Properties

Label 6023.2.a.b.1.3
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.63080 q^{2} -0.151619 q^{3} +4.92110 q^{4} -0.321250 q^{5} +0.398879 q^{6} -0.565304 q^{7} -7.68484 q^{8} -2.97701 q^{9} +O(q^{10})\) \(q-2.63080 q^{2} -0.151619 q^{3} +4.92110 q^{4} -0.321250 q^{5} +0.398879 q^{6} -0.565304 q^{7} -7.68484 q^{8} -2.97701 q^{9} +0.845143 q^{10} -4.63699 q^{11} -0.746133 q^{12} -0.0639167 q^{13} +1.48720 q^{14} +0.0487076 q^{15} +10.3751 q^{16} +1.37627 q^{17} +7.83192 q^{18} -1.00000 q^{19} -1.58090 q^{20} +0.0857108 q^{21} +12.1990 q^{22} +6.68613 q^{23} +1.16517 q^{24} -4.89680 q^{25} +0.168152 q^{26} +0.906229 q^{27} -2.78192 q^{28} +1.89444 q^{29} -0.128140 q^{30} -5.91732 q^{31} -11.9250 q^{32} +0.703057 q^{33} -3.62069 q^{34} +0.181604 q^{35} -14.6502 q^{36} -0.0360141 q^{37} +2.63080 q^{38} +0.00969099 q^{39} +2.46875 q^{40} +2.68462 q^{41} -0.225488 q^{42} +2.40508 q^{43} -22.8191 q^{44} +0.956364 q^{45} -17.5899 q^{46} +10.3758 q^{47} -1.57306 q^{48} -6.68043 q^{49} +12.8825 q^{50} -0.208668 q^{51} -0.314541 q^{52} +5.19462 q^{53} -2.38411 q^{54} +1.48963 q^{55} +4.34427 q^{56} +0.151619 q^{57} -4.98388 q^{58} +10.7496 q^{59} +0.239695 q^{60} +14.9701 q^{61} +15.5673 q^{62} +1.68292 q^{63} +10.6222 q^{64} +0.0205332 q^{65} -1.84960 q^{66} +3.00136 q^{67} +6.77276 q^{68} -1.01375 q^{69} -0.477763 q^{70} +6.28821 q^{71} +22.8779 q^{72} +6.93566 q^{73} +0.0947459 q^{74} +0.742448 q^{75} -4.92110 q^{76} +2.62131 q^{77} -0.0254950 q^{78} -12.4370 q^{79} -3.33298 q^{80} +8.79363 q^{81} -7.06270 q^{82} -4.10558 q^{83} +0.421792 q^{84} -0.442126 q^{85} -6.32729 q^{86} -0.287233 q^{87} +35.6346 q^{88} +15.6451 q^{89} -2.51600 q^{90} +0.0361323 q^{91} +32.9031 q^{92} +0.897179 q^{93} -27.2966 q^{94} +0.321250 q^{95} +1.80806 q^{96} -11.8503 q^{97} +17.5749 q^{98} +13.8044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} + O(q^{10}) \) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} - 6q^{10} - 9q^{11} - 27q^{12} - 28q^{13} - 13q^{14} - 10q^{15} + 38q^{16} - 36q^{17} - 14q^{18} - 99q^{19} - 34q^{20} - 20q^{21} - 53q^{22} - 38q^{23} - 25q^{24} - 8q^{25} - 3q^{26} - 3q^{27} - 63q^{28} - 34q^{29} - 30q^{30} - 16q^{31} - 43q^{32} - 41q^{33} - 14q^{34} - 25q^{35} - 16q^{36} - 80q^{37} + 4q^{38} - 48q^{39} - 10q^{40} - 32q^{41} - 37q^{42} - 76q^{43} - 21q^{44} - 53q^{45} - 23q^{46} - 31q^{47} - 74q^{48} - 32q^{49} - 29q^{50} - 30q^{51} - 71q^{52} - 35q^{53} - 80q^{54} - 45q^{55} - 33q^{56} + 3q^{57} - 91q^{58} + 12q^{59} - 56q^{60} - 61q^{61} - 46q^{62} - 43q^{63} - 30q^{64} - 46q^{65} - 75q^{66} - 26q^{67} - 55q^{68} - 45q^{69} - 76q^{70} - 41q^{71} - 77q^{72} - 143q^{73} - 64q^{74} - 8q^{75} - 80q^{76} - 58q^{77} - 34q^{78} - 22q^{79} - 36q^{80} - 81q^{81} - 109q^{82} - 7q^{83} - 6q^{84} - 80q^{85} + 32q^{86} - 57q^{87} - 120q^{88} - 28q^{89} - 12q^{90} - 30q^{91} - 107q^{92} - 121q^{93} + 8q^{94} + 15q^{95} + 4q^{96} - 128q^{97} + 54q^{98} - 34q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63080 −1.86026 −0.930128 0.367236i \(-0.880304\pi\)
−0.930128 + 0.367236i \(0.880304\pi\)
\(3\) −0.151619 −0.0875373 −0.0437687 0.999042i \(-0.513936\pi\)
−0.0437687 + 0.999042i \(0.513936\pi\)
\(4\) 4.92110 2.46055
\(5\) −0.321250 −0.143667 −0.0718336 0.997417i \(-0.522885\pi\)
−0.0718336 + 0.997417i \(0.522885\pi\)
\(6\) 0.398879 0.162842
\(7\) −0.565304 −0.213665 −0.106832 0.994277i \(-0.534071\pi\)
−0.106832 + 0.994277i \(0.534071\pi\)
\(8\) −7.68484 −2.71700
\(9\) −2.97701 −0.992337
\(10\) 0.845143 0.267258
\(11\) −4.63699 −1.39811 −0.699053 0.715070i \(-0.746395\pi\)
−0.699053 + 0.715070i \(0.746395\pi\)
\(12\) −0.746133 −0.215390
\(13\) −0.0639167 −0.0177273 −0.00886365 0.999961i \(-0.502821\pi\)
−0.00886365 + 0.999961i \(0.502821\pi\)
\(14\) 1.48720 0.397471
\(15\) 0.0487076 0.0125762
\(16\) 10.3751 2.59376
\(17\) 1.37627 0.333794 0.166897 0.985974i \(-0.446625\pi\)
0.166897 + 0.985974i \(0.446625\pi\)
\(18\) 7.83192 1.84600
\(19\) −1.00000 −0.229416
\(20\) −1.58090 −0.353501
\(21\) 0.0857108 0.0187036
\(22\) 12.1990 2.60084
\(23\) 6.68613 1.39415 0.697077 0.716996i \(-0.254483\pi\)
0.697077 + 0.716996i \(0.254483\pi\)
\(24\) 1.16517 0.237839
\(25\) −4.89680 −0.979360
\(26\) 0.168152 0.0329773
\(27\) 0.906229 0.174404
\(28\) −2.78192 −0.525733
\(29\) 1.89444 0.351788 0.175894 0.984409i \(-0.443718\pi\)
0.175894 + 0.984409i \(0.443718\pi\)
\(30\) −0.128140 −0.0233950
\(31\) −5.91732 −1.06278 −0.531391 0.847127i \(-0.678331\pi\)
−0.531391 + 0.847127i \(0.678331\pi\)
\(32\) −11.9250 −2.10806
\(33\) 0.703057 0.122386
\(34\) −3.62069 −0.620942
\(35\) 0.181604 0.0306966
\(36\) −14.6502 −2.44170
\(37\) −0.0360141 −0.00592069 −0.00296034 0.999996i \(-0.500942\pi\)
−0.00296034 + 0.999996i \(0.500942\pi\)
\(38\) 2.63080 0.426772
\(39\) 0.00969099 0.00155180
\(40\) 2.46875 0.390344
\(41\) 2.68462 0.419268 0.209634 0.977780i \(-0.432773\pi\)
0.209634 + 0.977780i \(0.432773\pi\)
\(42\) −0.225488 −0.0347936
\(43\) 2.40508 0.366772 0.183386 0.983041i \(-0.441294\pi\)
0.183386 + 0.983041i \(0.441294\pi\)
\(44\) −22.8191 −3.44011
\(45\) 0.956364 0.142566
\(46\) −17.5899 −2.59348
\(47\) 10.3758 1.51346 0.756732 0.653726i \(-0.226795\pi\)
0.756732 + 0.653726i \(0.226795\pi\)
\(48\) −1.57306 −0.227051
