Properties

Label 4010.2.a.k.1.4
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(4.22659\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.24378 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24378 q^{6} -2.96737 q^{7} -1.00000 q^{8} +2.03457 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.24378 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24378 q^{6} -2.96737 q^{7} -1.00000 q^{8} +2.03457 q^{9} +1.00000 q^{10} +3.78210 q^{11} -2.24378 q^{12} +1.59128 q^{13} +2.96737 q^{14} +2.24378 q^{15} +1.00000 q^{16} -1.08728 q^{17} -2.03457 q^{18} -1.19988 q^{19} -1.00000 q^{20} +6.65813 q^{21} -3.78210 q^{22} -9.20416 q^{23} +2.24378 q^{24} +1.00000 q^{25} -1.59128 q^{26} +2.16623 q^{27} -2.96737 q^{28} +4.24818 q^{29} -2.24378 q^{30} -7.57530 q^{31} -1.00000 q^{32} -8.48621 q^{33} +1.08728 q^{34} +2.96737 q^{35} +2.03457 q^{36} +3.06583 q^{37} +1.19988 q^{38} -3.57049 q^{39} +1.00000 q^{40} -0.377871 q^{41} -6.65813 q^{42} -0.242242 q^{43} +3.78210 q^{44} -2.03457 q^{45} +9.20416 q^{46} +2.92557 q^{47} -2.24378 q^{48} +1.80526 q^{49} -1.00000 q^{50} +2.43961 q^{51} +1.59128 q^{52} +3.63063 q^{53} -2.16623 q^{54} -3.78210 q^{55} +2.96737 q^{56} +2.69227 q^{57} -4.24818 q^{58} +10.1896 q^{59} +2.24378 q^{60} +14.0200 q^{61} +7.57530 q^{62} -6.03730 q^{63} +1.00000 q^{64} -1.59128 q^{65} +8.48621 q^{66} +9.43061 q^{67} -1.08728 q^{68} +20.6521 q^{69} -2.96737 q^{70} -6.13717 q^{71} -2.03457 q^{72} -0.754336 q^{73} -3.06583 q^{74} -2.24378 q^{75} -1.19988 q^{76} -11.2229 q^{77} +3.57049 q^{78} +14.7209 q^{79} -1.00000 q^{80} -10.9642 q^{81} +0.377871 q^{82} +3.77840 q^{83} +6.65813 q^{84} +1.08728 q^{85} +0.242242 q^{86} -9.53199 q^{87} -3.78210 q^{88} +5.67276 q^{89} +2.03457 q^{90} -4.72191 q^{91} -9.20416 q^{92} +16.9973 q^{93} -2.92557 q^{94} +1.19988 q^{95} +2.24378 q^{96} -12.0035 q^{97} -1.80526 q^{98} +7.69492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.24378 −1.29545 −0.647725 0.761875i \(-0.724279\pi\)
−0.647725 + 0.761875i \(0.724279\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.24378 0.916021
\(7\) −2.96737 −1.12156 −0.560779 0.827965i \(-0.689498\pi\)
−0.560779 + 0.827965i \(0.689498\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.03457 0.678188
\(10\) 1.00000 0.316228
\(11\) 3.78210 1.14035 0.570173 0.821525i \(-0.306876\pi\)
0.570173 + 0.821525i \(0.306876\pi\)
\(12\) −2.24378 −0.647725
\(13\) 1.59128 0.441342 0.220671 0.975348i \(-0.429175\pi\)
0.220671 + 0.975348i \(0.429175\pi\)
\(14\) 2.96737 0.793062
\(15\) 2.24378 0.579342
\(16\) 1.00000 0.250000
\(17\) −1.08728 −0.263703 −0.131852 0.991269i \(-0.542092\pi\)
−0.131852 + 0.991269i \(0.542092\pi\)
\(18\) −2.03457 −0.479552
\(19\) −1.19988 −0.275272 −0.137636 0.990483i \(-0.543950\pi\)
−0.137636 + 0.990483i \(0.543950\pi\)
\(20\) −1.00000 −0.223607
\(21\) 6.65813 1.45292
\(22\) −3.78210 −0.806346
\(23\) −9.20416 −1.91920 −0.959600 0.281369i \(-0.909211\pi\)
−0.959600 + 0.281369i \(0.909211\pi\)
\(24\) 2.24378 0.458010
\(25\) 1.00000 0.200000
\(26\) −1.59128 −0.312076
\(27\) 2.16623 0.416890
\(28\) −2.96737 −0.560779
\(29\) 4.24818 0.788867 0.394433 0.918925i \(-0.370941\pi\)
0.394433 + 0.918925i \(0.370941\pi\)
\(30\) −2.24378 −0.409657
\(31\) −7.57530 −1.36056 −0.680282 0.732950i \(-0.738143\pi\)
−0.680282 + 0.732950i \(0.738143\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.48621 −1.47726
\(34\) 1.08728 0.186466
\(35\) 2.96737 0.501576
\(36\) 2.03457 0.339094
\(37\) 3.06583 0.504019 0.252009 0.967725i \(-0.418909\pi\)
0.252009 + 0.967725i \(0.418909\pi\)
\(38\) 1.19988 0.194646
\(39\) −3.57049 −0.571736
\(40\) 1.00000 0.158114
\(41\) −0.377871 −0.0590135 −0.0295068 0.999565i \(-0.509394\pi\)
−0.0295068 + 0.999565i \(0.509394\pi\)
\(42\) −6.65813 −1.02737
\(43\) −0.242242 −0.0369416 −0.0184708 0.999829i \(-0.505880\pi\)
−0.0184708 + 0.999829i \(0.505880\pi\)
\(44\) 3.78210 0.570173
\(45\) −2.03457 −0.303295
\(46\) 9.20416 1.35708
\(47\) 2.92557 0.426738 0.213369 0.976972i \(-0.431556\pi\)
0.213369 + 0.976972i \(0.431556\pi\)
\(48\) −2.24378 −0.323862
\(49\) 1.80526 0.257894
\(50\) −1.00000 −0.141421
\(51\) 2.43961 0.341614
\(52\) 1.59128 0.220671
\(53\) 3.63063 0.498706 0.249353 0.968413i \(-0.419782\pi\)
0.249353 + 0.968413i \(0.419782\pi\)
\(54\) −2.16623 −0.294786
\(55\) −3.78210 −0.509978
\(56\) 2.96737 0.396531
\(57\) 2.69227 0.356600
\(58\) −4.24818 −0.557813
\(59\) 10.1896 1.32657 0.663284 0.748368i \(-0.269162\pi\)
0.663284 + 0.748368i \(0.269162\pi\)
\(60\) 2.24378 0.289671
\(61\) 14.0200 1.79508 0.897539 0.440935i \(-0.145353\pi\)
0.897539 + 0.440935i \(0.145353\pi\)
\(62\) 7.57530 0.962065
\(63\) −6.03730 −0.760628
\(64\) 1.00000 0.125000
\(65\) −1.59128 −0.197374
\(66\) 8.48621 1.04458
\(67\) 9.43061 1.15213 0.576066 0.817403i \(-0.304587\pi\)
0.576066 + 0.817403i \(0.304587\pi\)
\(68\) −1.08728 −0.131852
\(69\) 20.6521 2.48622
\(70\) −2.96737 −0.354668
\(71\) −6.13717 −0.728349 −0.364174 0.931331i \(-0.618649\pi\)
−0.364174 + 0.931331i \(0.618649\pi\)
\(72\) −2.03457 −0.239776
