Properties

Label 8041.2.a.i.1.8
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
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: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.35944 q^{2} +3.36081 q^{3} +3.56697 q^{4} -2.07702 q^{5} -7.92965 q^{6} -0.337523 q^{7} -3.69718 q^{8} +8.29507 q^{9} +O(q^{10})\) \(q-2.35944 q^{2} +3.36081 q^{3} +3.56697 q^{4} -2.07702 q^{5} -7.92965 q^{6} -0.337523 q^{7} -3.69718 q^{8} +8.29507 q^{9} +4.90061 q^{10} +1.00000 q^{11} +11.9879 q^{12} -4.41805 q^{13} +0.796366 q^{14} -6.98048 q^{15} +1.58935 q^{16} -1.00000 q^{17} -19.5718 q^{18} -3.97263 q^{19} -7.40868 q^{20} -1.13435 q^{21} -2.35944 q^{22} -1.36597 q^{23} -12.4255 q^{24} -0.685985 q^{25} +10.4241 q^{26} +17.7958 q^{27} -1.20393 q^{28} -3.07221 q^{29} +16.4700 q^{30} +10.8484 q^{31} +3.64439 q^{32} +3.36081 q^{33} +2.35944 q^{34} +0.701042 q^{35} +29.5883 q^{36} +8.29228 q^{37} +9.37320 q^{38} -14.8482 q^{39} +7.67912 q^{40} +7.25830 q^{41} +2.67644 q^{42} -1.00000 q^{43} +3.56697 q^{44} -17.2290 q^{45} +3.22293 q^{46} -1.36584 q^{47} +5.34150 q^{48} -6.88608 q^{49} +1.61854 q^{50} -3.36081 q^{51} -15.7590 q^{52} +5.56854 q^{53} -41.9881 q^{54} -2.07702 q^{55} +1.24788 q^{56} -13.3513 q^{57} +7.24871 q^{58} -6.38624 q^{59} -24.8992 q^{60} -4.07858 q^{61} -25.5962 q^{62} -2.79978 q^{63} -11.7774 q^{64} +9.17637 q^{65} -7.92965 q^{66} +8.90319 q^{67} -3.56697 q^{68} -4.59078 q^{69} -1.65407 q^{70} +2.21407 q^{71} -30.6684 q^{72} -8.86341 q^{73} -19.5652 q^{74} -2.30547 q^{75} -14.1703 q^{76} -0.337523 q^{77} +35.0336 q^{78} +12.6005 q^{79} -3.30111 q^{80} +34.9230 q^{81} -17.1255 q^{82} -2.84870 q^{83} -4.04620 q^{84} +2.07702 q^{85} +2.35944 q^{86} -10.3251 q^{87} -3.69718 q^{88} -2.02201 q^{89} +40.6509 q^{90} +1.49119 q^{91} -4.87238 q^{92} +36.4594 q^{93} +3.22263 q^{94} +8.25124 q^{95} +12.2481 q^{96} -4.54717 q^{97} +16.2473 q^{98} +8.29507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35944 −1.66838 −0.834189 0.551478i \(-0.814064\pi\)
−0.834189 + 0.551478i \(0.814064\pi\)
\(3\) 3.36081 1.94037 0.970184 0.242372i \(-0.0779253\pi\)
0.970184 + 0.242372i \(0.0779253\pi\)
\(4\) 3.56697 1.78349
\(5\) −2.07702 −0.928872 −0.464436 0.885607i \(-0.653743\pi\)
−0.464436 + 0.885607i \(0.653743\pi\)
\(6\) −7.92965 −3.23727
\(7\) −0.337523 −0.127572 −0.0637858 0.997964i \(-0.520317\pi\)
−0.0637858 + 0.997964i \(0.520317\pi\)
\(8\) −3.69718 −1.30715
\(9\) 8.29507 2.76502
\(10\) 4.90061 1.54971
\(11\) 1.00000 0.301511
\(12\) 11.9879 3.46062
\(13\) −4.41805 −1.22535 −0.612673 0.790337i \(-0.709906\pi\)
−0.612673 + 0.790337i \(0.709906\pi\)
\(14\) 0.796366 0.212838
\(15\) −6.98048 −1.80235
\(16\) 1.58935 0.397337
\(17\) −1.00000 −0.242536
\(18\) −19.5718 −4.61311
\(19\) −3.97263 −0.911384 −0.455692 0.890137i \(-0.650608\pi\)
−0.455692 + 0.890137i \(0.650608\pi\)
\(20\) −7.40868 −1.65663
\(21\) −1.13435 −0.247536
\(22\) −2.35944 −0.503035
\(23\) −1.36597 −0.284825 −0.142412 0.989807i \(-0.545486\pi\)
−0.142412 + 0.989807i \(0.545486\pi\)
\(24\) −12.4255 −2.53635
\(25\) −0.685985 −0.137197
\(26\) 10.4241 2.04434
\(27\) 17.7958 3.42479
\(28\) −1.20393 −0.227522
\(29\) −3.07221 −0.570495 −0.285248 0.958454i \(-0.592076\pi\)
−0.285248 + 0.958454i \(0.592076\pi\)
\(30\) 16.4700 3.00701
\(31\) 10.8484 1.94843 0.974214 0.225624i \(-0.0724422\pi\)
0.974214 + 0.225624i \(0.0724422\pi\)
\(32\) 3.64439 0.644243
\(33\) 3.36081 0.585043
\(34\) 2.35944 0.404641
\(35\) 0.701042 0.118498
\(36\) 29.5883 4.93138
\(37\) 8.29228 1.36324 0.681621 0.731706i \(-0.261275\pi\)
0.681621 + 0.731706i \(0.261275\pi\)
\(38\) 9.37320 1.52053
\(39\) −14.8482 −2.37762
\(40\) 7.67912 1.21418
\(41\) 7.25830 1.13356 0.566778 0.823871i \(-0.308190\pi\)
0.566778 + 0.823871i \(0.308190\pi\)
\(42\) 2.67644 0.412983
\(43\) −1.00000 −0.152499
\(44\) 3.56697 0.537741
\(45\) −17.2290 −2.56835
\(46\) 3.22293 0.475195
\(47\) −1.36584 −0.199229 −0.0996143 0.995026i \(-0.531761\pi\)
−0.0996143 + 0.995026i \(0.531761\pi\)
\(48\) 5.34150 0.770979
\(49\) −6.88608 −0.983725
\(50\) 1.61854 0.228897
\(51\) −3.36081 −0.470608
\(52\) −15.7590 −2.18539
\(53\) 5.56854 0.764898 0.382449 0.923977i \(-0.375081\pi\)
0.382449 + 0.923977i \(0.375081\pi\)
\(54\) −41.9881 −5.71385
\(55\) −2.07702 −0.280065
\(56\) 1.24788 0.166755
\(57\) −13.3513 −1.76842
\(58\) 7.24871 0.951802
\(59\) −6.38624 −0.831418 −0.415709 0.909498i \(-0.636467\pi\)
−0.415709 + 0.909498i \(0.636467\pi\)
\(60\) −24.8992 −3.21447
\(61\) −4.07858 −0.522208 −0.261104 0.965311i \(-0.584087\pi\)
−0.261104 + 0.965311i \(0.584087\pi\)
\(62\) −25.5962 −3.25072
\(63\) −2.79978 −0.352739
\(64\) −11.7774 −1.47218
\(65\) 9.17637 1.13819
\(66\) −7.92965 −0.976072
\(67\) 8.90319 1.08770 0.543849 0.839183i \(-0.316966\pi\)
0.543849 + 0.839183i \(0.316966\pi\)
\(68\) −3.56697 −0.432559
\(69\) −4.59078 −0.552664
\(70\) −1.65407 −0.197699
\(71\) 2.21407 0.262762 0.131381 0.991332i \(-0.458059\pi\)
0.131381 + 0.991332i \(0.458059\pi\)
\(72\) −30.6684 −3.61430