\(49\) −6.68043 −0.954347
\(50\) 12.8825 1.82186
\(51\) −0.208668 −0.0292194
\(52\) −0.314541 −0.0436189
\(53\) 5.19462 0.713535 0.356768 0.934193i \(-0.383879\pi\)
0.356768 + 0.934193i \(0.383879\pi\)
\(54\) −2.38411 −0.324436
\(55\) 1.48963 0.200862
\(56\) 4.34427 0.580527
\(57\) 0.151619 0.0200824
\(58\) −4.98388 −0.654415
\(59\) 10.7496 1.39948 0.699741 0.714396i \(-0.253299\pi\)
0.699741 + 0.714396i \(0.253299\pi\)
\(60\) 0.239695 0.0309445
\(61\) 14.9701 1.91673 0.958365 0.285547i \(-0.0921754\pi\)
0.958365 + 0.285547i \(0.0921754\pi\)
\(62\) 15.5673 1.97705
\(63\) 1.68292 0.212028
\(64\) 10.6222 1.32777
\(65\) 0.0205332 0.00254683
\(66\) −1.84960 −0.227670
\(67\) 3.00136 0.366674 0.183337 0.983050i \(-0.441310\pi\)
0.183337 + 0.983050i \(0.441310\pi\)
\(68\) 6.77276 0.821318
\(69\) −1.01375 −0.122041
\(70\) −0.477763 −0.0571036
\(71\) 6.28821 0.746273 0.373136 0.927776i \(-0.378282\pi\)
0.373136 + 0.927776i \(0.378282\pi\)
\(72\) 22.8779 2.69618
\(73\) 6.93566 0.811758 0.405879 0.913927i \(-0.366965\pi\)
0.405879 + 0.913927i \(0.366965\pi\)
\(74\) 0.0947459 0.0110140
\(75\) 0.742448 0.0857305
\(76\) −4.92110 −0.564489
\(77\) 2.62131 0.298726
\(78\) −0.0254950 −0.00288674
\(79\) −12.4370 −1.39927 −0.699637 0.714499i \(-0.746655\pi\)
−0.699637 + 0.714499i \(0.746655\pi\)
\(80\) −3.33298 −0.372639
\(81\) 8.79363 0.977070
\(82\) −7.06270 −0.779945
\(83\) −4.10558 −0.450646 −0.225323 0.974284i \(-0.572344\pi\)
−0.225323 + 0.974284i \(0.572344\pi\)
\(84\) 0.421792 0.0460213
\(85\) −0.442126 −0.0479553
\(86\) −6.32729 −0.682290
\(87\) −0.287233 −0.0307946
\(88\) 35.6346 3.79866
\(89\) 15.6451 1.65838 0.829188 0.558969i \(-0.188803\pi\)
0.829188 + 0.558969i \(0.188803\pi\)
\(90\) −2.51600 −0.265210
\(91\) 0.0361323 0.00378770
\(92\) 32.9031 3.43039
\(93\) 0.897179 0.0930331
\(94\) −27.2966 −2.81543
\(95\) 0.321250 0.0329595
\(96\) 1.80806 0.184534
\(97\) −11.8503 −1.20322 −0.601608 0.798792i \(-0.705473\pi\)
−0.601608 + 0.798792i \(0.705473\pi\)
\(98\) 17.5749 1.77533
\(99\) 13.8044 1.38739
\(100\) −24.0977 −2.40977
\(101\) −3.53917 −0.352161 −0.176080 0.984376i \(-0.556342\pi\)
−0.176080 + 0.984376i \(0.556342\pi\)
\(102\) 0.548965 0.0543556
\(103\) −1.50481 −0.148273 −0.0741366 0.997248i \(-0.523620\pi\)
−0.0741366 + 0.997248i \(0.523620\pi\)
\(104\) 0.491189 0.0481651
\(105\) −0.0275346 −0.00268710
\(106\) −13.6660 −1.32736
\(107\) 6.33333 0.612266 0.306133 0.951989i \(-0.400965\pi\)
0.306133 + 0.951989i \(0.400965\pi\)
\(108\) 4.45965 0.429130
\(109\) −6.89780 −0.660689 −0.330345 0.943860i \(-0.607165\pi\)
−0.330345 + 0.943860i \(0.607165\pi\)
\(110\) −3.91892 −0.373655
\(111\) 0.00546043 0.000518281 0
\(112\) −5.86506 −0.554196
\(113\) −19.3670 −1.82189 −0.910947 0.412523i \(-0.864648\pi\)
−0.910947 + 0.412523i \(0.864648\pi\)
\(114\) −0.398879 −0.0373585
\(115\) −2.14792 −0.200294
\(116\) 9.32271 0.865592
\(117\) 0.190281 0.0175915
\(118\) −28.2801 −2.60340
\(119\) −0.778010 −0.0713200
\(120\) −0.374310 −0.0341696
\(121\) 10.5017 0.954702
\(122\) −39.3834 −3.56561
\(123\) −0.407040 −0.0367016
\(124\) −29.1198 −2.61503
\(125\) 3.17934 0.284369
\(126\) −4.42741 −0.394425
\(127\) 0.628638 0.0557826 0.0278913 0.999611i \(-0.491121\pi\)
0.0278913 + 0.999611i \(0.491121\pi\)
\(128\) −4.09485 −0.361937
\(129\) −0.364657 −0.0321062
\(130\) −0.0540187 −0.00473776
\(131\) −18.9919 −1.65933 −0.829667 0.558259i \(-0.811470\pi\)
−0.829667 + 0.558259i \(0.811470\pi\)
\(132\) 3.45982 0.301138
\(133\) 0.565304 0.0490181
\(134\) −7.89596 −0.682107
\(135\) −0.291126 −0.0250561
\(136\) −10.5764 −0.906919
\(137\) 8.42134 0.719484 0.359742 0.933052i \(-0.382865\pi\)
0.359742 + 0.933052i \(0.382865\pi\)
\(138\) 2.66696 0.227027
\(139\) −1.38780 −0.117712 −0.0588558 0.998266i \(-0.518745\pi\)
−0.0588558 + 0.998266i \(0.518745\pi\)
\(140\) 0.893690 0.0755306
\(141\) −1.57317 −0.132484
\(142\) −16.5430 −1.38826
\(143\) 0.296381 0.0247846
\(144\) −30.8867 −2.57389
\(145\) −0.608587 −0.0505404
\(146\) −18.2463 −1.51008
\(147\) 1.01288 0.0835410
\(148\) −0.177229 −0.0145682
\(149\) 12.9671 1.06231 0.531154 0.847275i \(-0.321758\pi\)
0.531154 + 0.847275i \(0.321758\pi\)
\(150\) −1.95323 −0.159481
\(151\) −3.68039 −0.299506 −0.149753 0.988723i \(-0.547848\pi\)
−0.149753 + 0.988723i \(0.547848\pi\)
\(152\) 7.68484 0.623323
\(153\) −4.09717 −0.331236
\(154\) −6.89614 −0.555707
\(155\) 1.90094 0.152687
\(156\) 0.0476903 0.00381828
\(157\) −16.6159 −1.32609 −0.663046 0.748579i \(-0.730737\pi\)
−0.663046 + 0.748579i \(0.730737\pi\)
\(158\) 32.7193 2.60301
\(159\) −0.787603 −0.0624610
\(160\) 3.83091 0.302860
\(161\) −3.77970 −0.297882
\(162\) −23.1343 −1.81760
\(163\) −13.9917 −1.09592 −0.547959 0.836505i \(-0.684595\pi\)
−0.547959 + 0.836505i \(0.684595\pi\)
\(164\) 13.2113 1.03163
\(165\) −0.225857 −0.0175829
\(166\) 10.8010 0.838317
\(167\) −6.97817 −0.539987 −0.269994 0.962862i \(-0.587022\pi\)
−0.269994 + 0.962862i \(0.587022\pi\)
\(168\) −0.658674 −0.0508178
\(169\) −12.9959 −0.999686
\(170\) 1.16314 0.0892090
\(171\) 2.97701 0.227658
\(172\) 11.8357 0.902462
\(173\) −1.32835 −0.100992 −0.0504962 0.998724i \(-0.516080\pi\)
−0.0504962 + 0.998724i \(0.516080\pi\)
\(174\) 0.755651 0.0572858
\(175\) 2.76818 0.209255
\(176\) −48.1091 −3.62636
