Properties

Label 8041.2.a.j.1.17
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73828 q^{2} +2.71256 q^{3} +1.02162 q^{4} -1.00305 q^{5} -4.71518 q^{6} +1.91856 q^{7} +1.70071 q^{8} +4.35796 q^{9} +O(q^{10})\) \(q-1.73828 q^{2} +2.71256 q^{3} +1.02162 q^{4} -1.00305 q^{5} -4.71518 q^{6} +1.91856 q^{7} +1.70071 q^{8} +4.35796 q^{9} +1.74357 q^{10} +1.00000 q^{11} +2.77119 q^{12} +6.51880 q^{13} -3.33500 q^{14} -2.72082 q^{15} -4.99953 q^{16} +1.00000 q^{17} -7.57536 q^{18} -0.645703 q^{19} -1.02473 q^{20} +5.20421 q^{21} -1.73828 q^{22} +4.75758 q^{23} +4.61326 q^{24} -3.99390 q^{25} -11.3315 q^{26} +3.68355 q^{27} +1.96003 q^{28} +6.97508 q^{29} +4.72954 q^{30} +5.23359 q^{31} +5.28917 q^{32} +2.71256 q^{33} -1.73828 q^{34} -1.92441 q^{35} +4.45216 q^{36} -0.654072 q^{37} +1.12241 q^{38} +17.6826 q^{39} -1.70589 q^{40} +9.47139 q^{41} -9.04637 q^{42} +1.00000 q^{43} +1.02162 q^{44} -4.37124 q^{45} -8.27000 q^{46} +1.37344 q^{47} -13.5615 q^{48} -3.31912 q^{49} +6.94251 q^{50} +2.71256 q^{51} +6.65971 q^{52} -3.32487 q^{53} -6.40304 q^{54} -1.00305 q^{55} +3.26291 q^{56} -1.75151 q^{57} -12.1246 q^{58} -6.00887 q^{59} -2.77963 q^{60} -0.664019 q^{61} -9.09744 q^{62} +8.36103 q^{63} +0.805005 q^{64} -6.53865 q^{65} -4.71518 q^{66} +12.9481 q^{67} +1.02162 q^{68} +12.9052 q^{69} +3.34515 q^{70} -12.9188 q^{71} +7.41161 q^{72} +1.15650 q^{73} +1.13696 q^{74} -10.8337 q^{75} -0.659660 q^{76} +1.91856 q^{77} -30.7373 q^{78} +10.1389 q^{79} +5.01476 q^{80} -3.08204 q^{81} -16.4639 q^{82} -15.9249 q^{83} +5.31670 q^{84} -1.00305 q^{85} -1.73828 q^{86} +18.9203 q^{87} +1.70071 q^{88} +12.1599 q^{89} +7.59843 q^{90} +12.5067 q^{91} +4.86042 q^{92} +14.1964 q^{93} -2.38742 q^{94} +0.647670 q^{95} +14.3472 q^{96} -2.72699 q^{97} +5.76955 q^{98} +4.35796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 82q + 8q^{2} + 6q^{3} + 98q^{4} + 11q^{5} + 10q^{6} + 8q^{7} + 30q^{8} + 108q^{9} + O(q^{10}) \) \( 82q + 8q^{2} + 6q^{3} + 98q^{4} + 11q^{5} + 10q^{6} + 8q^{7} + 30q^{8} + 108q^{9} + q^{10} + 82q^{11} + 3q^{12} + 26q^{13} + 17q^{14} + 66q^{15} + 122q^{16} + 82q^{17} + 18q^{18} + 12q^{19} + 9q^{20} + 22q^{21} + 8q^{22} + 50q^{23} + 15q^{24} + 117q^{25} + 36q^{26} + 30q^{27} + 11q^{28} + 33q^{29} - 26q^{30} + 40q^{31} + 58q^{32} + 6q^{33} + 8q^{34} + 16q^{35} + 160q^{36} + 31q^{37} + 18q^{38} + 41q^{39} - 29q^{40} + 42q^{41} - 51q^{42} + 82q^{43} + 98q^{44} - 2q^{45} - 19q^{46} + 84q^{47} - 46q^{48} + 136q^{49} + 59q^{50} + 6q^{51} + 45q^{52} + 83q^{53} + 24q^{54} + 11q^{55} + 21q^{56} + 23q^{57} + 14q^{58} + 96q^{59} + 184q^{60} - 6q^{61} - 23q^{62} + 8q^{63} + 148q^{64} + 5q^{65} + 10q^{66} + 78q^{67} + 98q^{68} + 61q^{69} - 3q^{70} + 155q^{71} + 50q^{72} - 23q^{73} + 10q^{74} - 19q^{75} + 44q^{76} + 8q^{77} - 27q^{78} + 31q^{79} + 19q^{80} + 150q^{81} - 12q^{82} + 54q^{83} + 8q^{84} + 11q^{85} + 8q^{86} + 20q^{87} + 30q^{88} + 25q^{89} - 81q^{90} - 14q^{91} + 60q^{92} + 36q^{93} + 19q^{94} + 111q^{95} - 6q^{96} + 2q^{97} - 5q^{98} + 108q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73828 −1.22915 −0.614575 0.788859i \(-0.710672\pi\)
−0.614575 + 0.788859i \(0.710672\pi\)
\(3\) 2.71256 1.56610 0.783048 0.621962i \(-0.213664\pi\)
0.783048 + 0.621962i \(0.213664\pi\)
\(4\) 1.02162 0.510808
\(5\) −1.00305 −0.448576 −0.224288 0.974523i \(-0.572006\pi\)
−0.224288 + 0.974523i \(0.572006\pi\)
\(6\) −4.71518 −1.92496
\(7\) 1.91856 0.725149 0.362574 0.931955i \(-0.381898\pi\)
0.362574 + 0.931955i \(0.381898\pi\)
\(8\) 1.70071 0.601290
\(9\) 4.35796 1.45265
\(10\) 1.74357 0.551366
\(11\) 1.00000 0.301511
\(12\) 2.77119 0.799974
\(13\) 6.51880 1.80799 0.903995 0.427543i \(-0.140621\pi\)
0.903995 + 0.427543i \(0.140621\pi\)
\(14\) −3.33500 −0.891316
\(15\) −2.72082 −0.702512
\(16\) −4.99953 −1.24988
\(17\) 1.00000 0.242536
\(18\) −7.57536 −1.78553
\(19\) −0.645703 −0.148135 −0.0740673 0.997253i \(-0.523598\pi\)
−0.0740673 + 0.997253i \(0.523598\pi\)
\(20\) −1.02473 −0.229136
\(21\) 5.20421 1.13565
\(22\) −1.73828 −0.370602
\(23\) 4.75758 0.992024 0.496012 0.868316i \(-0.334797\pi\)
0.496012 + 0.868316i \(0.334797\pi\)
\(24\) 4.61326 0.941678
\(25\) −3.99390 −0.798780
\(26\) −11.3315 −2.22229
\(27\) 3.68355 0.708900
\(28\) 1.96003 0.370411
\(29\) 6.97508 1.29524 0.647620 0.761964i \(-0.275765\pi\)
0.647620 + 0.761964i \(0.275765\pi\)
\(30\) 4.72954 0.863492
\(31\) 5.23359 0.939980 0.469990 0.882672i \(-0.344257\pi\)
0.469990 + 0.882672i \(0.344257\pi\)
\(32\) 5.28917 0.935003
\(33\) 2.71256 0.472195
\(34\) −1.73828 −0.298112
\(35\) −1.92441 −0.325284
\(36\) 4.45216 0.742027
\(37\) −0.654072 −0.107529 −0.0537644 0.998554i \(-0.517122\pi\)
−0.0537644 + 0.998554i \(0.517122\pi\)
\(38\) 1.12241 0.182079
\(39\) 17.6826 2.83149
\(40\) −1.70589 −0.269724
\(41\) 9.47139 1.47918 0.739591 0.673056i \(-0.235019\pi\)
0.739591 + 0.673056i \(0.235019\pi\)
\(42\) −9.04637 −1.39589
\(43\) 1.00000 0.152499
\(44\) 1.02162 0.154014
\(45\) −4.37124 −0.651625
\(46\) −8.27000 −1.21935
\(47\) 1.37344 0.200336 0.100168 0.994971i \(-0.468062\pi\)
0.100168 + 0.994971i \(0.468062\pi\)
\(48\) −13.5615 −1.95744
\(49\) −3.31912 −0.474160
\(50\) 6.94251 0.981820
