557
\(364\) 0.140131 0.00734486
\(365\) −14.8156 −0.775485
\(366\) 20.8041 1.08745
\(367\) −11.5005 −0.600323 −0.300161 0.953888i \(-0.597041\pi\)
−0.300161 + 0.953888i \(0.597041\pi\)
\(368\) −4.57878 −0.238686
\(369\) 20.3340 1.05855
\(370\) −20.3001 −1.05535
\(371\) 15.2772 0.793154
\(372\) 15.2722 0.791825
\(373\) −36.0734 −1.86781 −0.933905 0.357521i \(-0.883622\pi\)
−0.933905 + 0.357521i \(0.883622\pi\)
\(374\) −1.94109 −0.100371
\(375\) −26.2519 −1.35564
\(376\) −6.50617 −0.335530
\(377\) 0.257364 0.0132549
\(378\) −2.54044 −0.130666
\(379\) −3.58163 −0.183976 −0.0919880 0.995760i \(-0.529322\pi\)
−0.0919880 + 0.995760i \(0.529322\pi\)
\(380\) −3.73021 −0.191356
\(381\) −22.9764 −1.17711
\(382\) −6.05149 −0.309621
\(383\) 21.0537 1.07579 0.537897 0.843011i \(-0.319219\pi\)
0.537897 + 0.843011i \(0.319219\pi\)
\(384\) −7.66298 −0.391050
\(385\) −25.8435 −1.31711
\(386\) −7.45534 −0.379467
\(387\) −2.82308 −0.143505
\(388\) −2.77145 −0.140699
\(389\) −8.55454 −0.433733 −0.216866 0.976201i \(-0.569584\pi\)
−0.216866 + 0.976201i \(0.569584\pi\)
\(390\) −0.227118 −0.0115006
\(391\) 2.69823 0.136456
\(392\) −11.0264 −0.556915
\(393\) 36.9469 1.86372
\(394\) 8.19502 0.412859
\(395\) −28.7850 −1.44833
\(396\) 9.43694 0.474224
\(397\) 20.4403 1.02587 0.512934 0.858428i \(-0.328559\pi\)
0.512934 + 0.858428i \(0.328559\pi\)
\(398\) 8.45606 0.423864
\(399\) 12.6548 0.633530
\(400\) −0.129151 −0.00645753
\(401\) −17.1022 −0.854042 −0.427021 0.904242i \(-0.640437\pi\)
−0.427021 + 0.904242i \(0.640437\pi\)
\(402\) 36.6763 1.82925
\(403\) 0.268216 0.0133608
\(404\) 2.57060 0.127892
\(405\) −22.3848 −1.11231
\(406\) −19.7410 −0.979731
\(407\) 31.4484 1.55884
\(408\) −3.99143 −0.197605
\(409\) 8.28369 0.409602 0.204801 0.978804i \(-0.434345\pi\)
0.204801 + 0.978804i \(0.434345\pi\)
\(410\) 17.1413 0.846549
\(411\) 1.73563 0.0856121
\(412\) −4.78843 −0.235909
\(413\) −21.8576 −1.07554
\(414\) 12.7953 0.628857
\(415\) −14.4816 −0.710875
\(416\) −0.213556 −0.0104704
\(417\) −29.6264 −1.45081
\(418\) −5.63663 −0.275696
\(419\) −23.9904 −1.17201 −0.586004 0.810308i \(-0.699300\pi\)
−0.586004 + 0.810308i \(0.699300\pi\)
\(420\) −17.8602 −0.871490
\(421\) −13.8202 −0.673556 −0.336778 0.941584i \(-0.609337\pi\)
−0.336778 + 0.941584i \(0.609337\pi\)
\(422\) −5.87381 −0.285933
\(423\) 5.80623 0.282309
\(424\) −13.9924 −0.679531
\(425\) 0.0761073 0.00369175
\(426\) −9.72754 −0.471301
\(427\) 28.7322 1.39045
\(428\) 1.12130 0.0542002
\(429\) 0.351845 0.0169872
\(430\) −2.37982 −0.114765
\(431\) 19.1258 0.921258 0.460629 0.887593i \(-0.347624\pi\)
0.460629 + 0.887593i \(0.347624\pi\)
\(432\) 0.743061 0.0357506
\(433\) −16.3174 −0.784166 −0.392083 0.919930i \(-0.628245\pi\)
−0.392083 + 0.919930i \(0.628245\pi\)
\(434\) −20.5735 −0.987558
\(435\) −32.8020 −1.57273
\(436\) 12.0294 0.576105
\(437\) 7.83526 0.374811
\(438\) −15.4718 −0.739273
\(439\) 29.5061 1.40825 0.704124 0.710077i \(-0.251340\pi\)
0.704124 + 0.710077i \(0.251340\pi\)
