Properties

Label 8007.2.a.j.1.16
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.62615 q^{2} -1.00000 q^{3} +0.644366 q^{4} +0.536374 q^{5} +1.62615 q^{6} +4.53678 q^{7} +2.20447 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.62615 q^{2} -1.00000 q^{3} +0.644366 q^{4} +0.536374 q^{5} +1.62615 q^{6} +4.53678 q^{7} +2.20447 q^{8} +1.00000 q^{9} -0.872225 q^{10} +2.87790 q^{11} -0.644366 q^{12} +1.05243 q^{13} -7.37748 q^{14} -0.536374 q^{15} -4.87352 q^{16} +1.00000 q^{17} -1.62615 q^{18} +6.13593 q^{19} +0.345621 q^{20} -4.53678 q^{21} -4.67990 q^{22} +2.66713 q^{23} -2.20447 q^{24} -4.71230 q^{25} -1.71140 q^{26} -1.00000 q^{27} +2.92334 q^{28} +4.14006 q^{29} +0.872225 q^{30} -2.93407 q^{31} +3.51615 q^{32} -2.87790 q^{33} -1.62615 q^{34} +2.43341 q^{35} +0.644366 q^{36} -5.20943 q^{37} -9.97794 q^{38} -1.05243 q^{39} +1.18242 q^{40} +0.258454 q^{41} +7.37748 q^{42} +0.594529 q^{43} +1.85442 q^{44} +0.536374 q^{45} -4.33715 q^{46} +4.62488 q^{47} +4.87352 q^{48} +13.5823 q^{49} +7.66291 q^{50} -1.00000 q^{51} +0.678147 q^{52} -4.78052 q^{53} +1.62615 q^{54} +1.54363 q^{55} +10.0012 q^{56} -6.13593 q^{57} -6.73235 q^{58} -2.88225 q^{59} -0.345621 q^{60} +10.4506 q^{61} +4.77124 q^{62} +4.53678 q^{63} +4.02926 q^{64} +0.564494 q^{65} +4.67990 q^{66} +16.2149 q^{67} +0.644366 q^{68} -2.66713 q^{69} -3.95709 q^{70} +9.88860 q^{71} +2.20447 q^{72} +2.83517 q^{73} +8.47132 q^{74} +4.71230 q^{75} +3.95378 q^{76} +13.0564 q^{77} +1.71140 q^{78} -4.89662 q^{79} -2.61403 q^{80} +1.00000 q^{81} -0.420286 q^{82} +2.12890 q^{83} -2.92334 q^{84} +0.536374 q^{85} -0.966794 q^{86} -4.14006 q^{87} +6.34423 q^{88} -10.2701 q^{89} -0.872225 q^{90} +4.77462 q^{91} +1.71860 q^{92} +2.93407 q^{93} -7.52076 q^{94} +3.29115 q^{95} -3.51615 q^{96} +11.9098 q^{97} -22.0869 q^{98} +2.87790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q + 5q^{2} - 64q^{3} + 77q^{4} - 3q^{5} - 5q^{6} + 5q^{7} + 18q^{8} + 64q^{9} + O(q^{10}) \) \( 64q + 5q^{2} - 64q^{3} + 77q^{4} - 3q^{5} - 5q^{6} + 5q^{7} + 18q^{8} + 64q^{9} + 12q^{10} - 7q^{11} - 77q^{12} + 24q^{13} - 14q^{14} + 3q^{15} + 103q^{16} + 64q^{17} + 5q^{18} + 26q^{19} - 24q^{20} - 5q^{21} + 25q^{22} + 20q^{23} - 18q^{24} + 141q^{25} + 9q^{26} - 64q^{27} + 14q^{28} + 5q^{29} - 12q^{30} + 11q^{31} + 31q^{32} + 7q^{33} + 5q^{34} - 3q^{35} + 77q^{36} + 50q^{37} + 8q^{38} - 24q^{39} + 28q^{40} - 9q^{41} + 14q^{42} + 59q^{43} - 6q^{44} - 3q^{45} + 11q^{47} - 103q^{48} + 163q^{49} + 20q^{50} - 64q^{51} + 65q^{52} + 39q^{53} - 5q^{54} + 35q^{55} - 34q^{56} - 26q^{57} - 27q^{58} - 65q^{59} + 24q^{60} + 15q^{61} + 18q^{62} + 5q^{63} + 152q^{64} + 49q^{65} - 25q^{66} + 56q^{67} + 77q^{68} - 20q^{69} + 28q^{70} - 18q^{71} + 18q^{72} + 37q^{73} - 76q^{74} - 141q^{75} + 30q^{76} + 80q^{77} - 9q^{78} + 20q^{79} - 144q^{80} + 64q^{81} + 27q^{82} + 3q^{83} - 14q^{84} - 3q^{85} + 12q^{86} - 5q^{87} + 108q^{88} + 42q^{89} + 12q^{90} + 25q^{91} + 18q^{92} - 11q^{93} + 60q^{94} + 42q^{95} - 31q^{96} + 72q^{97} + 18q^{98} - 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.62615 −1.14986 −0.574931 0.818202i \(-0.694971\pi\)