\(177\) −1.62985 −0.122507
\(178\) −41.1591 −3.08501
\(179\) 6.11145 0.456791 0.228396 0.973568i \(-0.426652\pi\)
0.228396 + 0.973568i \(0.426652\pi\)
\(180\) 4.70637 0.350792
\(181\) −1.97349 −0.146688 −0.0733441 0.997307i \(-0.523367\pi\)
−0.0733441 + 0.997307i \(0.523367\pi\)
\(182\) −0.0950569 −0.00704609
\(183\) −2.26976 −0.167785
\(184\) −51.3818 −3.78792
\(185\) 0.0115695 0.000850608 0
\(186\) −2.36030 −0.173065
\(187\) −6.38175 −0.466680
\(188\) 51.0603 3.72395
\(189\) −0.512295 −0.0372640
\(190\) −0.845143 −0.0613131
\(191\) 0.852529 0.0616869 0.0308434 0.999524i \(-0.490181\pi\)
0.0308434 + 0.999524i \(0.490181\pi\)
\(192\) −1.61053 −0.116230
\(193\) 11.1539 0.802876 0.401438 0.915886i \(-0.368511\pi\)
0.401438 + 0.915886i \(0.368511\pi\)
\(194\) 31.1757 2.23829
\(195\) −0.00311323 −0.000222943 0
\(196\) −32.8751 −2.34822
\(197\) −23.0857 −1.64479 −0.822395 0.568917i \(-0.807363\pi\)
−0.822395 + 0.568917i \(0.807363\pi\)
\(198\) −36.3166 −2.58091
\(199\) 13.4599 0.954151 0.477075 0.878862i \(-0.341697\pi\)
0.477075 + 0.878862i \(0.341697\pi\)
\(200\) 37.6311 2.66092
\(201\) −0.455063 −0.0320976
\(202\) 9.31085 0.655109
\(203\) −1.07093 −0.0751647
\(204\) −1.02688 −0.0718959
\(205\) −0.862434 −0.0602350
\(206\) 3.95885 0.275826
\(207\) −19.9047 −1.38347
\(208\) −0.663139 −0.0459804
\(209\) 4.63699 0.320748
\(210\) 0.0724379 0.00499869
\(211\) 8.16796 0.562306 0.281153 0.959663i \(-0.409283\pi\)
0.281153 + 0.959663i \(0.409283\pi\)
\(212\) 25.5632 1.75569
\(213\) −0.953412 −0.0653267
\(214\) −16.6617 −1.13897
\(215\) −0.772633 −0.0526931
\(216\) −6.96422 −0.473855
\(217\) 3.34508 0.227079
\(218\) 18.1467 1.22905
\(219\) −1.05158 −0.0710591
\(220\) 7.33064 0.494231
\(221\) −0.0879665 −0.00591727
\(222\) −0.0143653 −0.000964135 0
\(223\) −14.5992 −0.977637 −0.488819 0.872385i \(-0.662572\pi\)
−0.488819 + 0.872385i \(0.662572\pi\)
\(224\) 6.74126 0.450419
\(225\) 14.5778 0.971855
\(226\) 50.9507 3.38919
\(227\) −20.0319 −1.32957 −0.664783 0.747036i \(-0.731476\pi\)
−0.664783 + 0.747036i \(0.731476\pi\)
\(228\) 0.746133 0.0494139
\(229\) 9.62935 0.636326 0.318163 0.948036i \(-0.396934\pi\)
0.318163 + 0.948036i \(0.396934\pi\)
\(230\) 5.65074 0.372599
\(231\) −0.397441 −0.0261497
\(232\) −14.5584 −0.955808
\(233\) −4.48142 −0.293588 −0.146794 0.989167i \(-0.546895\pi\)
−0.146794 + 0.989167i \(0.546895\pi\)
\(234\) −0.500590 −0.0327246
\(235\) −3.33322 −0.217435
\(236\) 52.9000 3.44350
\(237\) 1.88569 0.122489
\(238\) 2.04679 0.132674
\(239\) 18.2607 1.18119 0.590594 0.806969i \(-0.298893\pi\)
0.590594 + 0.806969i \(0.298893\pi\)
\(240\) 0.505344 0.0326198
\(241\) 17.6080 1.13423 0.567115 0.823639i \(-0.308060\pi\)
0.567115 + 0.823639i \(0.308060\pi\)
\(242\) −27.6279 −1.77599
\(243\) −4.05197 −0.259934
\(244\) 73.6696 4.71621
\(245\) 2.14609 0.137108
\(246\) 1.07084 0.0682743
\(247\) 0.0639167 0.00406692
\(248\) 45.4737 2.88758
\(249\) 0.622484 0.0394483
\(250\) −8.36421 −0.528999
\(251\) −11.7241 −0.740021 −0.370010 0.929028i \(-0.620646\pi\)
−0.370010 + 0.929028i \(0.620646\pi\)
\(252\) 8.28181 0.521705
\(253\) −31.0036 −1.94918
\(254\) −1.65382 −0.103770
\(255\) 0.0670347 0.00419787
\(256\) −10.4717 −0.654480
\(257\) 1.90707 0.118960 0.0594798 0.998230i \(-0.481056\pi\)
0.0594798 + 0.998230i \(0.481056\pi\)
\(258\) 0.959339 0.0597258
\(259\) 0.0203589 0.00126504
\(260\) 0.101046 0.00626661
\(261\) −5.63976 −0.349092
\(262\) 49.9640 3.08679
\(263\) 5.84695 0.360538 0.180269 0.983617i \(-0.442303\pi\)
0.180269 + 0.983617i \(0.442303\pi\)
\(264\) −5.40288 −0.332524
\(265\) −1.66877 −0.102512
\(266\) −1.48720 −0.0911861
\(267\) −2.37209 −0.145170
\(268\) 14.7700 0.902220
\(269\) −14.3137 −0.872721 −0.436360 0.899772i \(-0.643733\pi\)
−0.436360 + 0.899772i \(0.643733\pi\)
\(270\) 0.765893 0.0466108
\(271\) −21.8420 −1.32681 −0.663404 0.748262i \(-0.730889\pi\)
−0.663404 + 0.748262i \(0.730889\pi\)
\(272\) 14.2789 0.865783
\(273\) −0.00547835 −0.000331565 0
\(274\) −22.1549 −1.33842
\(275\) 22.7064 1.36925
\(276\) −4.98874 −0.300287
\(277\) −20.9533 −1.25896 −0.629480 0.777017i \(-0.716732\pi\)
−0.629480 + 0.777017i \(0.716732\pi\)
\(278\) 3.65102 0.218974
\(279\) 17.6159 1.05464
\(280\) −1.39559 −0.0834027
\(281\) 12.2747 0.732246 0.366123 0.930567i \(-0.380685\pi\)
0.366123 + 0.930567i \(0.380685\pi\)
\(282\) 4.13868 0.246455
\(283\) 1.24217 0.0738396 0.0369198 0.999318i \(-0.488245\pi\)
0.0369198 + 0.999318i \(0.488245\pi\)
\(284\) 30.9449 1.83624
\(285\) −0.0487076 −0.00288519
\(286\) −0.779720 −0.0461058
\(287\) −1.51763 −0.0895827
\(288\) 35.5009 2.09191
\(289\) −15.1059 −0.888582
\(290\) 1.60107 0.0940180
\(291\) 1.79673 0.105326
\(292\) 34.1311 1.99737
\(293\) −2.87163 −0.167763 −0.0838813 0.996476i \(-0.526732\pi\)
−0.0838813 + 0.996476i \(0.526732\pi\)
\(294\) −2.66469 −0.155408
\(295\) −3.45331 −0.201060
\(296\) 0.276763 0.0160865
\(297\) −4.20218 −0.243835
\(298\) −34.1139 −1.97617
\(299\) −0.427355 −0.0247146
\(300\) 3.65366 0.210944
\(301\) −1.35960 −0.0783663
\(302\) 9.68236 0.557157
\(303\) 0.536606 0.0308272
\(304\) −10.3751 −0.595050
\(305\) −4.80915 −0.275371
\(306\) 10.7788 0.616184
\(307\) 24.9696 1.42509 0.712546 0.701626i \(-0.247542\pi\)
0.712546 + 0.701626i \(0.247542\pi\)
\(308\) 12.8997 0.735031