\(73\) −0.754336 −0.0882883 −0.0441441 0.999025i \(-0.514056\pi\)
−0.0441441 + 0.999025i \(0.514056\pi\)
\(74\) −3.06583 −0.356395
\(75\) −2.24378 −0.259090
\(76\) −1.19988 −0.137636
\(77\) −11.2229 −1.27896
\(78\) 3.57049 0.404279
\(79\) 14.7209 1.65623 0.828114 0.560560i \(-0.189414\pi\)
0.828114 + 0.560560i \(0.189414\pi\)
\(80\) −1.00000 −0.111803
\(81\) −10.9642 −1.21825
\(82\) 0.377871 0.0417289
\(83\) 3.77840 0.414733 0.207366 0.978263i \(-0.433511\pi\)
0.207366 + 0.978263i \(0.433511\pi\)
\(84\) 6.65813 0.726461
\(85\) 1.08728 0.117932
\(86\) 0.242242 0.0261217
\(87\) −9.53199 −1.02194
\(88\) −3.78210 −0.403173
\(89\) 5.67276 0.601312 0.300656 0.953733i \(-0.402794\pi\)
0.300656 + 0.953733i \(0.402794\pi\)
\(90\) 2.03457 0.214462
\(91\) −4.72191 −0.494991
\(92\) −9.20416 −0.959600
\(93\) 16.9973 1.76254
\(94\) −2.92557 −0.301749
\(95\) 1.19988 0.123105
\(96\) 2.24378 0.229005
\(97\) −12.0035 −1.21877 −0.609383 0.792876i \(-0.708583\pi\)
−0.609383 + 0.792876i \(0.708583\pi\)
\(98\) −1.80526 −0.182359
\(99\) 7.69492 0.773369
\(100\) 1.00000 0.100000
\(101\) 3.63273 0.361470 0.180735 0.983532i \(-0.442152\pi\)
0.180735 + 0.983532i \(0.442152\pi\)
\(102\) −2.43961 −0.241558
\(103\) −5.51088 −0.543003 −0.271501 0.962438i \(-0.587520\pi\)
−0.271501 + 0.962438i \(0.587520\pi\)
\(104\) −1.59128 −0.156038
\(105\) −6.65813 −0.649767
\(106\) −3.63063 −0.352638
\(107\) −15.1815 −1.46765 −0.733827 0.679336i \(-0.762268\pi\)
−0.733827 + 0.679336i \(0.762268\pi\)
\(108\) 2.16623 0.208445
\(109\) 5.50994 0.527756 0.263878 0.964556i \(-0.414998\pi\)
0.263878 + 0.964556i \(0.414998\pi\)
\(110\) 3.78210 0.360609
\(111\) −6.87905 −0.652930
\(112\) −2.96737 −0.280390
\(113\) 15.8093 1.48721 0.743605 0.668620i \(-0.233114\pi\)
0.743605 + 0.668620i \(0.233114\pi\)
\(114\) −2.69227 −0.252155
\(115\) 9.20416 0.858292
\(116\) 4.24818 0.394433
\(117\) 3.23757 0.299313
\(118\) −10.1896 −0.938025
\(119\) 3.22634 0.295759
\(120\) −2.24378 −0.204828
\(121\) 3.30426 0.300387
\(122\) −14.0200 −1.26931
\(123\) 0.847861 0.0764490
\(124\) −7.57530 −0.680282
\(125\) −1.00000 −0.0894427
\(126\) 6.03730 0.537845
\(127\) −10.7690 −0.955592 −0.477796 0.878471i \(-0.658564\pi\)
−0.477796 + 0.878471i \(0.658564\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.543539 0.0478560
\(130\) 1.59128 0.139565
\(131\) −0.543170 −0.0474569 −0.0237285 0.999718i \(-0.507554\pi\)
−0.0237285 + 0.999718i \(0.507554\pi\)
\(132\) −8.48621 −0.738630
\(133\) 3.56049 0.308733
\(134\) −9.43061 −0.814680
\(135\) −2.16623 −0.186439
\(136\) 1.08728 0.0932331
\(137\) 0.150966 0.0128979 0.00644894 0.999979i \(-0.497947\pi\)
0.00644894 + 0.999979i \(0.497947\pi\)
\(138\) −20.6521 −1.75803
\(139\) −2.83205 −0.240212 −0.120106 0.992761i \(-0.538323\pi\)
−0.120106 + 0.992761i \(0.538323\pi\)
\(140\) 2.96737 0.250788
\(141\) −6.56434 −0.552818
\(142\) 6.13717 0.515020
\(143\) 6.01838 0.503282
\(144\) 2.03457 0.169547
\(145\) −4.24818 −0.352792
\(146\) 0.754336 0.0624293
\(147\) −4.05061 −0.334089
\(148\) 3.06583 0.252009
\(149\) −3.14602 −0.257732 −0.128866 0.991662i \(-0.541134\pi\)
−0.128866 + 0.991662i \(0.541134\pi\)
\(150\) 2.24378 0.183204
\(151\) 1.76751 0.143838 0.0719191 0.997410i \(-0.477088\pi\)
0.0719191 + 0.997410i \(0.477088\pi\)
\(152\) 1.19988 0.0973232
\(153\) −2.21213 −0.178840
\(154\) 11.2229 0.904364
\(155\) 7.57530 0.608463
\(156\) −3.57049 −0.285868
\(157\) −2.40237 −0.191730 −0.0958650 0.995394i \(-0.530562\pi\)
−0.0958650 + 0.995394i \(0.530562\pi\)
\(158\) −14.7209 −1.17113
\(159\) −8.14636 −0.646048
\(160\) 1.00000 0.0790569
\(161\) 27.3121 2.15249
\(162\) 10.9642 0.861432
\(163\) −4.92711 −0.385921 −0.192961 0.981207i \(-0.561809\pi\)
−0.192961 + 0.981207i \(0.561809\pi\)
\(164\) −0.377871 −0.0295068
\(165\) 8.48621 0.660650
\(166\) −3.77840 −0.293260
\(167\) 4.05202 0.313555 0.156778 0.987634i \(-0.449889\pi\)
0.156778 + 0.987634i \(0.449889\pi\)
\(168\) −6.65813 −0.513686
\(169\) −10.4678 −0.805217
\(170\) −1.08728 −0.0833902
\(171\) −2.44124 −0.186686
\(172\) −0.242242 −0.0184708
\(173\) −10.4642 −0.795581 −0.397791 0.917476i \(-0.630223\pi\)
−0.397791 + 0.917476i \(0.630223\pi\)
\(174\) 9.53199 0.722619
\(175\) −2.96737 −0.224312
\(176\) 3.78210 0.285086
\(177\) −22.8632 −1.71850
\(178\) −5.67276 −0.425192
\(179\) −11.9204 −0.890973 −0.445486 0.895289i \(-0.646969\pi\)
−0.445486 + 0.895289i \(0.646969\pi\)
\(180\) −2.03457 −0.151648
\(181\) 9.17128 0.681696 0.340848 0.940118i \(-0.389286\pi\)
0.340848 + 0.940118i \(0.389286\pi\)
\(182\) 4.72191 0.350012
\(183\) −31.4579 −2.32543
\(184\) 9.20416 0.678539
\(185\) −3.06583 −0.225404
\(186\) −16.9973 −1.24631
\(187\) −4.11218 −0.300713
\(188\) 2.92557 0.213369
\(189\) −6.42799 −0.467567
\(190\) −1.19988 −0.0870486
\(191\) −21.6269 −1.56487 −0.782433 0.622735i \(-0.786022\pi\)
−0.782433 + 0.622735i \(0.786022\pi\)
\(192\) −2.24378 −0.161931
\(193\) −26.4655 −1.90503 −0.952513 0.304497i \(-0.901512\pi\)
−0.952513 + 0.304497i \(0.901512\pi\)
\(194\) 12.0035 0.861798
\(195\) 3.57049 0.255688
\(196\) 1.80526 0.128947