\(73\) −8.86341 −1.03738 −0.518692 0.854961i \(-0.673581\pi\)
−0.518692 + 0.854961i \(0.673581\pi\)
\(74\) −19.5652 −2.27440
\(75\) −2.30547 −0.266213
\(76\) −14.1703 −1.62544
\(77\) −0.337523 −0.0384643
\(78\) 35.0336 3.96677
\(79\) 12.6005 1.41767 0.708835 0.705374i \(-0.249221\pi\)
0.708835 + 0.705374i \(0.249221\pi\)
\(80\) −3.30111 −0.369075
\(81\) 34.9230 3.88033
\(82\) −17.1255 −1.89120
\(83\) −2.84870 −0.312686 −0.156343 0.987703i \(-0.549971\pi\)
−0.156343 + 0.987703i \(0.549971\pi\)
\(84\) −4.04620 −0.441477
\(85\) 2.07702 0.225285
\(86\) 2.35944 0.254425
\(87\) −10.3251 −1.10697
\(88\) −3.69718 −0.394121
\(89\) −2.02201 −0.214332 −0.107166 0.994241i \(-0.534178\pi\)
−0.107166 + 0.994241i \(0.534178\pi\)
\(90\) 40.6509 4.28498
\(91\) 1.49119 0.156319
\(92\) −4.87238 −0.507981
\(93\) 36.4594 3.78067
\(94\) 3.22263 0.332389
\(95\) 8.25124 0.846559
\(96\) 12.2481 1.25007
\(97\) −4.54717 −0.461695 −0.230848 0.972990i \(-0.574150\pi\)
−0.230848 + 0.972990i \(0.574150\pi\)
\(98\) 16.2473 1.64123
\(99\) 8.29507 0.833686
\(100\) −2.44689 −0.244689
\(101\) 9.41960 0.937285 0.468642 0.883388i \(-0.344743\pi\)
0.468642 + 0.883388i \(0.344743\pi\)
\(102\) 7.92965 0.785152
\(103\) −6.17442 −0.608384 −0.304192 0.952611i \(-0.598386\pi\)
−0.304192 + 0.952611i \(0.598386\pi\)
\(104\) 16.3343 1.60171
\(105\) 2.35607 0.229929
\(106\) −13.1386 −1.27614
\(107\) 9.65230 0.933123 0.466561 0.884489i \(-0.345493\pi\)
0.466561 + 0.884489i \(0.345493\pi\)
\(108\) 63.4770 6.10807
\(109\) −2.50036 −0.239491 −0.119745 0.992805i \(-0.538208\pi\)
−0.119745 + 0.992805i \(0.538208\pi\)
\(110\) 4.90061 0.467255
\(111\) 27.8688 2.64519
\(112\) −0.536441 −0.0506889
\(113\) −6.96650 −0.655353 −0.327677 0.944790i \(-0.606266\pi\)
−0.327677 + 0.944790i \(0.606266\pi\)
\(114\) 31.5016 2.95039
\(115\) 2.83715 0.264566
\(116\) −10.9585 −1.01747
\(117\) −36.6480 −3.38811
\(118\) 15.0680 1.38712
\(119\) 0.337523 0.0309407
\(120\) 25.8081 2.35595
\(121\) 1.00000 0.0909091
\(122\) 9.62317 0.871241
\(123\) 24.3938 2.19951
\(124\) 38.6959 3.47500
\(125\) 11.8099 1.05631
\(126\) 6.60591 0.588502
\(127\) 2.95295 0.262032 0.131016 0.991380i \(-0.458176\pi\)
0.131016 + 0.991380i \(0.458176\pi\)
\(128\) 20.4994 1.81191
\(129\) −3.36081 −0.295903
\(130\) −21.6511 −1.89893
\(131\) 12.9188 1.12872 0.564360 0.825529i \(-0.309123\pi\)
0.564360 + 0.825529i \(0.309123\pi\)
\(132\) 11.9879 1.04342
\(133\) 1.34085 0.116267
\(134\) −21.0066 −1.81469
\(135\) −36.9622 −3.18120
\(136\) 3.69718 0.317031
\(137\) 17.3914 1.48585 0.742925 0.669375i \(-0.233438\pi\)
0.742925 + 0.669375i \(0.233438\pi\)
\(138\) 10.8317 0.922053
\(139\) −16.9105 −1.43433 −0.717165 0.696904i \(-0.754561\pi\)
−0.717165 + 0.696904i \(0.754561\pi\)
\(140\) 2.50060 0.211339
\(141\) −4.59034 −0.386577
\(142\) −5.22397 −0.438386
\(143\) −4.41805 −0.369456
\(144\) 13.1837 1.09865
\(145\) 6.38105 0.529917
\(146\) 20.9127 1.73075
\(147\) −23.1428 −1.90879
\(148\) 29.5783 2.43132
\(149\) 21.5320 1.76397 0.881984 0.471280i \(-0.156208\pi\)
0.881984 + 0.471280i \(0.156208\pi\)
\(150\) 5.43962 0.444143
\(151\) 2.06410 0.167974 0.0839872 0.996467i \(-0.473235\pi\)
0.0839872 + 0.996467i \(0.473235\pi\)
\(152\) 14.6875 1.19132
\(153\) −8.29507 −0.670617
\(154\) 0.796366 0.0641730
\(155\) −22.5323 −1.80984
\(156\) −52.9632 −4.24045
\(157\) 13.4726 1.07523 0.537616 0.843190i \(-0.319325\pi\)
0.537616 + 0.843190i \(0.319325\pi\)
\(158\) −29.7302 −2.36521
\(159\) 18.7148 1.48418
\(160\) −7.56948 −0.598420
\(161\) 0.461046 0.0363356
\(162\) −82.3989 −6.47387
\(163\) 6.11928 0.479299 0.239650 0.970859i \(-0.422967\pi\)
0.239650 + 0.970859i \(0.422967\pi\)
\(164\) 25.8902 2.02168
\(165\) −6.98048 −0.543430
\(166\) 6.72136 0.521678
\(167\) 13.4644 1.04191 0.520953 0.853585i \(-0.325577\pi\)
0.520953 + 0.853585i \(0.325577\pi\)
\(168\) 4.19390 0.323567
\(169\) 6.51914 0.501472
\(170\) −4.90061 −0.375860
\(171\) −32.9533 −2.52000
\(172\) −3.56697 −0.271979
\(173\) 17.8587 1.35777 0.678886 0.734243i \(-0.262463\pi\)
0.678886 + 0.734243i \(0.262463\pi\)
\(174\) 24.3616 1.84685
\(175\) 0.231536 0.0175025
\(176\) 1.58935 0.119802
\(177\) −21.4630 −1.61326
\(178\) 4.77081 0.357587
\(179\) 13.4325 1.00399 0.501994 0.864871i \(-0.332600\pi\)
0.501994 + 0.864871i \(0.332600\pi\)
\(180\) −61.4555 −4.58062
\(181\) −10.8415 −0.805842 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(182\) −3.51838 −0.260800
\(183\) −13.7073 −1.01328
\(184\) 5.05024 0.372309
\(185\) −17.2232 −1.26628
\(186\) −86.0240 −6.30758
\(187\) −1.00000 −0.0731272
\(188\) −4.87192 −0.355321
\(189\) −6.00647 −0.436907
\(190\) −19.4683 −1.41238
\(191\) 0.770083 0.0557212 0.0278606 0.999612i \(-0.491131\pi\)
0.0278606 + 0.999612i \(0.491131\pi\)
\(192\) −39.5817 −2.85657
\(193\) 1.00907 0.0726342 0.0363171 0.999340i \(-0.488437\pi\)
0.0363171 + 0.999340i \(0.488437\pi\)
\(194\) 10.7288 0.770282
\(195\) 30.8401 2.20850
\(196\) −24.5625 −1.75446
\(197\) −3.76355 −0.268141 −0.134071 0.990972i \(-0.542805\pi\)
−0.134071 + 0.990972i \(0.542805\pi\)