\(309\) 0.228158 0.0129794
\(310\) −5.00098 −0.284037
\(311\) −22.1074 −1.25359 −0.626796 0.779183i \(-0.715634\pi\)
−0.626796 + 0.779183i \(0.715634\pi\)
\(312\) −0.0744736 −0.00421624
\(313\) −30.8405 −1.74321 −0.871605 0.490209i \(-0.836921\pi\)
−0.871605 + 0.490209i \(0.836921\pi\)
\(314\) 43.7130 2.46687
\(315\) −0.540636 −0.0304614
\(316\) −61.2038 −3.44298
\(317\) −1.00000 −0.0561656
\(318\) 2.07203 0.116193
\(319\) −8.78449 −0.491837
\(320\) −3.41238 −0.190758
\(321\) −0.960253 −0.0535961
\(322\) 9.94362 0.554136
\(323\) −1.37627 −0.0765776
\(324\) 43.2744 2.40413
\(325\) 0.312987 0.0173614
\(326\) 36.8095 2.03869
\(327\) 1.04584 0.0578349
\(328\) −20.6309 −1.13915
\(329\) −5.86547 −0.323374
\(330\) 0.594184 0.0327087
\(331\) 22.8745 1.25730 0.628649 0.777689i \(-0.283608\pi\)
0.628649 + 0.777689i \(0.283608\pi\)
\(332\) −20.2040 −1.10884
\(333\) 0.107214 0.00587532
\(334\) 18.3582 1.00451
\(335\) −0.964184 −0.0526790
\(336\) 0.889255 0.0485128
\(337\) 28.6553 1.56096 0.780478 0.625183i \(-0.214976\pi\)
0.780478 + 0.625183i \(0.214976\pi\)
\(338\) 34.1896 1.85967
\(339\) 2.93641 0.159484
\(340\) −2.17575 −0.117996
\(341\) 27.4386 1.48588
\(342\) −7.83192 −0.423502
\(343\) 7.73360 0.417575
\(344\) −18.4827 −0.996520
\(345\) 0.325665 0.0175332
\(346\) 3.49461 0.187872
\(347\) −32.5024 −1.74482 −0.872409 0.488777i \(-0.837443\pi\)
−0.872409 + 0.488777i \(0.837443\pi\)
\(348\) −1.41350 −0.0757716
\(349\) −11.4728 −0.614123 −0.307062 0.951690i \(-0.599346\pi\)
−0.307062 + 0.951690i \(0.599346\pi\)
\(350\) −7.28252 −0.389267
\(351\) −0.0579231 −0.00309171
\(352\) 55.2962 2.94730
\(353\) 16.1913 0.861776 0.430888 0.902405i \(-0.358200\pi\)
0.430888 + 0.902405i \(0.358200\pi\)
\(354\) 4.28780 0.227894
\(355\) −2.02008 −0.107215
\(356\) 76.9911 4.08052
\(357\) 0.117961 0.00624316
\(358\) −16.0780 −0.849749
\(359\) −25.2772 −1.33408 −0.667040 0.745022i \(-0.732439\pi\)
−0.667040 + 0.745022i \(0.732439\pi\)
\(360\) −7.34950 −0.387353
\(361\) 1.00000 0.0526316
\(362\) 5.19185 0.272878
\(363\) −1.59226 −0.0835720
\(364\) 0.177811 0.00931983
\(365\) −2.22808 −0.116623
\(366\) 5.97128 0.312124
\(367\) 29.3420 1.53164 0.765820 0.643055i \(-0.222333\pi\)
0.765820 + 0.643055i \(0.222333\pi\)
\(368\) 69.3690 3.61611
\(369\) −7.99215 −0.416055
\(370\) −0.0304371 −0.00158235
\(371\) −2.93654 −0.152457
\(372\) 4.41511 0.228913
\(373\) 6.89509 0.357014 0.178507 0.983939i \(-0.442873\pi\)
0.178507 + 0.983939i \(0.442873\pi\)
\(374\) 16.7891 0.868144
\(375\) −0.482049 −0.0248929
\(376\) −79.7362 −4.11208
\(377\) −0.121086 −0.00623625
\(378\) 1.34774 0.0693205
\(379\) −10.7299 −0.551157 −0.275579 0.961279i \(-0.588869\pi\)
−0.275579 + 0.961279i \(0.588869\pi\)
\(380\) 1.58090 0.0810986
\(381\) −0.0953134 −0.00488306
\(382\) −2.24283 −0.114753
\(383\) 13.6852 0.699283 0.349642 0.936884i \(-0.386303\pi\)
0.349642 + 0.936884i \(0.386303\pi\)
\(384\) 0.620857 0.0316830
\(385\) −0.842095 −0.0429171
\(386\) −29.3437 −1.49355
\(387\) −7.15997 −0.363962
\(388\) −58.3165 −2.96057
\(389\) −37.8353 −1.91832 −0.959162 0.282858i \(-0.908718\pi\)
−0.959162 + 0.282858i \(0.908718\pi\)
\(390\) 0.00819027 0.000414730 0
\(391\) 9.20191 0.465361
\(392\) 51.3380 2.59296
\(393\) 2.87954 0.145254
\(394\) 60.7339 3.05973
\(395\) 3.99539 0.201030
\(396\) 67.9328 3.41375
\(397\) −5.80187 −0.291187 −0.145594 0.989344i \(-0.546509\pi\)
−0.145594 + 0.989344i \(0.546509\pi\)
\(398\) −35.4104 −1.77496
\(399\) −0.0857108 −0.00429091
\(400\) −50.8046 −2.54023
\(401\) −0.140898 −0.00703612 −0.00351806 0.999994i \(-0.501120\pi\)
−0.00351806 + 0.999994i \(0.501120\pi\)
\(402\) 1.19718 0.0597098
\(403\) 0.378215 0.0188403
\(404\) −17.4166 −0.866510
\(405\) −2.82495 −0.140373
\(406\) 2.81741 0.139826
\(407\) 0.166997 0.00827775
\(408\) 1.60358 0.0793892
\(409\) 32.7166 1.61773 0.808865 0.587995i \(-0.200082\pi\)
0.808865 + 0.587995i \(0.200082\pi\)
\(410\) 2.26889 0.112053
\(411\) −1.27684 −0.0629817
\(412\) −7.40532 −0.364834
\(413\) −6.07681 −0.299020
\(414\) 52.3652 2.57361
\(415\) 1.31892 0.0647431
\(416\) 0.762207 0.0373703
\(417\) 0.210417 0.0103042
\(418\) −12.1990 −0.596673
\(419\) 16.7990 0.820686 0.410343 0.911931i \(-0.365409\pi\)
0.410343 + 0.911931i \(0.365409\pi\)
\(420\) −0.135501 −0.00661175
\(421\) 31.9117 1.55528 0.777640 0.628710i \(-0.216417\pi\)
0.777640 + 0.628710i \(0.216417\pi\)
\(422\) −21.4883 −1.04603
\(423\) −30.8888 −1.50187
\(424\) −39.9198 −1.93868
\(425\) −6.73931 −0.326904
\(426\) 2.50824 0.121524
\(427\) −8.46267 −0.409538
\(428\) 31.1670 1.50651
\(429\) −0.0449370 −0.00216958
\(430\) 2.03264 0.0980227
\(431\) 4.56161 0.219725 0.109863 0.993947i \(-0.464959\pi\)
0.109863 + 0.993947i \(0.464959\pi\)
\(432\) 9.40218 0.452362
\(433\) −24.2816 −1.16690 −0.583449 0.812150i \(-0.698297\pi\)
−0.583449 + 0.812150i \(0.698297\pi\)
\(434\) −8.80025 −0.422425
\(435\) 0.0922733 0.00442417
\(436\) −33.9448 −1.62566
\(437\) −6.68613 −0.319841
\(438\) 2.76649 0.132188
\(439\) 4.66088 0.222452 0.111226 0.993795i \(-0.464522\pi\)
0.111226 + 0.993795i \(0.464522\pi\)
\(440\) −11.4476 −0.545742
\(441\) 19.8877 0.947034
\(442\) 0.231422 0.0110076
\(443\) −27.2262 −1.29355 −0.646777 0.762679i \(-0.723883\pi\)
−0.646777 + 0.762679i \(0.723883\pi\)
\(444\) 0.0268713 0.00127526