\(197\) 18.2780 1.30225 0.651126 0.758969i \(-0.274297\pi\)
0.651126 + 0.758969i \(0.274297\pi\)
\(198\) −7.69492 −0.546854
\(199\) 20.6980 1.46724 0.733622 0.679558i \(-0.237828\pi\)
0.733622 + 0.679558i \(0.237828\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −21.1602 −1.49253
\(202\) −3.63273 −0.255598
\(203\) −12.6059 −0.884761
\(204\) 2.43961 0.170807
\(205\) 0.377871 0.0263917
\(206\) 5.51088 0.383961
\(207\) −18.7265 −1.30158
\(208\) 1.59128 0.110336
\(209\) −4.53807 −0.313905
\(210\) 6.65813 0.459454
\(211\) −16.9222 −1.16497 −0.582486 0.812841i \(-0.697920\pi\)
−0.582486 + 0.812841i \(0.697920\pi\)
\(212\) 3.63063 0.249353
\(213\) 13.7705 0.943539
\(214\) 15.1815 1.03779
\(215\) 0.242242 0.0165208
\(216\) −2.16623 −0.147393
\(217\) 22.4787 1.52595
\(218\) −5.50994 −0.373180
\(219\) 1.69257 0.114373
\(220\) −3.78210 −0.254989
\(221\) −1.73016 −0.116383
\(222\) 6.87905 0.461692
\(223\) 21.3560 1.43011 0.715053 0.699071i \(-0.246403\pi\)
0.715053 + 0.699071i \(0.246403\pi\)
\(224\) 2.96737 0.198265
\(225\) 2.03457 0.135638
\(226\) −15.8093 −1.05162
\(227\) 28.5483 1.89482 0.947408 0.320029i \(-0.103693\pi\)
0.947408 + 0.320029i \(0.103693\pi\)
\(228\) 2.69227 0.178300
\(229\) 0.261496 0.0172802 0.00864009 0.999963i \(-0.497250\pi\)
0.00864009 + 0.999963i \(0.497250\pi\)
\(230\) −9.20416 −0.606904
\(231\) 25.1817 1.65683
\(232\) −4.24818 −0.278907
\(233\) −2.81531 −0.184437 −0.0922187 0.995739i \(-0.529396\pi\)
−0.0922187 + 0.995739i \(0.529396\pi\)
\(234\) −3.23757 −0.211646
\(235\) −2.92557 −0.190843
\(236\) 10.1896 0.663284
\(237\) −33.0304 −2.14556
\(238\) −3.22634 −0.209133
\(239\) −18.5317 −1.19871 −0.599357 0.800482i \(-0.704577\pi\)
−0.599357 + 0.800482i \(0.704577\pi\)
\(240\) 2.24378 0.144836
\(241\) −15.2647 −0.983283 −0.491642 0.870798i \(-0.663603\pi\)
−0.491642 + 0.870798i \(0.663603\pi\)
\(242\) −3.30426 −0.212406
\(243\) 18.1027 1.16129
\(244\) 14.0200 0.897539
\(245\) −1.80526 −0.115334
\(246\) −0.847861 −0.0540576
\(247\) −1.90935 −0.121489
\(248\) 7.57530 0.481032
\(249\) −8.47790 −0.537265
\(250\) 1.00000 0.0632456
\(251\) −14.4528 −0.912253 −0.456127 0.889915i \(-0.650764\pi\)
−0.456127 + 0.889915i \(0.650764\pi\)
\(252\) −6.03730 −0.380314
\(253\) −34.8110 −2.18855
\(254\) 10.7690 0.675706
\(255\) −2.43961 −0.152774
\(256\) 1.00000 0.0625000
\(257\) 6.55811 0.409083 0.204542 0.978858i \(-0.434430\pi\)
0.204542 + 0.978858i \(0.434430\pi\)
\(258\) −0.543539 −0.0338393
\(259\) −9.09742 −0.565286
\(260\) −1.59128 −0.0986871
\(261\) 8.64320 0.535000
\(262\) 0.543170 0.0335571
\(263\) −1.30528 −0.0804872 −0.0402436 0.999190i \(-0.512813\pi\)
−0.0402436 + 0.999190i \(0.512813\pi\)
\(264\) 8.48621 0.522290
\(265\) −3.63063 −0.223028
\(266\) −3.56049 −0.218307
\(267\) −12.7285 −0.778969
\(268\) 9.43061 0.576066
\(269\) 18.5690 1.13217 0.566087 0.824345i \(-0.308457\pi\)
0.566087 + 0.824345i \(0.308457\pi\)
\(270\) 2.16623 0.131832
\(271\) −28.2537 −1.71629 −0.858146 0.513406i \(-0.828383\pi\)
−0.858146 + 0.513406i \(0.828383\pi\)
\(272\) −1.08728 −0.0659258
\(273\) 10.5950 0.641236
\(274\) −0.150966 −0.00912018
\(275\) 3.78210 0.228069
\(276\) 20.6521 1.24311
\(277\) −8.92264 −0.536110 −0.268055 0.963404i \(-0.586381\pi\)
−0.268055 + 0.963404i \(0.586381\pi\)
\(278\) 2.83205 0.169855
\(279\) −15.4125 −0.922719
\(280\) −2.96737 −0.177334
\(281\) 7.82655 0.466893 0.233447 0.972370i \(-0.425000\pi\)
0.233447 + 0.972370i \(0.425000\pi\)
\(282\) 6.56434 0.390901
\(283\) −13.7382 −0.816650 −0.408325 0.912837i \(-0.633887\pi\)
−0.408325 + 0.912837i \(0.633887\pi\)
\(284\) −6.13717 −0.364174
\(285\) −2.69227 −0.159477
\(286\) −6.01838 −0.355874
\(287\) 1.12128 0.0661872
\(288\) −2.03457 −0.119888
\(289\) −15.8178 −0.930461
\(290\) 4.24818 0.249462
\(291\) 26.9332 1.57885
\(292\) −0.754336 −0.0441441
\(293\) 18.6529 1.08971 0.544857 0.838529i \(-0.316584\pi\)
0.544857 + 0.838529i \(0.316584\pi\)
\(294\) 4.05061 0.236236
\(295\) −10.1896 −0.593259
\(296\) −3.06583 −0.178197
\(297\) 8.19288 0.475399
\(298\) 3.14602 0.182244
\(299\) −14.6464 −0.847023
\(300\) −2.24378 −0.129545
\(301\) 0.718822 0.0414322
\(302\) −1.76751 −0.101709
\(303\) −8.15105 −0.468266
\(304\) −1.19988 −0.0688179
\(305\) −14.0200 −0.802783
\(306\) 2.21213 0.126459
\(307\) −6.80077 −0.388140 −0.194070 0.980988i \(-0.562169\pi\)
−0.194070 + 0.980988i \(0.562169\pi\)
\(308\) −11.2229 −0.639482
\(309\) 12.3652 0.703432
\(310\) −7.57530 −0.430248
\(311\) 3.50135 0.198543 0.0992717 0.995060i \(-0.468349\pi\)
0.0992717 + 0.995060i \(0.468349\pi\)
\(312\) 3.57049 0.202139
\(313\) −15.8948 −0.898425 −0.449212 0.893425i \(-0.648295\pi\)
−0.449212 + 0.893425i \(0.648295\pi\)
\(314\) 2.40237 0.135574
\(315\) 6.03730 0.340163
\(316\) 14.7209 0.828114
\(317\) 21.6901 1.21824 0.609118 0.793080i \(-0.291524\pi\)
0.609118 + 0.793080i \(0.291524\pi\)
\(318\) 8.14636 0.456825
\(319\) 16.0670 0.899581
\(320\) −1.00000 −0.0559017
\(321\) 34.0641 1.90127
\(322\) −27.3121 −1.52204
\(323\) 1.30460 0.0725900
\(324\) −10.9642 −0.609124
\(325\) 1.59128 0.0882684
\(326\) 4.92711 0.272887