\(440\) 23.6700 1.12843
\(441\) 9.84013 0.468578
\(442\) −0.0235595 −0.00112061
\(443\) 7.94549 0.377502 0.188751 0.982025i \(-0.439556\pi\)
0.188751 + 0.982025i \(0.439556\pi\)
\(444\) 21.7337 1.03144
\(445\) 23.7500 1.12586
\(446\) −10.1589 −0.481040
\(447\) 8.85094 0.418635
\(448\) 22.5913 1.06734
\(449\) −37.2956 −1.76009 −0.880045 0.474890i \(-0.842488\pi\)
−0.880045 + 0.474890i \(0.842488\pi\)
\(450\) 0.360910 0.0170134
\(451\) −26.5548 −1.25042
\(452\) 8.38062 0.394191
\(453\) −23.6578 −1.11154
\(454\) 25.6195 1.20238
\(455\) −0.313669 −0.0147050
\(456\) −11.5905 −0.542774
\(457\) 17.0381 0.797007 0.398503 0.917167i \(-0.369530\pi\)
0.398503 + 0.917167i \(0.369530\pi\)
\(458\) 3.59940 0.168189
\(459\) −0.437879 −0.0204384
\(460\) −11.0582 −0.515593
\(461\) 36.9778 1.72223 0.861113 0.508413i \(-0.169768\pi\)
0.861113 + 0.508413i \(0.169768\pi\)
\(462\) −26.9882 −1.25560
\(463\) −42.0166 −1.95268 −0.976339 0.216245i \(-0.930619\pi\)
−0.976339 + 0.216245i \(0.930619\pi\)
\(464\) 5.77411 0.268056
\(465\) −34.1852 −1.58530
\(466\) −7.97261 −0.369324
\(467\) −11.6484 −0.539022 −0.269511 0.962997i \(-0.586862\pi\)
−0.269511 + 0.962997i \(0.586862\pi\)
\(468\) 0.114538 0.00529454
\(469\) 50.6530 2.33894
\(470\) 4.89458 0.225770
\(471\) 52.1523 2.40305
\(472\) 20.0194 0.921466
\(473\) 3.68676 0.169517
\(474\) −30.0599 −1.38070
\(475\) 0.221004 0.0101403
\(476\) −1.85268 −0.0849176
\(477\) 12.4871 0.571744
\(478\) −17.2816 −0.790441
\(479\) −11.2345 −0.513319 −0.256659 0.966502i \(-0.582622\pi\)
−0.256659 + 0.966502i \(0.582622\pi\)
\(480\) 27.2185 1.24235
\(481\) 0.381696 0.0174038
\(482\) 10.1507 0.462353
\(483\) 37.5152 1.70700
\(484\) −1.18708 −0.0539582
\(485\) 6.20360 0.281691
\(486\) −21.0445 −0.954597
\(487\) −12.7952 −0.579806 −0.289903 0.957056i \(-0.593623\pi\)
−0.289903 + 0.957056i \(0.593623\pi\)
\(488\) −26.3158 −1.19126
\(489\) 39.3540 1.77965
\(490\) 8.29511 0.374735
\(491\) −25.8706 −1.16753 −0.583763 0.811924i \(-0.698420\pi\)
−0.583763 + 0.811924i \(0.698420\pi\)
\(492\) −18.3518 −0.827364
\(493\) −3.40263 −0.153247
\(494\) −0.0684131 −0.00307805
\(495\) −21.1236 −0.949436
\(496\) 6.01759 0.270198
\(497\) −13.4345 −0.602622
\(498\) −15.1230 −0.677679
\(499\) −39.9900 −1.79020 −0.895099 0.445867i \(-0.852895\pi\)
−0.895099 + 0.445867i \(0.852895\pi\)
\(500\) 11.1605 0.499111
\(501\) 43.9067 1.96161
\(502\) 8.80396 0.392940
\(503\) 23.6258 1.05342 0.526712 0.850044i \(-0.323425\pi\)
0.526712 + 0.850044i \(0.323425\pi\)
\(504\) −26.1409 −1.16441
\(505\) −5.75402 −0.256051
\(506\) −16.7099 −0.742844
\(507\) −30.9553 −1.37477
\(508\) 9.76792 0.433381
\(509\) 30.6346 1.35786 0.678928 0.734204i \(-0.262445\pi\)
0.678928 + 0.734204i \(0.262445\pi\)
\(510\) 3.00274 0.132964
\(511\) −21.3679 −0.945260
\(512\) −10.4795 −0.463132
\(513\) −1.27153 −0.0561396
\(514\) 29.4078 1.29712
\(515\) 10.7184 0.472310
\(516\) 2.54789 0.112164
\(517\) −7.58255 −0.333480
\(518\) −29.2779 −1.28640
\(519\) 11.0197 0.483711