\(198\) −19.5718 −1.39090
\(199\) 8.12239 0.575781 0.287891 0.957663i \(-0.407046\pi\)
0.287891 + 0.957663i \(0.407046\pi\)
\(200\) 2.53621 0.179337
\(201\) 29.9220 2.11053
\(202\) −22.2250 −1.56375
\(203\) 1.03694 0.0727790
\(204\) −11.9879 −0.839323
\(205\) −15.0756 −1.05293
\(206\) 14.5682 1.01501
\(207\) −11.3308 −0.787547
\(208\) −7.02181 −0.486875
\(209\) −3.97263 −0.274793
\(210\) −5.55902 −0.383609
\(211\) −12.3384 −0.849407 −0.424704 0.905332i \(-0.639622\pi\)
−0.424704 + 0.905332i \(0.639622\pi\)
\(212\) 19.8628 1.36418
\(213\) 7.44108 0.509854
\(214\) −22.7740 −1.55680
\(215\) 2.07702 0.141652
\(216\) −65.7941 −4.47672
\(217\) −3.66158 −0.248564
\(218\) 5.89945 0.399561
\(219\) −29.7883 −2.01291
\(220\) −7.40868 −0.499493
\(221\) 4.41805 0.297190
\(222\) −65.7548 −4.41318
\(223\) 14.1723 0.949044 0.474522 0.880244i \(-0.342621\pi\)
0.474522 + 0.880244i \(0.342621\pi\)
\(224\) −1.23007 −0.0821872
\(225\) −5.69030 −0.379353
\(226\) 16.4371 1.09338
\(227\) 10.7318 0.712297 0.356149 0.934429i \(-0.384090\pi\)
0.356149 + 0.934429i \(0.384090\pi\)
\(228\) −47.6236 −3.15395
\(229\) 16.9360 1.11916 0.559580 0.828776i \(-0.310962\pi\)
0.559580 + 0.828776i \(0.310962\pi\)
\(230\) −6.69410 −0.441396
\(231\) −1.13435 −0.0746349
\(232\) 11.3585 0.745724
\(233\) −9.96306 −0.652702 −0.326351 0.945249i \(-0.605819\pi\)
−0.326351 + 0.945249i \(0.605819\pi\)
\(234\) 86.4689 5.65265
\(235\) 2.83688 0.185058
\(236\) −22.7795 −1.48282
\(237\) 42.3480 2.75080
\(238\) −0.796366 −0.0516207
\(239\) −1.81570 −0.117448 −0.0587240 0.998274i \(-0.518703\pi\)
−0.0587240 + 0.998274i \(0.518703\pi\)
\(240\) −11.0944 −0.716141
\(241\) −3.91834 −0.252402 −0.126201 0.992005i \(-0.540279\pi\)
−0.126201 + 0.992005i \(0.540279\pi\)
\(242\) −2.35944 −0.151671
\(243\) 63.9825 4.10448
\(244\) −14.5482 −0.931351
\(245\) 14.3025 0.913755
\(246\) −57.5558 −3.66962
\(247\) 17.5513 1.11676
\(248\) −40.1085 −2.54689
\(249\) −9.57397 −0.606725
\(250\) −27.8648 −1.76233
\(251\) −20.5519 −1.29722 −0.648611 0.761120i \(-0.724650\pi\)
−0.648611 + 0.761120i \(0.724650\pi\)
\(252\) −9.98672 −0.629105
\(253\) −1.36597 −0.0858779
\(254\) −6.96732 −0.437169
\(255\) 6.98048 0.437135
\(256\) −24.8123 −1.55077
\(257\) −20.4704 −1.27691 −0.638453 0.769660i \(-0.720426\pi\)
−0.638453 + 0.769660i \(0.720426\pi\)
\(258\) 7.92965 0.493678
\(259\) −2.79883 −0.173911
\(260\) 32.7319 2.02994
\(261\) −25.4842 −1.57743
\(262\) −30.4812 −1.88313
\(263\) 12.9079 0.795938 0.397969 0.917399i \(-0.369715\pi\)
0.397969 + 0.917399i \(0.369715\pi\)
\(264\) −12.4255 −0.764739
\(265\) −11.5660 −0.710492
\(266\) −3.16367 −0.193977
\(267\) −6.79559 −0.415883
\(268\) 31.7574 1.93989
\(269\) 22.5383 1.37419 0.687093 0.726570i \(-0.258887\pi\)
0.687093 + 0.726570i \(0.258887\pi\)
\(270\) 87.2101 5.30744
\(271\) 9.55883 0.580658 0.290329 0.956927i \(-0.406235\pi\)
0.290329 + 0.956927i \(0.406235\pi\)
\(272\) −1.58935 −0.0963683
\(273\) 5.01162 0.303317
\(274\) −41.0341 −2.47896
\(275\) −0.685985 −0.0413665
\(276\) −16.3752 −0.985669
\(277\) 30.9053 1.85692 0.928459 0.371434i \(-0.121134\pi\)
0.928459 + 0.371434i \(0.121134\pi\)
\(278\) 39.8994 2.39300
\(279\) 89.9882 5.38745
\(280\) −2.59188 −0.154894
\(281\) −4.37637 −0.261073 −0.130536 0.991444i \(-0.541670\pi\)
−0.130536 + 0.991444i \(0.541670\pi\)
\(282\) 10.8307 0.644956
\(283\) −2.52979 −0.150380 −0.0751902 0.997169i \(-0.523956\pi\)
−0.0751902 + 0.997169i \(0.523956\pi\)
\(284\) 7.89753 0.468632
\(285\) 27.7309 1.64264
\(286\) 10.4241 0.616392
\(287\) −2.44984 −0.144610
\(288\) 30.2305 1.78135
\(289\) 1.00000 0.0588235
\(290\) −15.0557 −0.884102
\(291\) −15.2822 −0.895858
\(292\) −31.6156 −1.85016
\(293\) −13.9521 −0.815090 −0.407545 0.913185i \(-0.633615\pi\)
−0.407545 + 0.913185i \(0.633615\pi\)
\(294\) 54.6042 3.18458
\(295\) 13.2644 0.772281
\(296\) −30.6581 −1.78196
\(297\) 17.7958 1.03261
\(298\) −50.8034 −2.94296
\(299\) 6.03492 0.349009
\(300\) −8.22354 −0.474786
\(301\) 0.337523 0.0194545
\(302\) −4.87014 −0.280245
\(303\) 31.6575 1.81868
\(304\) −6.31389 −0.362126
\(305\) 8.47129 0.485065
\(306\) 19.5718 1.11884
\(307\) −27.4919 −1.56904 −0.784522 0.620101i \(-0.787092\pi\)
−0.784522 + 0.620101i \(0.787092\pi\)
\(308\) −1.20393 −0.0686005
\(309\) −20.7511 −1.18049
\(310\) 53.1638 3.01950
\(311\) −6.52604 −0.370058 −0.185029 0.982733i \(-0.559238\pi\)
−0.185029 + 0.982733i \(0.559238\pi\)
\(312\) 54.8966 3.10791
\(313\) 12.7582 0.721139 0.360569 0.932732i \(-0.382582\pi\)
0.360569 + 0.932732i \(0.382582\pi\)
\(314\) −31.7879 −1.79389
\(315\) 5.81519 0.327649
\(316\) 44.9457 2.52840
\(317\) 25.2961 1.42077 0.710385 0.703814i \(-0.248521\pi\)
0.710385 + 0.703814i \(0.248521\pi\)
\(318\) −44.1566 −2.47618
\(319\) −3.07221 −0.172011
\(320\) 24.4620 1.36747
\(321\) 32.4396 1.81060
\(322\) −1.08781 −0.0606214
\(323\) 3.97263 0.221043
\(324\) 124.569 6.92052
\(325\) 3.03071 0.168114
\(326\) −14.4381 −0.799652
\(327\) −8.40323 −0.464700
\(328\) −26.8353 −1.48173
\(329\) 0.461003 0.0254159