\(327\) −12.3631 −0.683681
\(328\) 0.377871 0.0208644
\(329\) −8.68123 −0.478612
\(330\) −8.48621 −0.467150
\(331\) −28.5289 −1.56809 −0.784044 0.620705i \(-0.786847\pi\)
−0.784044 + 0.620705i \(0.786847\pi\)
\(332\) 3.77840 0.207366
\(333\) 6.23762 0.341820
\(334\) −4.05202 −0.221717
\(335\) −9.43061 −0.515249
\(336\) 6.65813 0.363231
\(337\) −13.8872 −0.756482 −0.378241 0.925707i \(-0.623471\pi\)
−0.378241 + 0.925707i \(0.623471\pi\)
\(338\) 10.4678 0.569375
\(339\) −35.4725 −1.92660
\(340\) 1.08728 0.0589658
\(341\) −28.6505 −1.55151
\(342\) 2.44124 0.132007
\(343\) 15.4147 0.832315
\(344\) 0.242242 0.0130608
\(345\) −20.6521 −1.11187
\(346\) 10.4642 0.562561
\(347\) −10.1110 −0.542785 −0.271393 0.962469i \(-0.587484\pi\)
−0.271393 + 0.962469i \(0.587484\pi\)
\(348\) −9.53199 −0.510968
\(349\) 7.91140 0.423488 0.211744 0.977325i \(-0.432086\pi\)
0.211744 + 0.977325i \(0.432086\pi\)
\(350\) 2.96737 0.158612
\(351\) 3.44708 0.183991
\(352\) −3.78210 −0.201586
\(353\) −18.0971 −0.963210 −0.481605 0.876389i \(-0.659946\pi\)
−0.481605 + 0.876389i \(0.659946\pi\)
\(354\) 22.8632 1.21516
\(355\) 6.13717 0.325727
\(356\) 5.67276 0.300656
\(357\) −7.23922 −0.383140
\(358\) 11.9204 0.630013
\(359\) −7.99822 −0.422130 −0.211065 0.977472i \(-0.567693\pi\)
−0.211065 + 0.977472i \(0.567693\pi\)
\(360\) 2.03457 0.107231
\(361\) −17.5603 −0.924225
\(362\) −9.17128 −0.482032
\(363\) −7.41404 −0.389136
\(364\) −4.72191 −0.247496
\(365\) 0.754336 0.0394837
\(366\) 31.4579 1.64433
\(367\) 17.2894 0.902498 0.451249 0.892398i \(-0.350979\pi\)
0.451249 + 0.892398i \(0.350979\pi\)
\(368\) −9.20416 −0.479800
\(369\) −0.768803 −0.0400223
\(370\) 3.06583 0.159385
\(371\) −10.7734 −0.559328
\(372\) 16.9973 0.881271
\(373\) −20.5070 −1.06181 −0.530906 0.847431i \(-0.678148\pi\)
−0.530906 + 0.847431i \(0.678148\pi\)
\(374\) 4.11218 0.212636
\(375\) 2.24378 0.115868
\(376\) −2.92557 −0.150875
\(377\) 6.76005 0.348160
\(378\) 6.42799 0.330620
\(379\) 13.1084 0.673332 0.336666 0.941624i \(-0.390701\pi\)
0.336666 + 0.941624i \(0.390701\pi\)
\(380\) 1.19988 0.0615526
\(381\) 24.1633 1.23792
\(382\) 21.6269 1.10653
\(383\) −27.3794 −1.39902 −0.699510 0.714623i \(-0.746598\pi\)
−0.699510 + 0.714623i \(0.746598\pi\)
\(384\) 2.24378 0.114503
\(385\) 11.2229 0.571970
\(386\) 26.4655 1.34706
\(387\) −0.492858 −0.0250534
\(388\) −12.0035 −0.609383
\(389\) 9.70549 0.492088 0.246044 0.969259i \(-0.420869\pi\)
0.246044 + 0.969259i \(0.420869\pi\)
\(390\) −3.57049 −0.180799
\(391\) 10.0075 0.506099
\(392\) −1.80526 −0.0911793
\(393\) 1.21875 0.0614781
\(394\) −18.2780 −0.920832
\(395\) −14.7209 −0.740687
\(396\) 7.69492 0.386684
\(397\) −16.3681 −0.821491 −0.410745 0.911750i \(-0.634732\pi\)
−0.410745 + 0.911750i \(0.634732\pi\)
\(398\) −20.6980 −1.03750
\(399\) −7.98896 −0.399948
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 21.1602 1.05538
\(403\) −12.0544 −0.600475
\(404\) 3.63273 0.180735
\(405\) 10.9642 0.544817
\(406\) 12.6059 0.625620
\(407\) 11.5952 0.574755
\(408\) −2.43961 −0.120779
\(409\) −21.5280 −1.06449 −0.532246 0.846590i \(-0.678652\pi\)
−0.532246 + 0.846590i \(0.678652\pi\)
\(410\) −0.377871 −0.0186617
\(411\) −0.338735 −0.0167085
\(412\) −5.51088 −0.271501
\(413\) −30.2361 −1.48782
\(414\) 18.7265 0.920355
\(415\) −3.77840 −0.185474
\(416\) −1.59128 −0.0780190
\(417\) 6.35451 0.311182
\(418\) 4.53807 0.221964
\(419\) −3.86254 −0.188697 −0.0943486 0.995539i \(-0.530077\pi\)
−0.0943486 + 0.995539i \(0.530077\pi\)
\(420\) −6.65813 −0.324883
\(421\) −16.9250 −0.824873 −0.412437 0.910986i \(-0.635322\pi\)
−0.412437 + 0.910986i \(0.635322\pi\)
\(422\) 16.9222 0.823760
\(423\) 5.95226 0.289409
\(424\) −3.63063 −0.176319
\(425\) −1.08728 −0.0527406
\(426\) −13.7705 −0.667183
\(427\) −41.6025 −2.01329
\(428\) −15.1815 −0.733827
\(429\) −13.5039 −0.651977
\(430\) −0.242242 −0.0116820
\(431\) −9.30456 −0.448185 −0.224093 0.974568i \(-0.571942\pi\)
−0.224093 + 0.974568i \(0.571942\pi\)
\(432\) 2.16623 0.104223
\(433\) 36.6921 1.76331 0.881655 0.471894i \(-0.156430\pi\)
0.881655 + 0.471894i \(0.156430\pi\)
\(434\) −22.4787 −1.07901
\(435\) 9.53199 0.457024
\(436\) 5.50994 0.263878
\(437\) 11.0439 0.528301
\(438\) −1.69257 −0.0808739
\(439\) 24.8310 1.18512 0.592560 0.805526i \(-0.298117\pi\)
0.592560 + 0.805526i \(0.298117\pi\)
\(440\) 3.78210 0.180304
\(441\) 3.67292 0.174901
\(442\) 1.73016 0.0822954
\(443\) 18.5611 0.881864 0.440932 0.897541i \(-0.354648\pi\)
0.440932 + 0.897541i \(0.354648\pi\)
\(444\) −6.87905 −0.326465
\(445\) −5.67276 −0.268915
\(446\) −21.3560 −1.01124
\(447\) 7.05899 0.333879
\(448\) −2.96737 −0.140195
\(449\) 22.2341 1.04929 0.524647 0.851320i \(-0.324197\pi\)
0.524647 + 0.851320i \(0.324197\pi\)
\(450\) −2.03457 −0.0959103
\(451\) −1.42915 −0.0672958
\(452\) 15.8093 0.743605
\(453\) −3.96592 −0.186335
\(454\) −28.5483 −1.33984
\(455\) 4.72191 0.221367
\(456\) −2.69227 −0.126077
\(457\) −15.5214 −0.726059 −0.363029 0.931778i \(-0.618258\pi\)
−0.363029 + 0.931778i \(0.618258\pi\)
\(458\) −0.261496 −0.0122189
\(459\) −2.35529 −0.109935