\(520\) 0.287289 0.0125984
\(521\) −8.18590 −0.358631 −0.179315 0.983792i \(-0.557388\pi\)
−0.179315 + 0.983792i \(0.557388\pi\)
\(522\) −16.1357 −0.706238
\(523\) −15.6310 −0.683497 −0.341749 0.939791i \(-0.611019\pi\)
−0.341749 + 0.939791i \(0.611019\pi\)
\(524\) −15.7072 −0.686172
\(525\) 1.05817 0.0461822
\(526\) 13.1006 0.571213
\(527\) −3.54611 −0.154471
\(528\) 7.89385 0.343536
\(529\) 0.227726 0.00990113
\(530\) 10.5265 0.457240
\(531\) −17.8657 −0.775304
\(532\) −5.37991 −0.233249
\(533\) −0.322302 −0.0139605
\(534\) 24.8020 1.07329
\(535\) −2.50992 −0.108513
\(536\) −46.3931 −2.00387
\(537\) 19.8773 0.857768
\(538\) 6.12679 0.264144
\(539\) −12.8506 −0.553513
\(540\) 1.79457 0.0772261
\(541\) 23.7414 1.02072 0.510360 0.859961i \(-0.329512\pi\)
0.510360 + 0.859961i \(0.329512\pi\)
\(542\) −7.38180 −0.317075
\(543\) 31.9058 1.36921
\(544\) 2.82344 0.121054
\(545\) −26.9266 −1.15341
\(546\) −0.327562 −0.0140183
\(547\) −15.5980 −0.666922 −0.333461 0.942764i \(-0.608217\pi\)
−0.333461 + 0.942764i \(0.608217\pi\)
\(548\) −0.737865 −0.0315200
\(549\) 23.4847 1.00230
\(550\) −0.471324 −0.0200973
\(551\) −9.88070 −0.420932
\(552\) −34.3601 −1.46246
\(553\) −41.5152 −1.76541
\(554\) 28.2544 1.20041
\(555\) −48.6486 −2.06502
\(556\) 12.5950 0.534149
\(557\) 35.0308 1.48430 0.742151 0.670233i \(-0.233806\pi\)
0.742151 + 0.670233i \(0.233806\pi\)
\(558\) −16.8161 −0.711880
\(559\) 0.0447470 0.00189260
\(560\) −7.03734 −0.297382
\(561\) −4.65177 −0.196398
\(562\) −1.91915 −0.0809545
\(563\) 24.0930 1.01540 0.507700 0.861534i \(-0.330496\pi\)
0.507700 + 0.861534i \(0.330496\pi\)
\(564\) −5.24023 −0.220654
\(565\) −18.7592 −0.789204
\(566\) −4.36972 −0.183673
\(567\) −32.2845 −1.35582
\(568\) 12.3047 0.516293
\(569\) −9.18857 −0.385205 −0.192603 0.981277i \(-0.561693\pi\)
−0.192603 + 0.981277i \(0.561693\pi\)
\(570\) 8.71951 0.365220
\(571\) −16.9178 −0.707989 −0.353994 0.935248i \(-0.615177\pi\)
−0.353994 + 0.935248i \(0.615177\pi\)
\(572\) −0.149579 −0.00625423
\(573\) −14.5022 −0.605840
\(574\) 24.7221 1.03188
\(575\) 0.655169 0.0273224
\(576\) 18.4654 0.769391
\(577\) 25.3727 1.05628 0.528141 0.849157i \(-0.322889\pi\)
0.528141 + 0.849157i \(0.322889\pi\)
\(578\) −16.5824 −0.689736
\(579\) −17.8665 −0.742507
\(580\) 13.9451 0.579038
\(581\) −20.8862 −0.866504
\(582\) 6.47838 0.268537
\(583\) −16.3073 −0.675379
\(584\) 19.5708 0.809847
\(585\) −0.256382 −0.0106001
\(586\) 28.2839 1.16840
\(587\) −42.0228 −1.73447 −0.867233 0.497902i \(-0.834104\pi\)
−0.867233 + 0.497902i \(0.834104\pi\)
\(588\) −8.88091 −0.366242
\(589\) −10.2974 −0.424295
\(590\) −15.0605 −0.620033
\(591\) 19.6391 0.807846
\(592\) 8.56358 0.351961
\(593\) −4.55651 −0.187114 −0.0935568 0.995614i \(-0.529824\pi\)
−0.0935568 + 0.995614i \(0.529824\pi\)
\(594\) 2.71174 0.111264
\(595\) 4.14704 0.170012
\(596\) −3.76279 −0.154130
\(597\) 20.2647 0.829379
\(598\) −0.202811 −0.00829358
\(599\) −29.9219 −1.22258 −0.611288 0.791409i \(-0.709348\pi\)
−0.611288 + 0.791409i \(0.709348\pi\)