\(51\) 2.71256 0.379834
\(52\) 6.65971 0.923535
\(53\) −3.32487 −0.456706 −0.228353 0.973578i \(-0.573334\pi\)
−0.228353 + 0.973578i \(0.573334\pi\)
\(54\) −6.40304 −0.871344
\(55\) −1.00305 −0.135251
\(56\) 3.26291 0.436025
\(57\) −1.75151 −0.231993
\(58\) −12.1246 −1.59204
\(59\) −6.00887 −0.782288 −0.391144 0.920330i \(-0.627921\pi\)
−0.391144 + 0.920330i \(0.627921\pi\)
\(60\) −2.77963 −0.358849
\(61\) −0.664019 −0.0850189 −0.0425095 0.999096i \(-0.513535\pi\)
−0.0425095 + 0.999096i \(0.513535\pi\)
\(62\) −9.09744 −1.15538
\(63\) 8.36103 1.05339
\(64\) 0.805005 0.100626
\(65\) −6.53865 −0.811020
\(66\) −4.71518 −0.580399
\(67\) 12.9481 1.58186 0.790931 0.611906i \(-0.209597\pi\)
0.790931 + 0.611906i \(0.209597\pi\)
\(68\) 1.02162 0.123889
\(69\) 12.9052 1.55360
\(70\) 3.34515 0.399822
\(71\) −12.9188 −1.53318 −0.766588 0.642140i \(-0.778047\pi\)
−0.766588 + 0.642140i \(0.778047\pi\)
\(72\) 7.41161 0.873467
\(73\) 1.15650 0.135358 0.0676788 0.997707i \(-0.478441\pi\)
0.0676788 + 0.997707i \(0.478441\pi\)
\(74\) 1.13696 0.132169
\(75\) −10.8337 −1.25097
\(76\) −0.659660 −0.0756682
\(77\) 1.91856 0.218641
\(78\) −30.7373 −3.48032
\(79\) 10.1389 1.14071 0.570356 0.821398i \(-0.306805\pi\)
0.570356 + 0.821398i \(0.306805\pi\)
\(80\) 5.01476 0.560667
\(81\) −3.08204 −0.342449
\(82\) −16.4639 −1.81814
\(83\) −15.9249 −1.74799 −0.873994 0.485938i \(-0.838478\pi\)
−0.873994 + 0.485938i \(0.838478\pi\)
\(84\) 5.31670 0.580100
\(85\) −1.00305 −0.108796
\(86\) −1.73828 −0.187443
\(87\) 18.9203 2.02847
\(88\) 1.70071 0.181296
\(89\) 12.1599 1.28895 0.644475 0.764625i \(-0.277076\pi\)
0.644475 + 0.764625i \(0.277076\pi\)
\(90\) 7.59843 0.800945
\(91\) 12.5067 1.31106
\(92\) 4.86042 0.506734
\(93\) 14.1964 1.47210
\(94\) −2.38742 −0.246243
\(95\) 0.647670 0.0664495
\(96\) 14.3472 1.46430
\(97\) −2.72699 −0.276884 −0.138442 0.990371i \(-0.544209\pi\)
−0.138442 + 0.990371i \(0.544209\pi\)
\(98\) 5.76955 0.582813
\(99\) 4.35796 0.437992
\(100\) −4.08023 −0.408023
\(101\) −8.59300 −0.855035 −0.427518 0.904007i \(-0.640612\pi\)
−0.427518 + 0.904007i \(0.640612\pi\)
\(102\) −4.71518 −0.466873
\(103\) −13.5679 −1.33688 −0.668440 0.743766i \(-0.733038\pi\)
−0.668440 + 0.743766i \(0.733038\pi\)
\(104\) 11.0866 1.08713
\(105\) −5.22006 −0.509426
\(106\) 5.77955 0.561360
\(107\) 7.34589 0.710154 0.355077 0.934837i \(-0.384455\pi\)
0.355077 + 0.934837i \(0.384455\pi\)
\(108\) 3.76317 0.362112
\(109\) −13.4662 −1.28983 −0.644916 0.764254i \(-0.723108\pi\)
−0.644916 + 0.764254i \(0.723108\pi\)
\(110\) 1.74357 0.166243
\(111\) −1.77421 −0.168400
\(112\) −9.59192 −0.906351
\(113\) 19.2657 1.81237 0.906185 0.422882i \(-0.138982\pi\)
0.906185 + 0.422882i \(0.138982\pi\)
\(114\) 3.04461 0.285154
\(115\) −4.77207 −0.444998
\(116\) 7.12585 0.661618
\(117\) 28.4087 2.62639
\(118\) 10.4451 0.961548
\(119\) 1.91856 0.175874
\(120\) −4.62731 −0.422414
\(121\) 1.00000 0.0909091
\(122\) 1.15425 0.104501
\(123\) 25.6917 2.31654
\(124\) 5.34672 0.480149
\(125\) 9.02129 0.806889
\(126\) −14.5338 −1.29477
\(127\) 3.91481 0.347383 0.173692 0.984800i \(-0.444430\pi\)
0.173692 + 0.984800i \(0.444430\pi\)
\(128\) −11.9777 −1.05869
\(129\) 2.71256 0.238827
\(130\) 11.3660 0.996865
\(131\) −8.42384 −0.735994 −0.367997 0.929827i \(-0.619956\pi\)
−0.367997 + 0.929827i \(0.619956\pi\)
\(132\) 2.77119 0.241201
\(133\) −1.23882 −0.107420
\(134\) −22.5074 −1.94434
\(135\) −3.69477 −0.317995
\(136\) 1.70071 0.145834
\(137\) 16.7671 1.43251 0.716253 0.697841i \(-0.245856\pi\)
0.716253 + 0.697841i \(0.245856\pi\)
\(138\) −22.4329 −1.90961
\(139\) 18.7394 1.58945 0.794726 0.606968i \(-0.207615\pi\)
0.794726 + 0.606968i \(0.207615\pi\)
\(140\) −1.96600 −0.166158
\(141\) 3.72552 0.313746
\(142\) 22.4564 1.88450
\(143\) 6.51880 0.545130
\(144\) −21.7878 −1.81565
\(145\) −6.99632 −0.581013
\(146\) −2.01031 −0.166375
\(147\) −9.00329 −0.742579
\(148\) −0.668210 −0.0549265
\(149\) −13.6632 −1.11933 −0.559665 0.828719i \(-0.689070\pi\)
−0.559665 + 0.828719i \(0.689070\pi\)
\(150\) 18.8320 1.53762
\(151\) 5.01324 0.407972 0.203986 0.978974i \(-0.434610\pi\)
0.203986 + 0.978974i \(0.434610\pi\)
\(152\) −1.09815 −0.0890718
\(153\) 4.35796 0.352320
\(154\) −3.33500 −0.268742
\(155\) −5.24953 −0.421652
\(156\) 18.0648 1.44634
\(157\) −22.6278 −1.80589 −0.902946 0.429753i \(-0.858601\pi\)
−0.902946 + 0.429753i \(0.858601\pi\)
\(158\) −17.6242 −1.40211
\(159\) −9.01890 −0.715245
\(160\) −5.30528 −0.419419
\(161\) 9.12772 0.719365
\(162\) 5.35746 0.420921
\(163\) −17.2810 −1.35355 −0.676777 0.736188i \(-0.736624\pi\)
−0.676777 + 0.736188i \(0.736624\pi\)
\(164\) 9.67612 0.755578
\(165\) −2.72082 −0.211815
\(166\) 27.6820 2.14854
\(167\) −13.1928 −1.02089 −0.510444 0.859911i \(-0.670519\pi\)
−0.510444 + 0.859911i \(0.670519\pi\)
\(168\) 8.85083 0.682856
\(169\) 29.4948 2.26883
\(170\) 1.74357 0.133726
\(171\) −2.81395 −0.215188
\(172\) 1.02162 0.0778974
\(173\) −2.00093 −0.152128 −0.0760638 0.997103i \(-0.524235\pi\)
−0.0760638 + 0.997103i \(0.524235\pi\)
\(174\) −32.8888 −2.49329
\(175\) −7.66255 −0.579234
\(176\) −4.99953 −0.376854
\(177\) −16.2994 −1.22514
\(178\) −21.1374 −1.58431