\(460\) 9.20416 0.429146
\(461\) −11.1142 −0.517639 −0.258819 0.965926i \(-0.583333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(462\) −25.1817 −1.17156
\(463\) −34.3965 −1.59854 −0.799270 0.600972i \(-0.794780\pi\)
−0.799270 + 0.600972i \(0.794780\pi\)
\(464\) 4.24818 0.197217
\(465\) −16.9973 −0.788233
\(466\) 2.81531 0.130417
\(467\) −33.5408 −1.55208 −0.776040 0.630683i \(-0.782775\pi\)
−0.776040 + 0.630683i \(0.782775\pi\)
\(468\) 3.23757 0.149657
\(469\) −27.9841 −1.29218
\(470\) 2.92557 0.134946
\(471\) 5.39040 0.248376
\(472\) −10.1896 −0.469013
\(473\) −0.916184 −0.0421262
\(474\) 33.0304 1.51714
\(475\) −1.19988 −0.0550543
\(476\) 3.22634 0.147879
\(477\) 7.38676 0.338217
\(478\) 18.5317 0.847619
\(479\) −4.84612 −0.221425 −0.110712 0.993852i \(-0.535313\pi\)
−0.110712 + 0.993852i \(0.535313\pi\)
\(480\) −2.24378 −0.102414
\(481\) 4.87859 0.222445
\(482\) 15.2647 0.695286
\(483\) −61.2824 −2.78845
\(484\) 3.30426 0.150194
\(485\) 12.0035 0.545049
\(486\) −18.1027 −0.821155
\(487\) −8.90754 −0.403639 −0.201820 0.979423i \(-0.564685\pi\)
−0.201820 + 0.979423i \(0.564685\pi\)
\(488\) −14.0200 −0.634656
\(489\) 11.0554 0.499941
\(490\) 1.80526 0.0815532
\(491\) −12.6983 −0.573066 −0.286533 0.958070i \(-0.592503\pi\)
−0.286533 + 0.958070i \(0.592503\pi\)
\(492\) 0.847861 0.0382245
\(493\) −4.61894 −0.208027
\(494\) 1.90935 0.0859057
\(495\) −7.69492 −0.345861
\(496\) −7.57530 −0.340141
\(497\) 18.2112 0.816886
\(498\) 8.47790 0.379904
\(499\) −22.7707 −1.01935 −0.509677 0.860366i \(-0.670235\pi\)
−0.509677 + 0.860366i \(0.670235\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −9.09186 −0.406195
\(502\) 14.4528 0.645061
\(503\) −27.5330 −1.22764 −0.613818 0.789447i \(-0.710367\pi\)
−0.613818 + 0.789447i \(0.710367\pi\)
\(504\) 6.03730 0.268923
\(505\) −3.63273 −0.161654
\(506\) 34.8110 1.54754
\(507\) 23.4875 1.04312
\(508\) −10.7690 −0.477796
\(509\) −25.8731 −1.14681 −0.573403 0.819273i \(-0.694377\pi\)
−0.573403 + 0.819273i \(0.694377\pi\)
\(510\) 2.43961 0.108028
\(511\) 2.23839 0.0990205
\(512\) −1.00000 −0.0441942
\(513\) −2.59921 −0.114758
\(514\) −6.55811 −0.289266
\(515\) 5.51088 0.242838
\(516\) 0.543539 0.0239280
\(517\) 11.0648 0.486629
\(518\) 9.09742 0.399718
\(519\) 23.4795 1.03063
\(520\) 1.59128 0.0697823
\(521\) 5.97102 0.261595 0.130798 0.991409i \(-0.458246\pi\)
0.130798 + 0.991409i \(0.458246\pi\)
\(522\) −8.64320 −0.378302
\(523\) −10.7992 −0.472218 −0.236109 0.971727i \(-0.575872\pi\)
−0.236109 + 0.971727i \(0.575872\pi\)
\(524\) −0.543170 −0.0237285
\(525\) 6.65813 0.290584
\(526\) 1.30528 0.0569131
\(527\) 8.23644 0.358785
\(528\) −8.48621 −0.369315
\(529\) 61.7165 2.68333
\(530\) 3.63063 0.157705
\(531\) 20.7313 0.899663
\(532\) 3.56049 0.154367
\(533\) −0.601299 −0.0260452
\(534\) 12.7285 0.550814
\(535\) 15.1815 0.656355
\(536\) −9.43061 −0.407340
\(537\) 26.7468 1.15421
\(538\) −18.5690 −0.800568
\(539\) 6.82766 0.294088
\(540\) −2.16623 −0.0932195
\(541\) 16.3100 0.701220 0.350610 0.936522i \(-0.385974\pi\)
0.350610 + 0.936522i \(0.385974\pi\)
\(542\) 28.2537 1.21360
\(543\) −20.5784 −0.883102
\(544\) 1.08728 0.0466166
\(545\) −5.50994 −0.236020
\(546\) −10.5950 −0.453422
\(547\) −44.9434 −1.92164 −0.960821 0.277170i \(-0.910604\pi\)
−0.960821 + 0.277170i \(0.910604\pi\)
\(548\) 0.150966 0.00644894
\(549\) 28.5246 1.21740
\(550\) −3.78210 −0.161269
\(551\) −5.09731 −0.217153
\(552\) −20.6521 −0.879013
\(553\) −43.6822 −1.85756
\(554\) 8.92264 0.379087
\(555\) 6.87905 0.291999
\(556\) −2.83205 −0.120106
\(557\) 24.3539 1.03191 0.515953 0.856617i \(-0.327438\pi\)
0.515953 + 0.856617i \(0.327438\pi\)
\(558\) 15.4125 0.652461
\(559\) −0.385476 −0.0163039
\(560\) 2.96737 0.125394
\(561\) 9.22685 0.389558
\(562\) −7.82655 −0.330143
\(563\) −12.2132 −0.514725 −0.257362 0.966315i \(-0.582853\pi\)
−0.257362 + 0.966315i \(0.582853\pi\)
\(564\) −6.56434 −0.276409
\(565\) −15.8093 −0.665100
\(566\) 13.7382 0.577459
\(567\) 32.5349 1.36634
\(568\) 6.13717 0.257510
\(569\) 2.29264 0.0961123 0.0480562 0.998845i \(-0.484697\pi\)
0.0480562 + 0.998845i \(0.484697\pi\)
\(570\) 2.69227 0.112767
\(571\) −9.26401 −0.387687 −0.193843 0.981032i \(-0.562095\pi\)
−0.193843 + 0.981032i \(0.562095\pi\)
\(572\) 6.01838 0.251641
\(573\) 48.5260 2.02720
\(574\) −1.12128 −0.0468014
\(575\) −9.20416 −0.383840
\(576\) 2.03457 0.0847736
\(577\) 6.56066 0.273124 0.136562 0.990632i \(-0.456395\pi\)
0.136562 + 0.990632i \(0.456395\pi\)
\(578\) 15.8178 0.657935
\(579\) 59.3828 2.46787
\(580\) −4.24818 −0.176396
\(581\) −11.2119 −0.465147
\(582\) −26.9332 −1.11642
\(583\) 13.7314 0.568697
\(584\) 0.754336 0.0312146
\(585\) −3.23757 −0.133857
\(586\) −18.6529 −0.770545
\(587\) −19.9120 −0.821855 −0.410928 0.911668i \(-0.634795\pi\)
−0.410928 + 0.911668i \(0.634795\pi\)
\(588\) −4.05061 −0.167044
\(589\) 9.08947 0.374525
\(590\) 10.1896 0.419498
\(591\) −41.0119 −1.68700
\(592\) 3.06583 0.126005
\(593\) −28.2049 −1.15824 −0.579119 0.815243i \(-0.696603\pi\)
−0.579119 + 0.815243i \(0.696603\pi\)
\(594\) −8.19288 −0.336158