\(600\) −0.969173 −0.0395663
\(601\) 18.2493 0.744404 0.372202 0.928152i \(-0.378603\pi\)
0.372202 + 0.928152i \(0.378603\pi\)
\(602\) −3.43231 −0.139891
\(603\) 41.4021 1.68602
\(604\) 10.0576 0.409238
\(605\) 2.65715 0.108029
\(606\) −6.00888 −0.244094
\(607\) −36.9675 −1.50046 −0.750232 0.661174i \(-0.770058\pi\)
−0.750232 + 0.661174i \(0.770058\pi\)
\(608\) 8.19884 0.332507
\(609\) −47.3088 −1.91705
\(610\) 19.7973 0.801570
\(611\) −0.0920311 −0.00372318
\(612\) −1.51432 −0.0612128
\(613\) 7.11423 0.287341 0.143670 0.989626i \(-0.454109\pi\)
0.143670 + 0.989626i \(0.454109\pi\)
\(614\) 31.5114 1.27170
\(615\) 41.0786 1.65645
\(616\) 34.1382 1.37547
\(617\) −21.3061 −0.857751 −0.428876 0.903364i \(-0.641090\pi\)
−0.428876 + 0.903364i \(0.641090\pi\)
\(618\) 11.1931 0.450255
\(619\) 1.00000 0.0401934
\(620\) 14.5331 0.583664
\(621\) −3.76948 −0.151264
\(622\) −17.4330 −0.699001
\(623\) 34.2536 1.37234
\(624\) 0.0958094 0.00383545
\(625\) −25.6612 −1.02645
\(626\) 23.9168 0.955907
\(627\) −13.5080 −0.539458
\(628\) −22.1714 −0.884737
\(629\) −5.04644 −0.201215
\(630\) 19.6657 0.783502
\(631\) −22.2473 −0.885650 −0.442825 0.896608i \(-0.646024\pi\)
−0.442825 + 0.896608i \(0.646024\pi\)
\(632\) 38.0238 1.51250
\(633\) −14.0764 −0.559487
\(634\) 30.1365 1.19687
\(635\) −21.8645 −0.867665
\(636\) −11.2698 −0.446878
\(637\) −0.155970 −0.00617976
\(638\) 21.0721 0.834252
\(639\) −10.9809 −0.434400
\(640\) −7.29215 −0.288248
\(641\) 28.1342 1.11124 0.555618 0.831438i \(-0.312482\pi\)
0.555618 + 0.831438i \(0.312482\pi\)
\(642\) −2.62109 −0.103446
\(643\) −32.9969 −1.30127 −0.650636 0.759390i \(-0.725498\pi\)
−0.650636 + 0.759390i \(0.725498\pi\)
\(644\) −15.9488 −0.628471
\(645\) −5.70318 −0.224562
\(646\) 0.904495 0.0355869
\(647\) −41.0699 −1.61463 −0.807313 0.590124i \(-0.799079\pi\)
−0.807313 + 0.590124i \(0.799079\pi\)
\(648\) 29.5694 1.16159
\(649\) 23.3314 0.915836
\(650\) −0.00572057 −0.000224379 0
\(651\) −49.3037 −1.93237
\(652\) −16.7306 −0.655219
\(653\) 39.9591 1.56372 0.781860 0.623454i \(-0.214271\pi\)
0.781860 + 0.623454i \(0.214271\pi\)
\(654\) −28.1193 −1.09955
\(655\) 35.1589 1.37377
\(656\) −7.23104 −0.282325
\(657\) −17.4654 −0.681390
\(658\) 7.05923 0.275197
\(659\) 26.4314 1.02962 0.514811 0.857304i \(-0.327862\pi\)
0.514811 + 0.857304i \(0.327862\pi\)
\(660\) 19.0645 0.742083
\(661\) 17.4319 0.678024 0.339012 0.940782i \(-0.389907\pi\)
0.339012 + 0.940782i \(0.389907\pi\)
\(662\) −14.0260 −0.545137
\(663\) −0.0564596 −0.00219271
\(664\) 19.1296 0.742374
\(665\) 12.0424 0.466983
\(666\) −23.9308 −0.927299
\(667\) −29.2915 −1.13417
\(668\) −18.6660 −0.722209
\(669\) −24.3456 −0.941255
\(670\) 34.9014 1.34836
\(671\) −30.6695 −1.18398
\(672\) 39.2561 1.51434
\(673\) 41.7040 1.60757 0.803785 0.594919i \(-0.202816\pi\)
0.803785 + 0.594919i \(0.202816\pi\)
\(674\) 33.1222 1.27582
\(675\) −0.106323 −0.00409238
\(676\) 13.1600 0.506154
\(677\) −6.10189 −0.234515 −0.117257 0.993102i \(-0.537410\pi\)