−0.574931 + 0.818202i \(0.694971\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.644366 0.322183
\(5\) 0.536374 0.239874 0.119937 0.992782i \(-0.461731\pi\)
0.119937 + 0.992782i \(0.461731\pi\)
\(6\) 1.62615 0.663873
\(7\) 4.53678 1.71474 0.857370 0.514701i \(-0.172097\pi\)
0.857370 + 0.514701i \(0.172097\pi\)
\(8\) 2.20447 0.779396
\(9\) 1.00000 0.333333
\(10\) −0.872225 −0.275822
\(11\) 2.87790 0.867719 0.433860 0.900981i \(-0.357151\pi\)
0.433860 + 0.900981i \(0.357151\pi\)
\(12\) −0.644366 −0.186012
\(13\) 1.05243 0.291890 0.145945 0.989293i \(-0.453378\pi\)
0.145945 + 0.989293i \(0.453378\pi\)
\(14\) −7.37748 −1.97171
\(15\) −0.536374 −0.138491
\(16\) −4.87352 −1.21838
\(17\) 1.00000 0.242536
\(18\) −1.62615 −0.383287
\(19\) 6.13593 1.40768 0.703839 0.710359i \(-0.251467\pi\)
0.703839 + 0.710359i \(0.251467\pi\)
\(20\) 0.345621 0.0772832
\(21\) −4.53678 −0.990006
\(22\) −4.67990 −0.997757
\(23\) 2.66713 0.556134 0.278067 0.960562i \(-0.410306\pi\)
0.278067 + 0.960562i \(0.410306\pi\)
\(24\) −2.20447 −0.449985
\(25\) −4.71230 −0.942461
\(26\) −1.71140 −0.335634
\(27\) −1.00000 −0.192450
\(28\) 2.92334 0.552460
\(29\) 4.14006 0.768789 0.384395 0.923169i \(-0.374410\pi\)
0.384395 + 0.923169i \(0.374410\pi\)
\(30\) 0.872225 0.159246
\(31\) −2.93407 −0.526974 −0.263487 0.964663i \(-0.584873\pi\)
−0.263487 + 0.964663i \(0.584873\pi\)
\(32\) 3.51615 0.621574
\(33\) −2.87790 −0.500978
\(34\) −1.62615 −0.278883
\(35\) 2.43341 0.411321
\(36\) 0.644366 0.107394
\(37\) −5.20943 −0.856425 −0.428212 0.903678i \(-0.640857\pi\)
−0.428212 + 0.903678i \(0.640857\pi\)
\(38\) −9.97794 −1.61864
\(39\) −1.05243 −0.168523
\(40\) 1.18242 0.186957
\(41\) 0.258454 0.0403638 0.0201819 0.999796i \(-0.493575\pi\)
0.0201819 + 0.999796i \(0.493575\pi\)
\(42\) 7.37748 1.13837
\(43\) 0.594529 0.0906649 0.0453324 0.998972i \(-0.485565\pi\)
0.0453324 + 0.998972i \(0.485565\pi\)
\(44\) 1.85442 0.279564
\(45\) 0.536374 0.0799579
\(46\) −4.33715 −0.639477
\(47\) 4.62488 0.674609 0.337304 0.941396i \(-0.390485\pi\)
0.337304 + 0.941396i \(0.390485\pi\)
\(48\) 4.87352 0.703433
\(49\) 13.5823 1.94033
\(50\) 7.66291 1.08370
\(51\) −1.00000 −0.140028
\(52\) 0.678147 0.0940421
\(53\) −4.78052 −0.656654 −0.328327 0.944564i \(-0.606485\pi\)
−0.328327 + 0.944564i \(0.606485\pi\)
\(54\) 1.62615 0.221291
\(55\) 1.54363 0.208143
\(56\) 10.0012 1.33646
\(57\) −6.13593 −0.812724
\(58\) −6.73235 −0.884001
\(59\) −2.88225 −0.375237 −0.187618 0.982242i \(-0.560077\pi\)
−0.187618 + 0.982242i \(0.560077\pi\)
\(60\) −0.345621 −0.0446195
\(61\) 10.4506 1.33806 0.669029 0.743237i \(-0.266710\pi\)
0.669029 + 0.743237i \(0.266710\pi\)
\(62\) 4.77124 0.605948
\(63\) 4.53678 0.571580
\(64\) 4.02926 0.503657
\(65\) 0.564494 0.0700168
\(66\) 4.67990 0.576055
\(67\) 16.2149 1.98096 0.990481 0.137648i \(-0.0439542\pi\)
0.990481 + 0.137648i \(0.0439542\pi\)
\(68\) 0.644366 0.0781408
\(69\) −2.66713 −0.321084
\(70\) −3.95709 −0.472962
\(71\) 9.88860 1.17356 0.586780 0.809746i \(-0.300395\pi\)
0.586780 + 0.809746i \(0.300395\pi\)
\(72\) 2.20447 0.259799
\(73\) 2.83517 0.331831 0.165916 0.986140i \(-0.446942\pi\)
0.165916 + 0.986140i \(0.446942\pi\)