\(445\) −5.02598 −0.238254
\(446\) 38.4077 1.81866
\(447\) −1.96606 −0.0929916
\(448\) −6.00477 −0.283699
\(449\) −10.9118 −0.514960 −0.257480 0.966284i \(-0.582892\pi\)
−0.257480 + 0.966284i \(0.582892\pi\)
\(450\) −38.3513 −1.80790
\(451\) −12.4486 −0.586181
\(452\) −95.3070 −4.48287
\(453\) 0.558017 0.0262179
\(454\) 52.7000 2.47333
\(455\) −0.0116075 −0.000544168 0
\(456\) −1.16517 −0.0545640
\(457\) −31.3364 −1.46585 −0.732927 0.680307i \(-0.761846\pi\)
−0.732927 + 0.680307i \(0.761846\pi\)
\(458\) −25.3329 −1.18373
\(459\) 1.24721 0.0582150
\(460\) −10.5701 −0.492835
\(461\) 11.5167 0.536385 0.268192 0.963365i \(-0.413574\pi\)
0.268192 + 0.963365i \(0.413574\pi\)
\(462\) 1.04559 0.0486451
\(463\) 9.94675 0.462265 0.231132 0.972922i \(-0.425757\pi\)
0.231132 + 0.972922i \(0.425757\pi\)
\(464\) 19.6549 0.912455
\(465\) −0.288218 −0.0133658
\(466\) 11.7897 0.546148
\(467\) 1.04001 0.0481257 0.0240629 0.999710i \(-0.492340\pi\)
0.0240629 + 0.999710i \(0.492340\pi\)
\(468\) 0.936391 0.0432847
\(469\) −1.69668 −0.0783453
\(470\) 8.76902 0.404485
\(471\) 2.51928 0.116082
\(472\) −82.6092 −3.80239
\(473\) −11.1524 −0.512786
\(474\) −4.96087 −0.227860
\(475\) 4.89680 0.224681
\(476\) −3.82867 −0.175487
\(477\) −15.4644 −0.708068
\(478\) −48.0403 −2.19731
\(479\) 29.6099 1.35291 0.676456 0.736483i \(-0.263515\pi\)
0.676456 + 0.736483i \(0.263515\pi\)
\(480\) −0.580838 −0.0265115
\(481\) 0.00230190 0.000104958 0
\(482\) −46.3231 −2.10996
\(483\) 0.573074 0.0260758
\(484\) 51.6801 2.34909
\(485\) 3.80690 0.172863
\(486\) 10.6599 0.483544
\(487\) 32.1482 1.45677 0.728387 0.685166i \(-0.240270\pi\)
0.728387 + 0.685166i \(0.240270\pi\)
\(488\) −115.043 −5.20775
\(489\) 2.12142 0.0959337
\(490\) −5.64592 −0.255057
\(491\) 22.4433 1.01285 0.506426 0.862283i \(-0.330966\pi\)
0.506426 + 0.862283i \(0.330966\pi\)
\(492\) −2.00309 −0.0903061
\(493\) 2.60725 0.117425
\(494\) −0.168152 −0.00756551
\(495\) −4.43465 −0.199323
\(496\) −61.3925 −2.75661
\(497\) −3.55475 −0.159452
\(498\) −1.63763 −0.0733840
\(499\) −0.137035 −0.00613454 −0.00306727 0.999995i \(-0.500976\pi\)
−0.00306727 + 0.999995i \(0.500976\pi\)
\(500\) 15.6459 0.699705
\(501\) 1.05802 0.0472690
\(502\) 30.8438 1.37663
\(503\) −41.9990 −1.87264 −0.936321 0.351144i \(-0.885793\pi\)
−0.936321 + 0.351144i \(0.885793\pi\)
\(504\) −12.9329 −0.576079
\(505\) 1.13696 0.0505940
\(506\) 81.5641 3.62597
\(507\) 1.97043 0.0875098
\(508\) 3.09359 0.137256
\(509\) −13.6595 −0.605445 −0.302722 0.953079i \(-0.597895\pi\)
−0.302722 + 0.953079i \(0.597895\pi\)
\(510\) −0.176355 −0.00780912
\(511\) −3.92076 −0.173444
\(512\) 35.7386 1.57944
\(513\) −0.906229 −0.0400110
\(514\) −5.01711 −0.221295
\(515\) 0.483419 0.0213020
\(516\) −1.79451 −0.0789991
\(517\) −48.1124 −2.11598
\(518\) −0.0535602 −0.00235330
\(519\) 0.201403 0.00884060
\(520\) −0.157794 −0.00691974
\(521\) −17.9553 −0.786635 −0.393318 0.919403i \(-0.628673\pi\)
−0.393318 + 0.919403i \(0.628673\pi\)
\(522\) 14.8371 0.649401
\(523\) −9.07837 −0.396970 −0.198485 0.980104i \(-0.563602\pi\)
−0.198485 + 0.980104i \(0.563602\pi\)
\(524\) −93.4613 −4.08288
\(525\) −0.419709 −0.0183176
\(526\) −15.3821 −0.670693
\(527\) −8.14382 −0.354750
\(528\) 7.29425 0.317442
\(529\) 21.7044 0.943668
\(530\) 4.39019 0.190698
\(531\) −32.0018 −1.38876
\(532\) 2.78192 0.120611
\(533\) −0.171592 −0.00743248
\(534\) 6.24050 0.270053
\(535\) −2.03458 −0.0879625
\(536\) −23.0649 −0.996253
\(537\) −0.926613 −0.0399863
\(538\) 37.6564 1.62348
\(539\) 30.9771 1.33428
\(540\) −1.43266 −0.0616519
\(541\) 8.70935 0.374444 0.187222 0.982318i \(-0.440052\pi\)
0.187222 + 0.982318i \(0.440052\pi\)
\(542\) 57.4619 2.46820
\(543\) 0.299218 0.0128407
\(544\) −16.4120 −0.703659
\(545\) 2.21591 0.0949193
\(546\) 0.0144124 0.000616796 0
\(547\) −19.0164 −0.813082 −0.406541 0.913632i \(-0.633265\pi\)
−0.406541 + 0.913632i \(0.633265\pi\)
\(548\) 41.4423 1.77033
\(549\) −44.5663 −1.90204
\(550\) −59.7361 −2.54715
\(551\) −1.89444 −0.0807057
\(552\) 7.79047 0.331584
\(553\) 7.03069 0.298975
\(554\) 55.1238 2.34199
\(555\) −0.00175416 −7.44600e−5 0
\(556\) −6.82950 −0.289635
\(557\) −33.4093 −1.41560 −0.707799 0.706413i \(-0.750312\pi\)
−0.707799 + 0.706413i \(0.750312\pi\)
\(558\) −46.3440 −1.96190
\(559\) −0.153725 −0.00650188
\(560\) 1.88415 0.0796198
\(561\) 0.967595 0.0408519
\(562\) −32.2922 −1.36216
\(563\) 33.5164 1.41255 0.706274 0.707939i \(-0.250375\pi\)
0.706274 + 0.707939i \(0.250375\pi\)
\(564\) −7.74171 −0.325985
\(565\) 6.22164 0.261746
\(566\) −3.26791 −0.137361
\(567\) −4.97108 −0.208766
\(568\) −48.3238 −2.02762
\(569\) 37.6232 1.57725 0.788624 0.614875i \(-0.210794\pi\)
0.788624 + 0.614875i \(0.210794\pi\)
\(570\) 0.128140 0.00536719
\(571\) −1.05810 −0.0442800 −0.0221400 0.999755i \(-0.507048\pi\)
−0.0221400 + 0.999755i \(0.507048\pi\)
\(572\) 1.45852 0.0609839
\(573\) −0.129260 −0.00539990
\(574\) 3.99257 0.166647
\(575\) −32.7406 −1.36538
\(576\) −31.6224 −1.31760
\(577\) −21.0600 −0.876738 −0.438369 0.898795i \(-0.644444\pi\)
−0.438369 + 0.898795i \(0.644444\pi\)
\(578\) 39.7406 1.65299
\(579\) −1.69114 −0.0702816
\(580\) −2.99492 −0.124357
\(581\) 2.32090 0.0962872
\(582\) −4.72684 −0.195934
\(583\) −24.0874 −0.997599