−0.117257 + 0.993102i \(0.537410\pi\)
\(678\) −19.5900 −0.752351
\(679\) 8.94718 0.343361
\(680\) −3.79827 −0.145657
\(681\) 61.3964 2.35271
\(682\) 21.9606 0.840917
\(683\) −0.724917 −0.0277382 −0.0138691 0.999904i \(-0.504415\pi\)
−0.0138691 + 0.999904i \(0.504415\pi\)
\(684\) −4.39735 −0.168137
\(685\) 1.65164 0.0631057
\(686\) −10.7732 −0.411321
\(687\) 8.62587 0.329097
\(688\) 1.00393 0.0382743
\(689\) −0.197925 −0.00754036
\(690\) 25.8491 0.984058
\(691\) −33.3019 −1.26686 −0.633432 0.773798i \(-0.718354\pi\)
−0.633432 + 0.773798i \(0.718354\pi\)
\(692\) −4.68480 −0.178089
\(693\) −30.4656 −1.15729
\(694\) −1.56681 −0.0594753
\(695\) −28.1927 −1.06941
\(696\) 43.3301 1.64242
\(697\) 4.26118 0.161404
\(698\) −5.50430 −0.208341
\(699\) −19.1061 −0.722661
\(700\) −0.449857 −0.0170030
\(701\) −22.5695 −0.852438 −0.426219 0.904620i \(-0.640155\pi\)
−0.426219 + 0.904620i \(0.640155\pi\)
\(702\) 0.0329130 0.00124222
\(703\) −14.6541 −0.552689
\(704\) −24.1145 −0.908851
\(705\) 11.7297 0.441767
\(706\) −11.5819 −0.435892
\(707\) −8.29877 −0.312107
\(708\) 16.1241 0.605981
\(709\) −9.58864 −0.360109 −0.180054 0.983657i \(-0.557627\pi\)
−0.180054 + 0.983657i \(0.557627\pi\)
\(710\) −9.25680 −0.347402
\(711\) −33.9332 −1.27259
\(712\) −31.3729 −1.17575
\(713\) −30.5266 −1.14323
\(714\) 4.33072 0.162073
\(715\) 0.334818 0.0125215
\(716\) −8.45041 −0.315807
\(717\) −41.4148 −1.54666
\(718\) 19.6996 0.735184
\(719\) −6.38603 −0.238159 −0.119079 0.992885i \(-0.537994\pi\)
−0.119079 + 0.992885i \(0.537994\pi\)
\(720\) −5.75209 −0.214368
\(721\) 15.4587 0.575711
\(722\) −16.2549 −0.604943
\(723\) 24.3259 0.904691
\(724\) −13.5641 −0.504105
\(725\) −0.826205 −0.0306845
\(726\) 2.77485 0.102984
\(727\) 34.5236 1.28041 0.640204 0.768205i \(-0.278850\pi\)
0.640204 + 0.768205i \(0.278850\pi\)
\(728\) 0.414344 0.0153566
\(729\) −20.8003 −0.770383
\(730\) −14.7231 −0.544927
\(731\) −0.591604 −0.0218813
\(732\) −21.1954 −0.783405
\(733\) 3.21274 0.118665 0.0593325 0.998238i \(-0.481103\pi\)
0.0593325 + 0.998238i \(0.481103\pi\)
\(734\) −11.4287 −0.421842
\(735\) 19.8790 0.733248
\(736\) 24.3056 0.895916
\(737\) −54.0683 −1.99163
\(738\) 20.2070 0.743831
\(739\) −34.8845 −1.28325 −0.641623 0.767020i \(-0.721738\pi\)
−0.641623 + 0.767020i \(0.721738\pi\)
\(740\) 20.6819 0.760284
\(741\) −0.163950 −0.00602285
\(742\) 15.1818 0.557343
\(743\) 47.5785 1.74549 0.872743 0.488181i \(-0.162339\pi\)
0.872743 + 0.488181i \(0.162339\pi\)
\(744\) 45.1572 1.65554
\(745\) 8.42262 0.308581
\(746\) −35.8482 −1.31250
\(747\) −17.0717 −0.624619
\(748\) 1.97760 0.0723083
\(749\) −3.61995 −0.132270
\(750\) −26.0880 −0.952599
\(751\) 21.7473 0.793569 0.396785 0.917912i \(-0.370126\pi\)
0.396785 + 0.917912i \(0.370126\pi\)
\(752\) −2.06477 −0.0752946
\(753\) 21.0985 0.768870
\(754\) 0.255757 0.00931411
\(755\) −22.5129 −0.819329
\(756\) 2.58823 0.0941330
\(757\) 25.0202 0.909375 0.454687 0.890651i \(-0.349751\pi\)
0.454687 + 0.890651i \(0.349751\pi\)