\(179\) 3.38728 0.253177 0.126589 0.991955i \(-0.459597\pi\)
0.126589 + 0.991955i \(0.459597\pi\)
\(180\) −4.46572 −0.332855
\(181\) −2.97143 −0.220865 −0.110432 0.993884i \(-0.535224\pi\)
−0.110432 + 0.993884i \(0.535224\pi\)
\(182\) −21.7402 −1.61149
\(183\) −1.80119 −0.133148
\(184\) 8.09125 0.596495
\(185\) 0.656064 0.0482348
\(186\) −24.6773 −1.80943
\(187\) 1.00000 0.0731272
\(188\) 1.40312 0.102333
\(189\) 7.06713 0.514058
\(190\) −1.12583 −0.0816764
\(191\) 26.6453 1.92799 0.963993 0.265928i \(-0.0856782\pi\)
0.963993 + 0.265928i \(0.0856782\pi\)
\(192\) 2.18362 0.157589
\(193\) −4.80106 −0.345588 −0.172794 0.984958i \(-0.555279\pi\)
−0.172794 + 0.984958i \(0.555279\pi\)
\(194\) 4.74028 0.340332
\(195\) −17.7365 −1.27014
\(196\) −3.39086 −0.242204
\(197\) −6.94457 −0.494780 −0.247390 0.968916i \(-0.579573\pi\)
−0.247390 + 0.968916i \(0.579573\pi\)
\(198\) −7.57536 −0.538357
\(199\) −15.0763 −1.06873 −0.534366 0.845253i \(-0.679449\pi\)
−0.534366 + 0.845253i \(0.679449\pi\)
\(200\) −6.79245 −0.480299
\(201\) 35.1224 2.47735
\(202\) 14.9370 1.05097
\(203\) 13.3821 0.939241
\(204\) 2.77119 0.194022
\(205\) −9.50023 −0.663525
\(206\) 23.5847 1.64323
\(207\) 20.7334 1.44107
\(208\) −32.5910 −2.25978
\(209\) −0.645703 −0.0446642
\(210\) 9.07392 0.626160
\(211\) −20.5176 −1.41249 −0.706245 0.707967i \(-0.749613\pi\)
−0.706245 + 0.707967i \(0.749613\pi\)
\(212\) −3.39674 −0.233289
\(213\) −35.0429 −2.40110
\(214\) −12.7692 −0.872885
\(215\) −1.00305 −0.0684071
\(216\) 6.26464 0.426255
\(217\) 10.0410 0.681625
\(218\) 23.4081 1.58540
\(219\) 3.13706 0.211983
\(220\) −1.02473 −0.0690871
\(221\) 6.51880 0.438502
\(222\) 3.08407 0.206989
\(223\) 16.6898 1.11763 0.558815 0.829292i \(-0.311256\pi\)
0.558815 + 0.829292i \(0.311256\pi\)
\(224\) 10.1476 0.678016
\(225\) −17.4053 −1.16035
\(226\) −33.4893 −2.22767
\(227\) −5.94499 −0.394583 −0.197291 0.980345i \(-0.563214\pi\)
−0.197291 + 0.980345i \(0.563214\pi\)
\(228\) −1.78937 −0.118504
\(229\) −25.5371 −1.68754 −0.843768 0.536708i \(-0.819668\pi\)
−0.843768 + 0.536708i \(0.819668\pi\)
\(230\) 8.29519 0.546969
\(231\) 5.20421 0.342412
\(232\) 11.8626 0.778815
\(233\) 18.3218 1.20030 0.600150 0.799888i \(-0.295108\pi\)
0.600150 + 0.799888i \(0.295108\pi\)
\(234\) −49.3823 −3.22822
\(235\) −1.37762 −0.0898659
\(236\) −6.13875 −0.399599
\(237\) 27.5023 1.78646
\(238\) −3.33500 −0.216176
\(239\) −1.51527 −0.0980149 −0.0490074 0.998798i \(-0.515606\pi\)
−0.0490074 + 0.998798i \(0.515606\pi\)
\(240\) 13.6028 0.878058
\(241\) −6.25007 −0.402602 −0.201301 0.979529i \(-0.564517\pi\)
−0.201301 + 0.979529i \(0.564517\pi\)
\(242\) −1.73828 −0.111741
\(243\) −19.4109 −1.24521
\(244\) −0.678372 −0.0434283
\(245\) 3.32923 0.212696
\(246\) −44.6593 −2.84737
\(247\) −4.20921 −0.267826
\(248\) 8.90080 0.565201
\(249\) −43.1972 −2.73751
\(250\) −15.6815 −0.991787
\(251\) −14.2921 −0.902107 −0.451053 0.892497i \(-0.648952\pi\)
−0.451053 + 0.892497i \(0.648952\pi\)
\(252\) 8.54175 0.538080
\(253\) 4.75758 0.299107
\(254\) −6.80503 −0.426986
\(255\) −2.72082 −0.170384
\(256\) 19.2105 1.20066
\(257\) −19.6832 −1.22781 −0.613903 0.789382i \(-0.710401\pi\)
−0.613903 + 0.789382i \(0.710401\pi\)
\(258\) −4.71518 −0.293554
\(259\) −1.25488 −0.0779743
\(260\) −6.67999 −0.414275
\(261\) 30.3971 1.88154
\(262\) 14.6430 0.904647
\(263\) −18.1031 −1.11629 −0.558143 0.829745i \(-0.688486\pi\)
−0.558143 + 0.829745i \(0.688486\pi\)
\(264\) 4.61326 0.283927
\(265\) 3.33500 0.204867
\(266\) 2.15342 0.132035
\(267\) 32.9845 2.01862
\(268\) 13.2280 0.808027
\(269\) 1.47461 0.0899086 0.0449543 0.998989i \(-0.485686\pi\)
0.0449543 + 0.998989i \(0.485686\pi\)
\(270\) 6.42254 0.390864
\(271\) −8.97382 −0.545121 −0.272560 0.962139i \(-0.587870\pi\)
−0.272560 + 0.962139i \(0.587870\pi\)
\(272\) −4.99953 −0.303141
\(273\) 33.9252 2.05325
\(274\) −29.1458 −1.76076
\(275\) −3.99390 −0.240841
\(276\) 13.1842 0.793593
\(277\) 14.9936 0.900879 0.450439 0.892807i \(-0.351267\pi\)
0.450439 + 0.892807i \(0.351267\pi\)
\(278\) −32.5742 −1.95367
\(279\) 22.8078 1.36547
\(280\) −3.27285 −0.195590
\(281\) 20.9991 1.25270 0.626349 0.779542i \(-0.284548\pi\)
0.626349 + 0.779542i \(0.284548\pi\)
\(282\) −6.47600 −0.385640
\(283\) 12.6634 0.752762 0.376381 0.926465i \(-0.377168\pi\)
0.376381 + 0.926465i \(0.377168\pi\)
\(284\) −13.1980 −0.783158
\(285\) 1.75684 0.104066
\(286\) −11.3315 −0.670046
\(287\) 18.1715 1.07263
\(288\) 23.0500 1.35824
\(289\) 1.00000 0.0588235
\(290\) 12.1616 0.714151
\(291\) −7.39712 −0.433627
\(292\) 1.18149 0.0691417
\(293\) −16.8401 −0.983809 −0.491904 0.870649i \(-0.663699\pi\)
−0.491904 + 0.870649i \(0.663699\pi\)
\(294\) 15.6502 0.912740
\(295\) 6.02717 0.350915
\(296\) −1.11238 −0.0646560
\(297\) 3.68355 0.213741
\(298\) 23.7504 1.37582
\(299\) 31.0137 1.79357
\(300\) −11.0679 −0.639003
\(301\) 1.91856 0.110584
\(302\) −8.71441 −0.501458
\(303\) −23.3090 −1.33907
\(304\) 3.22821 0.185151
\(305\) 0.666041 0.0381374
\(306\) −7.57536 −0.433054
\(307\) −11.2413 −0.641578 −0.320789 0.947151i \(-0.603948\pi\)
−0.320789 + 0.947151i \(0.603948\pi\)
\(308\) 1.96003 0.111683
\(309\) −36.8036 −2.09368
\(310\) 9.12515 0.518274