\(584\) −53.2994 −2.20555
\(585\) −0.0611276 −0.00252731
\(586\) 7.55469 0.312082
\(587\) 3.34088 0.137893 0.0689465 0.997620i \(-0.478036\pi\)
0.0689465 + 0.997620i \(0.478036\pi\)
\(588\) 4.98449 0.205557
\(589\) 5.91732 0.243819
\(590\) 9.08498 0.374023
\(591\) 3.50024 0.143980
\(592\) −0.373649 −0.0153569
\(593\) −16.7838 −0.689228 −0.344614 0.938744i \(-0.611990\pi\)
−0.344614 + 0.938744i \(0.611990\pi\)
\(594\) 11.0551 0.453596
\(595\) 0.249935 0.0102463
\(596\) 63.8126 2.61387
\(597\) −2.04078 −0.0835238
\(598\) 1.12429 0.0459755
\(599\) 5.98907 0.244707 0.122353 0.992487i \(-0.460956\pi\)
0.122353 + 0.992487i \(0.460956\pi\)
\(600\) −5.70559 −0.232930
\(601\) 9.32877 0.380529 0.190264 0.981733i \(-0.439066\pi\)
0.190264 + 0.981733i \(0.439066\pi\)
\(602\) 3.57684 0.145781
\(603\) −8.93507 −0.363864
\(604\) −18.1116 −0.736949
\(605\) −3.37367 −0.137159
\(606\) −1.41170 −0.0573465
\(607\) −17.6969 −0.718293 −0.359147 0.933281i \(-0.616932\pi\)
−0.359147 + 0.933281i \(0.616932\pi\)
\(608\) 11.9250 0.483623
\(609\) 0.162374 0.00657971
\(610\) 12.6519 0.512261
\(611\) −0.663185 −0.0268296
\(612\) −20.1626 −0.815024
\(613\) 11.5002 0.464490 0.232245 0.972657i \(-0.425393\pi\)
0.232245 + 0.972657i \(0.425393\pi\)
\(614\) −65.6901 −2.65103
\(615\) 0.130761 0.00527281
\(616\) −20.1444 −0.811639
\(617\) 35.8428 1.44298 0.721489 0.692426i \(-0.243458\pi\)
0.721489 + 0.692426i \(0.243458\pi\)
\(618\) −0.600237 −0.0241451
\(619\) 41.6671 1.67474 0.837372 0.546634i \(-0.184091\pi\)
0.837372 + 0.546634i \(0.184091\pi\)
\(620\) 9.35471 0.375694
\(621\) 6.05917 0.243146
\(622\) 58.1600 2.33200
\(623\) −8.84423 −0.354337
\(624\) 0.100545 0.00402500
\(625\) 23.4626 0.938505
\(626\) 81.1353 3.24282
\(627\) −0.703057 −0.0280774
\(628\) −81.7685 −3.26292
\(629\) −0.0495651 −0.00197629
\(630\) 1.42231 0.0566660
\(631\) −33.9208 −1.35036 −0.675182 0.737651i \(-0.735935\pi\)
−0.675182 + 0.737651i \(0.735935\pi\)
\(632\) 95.5764 3.80183
\(633\) −1.23842 −0.0492227
\(634\) 2.63080 0.104482
\(635\) −0.201950 −0.00801412
\(636\) −3.87588 −0.153688
\(637\) 0.426991 0.0169180
\(638\) 23.1102 0.914942
\(639\) −18.7201 −0.740554
\(640\) 1.31547 0.0519985
\(641\) −40.6684 −1.60631 −0.803153 0.595773i \(-0.796846\pi\)
−0.803153 + 0.595773i \(0.796846\pi\)
\(642\) 2.52623 0.0997025
\(643\) −9.39786 −0.370616 −0.185308 0.982681i \(-0.559328\pi\)
−0.185308 + 0.982681i \(0.559328\pi\)
\(644\) −18.6003 −0.732954
\(645\) 0.117146 0.00461261
\(646\) 3.62069 0.142454
\(647\) −29.3762 −1.15490 −0.577449 0.816427i \(-0.695952\pi\)
−0.577449 + 0.816427i \(0.695952\pi\)
\(648\) −67.5776 −2.65470
\(649\) −49.8460 −1.95663
\(650\) −0.823406 −0.0322966
\(651\) −0.507179 −0.0198779
\(652\) −68.8549 −2.69656
\(653\) 1.63436 0.0639576 0.0319788 0.999489i \(-0.489819\pi\)
0.0319788 + 0.999489i \(0.489819\pi\)
\(654\) −2.75139 −0.107588
\(655\) 6.10116 0.238392
\(656\) 27.8531 1.08748
\(657\) −20.6475 −0.805537
\(658\) 15.4309 0.601558
\(659\) 8.51844 0.331831 0.165916 0.986140i \(-0.446942\pi\)
0.165916 + 0.986140i \(0.446942\pi\)
\(660\) −1.11146 −0.0432637
\(661\) −35.6124 −1.38516 −0.692581 0.721340i \(-0.743526\pi\)
−0.692581 + 0.721340i \(0.743526\pi\)
\(662\) −60.1783 −2.33890
\(663\) 0.0133374 0.000517982 0
\(664\) 31.5507 1.22441
\(665\) −0.181604 −0.00704229
\(666\) −0.282060 −0.0109296
\(667\) 12.6664 0.490447
\(668\) −34.3403 −1.32867
\(669\) 2.21352 0.0855797
\(670\) 2.53658 0.0979964
\(671\) −69.4164 −2.67979
\(672\) −1.02210 −0.0394285
\(673\) −12.2901 −0.473748 −0.236874 0.971540i \(-0.576123\pi\)
−0.236874 + 0.971540i \(0.576123\pi\)
\(674\) −75.3864 −2.90378
\(675\) −4.43762 −0.170804
\(676\) −63.9542 −2.45978
\(677\) −32.1509 −1.23566 −0.617829 0.786312i \(-0.711988\pi\)
−0.617829 + 0.786312i \(0.711988\pi\)
\(678\) −7.72510 −0.296681
\(679\) 6.69902 0.257085
\(680\) 3.39766 0.130294
\(681\) 3.03722 0.116387
\(682\) −72.1854 −2.76412
\(683\) 39.7068 1.51934 0.759669 0.650309i \(-0.225361\pi\)
0.759669 + 0.650309i \(0.225361\pi\)
\(684\) 14.6502 0.560164
\(685\) −2.70535 −0.103366
\(686\) −20.3456 −0.776797
\(687\) −1.45999 −0.0557022
\(688\) 24.9529 0.951320
\(689\) −0.332023 −0.0126491
\(690\) −0.856760 −0.0326163
\(691\) 5.49492 0.209037 0.104518 0.994523i \(-0.466670\pi\)
0.104518 + 0.994523i \(0.466670\pi\)
\(692\) −6.53693 −0.248497
\(693\) −7.80367 −0.296437
\(694\) 85.5072 3.24581
\(695\) 0.445830 0.0169113
\(696\) 2.20734 0.0836688
\(697\) 3.69476 0.139949
\(698\) 30.1826 1.14243
\(699\) 0.679469 0.0256999
\(700\) 13.6225 0.514882
\(701\) 11.5975 0.438032 0.219016 0.975721i \(-0.429715\pi\)
0.219016 + 0.975721i \(0.429715\pi\)
\(702\) 0.152384 0.00575137
\(703\) 0.0360141 0.00135830
\(704\) −49.2551 −1.85637
\(705\) 0.505379 0.0190337
\(706\) −42.5960 −1.60312
\(707\) 2.00071 0.0752444
\(708\) −8.02066 −0.301435
\(709\) 17.7056 0.664949 0.332475 0.943112i \(-0.392116\pi\)
0.332475 + 0.943112i \(0.392116\pi\)
\(710\) 5.31443 0.199447
\(711\) 37.0251 1.38855
\(712\) −120.230 −4.50581
\(713\) −39.5640 −1.48168
\(714\) −0.310332 −0.0116139
\(715\) −0.0952124 −0.00356074
\(716\) 30.0751 1.12396
\(717\) −2.76867 −0.103398
\(718\) 66.4993 2.48173
\(719\) −23.4975 −0.876309 −0.438154 0.898900i \(-0.644368\pi\)
−0.438154 + 0.898900i \(0.644368\pi\)