\(330\) 16.4700 0.906646
\(331\) 25.9915 1.42862 0.714312 0.699827i \(-0.246740\pi\)
0.714312 + 0.699827i \(0.246740\pi\)
\(332\) −10.1612 −0.557671
\(333\) 68.7850 3.76940
\(334\) −31.7685 −1.73829
\(335\) −18.4921 −1.01033
\(336\) −1.80288 −0.0983550
\(337\) −11.3756 −0.619671 −0.309835 0.950790i \(-0.600274\pi\)
−0.309835 + 0.950790i \(0.600274\pi\)
\(338\) −15.3815 −0.836645
\(339\) −23.4131 −1.27163
\(340\) 7.40868 0.401792
\(341\) 10.8484 0.587473
\(342\) 77.7514 4.20431
\(343\) 4.68687 0.253067
\(344\) 3.69718 0.199339
\(345\) 9.53514 0.513354
\(346\) −42.1366 −2.26528
\(347\) 17.1926 0.922945 0.461472 0.887155i \(-0.347321\pi\)
0.461472 + 0.887155i \(0.347321\pi\)
\(348\) −36.8295 −1.97427
\(349\) 4.40790 0.235949 0.117975 0.993017i \(-0.462360\pi\)
0.117975 + 0.993017i \(0.462360\pi\)
\(350\) −0.546295 −0.0292007
\(351\) −78.6225 −4.19656
\(352\) 3.64439 0.194247
\(353\) −12.6940 −0.675636 −0.337818 0.941211i \(-0.609689\pi\)
−0.337818 + 0.941211i \(0.609689\pi\)
\(354\) 50.6407 2.69152
\(355\) −4.59867 −0.244072
\(356\) −7.21244 −0.382259
\(357\) 1.13435 0.0600363
\(358\) −31.6931 −1.67503
\(359\) 35.6820 1.88323 0.941613 0.336697i \(-0.109310\pi\)
0.941613 + 0.336697i \(0.109310\pi\)
\(360\) 63.6989 3.35723
\(361\) −3.21820 −0.169379
\(362\) 25.5799 1.34445
\(363\) 3.36081 0.176397
\(364\) 5.31904 0.278793
\(365\) 18.4095 0.963597
\(366\) 32.3417 1.69053
\(367\) −36.2408 −1.89175 −0.945877 0.324524i \(-0.894796\pi\)
−0.945877 + 0.324524i \(0.894796\pi\)
\(368\) −2.17100 −0.113171
\(369\) 60.2081 3.13431
\(370\) 40.6372 2.11263
\(371\) −1.87951 −0.0975792
\(372\) 130.050 6.74277
\(373\) −21.2432 −1.09993 −0.549967 0.835187i \(-0.685360\pi\)
−0.549967 + 0.835187i \(0.685360\pi\)
\(374\) 2.35944 0.122004
\(375\) 39.6909 2.04963
\(376\) 5.04977 0.260422
\(377\) 13.5732 0.699054
\(378\) 14.1719 0.728926
\(379\) −4.01803 −0.206393 −0.103196 0.994661i \(-0.532907\pi\)
−0.103196 + 0.994661i \(0.532907\pi\)
\(380\) 29.4319 1.50983
\(381\) 9.92432 0.508438
\(382\) −1.81697 −0.0929641
\(383\) −17.3698 −0.887556 −0.443778 0.896137i \(-0.646362\pi\)
−0.443778 + 0.896137i \(0.646362\pi\)
\(384\) 68.8946 3.51576
\(385\) 0.701042 0.0357284
\(386\) −2.38083 −0.121181
\(387\) −8.29507 −0.421662
\(388\) −16.2196 −0.823427
\(389\) 12.7440 0.646147 0.323074 0.946374i \(-0.395284\pi\)
0.323074 + 0.946374i \(0.395284\pi\)
\(390\) −72.7654 −3.68462
\(391\) 1.36597 0.0690801
\(392\) 25.4591 1.28588
\(393\) 43.4177 2.19013
\(394\) 8.87987 0.447361
\(395\) −26.1716 −1.31683
\(396\) 29.5883 1.48687
\(397\) −30.0644 −1.50889 −0.754445 0.656363i \(-0.772094\pi\)
−0.754445 + 0.656363i \(0.772094\pi\)
\(398\) −19.1643 −0.960621
\(399\) 4.50636 0.225600
\(400\) −1.09027 −0.0545134
\(401\) 14.6341 0.730794 0.365397 0.930852i \(-0.380933\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(402\) −70.5992 −3.52117
\(403\) −47.9287 −2.38750
\(404\) 33.5994 1.67163
\(405\) −72.5358 −3.60433
\(406\) −2.44661 −0.121423
\(407\) 8.29228 0.411033
\(408\) 12.4255 0.615156
\(409\) −5.37086 −0.265572 −0.132786 0.991145i \(-0.542392\pi\)
−0.132786 + 0.991145i \(0.542392\pi\)
\(410\) 35.5701 1.75668
\(411\) 58.4494 2.88309
\(412\) −22.0240 −1.08504
\(413\) 2.15550 0.106065
\(414\) 26.7345 1.31393
\(415\) 5.91682 0.290445
\(416\) −16.1011 −0.789421
\(417\) −56.8330 −2.78313
\(418\) 9.37320 0.458458
\(419\) −20.6886 −1.01070 −0.505352 0.862914i \(-0.668637\pi\)
−0.505352 + 0.862914i \(0.668637\pi\)
\(420\) 8.40404 0.410075
\(421\) 30.3001 1.47674 0.738369 0.674397i \(-0.235596\pi\)
0.738369 + 0.674397i \(0.235596\pi\)
\(422\) 29.1116 1.41713
\(423\) −11.3298 −0.550872
\(424\) −20.5879 −0.999837
\(425\) 0.685985 0.0332752
\(426\) −17.5568 −0.850630
\(427\) 1.37661 0.0666190
\(428\) 34.4295 1.66421
\(429\) −14.8482 −0.716879
\(430\) −4.90061 −0.236329
\(431\) 19.5301 0.940734 0.470367 0.882471i \(-0.344122\pi\)
0.470367 + 0.882471i \(0.344122\pi\)
\(432\) 28.2836 1.36080
\(433\) 16.0481 0.771224 0.385612 0.922661i \(-0.373990\pi\)
0.385612 + 0.922661i \(0.373990\pi\)
\(434\) 8.63929 0.414699
\(435\) 21.4455 1.02823
\(436\) −8.91870 −0.427128
\(437\) 5.42650 0.259585
\(438\) 70.2838 3.35829
\(439\) −2.35071 −0.112193 −0.0560966 0.998425i \(-0.517865\pi\)
−0.0560966 + 0.998425i \(0.517865\pi\)
\(440\) 7.67912 0.366088
\(441\) −57.1205 −2.72002
\(442\) −10.4241 −0.495825
\(443\) −0.379417 −0.0180266 −0.00901331 0.999959i \(-0.502869\pi\)
−0.00901331 + 0.999959i \(0.502869\pi\)
\(444\) 99.4072 4.71766
\(445\) 4.19975 0.199087
\(446\) −33.4386 −1.58336
\(447\) 72.3649 3.42274
\(448\) 3.97515 0.187808
\(449\) −17.1371 −0.808750 −0.404375 0.914593i \(-0.632511\pi\)
−0.404375 + 0.914593i \(0.632511\pi\)
\(450\) 13.4259 0.632905
\(451\) 7.25830 0.341780
\(452\) −24.8493 −1.16881
\(453\) 6.93707 0.325932
\(454\) −25.3212 −1.18838
\(455\) −3.09724 −0.145201
\(456\) 49.3621 2.31159
\(457\) −26.6400 −1.24617 −0.623084 0.782155i \(-0.714121\pi\)
−0.623084 + 0.782155i \(0.714121\pi\)
\(458\) −39.9594 −1.86718
\(459\) −17.7958 −0.830635