\(758\) −3.55927 −0.129278
\(759\) −40.0447 −1.45353
\(760\) −11.0296 −0.400085
\(761\) −21.1523 −0.766769 −0.383384 0.923589i \(-0.625242\pi\)
−0.383384 + 0.923589i \(0.625242\pi\)
\(762\) −22.8329 −0.827149
\(763\) −38.8350 −1.40592
\(764\) 6.16532 0.223054
\(765\) 3.38965 0.122553
\(766\) 20.9222 0.755951
\(767\) 0.283178 0.0102250
\(768\) −40.5360 −1.46272
\(769\) −24.5196 −0.884200 −0.442100 0.896966i \(-0.645766\pi\)
−0.442100 + 0.896966i \(0.645766\pi\)
\(770\) −25.6821 −0.925520
\(771\) 70.4750 2.53810
\(772\) 7.59557 0.273371
\(773\) −0.751017 −0.0270122 −0.0135061 0.999909i \(-0.504299\pi\)
−0.0135061 + 0.999909i \(0.504299\pi\)
\(774\) −2.80546 −0.100840
\(775\) −0.861044 −0.0309296
\(776\) −8.19471 −0.294173
\(777\) −70.1637 −2.51711
\(778\) −8.50113 −0.304780
\(779\) 12.3738 0.443338
\(780\) 0.231390 0.00828509
\(781\) 14.3404 0.513139
\(782\) 2.68139 0.0958862
\(783\) 4.75353 0.169877
\(784\) −3.49928 −0.124974
\(785\) 49.6285 1.77132
\(786\) 36.7162 1.30962
\(787\) −32.7650 −1.16795 −0.583973 0.811773i \(-0.698503\pi\)
−0.583973 + 0.811773i \(0.698503\pi\)
\(788\) −8.34917 −0.297427
\(789\) 31.3952 1.11770
\(790\) −28.6052 −1.01773
\(791\) −27.0555 −0.961982
\(792\) 27.9034 0.991506
\(793\) −0.372243 −0.0132187
\(794\) 20.3126 0.720868
\(795\) 25.2264 0.894687
\(796\) −8.61511 −0.305355
\(797\) −18.9303 −0.670547 −0.335274 0.942121i \(-0.608829\pi\)
−0.335274 + 0.942121i \(0.608829\pi\)
\(798\) 12.5757 0.445177
\(799\) 1.21675 0.0430456
\(800\) 0.685571 0.0242386
\(801\) 27.9978 0.989252
\(802\) −16.9954 −0.600128
\(803\) 22.8086 0.804899
\(804\) −37.3662 −1.31780
\(805\) 35.6998 1.25825
\(806\) 0.266541 0.00938852
\(807\) 14.6827 0.516854
\(808\) 7.60083 0.267396
\(809\) −34.3026 −1.20601 −0.603007 0.797736i \(-0.706031\pi\)
−0.603007 + 0.797736i \(0.706031\pi\)
\(810\) −22.2450 −0.781609
\(811\) −38.1606 −1.34000 −0.669999 0.742362i \(-0.733706\pi\)
−0.669999 + 0.742362i \(0.733706\pi\)
\(812\) 20.1123 0.705805
\(813\) −17.6903 −0.620425
\(814\) 31.2520 1.09538
\(815\) 37.4496 1.31180
\(816\) −1.26670 −0.0443435
\(817\) −1.71793 −0.0601027
\(818\) 8.23197 0.287824
\(819\) −0.369768 −0.0129208
\(820\) −17.4637 −0.609860
\(821\) −36.9014 −1.28787 −0.643935 0.765081i \(-0.722699\pi\)
−0.643935 + 0.765081i \(0.722699\pi\)
\(822\) 1.72479 0.0601589
\(823\) −2.42438 −0.0845085 −0.0422543 0.999107i \(-0.513454\pi\)
−0.0422543 + 0.999107i \(0.513454\pi\)
\(824\) −14.1586 −0.493238
\(825\) −1.12951 −0.0393246
\(826\) −21.7211 −0.755775
\(827\) 2.08456 0.0724874 0.0362437 0.999343i \(-0.488461\pi\)
0.0362437 + 0.999343i \(0.488461\pi\)
\(828\) −13.0360 −0.453033
\(829\) −46.0254 −1.59853 −0.799264 0.600980i \(-0.794777\pi\)
−0.799264 + 0.600980i \(0.794777\pi\)
\(830\) −14.3912 −0.499526
\(831\) 67.7109 2.34886
\(832\) −0.292684 −0.0101470
\(833\) 2.06209 0.0714474
\(834\) −29.4414 −1.01947
\(835\) 41.7819 1.44592
\(836\) 5.74265 0.198614
\(837\) 4.95397 0.171234
\(838\) −23.8406 −0.823560