\(311\) 5.57659 0.316219 0.158110 0.987422i \(-0.449460\pi\)
0.158110 + 0.987422i \(0.449460\pi\)
\(312\) 30.0729 1.70254
\(313\) −27.9294 −1.57866 −0.789331 0.613967i \(-0.789573\pi\)
−0.789331 + 0.613967i \(0.789573\pi\)
\(314\) 39.3334 2.21971
\(315\) −8.38649 −0.472525
\(316\) 10.3580 0.582684
\(317\) 34.2628 1.92439 0.962194 0.272364i \(-0.0878055\pi\)
0.962194 + 0.272364i \(0.0878055\pi\)
\(318\) 15.6774 0.879143
\(319\) 6.97508 0.390529
\(320\) −0.807456 −0.0451382
\(321\) 19.9261 1.11217
\(322\) −15.8665 −0.884207
\(323\) −0.645703 −0.0359279
\(324\) −3.14866 −0.174926
\(325\) −26.0354 −1.44419
\(326\) 30.0392 1.66372
\(327\) −36.5279 −2.02000
\(328\) 16.1080 0.889418
\(329\) 2.63502 0.145274
\(330\) 4.72954 0.260353
\(331\) 3.43714 0.188922 0.0944610 0.995529i \(-0.469887\pi\)
0.0944610 + 0.995529i \(0.469887\pi\)
\(332\) −16.2691 −0.892885
\(333\) −2.85042 −0.156202
\(334\) 22.9327 1.25482
\(335\) −12.9875 −0.709584
\(336\) −26.0186 −1.41943
\(337\) −0.346351 −0.0188669 −0.00943346 0.999956i \(-0.503003\pi\)
−0.00943346 + 0.999956i \(0.503003\pi\)
\(338\) −51.2702 −2.78873
\(339\) 52.2594 2.83834
\(340\) −1.02473 −0.0555736
\(341\) 5.23359 0.283415
\(342\) 4.89143 0.264498
\(343\) −19.7979 −1.06898
\(344\) 1.70071 0.0916959
\(345\) −12.9445 −0.696909
\(346\) 3.47817 0.186988
\(347\) 35.3760 1.89908 0.949542 0.313640i \(-0.101549\pi\)
0.949542 + 0.313640i \(0.101549\pi\)
\(348\) 19.3293 1.03616
\(349\) −8.72306 −0.466934 −0.233467 0.972365i \(-0.575007\pi\)
−0.233467 + 0.972365i \(0.575007\pi\)
\(350\) 13.3196 0.711965
\(351\) 24.0123 1.28168
\(352\) 5.28917 0.281914
\(353\) 7.34047 0.390694 0.195347 0.980734i \(-0.437417\pi\)
0.195347 + 0.980734i \(0.437417\pi\)
\(354\) 28.3329 1.50588
\(355\) 12.9581 0.687745
\(356\) 12.4228 0.658406
\(357\) 5.20421 0.275436
\(358\) −5.88804 −0.311193
\(359\) −3.09087 −0.163130 −0.0815650 0.996668i \(-0.525992\pi\)
−0.0815650 + 0.996668i \(0.525992\pi\)
\(360\) −7.43419 −0.391816
\(361\) −18.5831 −0.978056
\(362\) 5.16518 0.271476
\(363\) 2.71256 0.142372
\(364\) 12.7771 0.669700
\(365\) −1.16002 −0.0607182
\(366\) 3.13097 0.163658
\(367\) 26.5980 1.38840 0.694201 0.719781i \(-0.255758\pi\)
0.694201 + 0.719781i \(0.255758\pi\)
\(368\) −23.7857 −1.23991
\(369\) 41.2760 2.14874
\(370\) −1.14042 −0.0592877
\(371\) −6.37897 −0.331180
\(372\) 14.5033 0.751959
\(373\) −37.6039 −1.94706 −0.973529 0.228565i \(-0.926597\pi\)
−0.973529 + 0.228565i \(0.926597\pi\)
\(374\) −1.73828 −0.0898843
\(375\) 24.4708 1.26366
\(376\) 2.33581 0.120460
\(377\) 45.4692 2.34178
\(378\) −12.2846 −0.631854
\(379\) 7.62421 0.391629 0.195815 0.980641i \(-0.437265\pi\)
0.195815 + 0.980641i \(0.437265\pi\)
\(380\) 0.661669 0.0339429
\(381\) 10.6191 0.544035
\(382\) −46.3170 −2.36978
\(383\) 33.7237 1.72320 0.861601 0.507586i \(-0.169462\pi\)
0.861601 + 0.507586i \(0.169462\pi\)
\(384\) −32.4901 −1.65800
\(385\) −1.92441 −0.0980768
\(386\) 8.34559 0.424779
\(387\) 4.35796 0.221528
\(388\) −2.78594 −0.141435
\(389\) 24.4515 1.23974 0.619871 0.784704i \(-0.287185\pi\)
0.619871 + 0.784704i \(0.287185\pi\)
\(390\) 30.8309 1.56119
\(391\) 4.75758 0.240601
\(392\) −5.64484 −0.285108
\(393\) −22.8501 −1.15264
\(394\) 12.0716 0.608159
\(395\) −10.1697 −0.511696
\(396\) 4.45216 0.223730
\(397\) 0.404617 0.0203072 0.0101536 0.999948i \(-0.496768\pi\)
0.0101536 + 0.999948i \(0.496768\pi\)
\(398\) 26.2068 1.31363
\(399\) −3.36038 −0.168229
\(400\) 19.9676 0.998382
\(401\) 23.5867 1.17786 0.588931 0.808184i \(-0.299549\pi\)
0.588931 + 0.808184i \(0.299549\pi\)
\(402\) −61.0526 −3.04503
\(403\) 34.1167 1.69948
\(404\) −8.77874 −0.436759
\(405\) 3.09143 0.153614
\(406\) −23.2619 −1.15447
\(407\) −0.654072 −0.0324211
\(408\) 4.61326 0.228390
\(409\) 18.7932 0.929265 0.464633 0.885504i \(-0.346186\pi\)
0.464633 + 0.885504i \(0.346186\pi\)
\(410\) 16.5141 0.815571
\(411\) 45.4816 2.24344
\(412\) −13.8611 −0.682889
\(413\) −11.5284 −0.567275
\(414\) −36.0404 −1.77129
\(415\) 15.9734 0.784104
\(416\) 34.4791 1.69048
\(417\) 50.8316 2.48923
\(418\) 1.12241 0.0548990
\(419\) −4.88463 −0.238630 −0.119315 0.992856i \(-0.538070\pi\)
−0.119315 + 0.992856i \(0.538070\pi\)
\(420\) −5.33289 −0.260219
\(421\) −16.4314 −0.800815 −0.400408 0.916337i \(-0.631131\pi\)
−0.400408 + 0.916337i \(0.631131\pi\)
\(422\) 35.6654 1.73616
\(423\) 5.98538 0.291019
\(424\) −5.65463 −0.274613
\(425\) −3.99390 −0.193733
\(426\) 60.9143 2.95131
\(427\) −1.27396 −0.0616513
\(428\) 7.50468 0.362752
\(429\) 17.6826 0.853725
\(430\) 1.74357 0.0840826
\(431\) 37.8404 1.82271 0.911354 0.411623i \(-0.135038\pi\)
0.911354 + 0.411623i \(0.135038\pi\)
\(432\) −18.4160 −0.886042
\(433\) −16.3296 −0.784751 −0.392375 0.919805i \(-0.628347\pi\)
−0.392375 + 0.919805i \(0.628347\pi\)
\(434\) −17.4540 −0.837819
\(435\) −18.9779 −0.909921
\(436\) −13.7573 −0.658856
\(437\) −3.07199 −0.146953
\(438\) −5.45309 −0.260559
\(439\) −13.7765 −0.657514 −0.328757 0.944414i \(-0.606630\pi\)
−0.328757 + 0.944414i \(0.606630\pi\)
\(440\) −1.70589 −0.0813249
\(441\) −14.4646 −0.688790
\(442\) −11.3315 −0.538984
\(443\) 7.54597 0.358520 0.179260 0.983802i \(-0.442630\pi\)
0.179260 + 0.983802i \(0.442630\pi\)
\(444\) −1.81256 −0.0860201