\(595\) −3.22634 −0.132267
\(596\) −3.14602 −0.128866
\(597\) −46.4419 −1.90074
\(598\) 14.6464 0.598936
\(599\) −1.19218 −0.0487113 −0.0243557 0.999703i \(-0.507753\pi\)
−0.0243557 + 0.999703i \(0.507753\pi\)
\(600\) 2.24378 0.0916021
\(601\) −7.53346 −0.307296 −0.153648 0.988126i \(-0.549102\pi\)
−0.153648 + 0.988126i \(0.549102\pi\)
\(602\) −0.718822 −0.0292970
\(603\) 19.1872 0.781363
\(604\) 1.76751 0.0719191
\(605\) −3.30426 −0.134337
\(606\) 8.15105 0.331114
\(607\) 17.0915 0.693722 0.346861 0.937917i \(-0.387248\pi\)
0.346861 + 0.937917i \(0.387248\pi\)
\(608\) 1.19988 0.0486616
\(609\) 28.2849 1.14616
\(610\) 14.0200 0.567653
\(611\) 4.65540 0.188337
\(612\) −2.21213 −0.0894202
\(613\) 42.7942 1.72844 0.864221 0.503113i \(-0.167812\pi\)
0.864221 + 0.503113i \(0.167812\pi\)
\(614\) 6.80077 0.274457
\(615\) −0.847861 −0.0341891
\(616\) 11.2229 0.452182
\(617\) 30.7182 1.23667 0.618333 0.785916i \(-0.287808\pi\)
0.618333 + 0.785916i \(0.287808\pi\)
\(618\) −12.3652 −0.497402
\(619\) 16.8722 0.678151 0.339075 0.940759i \(-0.389886\pi\)
0.339075 + 0.940759i \(0.389886\pi\)
\(620\) 7.57530 0.304232
\(621\) −19.9383 −0.800096
\(622\) −3.50135 −0.140391
\(623\) −16.8332 −0.674406
\(624\) −3.57049 −0.142934
\(625\) 1.00000 0.0400000
\(626\) 15.8948 0.635282
\(627\) 10.1824 0.406648
\(628\) −2.40237 −0.0958650
\(629\) −3.33340 −0.132911
\(630\) −6.03730 −0.240532
\(631\) −23.1968 −0.923452 −0.461726 0.887023i \(-0.652770\pi\)
−0.461726 + 0.887023i \(0.652770\pi\)
\(632\) −14.7209 −0.585565
\(633\) 37.9698 1.50916
\(634\) −21.6901 −0.861423
\(635\) 10.7690 0.427354
\(636\) −8.14636 −0.323024
\(637\) 2.87267 0.113819
\(638\) −16.0670 −0.636100
\(639\) −12.4865 −0.493958
\(640\) 1.00000 0.0395285
\(641\) −15.1934 −0.600105 −0.300052 0.953923i \(-0.597004\pi\)
−0.300052 + 0.953923i \(0.597004\pi\)
\(642\) −34.0641 −1.34440
\(643\) 9.43775 0.372189 0.186094 0.982532i \(-0.440417\pi\)
0.186094 + 0.982532i \(0.440417\pi\)
\(644\) 27.3121 1.07625
\(645\) −0.543539 −0.0214018
\(646\) −1.30460 −0.0513289
\(647\) 16.9549 0.666565 0.333283 0.942827i \(-0.391844\pi\)
0.333283 + 0.942827i \(0.391844\pi\)
\(648\) 10.9642 0.430716
\(649\) 38.5379 1.51275
\(650\) −1.59128 −0.0624152
\(651\) −50.4373 −1.97680
\(652\) −4.92711 −0.192961
\(653\) 35.5957 1.39297 0.696484 0.717573i \(-0.254747\pi\)
0.696484 + 0.717573i \(0.254747\pi\)
\(654\) 12.3631 0.483436
\(655\) 0.543170 0.0212234
\(656\) −0.377871 −0.0147534
\(657\) −1.53475 −0.0598761
\(658\) 8.68123 0.338430
\(659\) 8.50494 0.331306 0.165653 0.986184i \(-0.447027\pi\)
0.165653 + 0.986184i \(0.447027\pi\)
\(660\) 8.48621 0.330325
\(661\) 10.5547 0.410532 0.205266 0.978706i \(-0.434194\pi\)
0.205266 + 0.978706i \(0.434194\pi\)
\(662\) 28.5289 1.10881
\(663\) 3.88211 0.150769
\(664\) −3.77840 −0.146630
\(665\) −3.56049 −0.138070
\(666\) −6.23762 −0.241703
\(667\) −39.1009 −1.51399
\(668\) 4.05202 0.156778
\(669\) −47.9183 −1.85263
\(670\) 9.43061 0.364336
\(671\) 53.0250 2.04701
\(672\) −6.65813 −0.256843
\(673\) −39.5530 −1.52465 −0.762327 0.647192i \(-0.775943\pi\)
−0.762327 + 0.647192i \(0.775943\pi\)
\(674\) 13.8872 0.534914
\(675\) 2.16623 0.0833781
\(676\) −10.4678 −0.402609
\(677\) 27.9532 1.07433 0.537164 0.843478i \(-0.319496\pi\)
0.537164 + 0.843478i \(0.319496\pi\)
\(678\) 35.4725 1.36231
\(679\) 35.6187 1.36692
\(680\) −1.08728 −0.0416951
\(681\) −64.0562 −2.45464
\(682\) 28.6505 1.09709
\(683\) 17.8758 0.683999 0.342000 0.939700i \(-0.388896\pi\)
0.342000 + 0.939700i \(0.388896\pi\)
\(684\) −2.44124 −0.0933430
\(685\) −0.150966 −0.00576811
\(686\) −15.4147 −0.588536
\(687\) −0.586741 −0.0223856
\(688\) −0.242242 −0.00923540
\(689\) 5.77736 0.220100
\(690\) 20.6521 0.786213
\(691\) −8.61554 −0.327751 −0.163875 0.986481i \(-0.552399\pi\)
−0.163875 + 0.986481i \(0.552399\pi\)
\(692\) −10.4642 −0.397791
\(693\) −22.8337 −0.867379
\(694\) 10.1110 0.383807
\(695\) 2.83205 0.107426
\(696\) 9.53199 0.361309
\(697\) 0.410850 0.0155621
\(698\) −7.91140 −0.299451
\(699\) 6.31695 0.238929
\(700\) −2.96737 −0.112156
\(701\) 24.2297 0.915143 0.457571 0.889173i \(-0.348719\pi\)
0.457571 + 0.889173i \(0.348719\pi\)
\(702\) −3.44708 −0.130102
\(703\) −3.67863 −0.138742
\(704\) 3.78210 0.142543
\(705\) 6.56434 0.247228
\(706\) 18.0971 0.681092
\(707\) −10.7796 −0.405410
\(708\) −22.8632 −0.859251
\(709\) 6.55294 0.246101 0.123050 0.992400i \(-0.460732\pi\)
0.123050 + 0.992400i \(0.460732\pi\)
\(710\) −6.13717 −0.230324
\(711\) 29.9506 1.12323
\(712\) −5.67276 −0.212596
\(713\) 69.7243 2.61120
\(714\) 7.23922 0.270921
\(715\) −6.01838 −0.225075
\(716\) −11.9204 −0.445486
\(717\) 41.5811 1.55287
\(718\) 7.99822 0.298491
\(719\) −24.7982 −0.924818 −0.462409 0.886667i \(-0.653015\pi\)
−0.462409 + 0.886667i \(0.653015\pi\)
\(720\) −2.03457 −0.0758238
\(721\) 16.3528 0.609009
\(722\) 17.5603 0.653526
\(723\) 34.2506 1.27379
\(724\) 9.17128 0.340848
\(725\) 4.24818 0.157773
\(726\) 7.41404 0.275161
\(727\) −12.7303 −0.472142 −0.236071 0.971736i \(-0.575860\pi\)
−0.236071 + 0.971736i \(0.575860\pi\)