\(460\) 10.1200 0.471849
\(461\) −16.2355 −0.756162 −0.378081 0.925773i \(-0.623416\pi\)
−0.378081 + 0.925773i \(0.623416\pi\)
\(462\) 2.67644 0.124519
\(463\) −11.0304 −0.512628 −0.256314 0.966594i \(-0.582508\pi\)
−0.256314 + 0.966594i \(0.582508\pi\)
\(464\) −4.88281 −0.226679
\(465\) −75.7270 −3.51176
\(466\) 23.5073 1.08895
\(467\) −29.4707 −1.36374 −0.681870 0.731473i \(-0.738833\pi\)
−0.681870 + 0.731473i \(0.738833\pi\)
\(468\) −130.722 −6.04265
\(469\) −3.00503 −0.138759
\(470\) −6.69347 −0.308747
\(471\) 45.2790 2.08635
\(472\) 23.6111 1.08679
\(473\) −1.00000 −0.0459800
\(474\) −99.9178 −4.58938
\(475\) 2.72517 0.125039
\(476\) 1.20393 0.0551823
\(477\) 46.1914 2.11496
\(478\) 4.28404 0.195948
\(479\) 4.34472 0.198515 0.0992576 0.995062i \(-0.468353\pi\)
0.0992576 + 0.995062i \(0.468353\pi\)
\(480\) −25.4396 −1.16115
\(481\) −36.6357 −1.67044
\(482\) 9.24510 0.421103
\(483\) 1.54949 0.0705043
\(484\) 3.56697 0.162135
\(485\) 9.44456 0.428856
\(486\) −150.963 −6.84782
\(487\) 13.3720 0.605944 0.302972 0.952999i \(-0.402021\pi\)
0.302972 + 0.952999i \(0.402021\pi\)
\(488\) 15.0792 0.682605
\(489\) 20.5658 0.930016
\(490\) −33.7460 −1.52449
\(491\) 25.4078 1.14664 0.573319 0.819333i \(-0.305656\pi\)
0.573319 + 0.819333i \(0.305656\pi\)
\(492\) 87.0120 3.92280
\(493\) 3.07221 0.138365
\(494\) −41.4112 −1.86318
\(495\) −17.2290 −0.774388
\(496\) 17.2419 0.774182
\(497\) −0.747299 −0.0335210
\(498\) 22.5892 1.01225
\(499\) 7.54504 0.337762 0.168881 0.985636i \(-0.445985\pi\)
0.168881 + 0.985636i \(0.445985\pi\)
\(500\) 42.1256 1.88391
\(501\) 45.2514 2.02168
\(502\) 48.4909 2.16426
\(503\) −17.2015 −0.766975 −0.383488 0.923546i \(-0.625277\pi\)
−0.383488 + 0.923546i \(0.625277\pi\)
\(504\) 10.3513 0.461083
\(505\) −19.5647 −0.870618
\(506\) 3.22293 0.143277
\(507\) 21.9096 0.973040
\(508\) 10.5331 0.467330
\(509\) 39.4081 1.74674 0.873368 0.487062i \(-0.161931\pi\)
0.873368 + 0.487062i \(0.161931\pi\)
\(510\) −16.4700 −0.729306
\(511\) 2.99160 0.132341
\(512\) 17.5444 0.775361
\(513\) −70.6960 −3.12130
\(514\) 48.2987 2.13036
\(515\) 12.8244 0.565111
\(516\) −11.9879 −0.527739
\(517\) −1.36584 −0.0600697
\(518\) 6.60369 0.290149
\(519\) 60.0198 2.63458
\(520\) −33.9267 −1.48779
\(521\) −12.2266 −0.535656 −0.267828 0.963467i \(-0.586306\pi\)
−0.267828 + 0.963467i \(0.586306\pi\)
\(522\) 60.1286 2.63176
\(523\) −23.0443 −1.00766 −0.503828 0.863804i \(-0.668075\pi\)
−0.503828 + 0.863804i \(0.668075\pi\)
\(524\) 46.0810 2.01306
\(525\) 0.778148 0.0339612
\(526\) −30.4556 −1.32793
\(527\) −10.8484 −0.472563
\(528\) 5.34150 0.232459
\(529\) −21.1341 −0.918875
\(530\) 27.2892 1.18537
\(531\) −52.9743 −2.29889
\(532\) 4.78279 0.207360
\(533\) −32.0675 −1.38900
\(534\) 16.0338 0.693850
\(535\) −20.0480 −0.866751
\(536\) −32.9167 −1.42179
\(537\) 45.1440 1.94811
\(538\) −53.1779 −2.29266
\(539\) −6.88608 −0.296604
\(540\) −131.843 −5.67362
\(541\) −2.70828 −0.116438 −0.0582189 0.998304i \(-0.518542\pi\)
−0.0582189 + 0.998304i \(0.518542\pi\)
\(542\) −22.5535 −0.968757
\(543\) −36.4363 −1.56363
\(544\) −3.64439 −0.156252
\(545\) 5.19329 0.222456
\(546\) −11.8246 −0.506047
\(547\) 5.03151 0.215132 0.107566 0.994198i \(-0.465694\pi\)
0.107566 + 0.994198i \(0.465694\pi\)
\(548\) 62.0347 2.64999
\(549\) −33.8321 −1.44392
\(550\) 1.61854 0.0690149
\(551\) 12.2048 0.519941
\(552\) 16.9729 0.722416
\(553\) −4.25297 −0.180855
\(554\) −72.9193 −3.09804
\(555\) −57.8841 −2.45704
\(556\) −60.3193 −2.55811
\(557\) 0.182720 0.00774211 0.00387106 0.999993i \(-0.498768\pi\)
0.00387106 + 0.999993i \(0.498768\pi\)
\(558\) −212.322 −8.98831
\(559\) 4.41805 0.186863
\(560\) 1.11420 0.0470835
\(561\) −3.36081 −0.141894
\(562\) 10.3258 0.435568
\(563\) −0.876473 −0.0369389 −0.0184695 0.999829i \(-0.505879\pi\)
−0.0184695 + 0.999829i \(0.505879\pi\)
\(564\) −16.3736 −0.689454
\(565\) 14.4696 0.608739
\(566\) 5.96890 0.250891
\(567\) −11.7873 −0.495021
\(568\) −8.18582 −0.343469
\(569\) 24.0649 1.00885 0.504426 0.863455i \(-0.331704\pi\)
0.504426 + 0.863455i \(0.331704\pi\)
\(570\) −65.4294 −2.74054
\(571\) 2.91979 0.122189 0.0610947 0.998132i \(-0.480541\pi\)
0.0610947 + 0.998132i \(0.480541\pi\)
\(572\) −15.7590 −0.658919
\(573\) 2.58811 0.108120
\(574\) 5.78026 0.241264
\(575\) 0.937036 0.0390771
\(576\) −97.6946 −4.07061
\(577\) 33.2108 1.38258 0.691291 0.722576i \(-0.257042\pi\)
0.691291 + 0.722576i \(0.257042\pi\)
\(578\) −2.35944 −0.0981399
\(579\) 3.39128 0.140937
\(580\) 22.7610 0.945100
\(581\) 0.961503 0.0398899
\(582\) 36.0575 1.49463
\(583\) 5.56854 0.230625
\(584\) 32.7697 1.35602
\(585\) 76.1187 3.14712
\(586\) 32.9192 1.35988
\(587\) 11.3106 0.466838 0.233419 0.972376i \(-0.425009\pi\)
0.233419 + 0.972376i \(0.425009\pi\)
\(588\) −82.5498 −3.40430
\(589\) −43.0967 −1.77577
\(590\) −31.2965 −1.28846
\(591\) −12.6486 −0.520293
\(592\) 13.1793 0.541666
\(593\) 22.2422 0.913376 0.456688 0.889627i \(-0.349036\pi\)
0.456688 + 0.889627i \(0.349036\pi\)
\(594\) −41.9881 −1.72279
\(595\) −0.701042 −0.0287399