\(720\) 9.92233 0.369783
\(721\) 0.850675 0.0316808
\(722\) −2.63080 −0.0979082
\(723\) −2.66971 −0.0992874
\(724\) −9.71174 −0.360934
\(725\) −9.27667 −0.344527
\(726\) 4.18892 0.155465
\(727\) 29.2908 1.08634 0.543168 0.839624i \(-0.317225\pi\)
0.543168 + 0.839624i \(0.317225\pi\)
\(728\) −0.277671 −0.0102912
\(729\) −25.7665 −0.954316
\(730\) 5.86163 0.216949
\(731\) 3.31004 0.122426
\(732\) −11.1697 −0.412844
\(733\) −18.3142 −0.676449 −0.338224 0.941065i \(-0.609826\pi\)
−0.338224 + 0.941065i \(0.609826\pi\)
\(734\) −77.1929 −2.84924
\(735\) −0.325388 −0.0120021
\(736\) −79.7322 −2.93897
\(737\) −13.9173 −0.512649
\(738\) 21.0257 0.773968
\(739\) −0.866860 −0.0318880 −0.0159440 0.999873i \(-0.505075\pi\)
−0.0159440 + 0.999873i \(0.505075\pi\)
\(740\) 0.0569348 0.00209297
\(741\) −0.00969099 −0.000356007 0
\(742\) 7.72544 0.283610
\(743\) 12.6859 0.465400 0.232700 0.972549i \(-0.425244\pi\)
0.232700 + 0.972549i \(0.425244\pi\)
\(744\) −6.89467 −0.252771
\(745\) −4.16569 −0.152619
\(746\) −18.1396 −0.664138
\(747\) 12.2224 0.447193
\(748\) −31.4052 −1.14829
\(749\) −3.58025 −0.130820
\(750\) 1.26817 0.0463072
\(751\) −25.8972 −0.945001 −0.472501 0.881330i \(-0.656649\pi\)
−0.472501 + 0.881330i \(0.656649\pi\)
\(752\) 107.649 3.92557
\(753\) 1.77760 0.0647794
\(754\) 0.318553 0.0116010
\(755\) 1.18232 0.0430291
\(756\) −2.52106 −0.0916899
\(757\) −7.65024 −0.278053 −0.139026 0.990289i \(-0.544397\pi\)
−0.139026 + 0.990289i \(0.544397\pi\)
\(758\) 28.2282 1.02529
\(759\) 4.70073 0.170626
\(760\) −2.46875 −0.0895510
\(761\) 14.0560 0.509530 0.254765 0.967003i \(-0.418002\pi\)
0.254765 + 0.967003i \(0.418002\pi\)
\(762\) 0.250751 0.00908373
\(763\) 3.89935 0.141166
\(764\) 4.19538 0.151784
\(765\) 1.31621 0.0475878
\(766\) −36.0031 −1.30085
\(767\) −0.687081 −0.0248090
\(768\) 1.58771 0.0572914
\(769\) −16.8386 −0.607214 −0.303607 0.952797i \(-0.598191\pi\)
−0.303607 + 0.952797i \(0.598191\pi\)
\(770\) 2.21538 0.0798369
\(771\) −0.289148 −0.0104134
\(772\) 54.8895 1.97552
\(773\) −3.71644 −0.133671 −0.0668355 0.997764i \(-0.521290\pi\)
−0.0668355 + 0.997764i \(0.521290\pi\)
\(774\) 18.8364 0.677062
\(775\) 28.9759 1.04085
\(776\) 91.0676 3.26914
\(777\) −0.00308680 −0.000110738 0
\(778\) 99.5370 3.56857
\(779\) −2.68462 −0.0961866
\(780\) −0.0153205 −0.000548562 0
\(781\) −29.1584 −1.04337
\(782\) −24.2084 −0.865690
\(783\) 1.71679 0.0613531
\(784\) −69.3098 −2.47535
\(785\) 5.33785 0.190516
\(786\) −7.57549 −0.270209
\(787\) 0.0309705 0.00110398 0.000551989 1.00000i \(-0.499824\pi\)
0.000551989 1.00000i \(0.499824\pi\)
\(788\) −113.607 −4.04709
\(789\) −0.886509 −0.0315605
\(790\) −10.5111 −0.373967
\(791\) 10.9482 0.389275
\(792\) −106.084 −3.76955
\(793\) −0.956841 −0.0339784
\(794\) 15.2635 0.541683
\(795\) 0.253017 0.00897359
\(796\) 66.2378 2.34774
\(797\) −12.2109 −0.432531 −0.216265 0.976335i \(-0.569388\pi\)
−0.216265 + 0.976335i \(0.569388\pi\)
\(798\) 0.225488 0.00798219
\(799\) 14.2799 0.505185
\(800\) 58.3944 2.06455
\(801\) −46.5756 −1.64567
\(802\) 0.370675 0.0130890
\(803\) −32.1606 −1.13492
\(804\) −2.23941 −0.0789779
\(805\) 1.21423 0.0427958
\(806\) −0.995009 −0.0350477
\(807\) 2.17023 0.0763956
\(808\) 27.1980 0.956821
\(809\) 16.7603 0.589262 0.294631 0.955611i \(-0.404803\pi\)
0.294631 + 0.955611i \(0.404803\pi\)
\(810\) 7.43188 0.261130
\(811\) −5.39693 −0.189512 −0.0947559 0.995501i \(-0.530207\pi\)
−0.0947559 + 0.995501i \(0.530207\pi\)
\(812\) −5.27017 −0.184947
\(813\) 3.31166 0.116145
\(814\) −0.439336 −0.0153987
\(815\) 4.49484 0.157448
\(816\) −2.16495 −0.0757883
\(817\) −2.40508 −0.0841433
\(818\) −86.0707 −3.00939
\(819\) −0.107566 −0.00375867
\(820\) −4.24413 −0.148211
\(821\) −16.8878 −0.589389 −0.294694 0.955592i \(-0.595218\pi\)
−0.294694 + 0.955592i \(0.595218\pi\)
\(822\) 3.35910 0.117162
\(823\) 37.1374 1.29453 0.647265 0.762265i \(-0.275913\pi\)
0.647265 + 0.762265i \(0.275913\pi\)
\(824\) 11.5642 0.402859
\(825\) −3.44273 −0.119860
\(826\) 15.9869 0.556254
\(827\) −43.2715 −1.50470 −0.752349 0.658765i \(-0.771079\pi\)
−0.752349 + 0.658765i \(0.771079\pi\)
\(828\) −97.9531 −3.40410
\(829\) 51.3812 1.78454 0.892271 0.451501i \(-0.149111\pi\)
0.892271 + 0.451501i \(0.149111\pi\)
\(830\) −3.46980 −0.120439
\(831\) 3.17691 0.110206
\(832\) −0.678936 −0.0235379
\(833\) −9.19407 −0.318555
\(834\) −0.553564 −0.0191684
\(835\) 2.24174 0.0775785
\(836\) 22.8191 0.789216
\(837\) −5.36245 −0.185353
\(838\) −44.1949 −1.52669
\(839\) 22.2169 0.767013 0.383506 0.923538i \(-0.374716\pi\)
0.383506 + 0.923538i \(0.374716\pi\)
\(840\) 0.211599 0.00730085
\(841\) −25.4111 −0.876245
\(842\) −83.9532 −2.89322
\(843\) −1.86107 −0.0640988
\(844\) 40.1954 1.38358
\(845\) 4.17493 0.143622
\(846\) 81.2623 2.79385
\(847\) −5.93666 −0.203986
\(848\) 53.8944 1.85074
\(849\) −0.188337 −0.00646372
\(850\) 17.7298 0.608126
\(851\) −0.240795 −0.00825435
\(852\) −4.69184 −0.160740
\(853\) −35.8616 −1.22788 −0.613939 0.789353i \(-0.710416\pi\)
−0.613939 + 0.789353i \(0.710416\pi\)
\(854\) 22.2636 0.761845
\(855\) −0.956364 −0.0327070
\(856\) −48.6706 −1.66353
\(857\) 36.4588 1.24541 0.622704 0.782457i \(-0.286034\pi\)
0.622704 + 0.782457i \(0.286034\pi\)
\(858\) 0.118220 0.00403598
\(859\) −8.92090 −0.304377 −0.152189 0.988351i \(-0.548632\pi\)