\(445\) −12.1970 −0.578191
\(446\) −29.0115 −1.37373
\(447\) −37.0621 −1.75298
\(448\) 1.54445 0.0729685
\(449\) 10.0748 0.475461 0.237730 0.971331i \(-0.423597\pi\)
0.237730 + 0.971331i \(0.423597\pi\)
\(450\) 30.2552 1.42624
\(451\) 9.47139 0.445990
\(452\) 19.6822 0.925772
\(453\) 13.5987 0.638922
\(454\) 10.3340 0.485001
\(455\) −12.5448 −0.588110
\(456\) −2.97880 −0.139495
\(457\) 14.8430 0.694327 0.347163 0.937805i \(-0.387145\pi\)
0.347163 + 0.937805i \(0.387145\pi\)
\(458\) 44.3905 2.07423
\(459\) 3.68355 0.171934
\(460\) −4.87522 −0.227308
\(461\) 3.00223 0.139828 0.0699139 0.997553i \(-0.477728\pi\)
0.0699139 + 0.997553i \(0.477728\pi\)
\(462\) −9.04637 −0.420875
\(463\) −7.04016 −0.327184 −0.163592 0.986528i \(-0.552308\pi\)
−0.163592 + 0.986528i \(0.552308\pi\)
\(464\) −34.8721 −1.61890
\(465\) −14.2396 −0.660348
\(466\) −31.8484 −1.47535
\(467\) −32.8334 −1.51935 −0.759675 0.650303i \(-0.774642\pi\)
−0.759675 + 0.650303i \(0.774642\pi\)
\(468\) 29.0228 1.34158
\(469\) 24.8417 1.14708
\(470\) 2.39469 0.110459
\(471\) −61.3791 −2.82820
\(472\) −10.2193 −0.470382
\(473\) 1.00000 0.0459800
\(474\) −47.8066 −2.19583
\(475\) 2.57887 0.118327
\(476\) 1.96003 0.0898380
\(477\) −14.4897 −0.663436
\(478\) 2.63397 0.120475
\(479\) −34.1397 −1.55988 −0.779942 0.625851i \(-0.784752\pi\)
−0.779942 + 0.625851i \(0.784752\pi\)
\(480\) −14.3909 −0.656851
\(481\) −4.26376 −0.194411
\(482\) 10.8644 0.494858
\(483\) 24.7594 1.12659
\(484\) 1.02162 0.0464371
\(485\) 2.73530 0.124203
\(486\) 33.7415 1.53055
\(487\) 28.1357 1.27495 0.637476 0.770471i \(-0.279979\pi\)
0.637476 + 0.770471i \(0.279979\pi\)
\(488\) −1.12930 −0.0511211
\(489\) −46.8758 −2.11980
\(490\) −5.78712 −0.261436
\(491\) −30.6172 −1.38174 −0.690868 0.722981i \(-0.742772\pi\)
−0.690868 + 0.722981i \(0.742772\pi\)
\(492\) 26.2470 1.18331
\(493\) 6.97508 0.314142
\(494\) 7.31679 0.329198
\(495\) −4.37124 −0.196472
\(496\) −26.1655 −1.17487
\(497\) −24.7855 −1.11178
\(498\) 75.0889 3.36481
\(499\) −10.2086 −0.457001 −0.228501 0.973544i \(-0.573382\pi\)
−0.228501 + 0.973544i \(0.573382\pi\)
\(500\) 9.21629 0.412165
\(501\) −35.7862 −1.59881
\(502\) 24.8436 1.10882
\(503\) 35.4049 1.57863 0.789313 0.613991i \(-0.210437\pi\)
0.789313 + 0.613991i \(0.210437\pi\)
\(504\) 14.2196 0.633393
\(505\) 8.61917 0.383548
\(506\) −8.27000 −0.367647
\(507\) 80.0062 3.55320
\(508\) 3.99943 0.177446
\(509\) 0.0822089 0.00364384 0.00182192 0.999998i \(-0.499420\pi\)
0.00182192 + 0.999998i \(0.499420\pi\)
\(510\) 4.72954 0.209428
\(511\) 2.21881 0.0981544
\(512\) −9.43793 −0.417101
\(513\) −2.37848 −0.105013
\(514\) 34.2149 1.50916
\(515\) 13.6092 0.599692
\(516\) 2.77119 0.121995
\(517\) 1.37344 0.0604036
\(518\) 2.18133 0.0958421
\(519\) −5.42763 −0.238246
\(520\) −11.1203 −0.487659
\(521\) −25.0397 −1.09701 −0.548504 0.836148i \(-0.684803\pi\)
−0.548504 + 0.836148i \(0.684803\pi\)
\(522\) −52.8387 −2.31269
\(523\) 7.13145 0.311837 0.155918 0.987770i \(-0.450166\pi\)
0.155918 + 0.987770i \(0.450166\pi\)
\(524\) −8.60592 −0.375951
\(525\) −20.7851 −0.907136
\(526\) 31.4683 1.37208
\(527\) 5.23359 0.227979
\(528\) −13.5615 −0.590189
\(529\) −0.365427 −0.0158881
\(530\) −5.79715 −0.251812
\(531\) −26.1864 −1.13639
\(532\) −1.26560 −0.0548707
\(533\) 61.7421 2.67435
\(534\) −57.3363 −2.48118
\(535\) −7.36826 −0.318558
\(536\) 22.0209 0.951158
\(537\) 9.18820 0.396500
\(538\) −2.56329 −0.110511
\(539\) −3.31912 −0.142964
\(540\) −3.77463 −0.162434
\(541\) −2.08035 −0.0894413 −0.0447207 0.999000i \(-0.514240\pi\)
−0.0447207 + 0.999000i \(0.514240\pi\)
\(542\) 15.5990 0.670035
\(543\) −8.06017 −0.345895
\(544\) 5.28917 0.226771
\(545\) 13.5072 0.578587
\(546\) −58.9715 −2.52375
\(547\) 12.6144 0.539351 0.269675 0.962951i \(-0.413084\pi\)
0.269675 + 0.962951i \(0.413084\pi\)
\(548\) 17.1295 0.731735
\(549\) −2.89377 −0.123503
\(550\) 6.94251 0.296030
\(551\) −4.50383 −0.191870
\(552\) 21.9480 0.934167
\(553\) 19.4521 0.827186
\(554\) −26.0631 −1.10731
\(555\) 1.77961 0.0755402
\(556\) 19.1444 0.811904
\(557\) −29.4322 −1.24708 −0.623542 0.781790i \(-0.714307\pi\)
−0.623542 + 0.781790i \(0.714307\pi\)
\(558\) −39.6463 −1.67836
\(559\) 6.51880 0.275716
\(560\) 9.62113 0.406567
\(561\) 2.71256 0.114524
\(562\) −36.5022 −1.53975
\(563\) 7.86597 0.331511 0.165756 0.986167i \(-0.446994\pi\)
0.165756 + 0.986167i \(0.446994\pi\)
\(564\) 3.80605 0.160264
\(565\) −19.3244 −0.812985
\(566\) −22.0126 −0.925257
\(567\) −5.91310 −0.248327
\(568\) −21.9710 −0.921884
\(569\) −30.0944 −1.26162 −0.630811 0.775936i \(-0.717278\pi\)
−0.630811 + 0.775936i \(0.717278\pi\)
\(570\) −3.05388 −0.127913
\(571\) −3.99271 −0.167090 −0.0835449 0.996504i \(-0.526624\pi\)
−0.0835449 + 0.996504i \(0.526624\pi\)
\(572\) 6.65971 0.278456
\(573\) 72.2769 3.01941
\(574\) −31.5871 −1.31842
\(575\) −19.0013 −0.792409
\(576\) 3.50818 0.146174
\(577\) −20.9039 −0.870241 −0.435120 0.900372i \(-0.643294\pi\)
−0.435120 + 0.900372i \(0.643294\pi\)
\(578\) −1.73828 −0.0723029
\(579\) −13.0232 −0.541224
\(580\) −7.14755 −0.296786
\(581\) −30.5530 −1.26755
\(582\) 12.8583 0.532992
\(583\) −3.32487 −0.137702
\(584\) 1.96686 0.0813893