\(596\) 76.8039 3.14601
\(597\) 27.2979 1.11723
\(598\) −14.2391 −0.582279
\(599\) 43.8440 1.79142 0.895709 0.444640i \(-0.146669\pi\)
0.895709 + 0.444640i \(0.146669\pi\)
\(600\) 8.52374 0.347980
\(601\) −39.7992 −1.62344 −0.811722 0.584043i \(-0.801470\pi\)
−0.811722 + 0.584043i \(0.801470\pi\)
\(602\) −0.796366 −0.0324575
\(603\) 73.8526 3.00751
\(604\) 7.36260 0.299580
\(605\) −2.07702 −0.0844429
\(606\) −74.6941 −3.03424
\(607\) −1.22924 −0.0498934 −0.0249467 0.999689i \(-0.507942\pi\)
−0.0249467 + 0.999689i \(0.507942\pi\)
\(608\) −14.4778 −0.587153
\(609\) 3.48497 0.141218
\(610\) −19.9875 −0.809271
\(611\) 6.03436 0.244124
\(612\) −29.5883 −1.19604
\(613\) −30.0021 −1.21177 −0.605887 0.795551i \(-0.707181\pi\)
−0.605887 + 0.795551i \(0.707181\pi\)
\(614\) 64.8655 2.61776
\(615\) −50.6664 −2.04307
\(616\) 1.24788 0.0502787
\(617\) 37.2819 1.50091 0.750456 0.660920i \(-0.229834\pi\)
0.750456 + 0.660920i \(0.229834\pi\)
\(618\) 48.9610 1.96950
\(619\) 20.8779 0.839153 0.419577 0.907720i \(-0.362179\pi\)
0.419577 + 0.907720i \(0.362179\pi\)
\(620\) −80.3722 −3.22783
\(621\) −24.3085 −0.975466
\(622\) 15.3978 0.617397
\(623\) 0.682473 0.0273427
\(624\) −23.5990 −0.944716
\(625\) −21.0995 −0.843980
\(626\) −30.1024 −1.20313
\(627\) −13.3513 −0.533199
\(628\) 48.0565 1.91766
\(629\) −8.29228 −0.330635
\(630\) −13.7206 −0.546643
\(631\) 41.5113 1.65254 0.826270 0.563275i \(-0.190459\pi\)
0.826270 + 0.563275i \(0.190459\pi\)
\(632\) −46.5865 −1.85311
\(633\) −41.4669 −1.64816
\(634\) −59.6847 −2.37038
\(635\) −6.13334 −0.243394
\(636\) 66.7553 2.64702
\(637\) 30.4230 1.20540
\(638\) 7.24871 0.286979
\(639\) 18.3659 0.726543
\(640\) −42.5777 −1.68303
\(641\) 24.9781 0.986574 0.493287 0.869867i \(-0.335795\pi\)
0.493287 + 0.869867i \(0.335795\pi\)
\(642\) −76.5393 −3.02077
\(643\) −44.5545 −1.75706 −0.878528 0.477691i \(-0.841474\pi\)
−0.878528 + 0.477691i \(0.841474\pi\)
\(644\) 1.64454 0.0648040
\(645\) 6.98048 0.274856
\(646\) −9.37320 −0.368784
\(647\) −22.1384 −0.870352 −0.435176 0.900345i \(-0.643314\pi\)
−0.435176 + 0.900345i \(0.643314\pi\)
\(648\) −129.117 −5.07218
\(649\) −6.38624 −0.250682
\(650\) −7.15080 −0.280477
\(651\) −12.3059 −0.482306
\(652\) 21.8273 0.854823
\(653\) −31.4314 −1.23001 −0.615004 0.788524i \(-0.710846\pi\)
−0.615004 + 0.788524i \(0.710846\pi\)
\(654\) 19.8269 0.775295
\(655\) −26.8326 −1.04844
\(656\) 11.5360 0.450403
\(657\) −73.5227 −2.86839
\(658\) −1.08771 −0.0424034
\(659\) 1.53993 0.0599872 0.0299936 0.999550i \(-0.490451\pi\)
0.0299936 + 0.999550i \(0.490451\pi\)
\(660\) −24.8992 −0.969199
\(661\) −3.03722 −0.118134 −0.0590670 0.998254i \(-0.518813\pi\)
−0.0590670 + 0.998254i \(0.518813\pi\)
\(662\) −61.3256 −2.38349
\(663\) 14.8482 0.576658
\(664\) 10.5322 0.408728
\(665\) −2.78498 −0.107997
\(666\) −162.294 −6.28878
\(667\) 4.19655 0.162491
\(668\) 48.0271 1.85823
\(669\) 47.6303 1.84149
\(670\) 43.6311 1.68562
\(671\) −4.07858 −0.157452
\(672\) −4.13402 −0.159473
\(673\) −33.5405 −1.29289 −0.646445 0.762960i \(-0.723745\pi\)
−0.646445 + 0.762960i \(0.723745\pi\)
\(674\) 26.8402 1.03385
\(675\) −12.2076 −0.469872
\(676\) 23.2536 0.894368
\(677\) −1.78472 −0.0685922 −0.0342961 0.999412i \(-0.510919\pi\)
−0.0342961 + 0.999412i \(0.510919\pi\)
\(678\) 55.2419 2.12155
\(679\) 1.53477 0.0588992
\(680\) −7.67912 −0.294481
\(681\) 36.0677 1.38212
\(682\) −25.5962 −0.980128
\(683\) 4.28474 0.163951 0.0819756 0.996634i \(-0.473877\pi\)
0.0819756 + 0.996634i \(0.473877\pi\)
\(684\) −117.543 −4.49438
\(685\) −36.1224 −1.38016
\(686\) −11.0584 −0.422212
\(687\) 56.9186 2.17158
\(688\) −1.58935 −0.0605933
\(689\) −24.6021 −0.937264
\(690\) −22.4976 −0.856469
\(691\) 48.2437 1.83528 0.917639 0.397415i \(-0.130093\pi\)
0.917639 + 0.397415i \(0.130093\pi\)
\(692\) 63.7015 2.42157
\(693\) −2.79978 −0.106355
\(694\) −40.5649 −1.53982
\(695\) 35.1234 1.33231
\(696\) 38.1739 1.44698
\(697\) −7.25830 −0.274928
\(698\) −10.4002 −0.393653
\(699\) −33.4840 −1.26648
\(700\) 0.825881 0.0312154
\(701\) 31.9011 1.20489 0.602444 0.798161i \(-0.294194\pi\)
0.602444 + 0.798161i \(0.294194\pi\)
\(702\) 185.505 7.00144
\(703\) −32.9422 −1.24244
\(704\) −11.7774 −0.443878
\(705\) 9.53424 0.359080
\(706\) 29.9509 1.12722
\(707\) −3.17933 −0.119571
\(708\) −76.5578 −2.87722
\(709\) −13.9798 −0.525021 −0.262511 0.964929i \(-0.584551\pi\)
−0.262511 + 0.964929i \(0.584551\pi\)
\(710\) 10.8503 0.407205
\(711\) 104.522 3.91989
\(712\) 7.47572 0.280165
\(713\) −14.8186 −0.554961
\(714\) −2.67644 −0.100163
\(715\) 9.17637 0.343177
\(716\) 47.9132 1.79060
\(717\) −6.10224 −0.227892
\(718\) −84.1898 −3.14193
\(719\) −11.9355 −0.445119 −0.222560 0.974919i \(-0.571441\pi\)
−0.222560 + 0.974919i \(0.571441\pi\)
\(720\) −27.3829 −1.02050
\(721\) 2.08401 0.0776125
\(722\) 7.59316 0.282588
\(723\) −13.1688 −0.489753
\(724\) −38.6713 −1.43721
\(725\) 2.10749 0.0782703
\(726\) −7.92965 −0.294297
\(727\) −27.7919 −1.03074 −0.515372 0.856967i \(-0.672346\pi\)
−0.515372 + 0.856967i \(0.672346\pi\)