\(728\) 4.72191 0.175006
\(729\) −7.72583 −0.286142
\(730\) −0.754336 −0.0279192
\(731\) 0.263384 0.00974162
\(732\) −31.4579 −1.16272
\(733\) −12.6583 −0.467544 −0.233772 0.972291i \(-0.575107\pi\)
−0.233772 + 0.972291i \(0.575107\pi\)
\(734\) −17.2894 −0.638162
\(735\) 4.05061 0.149409
\(736\) 9.20416 0.339270
\(737\) 35.6675 1.31383
\(738\) 0.768803 0.0283000
\(739\) −22.9874 −0.845607 −0.422803 0.906221i \(-0.638954\pi\)
−0.422803 + 0.906221i \(0.638954\pi\)
\(740\) −3.06583 −0.112702
\(741\) 4.28417 0.157383
\(742\) 10.7734 0.395505
\(743\) 5.79413 0.212566 0.106283 0.994336i \(-0.466105\pi\)
0.106283 + 0.994336i \(0.466105\pi\)
\(744\) −16.9973 −0.623153
\(745\) 3.14602 0.115261
\(746\) 20.5070 0.750814
\(747\) 7.68739 0.281267
\(748\) −4.11218 −0.150356
\(749\) 45.0492 1.64606
\(750\) −2.24378 −0.0819314
\(751\) −25.6154 −0.934719 −0.467359 0.884067i \(-0.654795\pi\)
−0.467359 + 0.884067i \(0.654795\pi\)
\(752\) 2.92557 0.106685
\(753\) 32.4290 1.18178
\(754\) −6.76005 −0.246186
\(755\) −1.76751 −0.0643264
\(756\) −6.42799 −0.233784
\(757\) 5.83461 0.212063 0.106031 0.994363i \(-0.466186\pi\)
0.106031 + 0.994363i \(0.466186\pi\)
\(758\) −13.1084 −0.476118
\(759\) 78.1084 2.83515
\(760\) −1.19988 −0.0435243
\(761\) 31.0981 1.12730 0.563652 0.826012i \(-0.309396\pi\)
0.563652 + 0.826012i \(0.309396\pi\)
\(762\) −24.1633 −0.875343
\(763\) −16.3500 −0.591910
\(764\) −21.6269 −0.782433
\(765\) 2.21213 0.0799799
\(766\) 27.3794 0.989257
\(767\) 16.2145 0.585470
\(768\) −2.24378 −0.0809656
\(769\) −26.6210 −0.959978 −0.479989 0.877274i \(-0.659359\pi\)
−0.479989 + 0.877274i \(0.659359\pi\)
\(770\) −11.2229 −0.404444
\(771\) −14.7150 −0.529947
\(772\) −26.4655 −0.952513
\(773\) 35.6842 1.28347 0.641735 0.766926i \(-0.278215\pi\)
0.641735 + 0.766926i \(0.278215\pi\)
\(774\) 0.492858 0.0177154
\(775\) −7.57530 −0.272113
\(776\) 12.0035 0.430899
\(777\) 20.4127 0.732300
\(778\) −9.70549 −0.347959
\(779\) 0.453400 0.0162448
\(780\) 3.57049 0.127844
\(781\) −23.2114 −0.830569
\(782\) −10.0075 −0.357866
\(783\) 9.20252 0.328871
\(784\) 1.80526 0.0644735
\(785\) 2.40237 0.0857442
\(786\) −1.21875 −0.0434716
\(787\) −6.90653 −0.246191 −0.123096 0.992395i \(-0.539282\pi\)
−0.123096 + 0.992395i \(0.539282\pi\)
\(788\) 18.2780 0.651126
\(789\) 2.92877 0.104267
\(790\) 14.7209 0.523745
\(791\) −46.9118 −1.66799
\(792\) −7.69492 −0.273427
\(793\) 22.3098 0.792243
\(794\) 16.3681 0.580882
\(795\) 8.14636 0.288921
\(796\) 20.6980 0.733622
\(797\) 4.88962 0.173199 0.0865996 0.996243i \(-0.472400\pi\)
0.0865996 + 0.996243i \(0.472400\pi\)
\(798\) 7.98896 0.282806
\(799\) −3.18090 −0.112532
\(800\) −1.00000 −0.0353553
\(801\) 11.5416 0.407803
\(802\) 1.00000 0.0353112
\(803\) −2.85297 −0.100679
\(804\) −21.1602 −0.746264
\(805\) −27.3121 −0.962625
\(806\) 12.0544 0.424600
\(807\) −41.6649 −1.46667
\(808\) −3.63273 −0.127799
\(809\) 23.3285 0.820188 0.410094 0.912043i \(-0.365496\pi\)
0.410094 + 0.912043i \(0.365496\pi\)
\(810\) −10.9642 −0.385244
\(811\) 3.86206 0.135615 0.0678076 0.997698i \(-0.478400\pi\)
0.0678076 + 0.997698i \(0.478400\pi\)
\(812\) −12.6059 −0.442380
\(813\) 63.3952 2.22337
\(814\) −11.5952 −0.406413
\(815\) 4.92711 0.172589
\(816\) 2.43961 0.0854035
\(817\) 0.290662 0.0101690
\(818\) 21.5280 0.752709
\(819\) −9.60704 −0.335697
\(820\) 0.377871 0.0131958
\(821\) 25.3816 0.885825 0.442912 0.896565i \(-0.353945\pi\)
0.442912 + 0.896565i \(0.353945\pi\)
\(822\) 0.338735 0.0118147
\(823\) 17.3917 0.606238 0.303119 0.952953i \(-0.401972\pi\)
0.303119 + 0.952953i \(0.401972\pi\)
\(824\) 5.51088 0.191980
\(825\) −8.48621 −0.295452
\(826\) 30.2361 1.05205
\(827\) −36.9925 −1.28636 −0.643178 0.765716i \(-0.722385\pi\)
−0.643178 + 0.765716i \(0.722385\pi\)
\(828\) −18.7265 −0.650789
\(829\) −35.9495 −1.24858 −0.624289 0.781194i \(-0.714611\pi\)
−0.624289 + 0.781194i \(0.714611\pi\)
\(830\) 3.77840 0.131150
\(831\) 20.0205 0.694503
\(832\) 1.59128 0.0551678
\(833\) −1.96281 −0.0680074
\(834\) −6.35451 −0.220039
\(835\) −4.05202 −0.140226
\(836\) −4.53807 −0.156952
\(837\) −16.4098 −0.567207
\(838\) 3.86254 0.133429
\(839\) 50.3204 1.73725 0.868627 0.495467i \(-0.165003\pi\)
0.868627 + 0.495467i \(0.165003\pi\)
\(840\) 6.65813 0.229727
\(841\) −10.9530 −0.377689
\(842\) 16.9250 0.583274
\(843\) −17.5611 −0.604836
\(844\) −16.9222 −0.582486
\(845\) 10.4678 0.360104
\(846\) −5.95226 −0.204643
\(847\) −9.80494 −0.336902
\(848\) 3.63063 0.124676
\(849\) 30.8255 1.05793
\(850\) 1.08728 0.0372932
\(851\) −28.2183 −0.967312
\(852\) 13.7705 0.471769
\(853\) −29.0949 −0.996189 −0.498095 0.867123i \(-0.665967\pi\)
−0.498095 + 0.867123i \(0.665967\pi\)
\(854\) 41.6025 1.42361
\(855\) 2.44124 0.0834886
\(856\) 15.1815 0.518894
\(857\) 53.6120 1.83135 0.915676 0.401918i \(-0.131656\pi\)
0.915676 + 0.401918i \(0.131656\pi\)
\(858\) 13.5039 0.461017
\(859\) −17.8064 −0.607547 −0.303774 0.952744i \(-0.598247\pi\)
−0.303774 + 0.952744i \(0.598247\pi\)
\(860\) 0.242242 0.00826040
\(861\) −2.51591 −0.0857421
\(862\) 9.30456 0.316915