\(585\) −28.4952 −1.17813
\(586\) 29.2728 1.20925
\(587\) 38.0186 1.56920 0.784598 0.620004i \(-0.212869\pi\)
0.784598 + 0.620004i \(0.212869\pi\)
\(588\) −9.19790 −0.379315
\(589\) −3.37935 −0.139244
\(590\) −10.4769 −0.431327
\(591\) −18.8375 −0.774873
\(592\) 3.27005 0.134398
\(593\) −36.3283 −1.49182 −0.745911 0.666045i \(-0.767986\pi\)
−0.745911 + 0.666045i \(0.767986\pi\)
\(594\) −6.40304 −0.262720
\(595\) −1.92441 −0.0788929
\(596\) −13.9585 −0.571763
\(597\) −40.8953 −1.67374
\(598\) −53.9105 −2.20457
\(599\) 25.9606 1.06072 0.530362 0.847772i \(-0.322056\pi\)
0.530362 + 0.847772i \(0.322056\pi\)
\(600\) −18.4249 −0.752193
\(601\) −1.84844 −0.0753993 −0.0376996 0.999289i \(-0.512003\pi\)
−0.0376996 + 0.999289i \(0.512003\pi\)
\(602\) −3.33500 −0.135924
\(603\) 56.4273 2.29790
\(604\) 5.12160 0.208395
\(605\) −1.00305 −0.0407796
\(606\) 40.5175 1.64591
\(607\) 35.5192 1.44168 0.720840 0.693102i \(-0.243756\pi\)
0.720840 + 0.693102i \(0.243756\pi\)
\(608\) −3.41524 −0.138506
\(609\) 36.2998 1.47094
\(610\) −1.15777 −0.0468766
\(611\) 8.95315 0.362206
\(612\) 4.45216 0.179968
\(613\) 20.0787 0.810973 0.405486 0.914101i \(-0.367102\pi\)
0.405486 + 0.914101i \(0.367102\pi\)
\(614\) 19.5406 0.788595
\(615\) −25.7699 −1.03914
\(616\) 3.26291 0.131466
\(617\) 46.1262 1.85697 0.928484 0.371371i \(-0.121112\pi\)
0.928484 + 0.371371i \(0.121112\pi\)
\(618\) 63.9749 2.57345
\(619\) −37.7568 −1.51757 −0.758787 0.651339i \(-0.774208\pi\)
−0.758787 + 0.651339i \(0.774208\pi\)
\(620\) −5.36300 −0.215383
\(621\) 17.5248 0.703246
\(622\) −9.69367 −0.388681
\(623\) 23.3296 0.934680
\(624\) −88.4048 −3.53903
\(625\) 10.9207 0.436829
\(626\) 48.5491 1.94041
\(627\) −1.75151 −0.0699484
\(628\) −23.1169 −0.922464
\(629\) −0.654072 −0.0260796
\(630\) 14.5781 0.580804
\(631\) 1.49485 0.0595092 0.0297546 0.999557i \(-0.490527\pi\)
0.0297546 + 0.999557i \(0.490527\pi\)
\(632\) 17.2432 0.685899
\(633\) −55.6552 −2.21210
\(634\) −59.5583 −2.36536
\(635\) −3.92673 −0.155828
\(636\) −9.21385 −0.365353
\(637\) −21.6367 −0.857276
\(638\) −12.1246 −0.480019
\(639\) −56.2995 −2.22717
\(640\) 12.0141 0.474901
\(641\) 41.7650 1.64962 0.824809 0.565411i \(-0.191283\pi\)
0.824809 + 0.565411i \(0.191283\pi\)
\(642\) −34.6372 −1.36702
\(643\) −2.01265 −0.0793710 −0.0396855 0.999212i \(-0.512636\pi\)
−0.0396855 + 0.999212i \(0.512636\pi\)
\(644\) 9.32502 0.367457
\(645\) −2.72082 −0.107132
\(646\) 1.12241 0.0441607
\(647\) −10.5484 −0.414701 −0.207351 0.978267i \(-0.566484\pi\)
−0.207351 + 0.978267i \(0.566484\pi\)
\(648\) −5.24165 −0.205912
\(649\) −6.00887 −0.235869
\(650\) 45.2569 1.77512
\(651\) 27.2367 1.06749
\(652\) −17.6546 −0.691406
\(653\) 32.3630 1.26646 0.633230 0.773963i \(-0.281729\pi\)
0.633230 + 0.773963i \(0.281729\pi\)
\(654\) 63.4957 2.48288
\(655\) 8.44949 0.330149
\(656\) −47.3525 −1.84881
\(657\) 5.03997 0.196628
\(658\) −4.58041 −0.178563
\(659\) 22.0220 0.857855 0.428927 0.903339i \(-0.358892\pi\)
0.428927 + 0.903339i \(0.358892\pi\)
\(660\) −2.77963 −0.108197
\(661\) −23.5021 −0.914127 −0.457063 0.889434i \(-0.651099\pi\)
−0.457063 + 0.889434i \(0.651099\pi\)
\(662\) −5.97470 −0.232213
\(663\) 17.6826 0.686736
\(664\) −27.0836 −1.05105
\(665\) 1.24260 0.0481858
\(666\) 4.95483 0.191996
\(667\) 33.1845 1.28491
\(668\) −13.4780 −0.521478
\(669\) 45.2720 1.75032
\(670\) 22.5759 0.872185
\(671\) −0.664019 −0.0256342
\(672\) 27.5260 1.06184
\(673\) −9.40321 −0.362467 −0.181234 0.983440i \(-0.558009\pi\)
−0.181234 + 0.983440i \(0.558009\pi\)
\(674\) 0.602054 0.0231903
\(675\) −14.7117 −0.566255
\(676\) 30.1323 1.15894
\(677\) 34.4457 1.32386 0.661929 0.749567i \(-0.269738\pi\)
0.661929 + 0.749567i \(0.269738\pi\)
\(678\) −90.8415 −3.48875
\(679\) −5.23191 −0.200782
\(680\) −1.70589 −0.0654177
\(681\) −16.1261 −0.617954
\(682\) −9.09744 −0.348359
\(683\) 18.5880 0.711249 0.355624 0.934629i \(-0.384268\pi\)
0.355624 + 0.934629i \(0.384268\pi\)
\(684\) −2.87478 −0.109920
\(685\) −16.8181 −0.642587
\(686\) 34.4142 1.31394
\(687\) −69.2707 −2.64284
\(688\) −4.99953 −0.190605
\(689\) −21.6742 −0.825720
\(690\) 22.5012 0.856605
\(691\) −14.8211 −0.563822 −0.281911 0.959441i \(-0.590968\pi\)
−0.281911 + 0.959441i \(0.590968\pi\)
\(692\) −2.04418 −0.0777080
\(693\) 8.36103 0.317609
\(694\) −61.4934 −2.33426
\(695\) −18.7964 −0.712989
\(696\) 32.1779 1.21970
\(697\) 9.47139 0.358754
\(698\) 15.1631 0.573932
\(699\) 49.6989 1.87978
\(700\) −7.82818 −0.295877
\(701\) 6.34593 0.239682 0.119841 0.992793i \(-0.461761\pi\)
0.119841 + 0.992793i \(0.461761\pi\)
\(702\) −41.7402 −1.57538
\(703\) 0.422336 0.0159287
\(704\) 0.805005 0.0303397
\(705\) −3.73687 −0.140739
\(706\) −12.7598 −0.480221
\(707\) −16.4862 −0.620028
\(708\) −16.6517 −0.625810
\(709\) 10.1001 0.379318 0.189659 0.981850i \(-0.439262\pi\)
0.189659 + 0.981850i \(0.439262\pi\)
\(710\) −22.5248 −0.845341
\(711\) 44.1848 1.65706
\(712\) 20.6805 0.775033
\(713\) 24.8992 0.932483
\(714\) −9.04637 −0.338552
\(715\) −6.53865 −0.244532
\(716\) 3.46050 0.129325
\(717\) −4.11026 −0.153501
\(718\) 5.37280 0.200511
\(719\) 22.9728 0.856739 0.428370 0.903604i \(-0.359088\pi\)
0.428370 + 0.903604i \(0.359088\pi\)