\(728\) −5.51321 −0.204333
\(729\) 110.264 4.08386
\(730\) −43.4362 −1.60764
\(731\) 1.00000 0.0369863
\(732\) −48.8937 −1.80716
\(733\) 40.5665 1.49836 0.749179 0.662368i \(-0.230448\pi\)
0.749179 + 0.662368i \(0.230448\pi\)
\(734\) 85.5081 3.15616
\(735\) 48.0681 1.77302
\(736\) −4.97813 −0.183496
\(737\) 8.90319 0.327953
\(738\) −142.058 −5.22921
\(739\) 15.8992 0.584861 0.292430 0.956287i \(-0.405536\pi\)
0.292430 + 0.956287i \(0.405536\pi\)
\(740\) −61.4348 −2.25839
\(741\) 58.9866 2.16693
\(742\) 4.43459 0.162799
\(743\) 40.0958 1.47097 0.735486 0.677540i \(-0.236954\pi\)
0.735486 + 0.677540i \(0.236954\pi\)
\(744\) −134.797 −4.94190
\(745\) −44.7223 −1.63850
\(746\) 50.1222 1.83510
\(747\) −23.6302 −0.864584
\(748\) −3.56697 −0.130421
\(749\) −3.25787 −0.119040
\(750\) −93.6484 −3.41956
\(751\) −5.93359 −0.216520 −0.108260 0.994123i \(-0.534528\pi\)
−0.108260 + 0.994123i \(0.534528\pi\)
\(752\) −2.17080 −0.0791608
\(753\) −69.0710 −2.51709
\(754\) −32.0251 −1.16629
\(755\) −4.28719 −0.156027
\(756\) −21.4249 −0.779217
\(757\) 51.6664 1.87785 0.938924 0.344125i \(-0.111824\pi\)
0.938924 + 0.344125i \(0.111824\pi\)
\(758\) 9.48032 0.344341
\(759\) −4.59078 −0.166635
\(760\) −30.5063 −1.10658
\(761\) 2.99731 0.108652 0.0543262 0.998523i \(-0.482699\pi\)
0.0543262 + 0.998523i \(0.482699\pi\)
\(762\) −23.4159 −0.848267
\(763\) 0.843927 0.0305522
\(764\) 2.74686 0.0993780
\(765\) 17.2290 0.622917
\(766\) 40.9831 1.48078
\(767\) 28.2147 1.01877
\(768\) −83.3895 −3.00906
\(769\) 10.3755 0.374150 0.187075 0.982346i \(-0.440099\pi\)
0.187075 + 0.982346i \(0.440099\pi\)
\(770\) −1.65407 −0.0596085
\(771\) −68.7971 −2.47767
\(772\) 3.59931 0.129542
\(773\) 14.3298 0.515408 0.257704 0.966224i \(-0.417034\pi\)
0.257704 + 0.966224i \(0.417034\pi\)
\(774\) 19.5718 0.703492
\(775\) −7.44184 −0.267319
\(776\) 16.8117 0.603505
\(777\) −9.40636 −0.337451
\(778\) −30.0688 −1.07802
\(779\) −28.8345 −1.03310
\(780\) 110.006 3.93884
\(781\) 2.21407 0.0792257
\(782\) −3.22293 −0.115252
\(783\) −54.6723 −1.95383
\(784\) −10.9444 −0.390870
\(785\) −27.9829 −0.998753
\(786\) −102.442 −3.65397
\(787\) 1.35046 0.0481386 0.0240693 0.999710i \(-0.492338\pi\)
0.0240693 + 0.999710i \(0.492338\pi\)
\(788\) −13.4245 −0.478227
\(789\) 43.3812 1.54441
\(790\) 61.7503 2.19698
\(791\) 2.35135 0.0836045
\(792\) −30.6684 −1.08975
\(793\) 18.0193 0.639886
\(794\) 70.9353 2.51740
\(795\) −38.8711 −1.37861
\(796\) 28.9723 1.02690
\(797\) −17.0552 −0.604125 −0.302063 0.953288i \(-0.597675\pi\)
−0.302063 + 0.953288i \(0.597675\pi\)
\(798\) −10.6325 −0.376386
\(799\) 1.36584 0.0483200
\(800\) −2.50000 −0.0883883
\(801\) −16.7727 −0.592634
\(802\) −34.5284 −1.21924
\(803\) −8.86341 −0.312783
\(804\) 106.731 3.76411
\(805\) −0.957603 −0.0337511
\(806\) 113.085 3.98325
\(807\) 75.7471 2.66642
\(808\) −34.8260 −1.22517
\(809\) 20.0216 0.703921 0.351960 0.936015i \(-0.385515\pi\)
0.351960 + 0.936015i \(0.385515\pi\)
\(810\) 171.144 6.01339
\(811\) 45.0362 1.58144 0.790718 0.612180i \(-0.209707\pi\)
0.790718 + 0.612180i \(0.209707\pi\)
\(812\) 3.69874 0.129800
\(813\) 32.1255 1.12669
\(814\) −19.5652 −0.685758
\(815\) −12.7099 −0.445207
\(816\) −5.34150 −0.186990
\(817\) 3.97263 0.138985
\(818\) 12.6722 0.443074
\(819\) 12.3695 0.432227
\(820\) −53.7744 −1.87788
\(821\) −30.3782 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(822\) −137.908 −4.81009
\(823\) −52.8826 −1.84337 −0.921686 0.387936i \(-0.873188\pi\)
−0.921686 + 0.387936i \(0.873188\pi\)
\(824\) 22.8280 0.795250
\(825\) −2.30547 −0.0802661
\(826\) −5.08579 −0.176957
\(827\) −12.6229 −0.438942 −0.219471 0.975619i \(-0.570433\pi\)
−0.219471 + 0.975619i \(0.570433\pi\)
\(828\) −40.4168 −1.40458
\(829\) −25.8805 −0.898865 −0.449433 0.893314i \(-0.648374\pi\)
−0.449433 + 0.893314i \(0.648374\pi\)
\(830\) −13.9604 −0.484572
\(831\) 103.867 3.60310
\(832\) 52.0332 1.80393
\(833\) 6.88608 0.238588
\(834\) 134.094 4.64331
\(835\) −27.9658 −0.967798
\(836\) −14.1703 −0.490089
\(837\) 193.055 6.67297
\(838\) 48.8135 1.68623
\(839\) −26.1294 −0.902085 −0.451043 0.892502i \(-0.648948\pi\)
−0.451043 + 0.892502i \(0.648948\pi\)
\(840\) −8.71083 −0.300552
\(841\) −19.5615 −0.674535
\(842\) −71.4914 −2.46376
\(843\) −14.7082 −0.506576
\(844\) −44.0106 −1.51491
\(845\) −13.5404 −0.465803
\(846\) 26.7319 0.919063
\(847\) −0.337523 −0.0115974
\(848\) 8.85034 0.303922
\(849\) −8.50215 −0.291793
\(850\) −1.61854 −0.0555156
\(851\) −11.3270 −0.388285
\(852\) 26.5421 0.909318
\(853\) 26.0421 0.891666 0.445833 0.895116i \(-0.352908\pi\)
0.445833 + 0.895116i \(0.352908\pi\)
\(854\) −3.24804 −0.111146
\(855\) 68.4446 2.34076
\(856\) −35.6863 −1.21973
\(857\) 46.5265 1.58931 0.794657 0.607059i \(-0.207651\pi\)
0.794657 + 0.607059i \(0.207651\pi\)
\(858\) 35.0336 1.19603
\(859\) −27.4136 −0.935340 −0.467670 0.883903i \(-0.654906\pi\)
−0.467670 + 0.883903i \(0.654906\pi\)
\(860\) 7.40868 0.252634
\(861\) −8.23346 −0.280596
\(862\) −46.0803 −1.56950