−0.152189 + 0.988351i \(0.548632\pi\)
\(860\) −3.80221 −0.129654
\(861\) 0.230101 0.00784183
\(862\) −12.0007 −0.408745
\(863\) −4.50948 −0.153505 −0.0767523 0.997050i \(-0.524455\pi\)
−0.0767523 + 0.997050i \(0.524455\pi\)
\(864\) −10.8068 −0.367654
\(865\) 0.426731 0.0145093
\(866\) 63.8799 2.17073
\(867\) 2.29034 0.0777840
\(868\) 16.4615 0.558740
\(869\) 57.6704 1.95633
\(870\) −0.242753 −0.00823008
\(871\) −0.191837 −0.00650014
\(872\) 53.0084 1.79509
\(873\) 35.2785 1.19400
\(874\) 17.5899 0.594986
\(875\) −1.79729 −0.0607597
\(876\) −5.17493 −0.174845
\(877\) −49.7290 −1.67923 −0.839615 0.543182i \(-0.817219\pi\)
−0.839615 + 0.543182i \(0.817219\pi\)
\(878\) −12.2618 −0.413817
\(879\) 0.435395 0.0146855
\(880\) 15.4550 0.520989
\(881\) −33.5212 −1.12936 −0.564678 0.825311i \(-0.691000\pi\)
−0.564678 + 0.825311i \(0.691000\pi\)
\(882\) −52.3206 −1.76173
\(883\) −36.6933 −1.23483 −0.617414 0.786638i \(-0.711820\pi\)
−0.617414 + 0.786638i \(0.711820\pi\)
\(884\) −0.432892 −0.0145597
\(885\) 0.523588 0.0176002
\(886\) 71.6265 2.40634
\(887\) −45.1876 −1.51725 −0.758625 0.651528i \(-0.774128\pi\)
−0.758625 + 0.651528i \(0.774128\pi\)
\(888\) −0.0419625 −0.00140817
\(889\) −0.355371 −0.0119188
\(890\) 13.2223 0.443214
\(891\) −40.7760 −1.36605
\(892\) −71.8444 −2.40553
\(893\) −10.3758 −0.347212
\(894\) 5.17232 0.172988
\(895\) −1.96330 −0.0656259
\(896\) 2.31483 0.0773332
\(897\) 0.0647952 0.00216345
\(898\) 28.7067 0.957957
\(899\) −11.2100 −0.373874
\(900\) 71.7390 2.39130
\(901\) 7.14919 0.238174
\(902\) 32.7497 1.09045
\(903\) 0.206142 0.00685997
\(904\) 148.832 4.95009
\(905\) 0.633982 0.0210743
\(906\) −1.46803 −0.0487720
\(907\) 38.4521 1.27678 0.638390 0.769713i \(-0.279601\pi\)
0.638390 + 0.769713i \(0.279601\pi\)
\(908\) −98.5792 −3.27147
\(909\) 10.5362 0.349462
\(910\) 0.0305370 0.00101229
\(911\) −49.4790 −1.63931 −0.819655 0.572857i \(-0.805835\pi\)
−0.819655 + 0.572857i \(0.805835\pi\)
\(912\) 1.57306 0.0520891
\(913\) 19.0376 0.630051
\(914\) 82.4397 2.72686
\(915\) 0.729159 0.0241052
\(916\) 47.3870 1.56571
\(917\) 10.7362 0.354541
\(918\) −3.28117 −0.108295
\(919\) −31.2817 −1.03189 −0.515944 0.856622i \(-0.672559\pi\)
−0.515944 + 0.856622i \(0.672559\pi\)
\(920\) 16.5064 0.544200
\(921\) −3.78587 −0.124749
\(922\) −30.2980 −0.997813
\(923\) −0.401921 −0.0132294
\(924\) −1.95585 −0.0643427
\(925\) 0.176354 0.00579848
\(926\) −26.1679 −0.859930
\(927\) 4.47984 0.147137
\(928\) −22.5912 −0.741591
\(929\) −45.2490 −1.48457 −0.742286 0.670083i \(-0.766258\pi\)
−0.742286 + 0.670083i \(0.766258\pi\)
\(930\) 0.758244 0.0248638
\(931\) 6.68043 0.218942
\(932\) −22.0535 −0.722387
\(933\) 3.35190 0.109736
\(934\) −2.73605 −0.0895262
\(935\) 2.05013 0.0670466
\(936\) −1.46228 −0.0477960
\(937\) −33.0824 −1.08076 −0.540378 0.841422i \(-0.681719\pi\)
−0.540378 + 0.841422i \(0.681719\pi\)
\(938\) 4.46362 0.145742
\(939\) 4.67601 0.152596
\(940\) −16.4031 −0.535010
\(941\) −41.1036 −1.33994 −0.669970 0.742388i \(-0.733693\pi\)
−0.669970 + 0.742388i \(0.733693\pi\)
\(942\) −6.62773 −0.215943
\(943\) 17.9497 0.584524
\(944\) 111.528 3.62993
\(945\) 0.164574 0.00535361
\(946\) 29.3396 0.953914
\(947\) 45.8518 1.48998 0.744992 0.667074i \(-0.232453\pi\)
0.744992 + 0.667074i \(0.232453\pi\)
\(948\) 9.27967 0.301390
\(949\) −0.443304 −0.0143903
\(950\) −12.8825 −0.417963
\(951\) 0.151619 0.00491659
\(952\) 5.97888 0.193777
\(953\) 22.9627 0.743834 0.371917 0.928266i \(-0.378701\pi\)
0.371917 + 0.928266i \(0.378701\pi\)
\(954\) 40.6838 1.31719
\(955\) −0.273875 −0.00886238
\(956\) 89.8629 2.90637
\(957\) 1.33190 0.0430541
\(958\) −77.8978 −2.51676
\(959\) −4.76062 −0.153728
\(960\) 0.517381 0.0166984
\(961\) 4.01469 0.129506
\(962\) −0.00605584 −0.000195248 0
\(963\) −18.8544 −0.607574
\(964\) 86.6507 2.79083
\(965\) −3.58319 −0.115347
\(966\) −1.50764 −0.0485076
\(967\) 29.0541 0.934317 0.467158 0.884174i \(-0.345278\pi\)
0.467158 + 0.884174i \(0.345278\pi\)
\(968\) −80.7040 −2.59393
\(969\) 0.208668 0.00670340
\(970\) −10.0152 −0.321569
\(971\) −17.3161 −0.555702 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(972\) −19.9402 −0.639581
\(973\) 0.784528 0.0251508
\(974\) −84.5755 −2.70997
\(975\) −0.0474548 −0.00151977
\(976\) 155.316 4.97154
\(977\) 19.5146 0.624328 0.312164 0.950028i \(-0.398946\pi\)
0.312164 + 0.950028i \(0.398946\pi\)
\(978\) −5.58102 −0.178461
\(979\) −72.5462 −2.31859
\(980\) 10.5611 0.337362
\(981\) 20.5348 0.655626
\(982\) −59.0439 −1.88416
\(983\) −15.8203 −0.504591 −0.252295 0.967650i \(-0.581185\pi\)
−0.252295 + 0.967650i \(0.581185\pi\)
\(984\) 3.12804 0.0997181
\(985\) 7.41628 0.236302
\(986\) −6.85915 −0.218440
\(987\) 0.889317 0.0283073
\(988\) 0.314541 0.0100069
\(989\) 16.0807 0.511337
\(990\) 11.6667 0.370792
\(991\) −15.0747 −0.478862 −0.239431 0.970913i \(-0.576961\pi\)
−0.239431 + 0.970913i \(0.576961\pi\)
\(992\) 70.5641 2.24041
\(993\) −3.46821 −0.110060
\(994\) 9.35183 0.296622
\(995\) −4.32400 −0.137080
\(996\) 3.06331 0.0970647
\(997\) −42.2096 −1.33679 −0.668396 0.743805i \(-0.733019\pi\)
−0.668396 + 0.743805i \(0.733019\pi\)
\(998\) 0.360512 0.0114118
\(999\) −0.0326370 −0.00103259
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 \(a_p\))