\(839\) −8.54263 −0.294924 −0.147462 0.989068i \(-0.547110\pi\)
−0.147462 + 0.989068i \(0.547110\pi\)
\(840\) −52.8097 −1.82211
\(841\) 7.93822 0.273732
\(842\) −13.7339 −0.473302
\(843\) −4.59919 −0.158405
\(844\) 5.98430 0.205988
\(845\) −29.4573 −1.01336
\(846\) 5.76998 0.198376
\(847\) 3.83229 0.131679
\(848\) −4.44058 −0.152490
\(849\) −10.4719 −0.359395
\(850\) 0.0756321 0.00259416
\(851\) −43.4422 −1.48918
\(852\) 9.91052 0.339529
\(853\) −24.5758 −0.841461 −0.420730 0.907186i \(-0.638226\pi\)
−0.420730 + 0.907186i \(0.638226\pi\)
\(854\) 28.5528 0.977056
\(855\) 9.84302 0.336624
\(856\) 3.31550 0.113322
\(857\) 49.6423 1.69575 0.847874 0.530198i \(-0.177882\pi\)
0.847874 + 0.530198i \(0.177882\pi\)
\(858\) 0.349648 0.0119368
\(859\) −30.2314 −1.03148 −0.515740 0.856745i \(-0.672483\pi\)
−0.515740 + 0.856745i \(0.672483\pi\)
\(860\) 2.42459 0.0826777
\(861\) 59.2459 2.01909
\(862\) 19.0064 0.647360
\(863\) −27.9588 −0.951728 −0.475864 0.879519i \(-0.657865\pi\)
−0.475864 + 0.879519i \(0.657865\pi\)
\(864\) −3.94440 −0.134191
\(865\) 10.4864 0.356549
\(866\) −16.2156 −0.551027
\(867\) −39.7392 −1.34961
\(868\) 20.9604 0.711444
\(869\) 44.3144 1.50326
\(870\) −32.5972 −1.10515
\(871\) −0.656240 −0.0222358
\(872\) 35.5690 1.20452
\(873\) 7.31312 0.247512
\(874\) 7.78633 0.263377
\(875\) −36.0297 −1.21803
\(876\) 15.7629 0.532577
\(877\) −8.94803 −0.302153 −0.151077 0.988522i \(-0.548274\pi\)
−0.151077 + 0.988522i \(0.548274\pi\)
\(878\) 29.3218 0.989564
\(879\) 67.7815 2.28621
\(880\) 7.51184 0.253224
\(881\) 52.7351 1.77669 0.888345 0.459176i \(-0.151855\pi\)
0.888345 + 0.459176i \(0.151855\pi\)
\(882\) 9.77869 0.329266
\(883\) −12.0557 −0.405707 −0.202854 0.979209i \(-0.565022\pi\)
−0.202854 + 0.979209i \(0.565022\pi\)
\(884\) 0.0240026 0.000807295 0
\(885\) −36.0922 −1.21322
\(886\) 7.89588 0.265267
\(887\) 13.3652 0.448760 0.224380 0.974502i \(-0.427964\pi\)
0.224380 + 0.974502i \(0.427964\pi\)
\(888\) 64.2629 2.15652
\(889\) −31.5341 −1.05762
\(890\) 23.6018 0.791133
\(891\) 34.4613 1.15450
\(892\) 10.3500 0.346544
\(893\) 3.53326 0.118236
\(894\) 8.79567 0.294171
\(895\) 18.9154 0.632271
\(896\) −10.5171 −0.351353
\(897\) −0.486032 −0.0162281
\(898\) −37.0628 −1.23680
\(899\) 38.4958 1.28391
\(900\) −0.367698 −0.0122566
\(901\) 2.61679 0.0871779
\(902\) −26.3890 −0.878659
\(903\) −8.22544 −0.273725
\(904\) 24.7801 0.824174
\(905\) 30.3618 1.00926
\(906\) −23.5101 −0.781070
\(907\) −17.4678 −0.580007 −0.290004 0.957026i \(-0.593657\pi\)
−0.290004 + 0.957026i \(0.593657\pi\)
\(908\) −26.1014 −0.866205
\(909\) −6.78313 −0.224982
\(910\) −0.311710 −0.0103331
\(911\) 47.8184 1.58429 0.792147 0.610331i \(-0.208964\pi\)
0.792147 + 0.610331i \(0.208964\pi\)
\(912\) −3.67831 −0.121801
\(913\) 22.2944 0.737838
\(914\) 16.9317 0.560050
\(915\) 47.4437 1.56844
\(916\) −3.66711 −0.121165
\(917\) 50.7081 1.67453
\(918\) −0.435145 −0.0143619
\(919\) 0.0733749 0.00242041 0.00121021 0.999999i \(-0.499615\pi\)
0.00121021 + 0.999999i \(0.499615\pi\)