\(863\) 28.5879 0.973143 0.486571 0.873641i \(-0.338247\pi\)
0.486571 + 0.873641i \(0.338247\pi\)
\(864\) 64.8547 2.20640
\(865\) −37.0929 −1.26120
\(866\) −37.8647 −1.28669
\(867\) 3.36081 0.114139
\(868\) −13.0608 −0.443311
\(869\) 12.6005 0.427444
\(870\) −50.5995 −1.71548
\(871\) −39.3347 −1.33281
\(872\) 9.24427 0.313050
\(873\) −37.7191 −1.27660
\(874\) −12.8035 −0.433085
\(875\) −3.98611 −0.134755
\(876\) −106.254 −3.58999
\(877\) −21.0458 −0.710667 −0.355334 0.934740i \(-0.615633\pi\)
−0.355334 + 0.934740i \(0.615633\pi\)
\(878\) 5.54636 0.187181
\(879\) −46.8904 −1.58157
\(880\) −3.30111 −0.111280
\(881\) 50.2925 1.69440 0.847199 0.531275i \(-0.178287\pi\)
0.847199 + 0.531275i \(0.178287\pi\)
\(882\) 134.773 4.53803
\(883\) −8.48445 −0.285525 −0.142762 0.989757i \(-0.545598\pi\)
−0.142762 + 0.989757i \(0.545598\pi\)
\(884\) 15.7590 0.530034
\(885\) 44.5790 1.49851
\(886\) 0.895212 0.0300752
\(887\) −43.9041 −1.47416 −0.737078 0.675807i \(-0.763795\pi\)
−0.737078 + 0.675807i \(0.763795\pi\)
\(888\) −103.036 −3.45766
\(889\) −0.996688 −0.0334279
\(890\) −9.90907 −0.332153
\(891\) 34.9230 1.16996
\(892\) 50.5520 1.69261
\(893\) 5.42599 0.181574
\(894\) −170.741 −5.71043
\(895\) −27.8995 −0.932577
\(896\) −6.91901 −0.231148
\(897\) 20.2823 0.677205
\(898\) 40.4341 1.34930
\(899\) −33.3286 −1.11157
\(900\) −20.2971 −0.676571
\(901\) −5.56854 −0.185515
\(902\) −17.1255 −0.570218
\(903\) 1.13435 0.0377489
\(904\) 25.7564 0.856646
\(905\) 22.5180 0.748524
\(906\) −16.3676 −0.543778
\(907\) 13.1570 0.436870 0.218435 0.975852i \(-0.429905\pi\)
0.218435 + 0.975852i \(0.429905\pi\)
\(908\) 38.2802 1.27037
\(909\) 78.1362 2.59162
\(910\) 7.30775 0.242250
\(911\) −51.9515 −1.72123 −0.860616 0.509255i \(-0.829921\pi\)
−0.860616 + 0.509255i \(0.829921\pi\)
\(912\) −21.2198 −0.702658
\(913\) −2.84870 −0.0942784
\(914\) 62.8556 2.07908
\(915\) 28.4704 0.941203
\(916\) 60.4101 1.99601
\(917\) −4.36039 −0.143993
\(918\) 41.9881 1.38581
\(919\) 37.0574 1.22241 0.611206 0.791472i \(-0.290685\pi\)
0.611206 + 0.791472i \(0.290685\pi\)
\(920\) −10.4895 −0.345827
\(921\) −92.3951 −3.04452
\(922\) 38.3067 1.26156
\(923\) −9.78187 −0.321974
\(924\) −4.04620 −0.133110
\(925\) −5.68838 −0.187033
\(926\) 26.0257 0.855258
\(927\) −51.2173 −1.68220
\(928\) −11.1963 −0.367538
\(929\) 41.6931 1.36791 0.683953 0.729526i \(-0.260259\pi\)
0.683953 + 0.729526i \(0.260259\pi\)
\(930\) 178.674 5.85894
\(931\) 27.3559 0.896552
\(932\) −35.5380 −1.16408
\(933\) −21.9328 −0.718048
\(934\) 69.5344 2.27524
\(935\) 2.07702 0.0679258
\(936\) 135.494 4.42877
\(937\) 38.0417 1.24277 0.621384 0.783506i \(-0.286571\pi\)
0.621384 + 0.783506i \(0.286571\pi\)
\(938\) 7.09020 0.231503
\(939\) 42.8781 1.39927
\(940\) 10.1191 0.330048
\(941\) −48.6921 −1.58732 −0.793658 0.608364i \(-0.791826\pi\)
−0.793658 + 0.608364i \(0.791826\pi\)
\(942\) −106.833 −3.48081
\(943\) −9.91463 −0.322865
\(944\) −10.1500 −0.330353
\(945\) 12.4756 0.405830
\(946\) 2.35944 0.0767121
\(947\) −6.18677 −0.201043 −0.100522 0.994935i \(-0.532051\pi\)
−0.100522 + 0.994935i \(0.532051\pi\)
\(948\) 151.054 4.90602
\(949\) 39.1590 1.27115
\(950\) −6.42988 −0.208613
\(951\) 85.0154 2.75681
\(952\) −1.24788 −0.0404441
\(953\) −27.0302 −0.875594 −0.437797 0.899074i \(-0.644241\pi\)
−0.437797 + 0.899074i \(0.644241\pi\)
\(954\) −108.986 −3.52855
\(955\) −1.59948 −0.0517579
\(956\) −6.47656 −0.209467
\(957\) −10.3251 −0.333764
\(958\) −10.2511 −0.331198
\(959\) −5.87000 −0.189552
\(960\) 82.2121 2.65338
\(961\) 86.6876 2.79637
\(962\) 86.4398 2.78693
\(963\) 80.0665 2.58011
\(964\) −13.9766 −0.450156
\(965\) −2.09585 −0.0674678
\(966\) −3.65594 −0.117628
\(967\) 35.3552 1.13695 0.568473 0.822702i \(-0.307534\pi\)
0.568473 + 0.822702i \(0.307534\pi\)
\(968\) −3.69718 −0.118832
\(969\) 13.3513 0.428905
\(970\) −22.2839 −0.715493
\(971\) 46.4813 1.49165 0.745827 0.666139i \(-0.232054\pi\)
0.745827 + 0.666139i \(0.232054\pi\)
\(972\) 228.224 7.32028
\(973\) 5.70768 0.182980
\(974\) −31.5505 −1.01094
\(975\) 10.1857 0.326202
\(976\) −6.48227 −0.207492
\(977\) −5.89654 −0.188647 −0.0943235 0.995542i \(-0.530069\pi\)
−0.0943235 + 0.995542i \(0.530069\pi\)
\(978\) −48.5238 −1.55162
\(979\) −2.02201 −0.0646236
\(980\) 51.0167 1.62967
\(981\) −20.7406 −0.662197
\(982\) −59.9482 −1.91302
\(983\) 6.13640 0.195721 0.0978604 0.995200i \(-0.468800\pi\)
0.0978604 + 0.995200i \(0.468800\pi\)
\(984\) −90.1883 −2.87510
\(985\) 7.81696 0.249069
\(986\) −7.24871 −0.230846
\(987\) 1.54935 0.0493162
\(988\) 62.6049 1.99173
\(989\) 1.36597 0.0434354
\(990\) 40.6509 1.29197
\(991\) 18.5991 0.590819 0.295409 0.955371i \(-0.404544\pi\)
0.295409 + 0.955371i \(0.404544\pi\)
\(992\) 39.5358 1.25526
\(993\) 87.3527 2.77206
\(994\) 1.76321 0.0559256
\(995\) −16.8704 −0.534827
\(996\) −34.1501 −1.08209
\(997\) 2.40123 0.0760476 0.0380238 0.999277i \(-0.487894\pi\)
0.0380238 + 0.999277i \(0.487894\pi\)
\(998\) −17.8021 −0.563515
\(999\) 147.567 4.66882
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 \(a_p\))