\(720\) 21.8541 0.814456
\(721\) −26.0308 −0.969437
\(722\) 32.3026 1.20218
\(723\) −16.9537 −0.630514
\(724\) −3.03566 −0.112819
\(725\) −27.8578 −1.03461
\(726\) −4.71518 −0.174997
\(727\) 11.7756 0.436735 0.218367 0.975867i \(-0.429927\pi\)
0.218367 + 0.975867i \(0.429927\pi\)
\(728\) 21.2703 0.788329
\(729\) −43.4070 −1.60767
\(730\) 2.01644 0.0746317
\(731\) 1.00000 0.0369863
\(732\) −1.84012 −0.0680129
\(733\) −5.16842 −0.190900 −0.0954500 0.995434i \(-0.530429\pi\)
−0.0954500 + 0.995434i \(0.530429\pi\)
\(734\) −46.2347 −1.70655
\(735\) 9.03071 0.333103
\(736\) 25.1637 0.927545
\(737\) 12.9481 0.476949
\(738\) −71.7492 −2.64112
\(739\) −41.0301 −1.50932 −0.754659 0.656117i \(-0.772198\pi\)
−0.754659 + 0.656117i \(0.772198\pi\)
\(740\) 0.670245 0.0246387
\(741\) −11.4177 −0.419441
\(742\) 11.0884 0.407069
\(743\) 24.1532 0.886096 0.443048 0.896498i \(-0.353897\pi\)
0.443048 + 0.896498i \(0.353897\pi\)
\(744\) 24.1439 0.885159
\(745\) 13.7048 0.502104
\(746\) 65.3661 2.39322
\(747\) −69.4002 −2.53922
\(748\) 1.02162 0.0373540
\(749\) 14.0936 0.514967
\(750\) −42.5370 −1.55323
\(751\) −1.22172 −0.0445811 −0.0222906 0.999752i \(-0.507096\pi\)
−0.0222906 + 0.999752i \(0.507096\pi\)
\(752\) −6.86654 −0.250397
\(753\) −38.7680 −1.41279
\(754\) −79.0381 −2.87840
\(755\) −5.02851 −0.183006
\(756\) 7.21989 0.262585
\(757\) 30.2803 1.10056 0.550278 0.834982i \(-0.314522\pi\)
0.550278 + 0.834982i \(0.314522\pi\)
\(758\) −13.2530 −0.481371
\(759\) 12.9052 0.468429
\(760\) 1.10150 0.0399555
\(761\) −54.4394 −1.97343 −0.986713 0.162471i \(-0.948054\pi\)
−0.986713 + 0.162471i \(0.948054\pi\)
\(762\) −18.4590 −0.668700
\(763\) −25.8358 −0.935319
\(764\) 27.2212 0.984830
\(765\) −4.37124 −0.158042
\(766\) −58.6213 −2.11807
\(767\) −39.1706 −1.41437
\(768\) 52.1096 1.88034
\(769\) 2.75387 0.0993070 0.0496535 0.998767i \(-0.484188\pi\)
0.0496535 + 0.998767i \(0.484188\pi\)
\(770\) 3.34515 0.120551
\(771\) −53.3918 −1.92286
\(772\) −4.90484 −0.176529
\(773\) −9.54228 −0.343212 −0.171606 0.985166i \(-0.554896\pi\)
−0.171606 + 0.985166i \(0.554896\pi\)
\(774\) −7.57536 −0.272291
\(775\) −20.9024 −0.750837
\(776\) −4.63781 −0.166488
\(777\) −3.40393 −0.122115
\(778\) −42.5036 −1.52383
\(779\) −6.11571 −0.219118
\(780\) −18.1199 −0.648795
\(781\) −12.9188 −0.462270
\(782\) −8.27000 −0.295735
\(783\) 25.6931 0.918195
\(784\) 16.5940 0.592644
\(785\) 22.6967 0.810079
\(786\) 39.7199 1.41676
\(787\) −45.7605 −1.63119 −0.815593 0.578625i \(-0.803589\pi\)
−0.815593 + 0.578625i \(0.803589\pi\)
\(788\) −7.09468 −0.252738
\(789\) −49.1057 −1.74821
\(790\) 17.6779 0.628950
\(791\) 36.9626 1.31424
\(792\) 7.41161 0.263360
\(793\) −4.32861 −0.153713
\(794\) −0.703338 −0.0249605
\(795\) 9.04636 0.320842
\(796\) −15.4022 −0.545916
\(797\) 37.3345 1.32246 0.661229 0.750184i \(-0.270035\pi\)
0.661229 + 0.750184i \(0.270035\pi\)
\(798\) 5.84127 0.206779
\(799\) 1.37344 0.0485887
\(800\) −21.1244 −0.746861
\(801\) 52.9925 1.87240
\(802\) −41.0002 −1.44777
\(803\) 1.15650 0.0408119
\(804\) 35.8816 1.26545
\(805\) −9.15552 −0.322690
\(806\) −59.3044 −2.08891
\(807\) 3.99997 0.140805
\(808\) −14.6142 −0.514124
\(809\) 0.383409 0.0134799 0.00673996 0.999977i \(-0.497855\pi\)
0.00673996 + 0.999977i \(0.497855\pi\)
\(810\) −5.37377 −0.188815
\(811\) 6.83317 0.239945 0.119973 0.992777i \(-0.461719\pi\)
0.119973 + 0.992777i \(0.461719\pi\)
\(812\) 13.6714 0.479772
\(813\) −24.3420 −0.853711
\(814\) 1.13696 0.0398504
\(815\) 17.3337 0.607171
\(816\) −13.5615 −0.474748
\(817\) −0.645703 −0.0225903
\(818\) −32.6679 −1.14221
\(819\) 54.5039 1.90452
\(820\) −9.70559 −0.338934
\(821\) −38.7817 −1.35349 −0.676746 0.736217i \(-0.736610\pi\)
−0.676746 + 0.736217i \(0.736610\pi\)
\(822\) −79.0597 −2.75752
\(823\) 7.00732 0.244260 0.122130 0.992514i \(-0.461028\pi\)
0.122130 + 0.992514i \(0.461028\pi\)
\(824\) −23.0749 −0.803853
\(825\) −10.8337 −0.377180
\(826\) 20.0396 0.697265
\(827\) 13.5718 0.471937 0.235968 0.971761i \(-0.424174\pi\)
0.235968 + 0.971761i \(0.424174\pi\)
\(828\) 21.1815 0.736109
\(829\) −38.3815 −1.33304 −0.666521 0.745486i \(-0.732218\pi\)
−0.666521 + 0.745486i \(0.732218\pi\)
\(830\) −27.7663 −0.963781
\(831\) 40.6710 1.41086
\(832\) 5.24766 0.181930
\(833\) −3.31912 −0.115001
\(834\) −88.3595 −3.05964
\(835\) 13.2330 0.457946
\(836\) −0.659660 −0.0228148
\(837\) 19.2782 0.666352
\(838\) 8.49084 0.293311
\(839\) −8.30321 −0.286659 −0.143329 0.989675i \(-0.545781\pi\)
−0.143329 + 0.989675i \(0.545781\pi\)
\(840\) −8.87779 −0.306313
\(841\) 19.6517 0.677646
\(842\) 28.5623 0.984322
\(843\) 56.9611 1.96185
\(844\) −20.9611 −0.721511
\(845\) −29.5846 −1.01774
\(846\) −10.4043 −0.357706
\(847\) 1.91856 0.0659226
\(848\) 16.6228 0.570829
\(849\) 34.3502 1.17890
\(850\) 6.94251 0.238126
\(851\) −3.11180 −0.106671
\(852\) −35.8004 −1.22650
\(853\) −19.3929 −0.663999 −0.331999 0.943280i \(-0.607723\pi\)
−0.331999 + 0.943280i \(0.607723\pi\)
\(854\) 2.21450 0.0757787
\(855\) 2.82252 0.0965282
\(856\) 12.4932 0.427009
\(857\) 39.6359 1.35394 0.676969 0.736012i \(-0.263293\pi\)
0.676969 + 0.736012i \(0.263293\pi\)
\(858\) −30.7373 −1.04936
\(859\) 31.1168 1.06169 0.530846 0.847468i \(-0.321874\pi\)