\(863\) −22.2473 −0.757306 −0.378653 0.925539i \(-0.623613\pi\)
−0.378653 + 0.925539i \(0.623613\pi\)
\(864\) −2.16623 −0.0736965
\(865\) 10.4642 0.355795
\(866\) −36.6921 −1.24685
\(867\) 35.4918 1.20536
\(868\) 22.4787 0.762977
\(869\) 55.6758 1.88867
\(870\) −9.53199 −0.323165
\(871\) 15.0068 0.508484
\(872\) −5.50994 −0.186590
\(873\) −24.4218 −0.826554
\(874\) −11.0439 −0.373565
\(875\) 2.96737 0.100315
\(876\) 1.69257 0.0571865
\(877\) −0.116856 −0.00394594 −0.00197297 0.999998i \(-0.500628\pi\)
−0.00197297 + 0.999998i \(0.500628\pi\)
\(878\) −24.8310 −0.838006
\(879\) −41.8531 −1.41167
\(880\) −3.78210 −0.127494
\(881\) 43.9679 1.48131 0.740657 0.671883i \(-0.234514\pi\)
0.740657 + 0.671883i \(0.234514\pi\)
\(882\) −3.67292 −0.123674
\(883\) −8.04145 −0.270616 −0.135308 0.990804i \(-0.543202\pi\)
−0.135308 + 0.990804i \(0.543202\pi\)
\(884\) −1.73016 −0.0581916
\(885\) 22.8632 0.768537
\(886\) −18.5611 −0.623572
\(887\) 19.6128 0.658533 0.329267 0.944237i \(-0.393199\pi\)
0.329267 + 0.944237i \(0.393199\pi\)
\(888\) 6.87905 0.230846
\(889\) 31.9555 1.07175
\(890\) 5.67276 0.190151
\(891\) −41.4678 −1.38922
\(892\) 21.3560 0.715053
\(893\) −3.51034 −0.117469
\(894\) −7.05899 −0.236088
\(895\) 11.9204 0.398455
\(896\) 2.96737 0.0991327
\(897\) 32.8634 1.09728
\(898\) −22.2341 −0.741962
\(899\) −32.1812 −1.07330
\(900\) 2.03457 0.0678188
\(901\) −3.94750 −0.131510
\(902\) 1.42915 0.0475853
\(903\) −1.61288 −0.0536733
\(904\) −15.8093 −0.525808
\(905\) −9.17128 −0.304864
\(906\) 3.96592 0.131759
\(907\) 17.0659 0.566662 0.283331 0.959022i \(-0.408560\pi\)
0.283331 + 0.959022i \(0.408560\pi\)
\(908\) 28.5483 0.947408
\(909\) 7.39102 0.245145
\(910\) −4.72191 −0.156530
\(911\) −3.20485 −0.106181 −0.0530907 0.998590i \(-0.516907\pi\)
−0.0530907 + 0.998590i \(0.516907\pi\)
\(912\) 2.69227 0.0891501
\(913\) 14.2903 0.472939
\(914\) 15.5214 0.513401
\(915\) 31.4579 1.03996
\(916\) 0.261496 0.00864009
\(917\) 1.61178 0.0532257
\(918\) 2.35529 0.0777360
\(919\) 34.9045 1.15139 0.575697 0.817663i \(-0.304731\pi\)
0.575697 + 0.817663i \(0.304731\pi\)
\(920\) −9.20416 −0.303452
\(921\) 15.2595 0.502816
\(922\) 11.1142 0.366026
\(923\) −9.76597 −0.321451
\(924\) 25.1817 0.828416
\(925\) 3.06583 0.100804
\(926\) 34.3965 1.13034
\(927\) −11.2122 −0.368258
\(928\) −4.24818 −0.139453
\(929\) −55.6170 −1.82473 −0.912367 0.409373i \(-0.865747\pi\)
−0.912367 + 0.409373i \(0.865747\pi\)
\(930\) 16.9973 0.557365
\(931\) −2.16610 −0.0709909
\(932\) −2.81531 −0.0922187
\(933\) −7.85627 −0.257203
\(934\) 33.5408 1.09749
\(935\) 4.11218 0.134483
\(936\) −3.23757 −0.105823
\(937\) −9.00724 −0.294254 −0.147127 0.989118i \(-0.547003\pi\)
−0.147127 + 0.989118i \(0.547003\pi\)
\(938\) 27.9841 0.913712
\(939\) 35.6644 1.16386
\(940\) −2.92557 −0.0954215
\(941\) −61.0321 −1.98959 −0.994795 0.101896i \(-0.967509\pi\)
−0.994795 + 0.101896i \(0.967509\pi\)
\(942\) −5.39040 −0.175629
\(943\) 3.47798 0.113259
\(944\) 10.1896 0.331642
\(945\) 6.42799 0.209102
\(946\) 0.916184 0.0297877
\(947\) 27.6805 0.899496 0.449748 0.893156i \(-0.351514\pi\)
0.449748 + 0.893156i \(0.351514\pi\)
\(948\) −33.0304 −1.07278
\(949\) −1.20036 −0.0389653
\(950\) 1.19988 0.0389293
\(951\) −48.6678 −1.57816
\(952\) −3.22634 −0.104566
\(953\) −43.8513 −1.42048 −0.710242 0.703958i \(-0.751414\pi\)
−0.710242 + 0.703958i \(0.751414\pi\)
\(954\) −7.38676 −0.239155
\(955\) 21.6269 0.699829
\(956\) −18.5317 −0.599357
\(957\) −36.0509 −1.16536
\(958\) 4.84612 0.156571
\(959\) −0.447971 −0.0144657
\(960\) 2.24378 0.0724178
\(961\) 26.3852 0.851137
\(962\) −4.87859 −0.157292
\(963\) −30.8878 −0.995346
\(964\) −15.2647 −0.491642
\(965\) 26.4655 0.851954
\(966\) 61.2824 1.97173
\(967\) −31.0514 −0.998546 −0.499273 0.866445i \(-0.666399\pi\)
−0.499273 + 0.866445i \(0.666399\pi\)
\(968\) −3.30426 −0.106203
\(969\) −2.92724 −0.0940366
\(970\) −12.0035 −0.385408
\(971\) 37.2884 1.19664 0.598321 0.801257i \(-0.295835\pi\)
0.598321 + 0.801257i \(0.295835\pi\)
\(972\) 18.1027 0.580644
\(973\) 8.40374 0.269411
\(974\) 8.90754 0.285416
\(975\) −3.57049 −0.114347
\(976\) 14.0200 0.448769
\(977\) −5.67674 −0.181615 −0.0908075 0.995868i \(-0.528945\pi\)
−0.0908075 + 0.995868i \(0.528945\pi\)
\(978\) −11.0554 −0.353512
\(979\) 21.4549 0.685703
\(980\) −1.80526 −0.0576669
\(981\) 11.2103 0.357918
\(982\) 12.6983 0.405219
\(983\) 45.5812 1.45381 0.726907 0.686736i \(-0.240957\pi\)
0.726907 + 0.686736i \(0.240957\pi\)
\(984\) −0.847861 −0.0270288
\(985\) −18.2780 −0.582385
\(986\) 4.61894 0.147097
\(987\) 19.4788 0.620017
\(988\) −1.90935 −0.0607445
\(989\) 2.22964 0.0708983
\(990\) 7.69492 0.244561
\(991\) −5.13391 −0.163084 −0.0815420 0.996670i \(-0.525984\pi\)
−0.0815420 + 0.996670i \(0.525984\pi\)
\(992\) 7.57530 0.240516
\(993\) 64.0126 2.03138
\(994\) −18.2112 −0.577625
\(995\) −20.6980 −0.656171
\(996\) −8.47790 −0.268633
\(997\) 60.1615 1.90533 0.952666 0.304017i \(-0.0983281\pi\)
0.952666 + 0.304017i \(0.0983281\pi\)
\(998\) 22.7707 0.720793
\(999\) 6.64127 0.210121
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 \(a_p\))