\(920\) −32.6974 −1.07800
\(921\) 75.5161 2.48834
\(922\) 36.7469 1.21019
\(923\) 0.174053 0.00572901
\(924\) 27.4958 0.904546
\(925\) −1.22534 −0.0402891
\(926\) −41.7543 −1.37213
\(927\) 12.6354 0.415001
\(928\) −30.6507 −1.00616
\(929\) 37.0409 1.21527 0.607636 0.794216i \(-0.292118\pi\)
0.607636 + 0.794216i \(0.292118\pi\)
\(930\) −33.9717 −1.11398
\(931\) 5.98801 0.196249
\(932\) 8.12258 0.266064
\(933\) −41.7778 −1.36774
\(934\) −11.5756 −0.378766
\(935\) −4.42666 −0.144767
\(936\) 0.338671 0.0110698
\(937\) 37.6030 1.22844 0.614219 0.789136i \(-0.289471\pi\)
0.614219 + 0.789136i \(0.289471\pi\)
\(938\) 50.3368 1.64355
\(939\) 57.3159 1.87043
\(940\) −4.98665 −0.162646
\(941\) 37.0302 1.20715 0.603576 0.797306i \(-0.293742\pi\)
0.603576 + 0.797306i \(0.293742\pi\)
\(942\) 51.8266 1.68860
\(943\) 36.6824 1.19454
\(944\) 6.35327 0.206781
\(945\) −5.79348 −0.188462
\(946\) 3.66374 0.119118
\(947\) 4.21444 0.136951 0.0684754 0.997653i \(-0.478187\pi\)
0.0684754 + 0.997653i \(0.478187\pi\)
\(948\) 30.6253 0.994665
\(949\) 0.276834 0.00898640
\(950\) 0.219624 0.00712554
\(951\) 72.2213 2.34194
\(952\) −5.47807 −0.177545
\(953\) 27.4562 0.889392 0.444696 0.895682i \(-0.353312\pi\)
0.444696 + 0.895682i \(0.353312\pi\)
\(954\) 12.4091 0.401760
\(955\) −13.8004 −0.446572
\(956\) 17.6066 0.569440
\(957\) 50.4986 1.63239
\(958\) −11.1644 −0.360705
\(959\) 2.38208 0.0769213
\(960\) 37.3037 1.20397
\(961\) 9.11911 0.294165
\(962\) 0.379313 0.0122295
\(963\) −2.95882 −0.0953467
\(964\) −10.3417 −0.333082
\(965\) −17.0019 −0.547311
\(966\) 37.2810 1.19950
\(967\) −17.0797 −0.549246 −0.274623 0.961552i \(-0.588553\pi\)
−0.274623 + 0.961552i \(0.588553\pi\)
\(968\) −3.50999 −0.112815
\(969\) 2.16760 0.0696332
\(970\) 6.16487 0.197942
\(971\) −18.9414 −0.607859 −0.303929 0.952695i \(-0.598299\pi\)
−0.303929 + 0.952695i \(0.598299\pi\)
\(972\) 21.4403 0.687699
\(973\) −40.6611 −1.30353
\(974\) −12.7153 −0.407425
\(975\) −0.0137092 −0.000439045 0
\(976\) −8.35148 −0.267324
\(977\) −52.5608 −1.68157 −0.840785 0.541369i \(-0.817906\pi\)
−0.840785 + 0.541369i \(0.817906\pi\)
\(978\) 39.1083 1.25055
\(979\) −36.5632 −1.16856
\(980\) −8.45114 −0.269962
\(981\) −31.7425 −1.01346
\(982\) −25.7091 −0.820411
\(983\) −47.3712 −1.51091 −0.755453 0.655203i \(-0.772583\pi\)
−0.755453 + 0.655203i \(0.772583\pi\)
\(984\) −54.2632 −1.72985
\(985\) 18.6887 0.595473
\(986\) −3.38138 −0.107685
\(987\) 16.9172 0.538482
\(988\) 0.0696999 0.00221745
\(989\) −5.09282 −0.161942
\(990\) −20.9917 −0.667161
\(991\) −31.7535 −1.00868 −0.504342 0.863504i \(-0.668265\pi\)
−0.504342 + 0.863504i \(0.668265\pi\)
\(992\) −31.9432 −1.01420
\(993\) −33.6129 −1.06667
\(994\) −13.3507 −0.423457
\(995\) 19.2840 0.611345
\(996\) 15.4075 0.488205
\(997\) −44.9981 −1.42510 −0.712552 0.701619i \(-0.752461\pi\)
−0.712552 + 0.701619i \(0.752461\pi\)
\(998\) −39.7403 −1.25796
\(999\) 7.04996 0.223051
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 \(a_p\))