0.530846 + 0.847468i \(0.321874\pi\)
\(860\) −1.02473 −0.0349429
\(861\) 49.2911 1.67984
\(862\) −65.7772 −2.24038
\(863\) −17.1350 −0.583282 −0.291641 0.956528i \(-0.594201\pi\)
−0.291641 + 0.956528i \(0.594201\pi\)
\(864\) 19.4829 0.662823
\(865\) 2.00702 0.0682407
\(866\) 28.3854 0.964576
\(867\) 2.71256 0.0921233
\(868\) 10.2580 0.348180
\(869\) 10.1389 0.343938
\(870\) 32.9889 1.11843
\(871\) 84.4060 2.85999
\(872\) −22.9021 −0.775563
\(873\) −11.8841 −0.402217
\(874\) 5.33997 0.180627
\(875\) 17.3079 0.585114
\(876\) 3.20487 0.108283
\(877\) 39.4066 1.33067 0.665333 0.746546i \(-0.268289\pi\)
0.665333 + 0.746546i \(0.268289\pi\)
\(878\) 23.9473 0.808183
\(879\) −45.6797 −1.54074
\(880\) 5.01476 0.169047
\(881\) −29.4027 −0.990602 −0.495301 0.868721i \(-0.664942\pi\)
−0.495301 + 0.868721i \(0.664942\pi\)
\(882\) 25.1435 0.846626
\(883\) 34.3859 1.15718 0.578588 0.815620i \(-0.303604\pi\)
0.578588 + 0.815620i \(0.303604\pi\)
\(884\) 6.65971 0.223990
\(885\) 16.3490 0.549567
\(886\) −13.1170 −0.440675
\(887\) −12.2822 −0.412398 −0.206199 0.978510i \(-0.566109\pi\)
−0.206199 + 0.978510i \(0.566109\pi\)
\(888\) −3.01740 −0.101257
\(889\) 7.51080 0.251904
\(890\) 21.2017 0.710684
\(891\) −3.08204 −0.103252
\(892\) 17.0505 0.570894
\(893\) −0.886832 −0.0296767
\(894\) 64.4243 2.15467
\(895\) −3.39760 −0.113569
\(896\) −22.9799 −0.767705
\(897\) 84.1265 2.80890
\(898\) −17.5129 −0.584412
\(899\) 36.5047 1.21750
\(900\) −17.7815 −0.592716
\(901\) −3.32487 −0.110767
\(902\) −16.4639 −0.548189
\(903\) 5.20421 0.173185
\(904\) 32.7654 1.08976
\(905\) 2.98048 0.0990745
\(906\) −23.6383 −0.785331
\(907\) −30.4473 −1.01099 −0.505494 0.862830i \(-0.668690\pi\)
−0.505494 + 0.862830i \(0.668690\pi\)
\(908\) −6.07349 −0.201556
\(909\) −37.4480 −1.24207
\(910\) 21.8064 0.722875
\(911\) −20.4981 −0.679133 −0.339566 0.940582i \(-0.610280\pi\)
−0.339566 + 0.940582i \(0.610280\pi\)
\(912\) 8.75672 0.289964
\(913\) −15.9249 −0.527038
\(914\) −25.8013 −0.853431
\(915\) 1.80667 0.0597268
\(916\) −26.0890 −0.862006
\(917\) −16.1617 −0.533705
\(918\) −6.40304 −0.211332
\(919\) 46.1231 1.52146 0.760730 0.649068i \(-0.224841\pi\)
0.760730 + 0.649068i \(0.224841\pi\)
\(920\) −8.11589 −0.267573
\(921\) −30.4928 −1.00477
\(922\) −5.21871 −0.171869
\(923\) −84.2149 −2.77197
\(924\) 5.31670 0.174907
\(925\) 2.61230 0.0858918
\(926\) 12.2378 0.402158
\(927\) −59.1282 −1.94203
\(928\) 36.8924 1.21105
\(929\) 17.3747 0.570046 0.285023 0.958521i \(-0.407999\pi\)
0.285023 + 0.958521i \(0.407999\pi\)
\(930\) 24.7525 0.811666
\(931\) 2.14316 0.0702394
\(932\) 18.7178 0.613122
\(933\) 15.1268 0.495230
\(934\) 57.0737 1.86751
\(935\) −1.00305 −0.0328031
\(936\) 48.3148 1.57922
\(937\) 10.2370 0.334427 0.167213 0.985921i \(-0.446523\pi\)
0.167213 + 0.985921i \(0.446523\pi\)
\(938\) −43.1819 −1.40994
\(939\) −75.7601 −2.47234
\(940\) −1.40740 −0.0459042
\(941\) 34.1405 1.11295 0.556475 0.830865i \(-0.312154\pi\)
0.556475 + 0.830865i \(0.312154\pi\)
\(942\) 106.694 3.47628
\(943\) 45.0609 1.46738
\(944\) 30.0415 0.977768
\(945\) −7.08865 −0.230594
\(946\) −1.73828 −0.0565163
\(947\) −6.07427 −0.197387 −0.0986936 0.995118i \(-0.531466\pi\)
−0.0986936 + 0.995118i \(0.531466\pi\)
\(948\) 28.0967 0.912539
\(949\) 7.53897 0.244725
\(950\) −4.48280 −0.145441
\(951\) 92.9397 3.01378
\(952\) 3.26291 0.105752
\(953\) −37.4663 −1.21365 −0.606825 0.794835i \(-0.707557\pi\)
−0.606825 + 0.794835i \(0.707557\pi\)
\(954\) 25.1871 0.815462
\(955\) −26.7264 −0.864847
\(956\) −1.54803 −0.0500668
\(957\) 18.9203 0.611606
\(958\) 59.3444 1.91733
\(959\) 32.1686 1.03878
\(960\) −2.19027 −0.0706907
\(961\) −3.60954 −0.116437
\(962\) 7.41161 0.238960
\(963\) 32.0131 1.03161
\(964\) −6.38517 −0.205652
\(965\) 4.81568 0.155022
\(966\) −43.0388 −1.38475
\(967\) −24.4207 −0.785317 −0.392659 0.919684i \(-0.628445\pi\)
−0.392659 + 0.919684i \(0.628445\pi\)
\(968\) 1.70071 0.0546628
\(969\) −1.75151 −0.0562665
\(970\) −4.75471 −0.152665
\(971\) −49.7852 −1.59768 −0.798841 0.601542i \(-0.794553\pi\)
−0.798841 + 0.601542i \(0.794553\pi\)
\(972\) −19.8305 −0.636062
\(973\) 35.9526 1.15259
\(974\) −48.9077 −1.56710
\(975\) −70.6226 −2.26173
\(976\) 3.31978 0.106264
\(977\) 23.9893 0.767485 0.383743 0.923440i \(-0.374635\pi\)
0.383743 + 0.923440i \(0.374635\pi\)
\(978\) 81.4832 2.60554
\(979\) 12.1599 0.388633
\(980\) 3.40119 0.108647
\(981\) −58.6854 −1.87368
\(982\) 53.2213 1.69836
\(983\) −48.8932 −1.55945 −0.779726 0.626121i \(-0.784642\pi\)
−0.779726 + 0.626121i \(0.784642\pi\)
\(984\) 43.6940 1.39291
\(985\) 6.96572 0.221946
\(986\) −12.1246 −0.386127
\(987\) 7.14765 0.227512
\(988\) −4.30020 −0.136807
\(989\) 4.75758 0.151282
\(990\) 7.59843 0.241494
\(991\) 18.6807 0.593412 0.296706 0.954969i \(-0.404112\pi\)
0.296706 + 0.954969i \(0.404112\pi\)
\(992\) 27.6814 0.878884
\(993\) 9.32342 0.295870
\(994\) 43.0841 1.36654
\(995\) 15.1222 0.479407
\(996\) −44.1310 −1.39834
\(997\) −18.5437 −0.587286 −0.293643 0.955915i \(-0.594868\pi\)
−0.293643 + 0.955915i \(0.594868\pi\)
\(998\) 17.7455 0.561723
\(999\) −2.40931 −0.0762271
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 \(a_p\))