\(74\) 8.47132 0.984770
\(75\) 4.71230 0.544130
\(76\) 3.95378 0.453530
\(77\) 13.0564 1.48791
\(78\) 1.71140 0.193778
\(79\) −4.89662 −0.550913 −0.275456 0.961314i \(-0.588829\pi\)
−0.275456 + 0.961314i \(0.588829\pi\)
\(80\) −2.61403 −0.292258
\(81\) 1.00000 0.111111
\(82\) −0.420286 −0.0464128
\(83\) 2.12890 0.233678 0.116839 0.993151i \(-0.462724\pi\)
0.116839 + 0.993151i \(0.462724\pi\)
\(84\) −2.92334 −0.318963
\(85\) 0.536374 0.0581779
\(86\) −0.966794 −0.104252
\(87\) −4.14006 −0.443861
\(88\) 6.34423 0.676297
\(89\) −10.2701 −1.08863 −0.544313 0.838882i \(-0.683210\pi\)
−0.544313 + 0.838882i \(0.683210\pi\)
\(90\) −0.872225 −0.0919406
\(91\) 4.77462 0.500516
\(92\) 1.71860 0.179177
\(93\) 2.93407 0.304249
\(94\) −7.52076 −0.775707
\(95\) 3.29115 0.337665
\(96\) −3.51615 −0.358866
\(97\) 11.9098 1.20925 0.604627 0.796508i \(-0.293322\pi\)
0.604627 + 0.796508i \(0.293322\pi\)
\(98\) −22.0869 −2.23112
\(99\) 2.87790 0.289240
\(100\) −3.03645 −0.303645
\(101\) −13.8417 −1.37730 −0.688651 0.725093i \(-0.741797\pi\)
−0.688651 + 0.725093i \(0.741797\pi\)
\(102\) 1.62615 0.161013
\(103\) 15.2504 1.50267 0.751333 0.659923i \(-0.229411\pi\)
0.751333 + 0.659923i \(0.229411\pi\)
\(104\) 2.32004 0.227498
\(105\) −2.43341 −0.237476
\(106\) 7.77384 0.755062
\(107\) −13.9722 −1.35074 −0.675372 0.737477i \(-0.736017\pi\)
−0.675372 + 0.737477i \(0.736017\pi\)
\(108\) −0.644366 −0.0620041
\(109\) −6.26962 −0.600520 −0.300260 0.953857i \(-0.597074\pi\)
−0.300260 + 0.953857i \(0.597074\pi\)
\(110\) −2.51017 −0.239336
\(111\) 5.20943 0.494457
\(112\) −22.1101 −2.08921
\(113\) −3.82481 −0.359808 −0.179904 0.983684i \(-0.557579\pi\)
−0.179904 + 0.983684i \(0.557579\pi\)
\(114\) 9.97794 0.934520
\(115\) 1.43058 0.133402
\(116\) 2.66771 0.247691
\(117\) 1.05243 0.0972968
\(118\) 4.68697 0.431470
\(119\) 4.53678 0.415886
\(120\) −1.18242 −0.107939
\(121\) −2.71770 −0.247064
\(122\) −16.9942 −1.53858
\(123\) −0.258454 −0.0233040
\(124\) −1.89061 −0.169782
\(125\) −5.20943 −0.465945
\(126\) −7.37748 −0.657238
\(127\) 11.5276 1.02291 0.511455 0.859310i \(-0.329107\pi\)
0.511455 + 0.859310i \(0.329107\pi\)
\(128\) −13.5845 −1.20071
\(129\) −0.594529 −0.0523454
\(130\) −0.917952 −0.0805097
\(131\) 8.80112 0.768958 0.384479 0.923134i \(-0.374381\pi\)
0.384479 + 0.923134i \(0.374381\pi\)
\(132\) −1.85442 −0.161406
\(133\) 27.8373 2.41380
\(134\) −26.3678 −2.27783
\(135\) −0.536374 −0.0461637
\(136\) 2.20447 0.189031
\(137\) −15.2872 −1.30607 −0.653037 0.757326i \(-0.726505\pi\)
−0.653037 + 0.757326i \(0.726505\pi\)
\(138\) 4.33715 0.369203
\(139\) 13.7436 1.16572 0.582858 0.812574i \(-0.301934\pi\)
0.582858 + 0.812574i \(0.301934\pi\)
\(140\) 1.56800 0.132521
\(141\) −4.62488 −0.389486
\(142\) −16.0803 −1.34943
\(143\) 3.02878 0.253279
\(144\) −4.87352 −0.406127
\(145\) 2.22062 0.184412
\(146\) −4.61041 −0.381560
\(147\) −13.5823 −1.12025
\(148\) −3.35678 −0.275925
\(149\) 2.98768 0.244761 0.122380 0.992483i \(-0.460947\pi\)
0.122380 + 0.992483i \(0.460947\pi\)
\(150\) −7.66291 −0.625674
\(151\) 23.0024 1.87191 0.935955 0.352118i \(-0.114539\pi\)
0.935955 + 0.352118i \(0.114539\pi\)
\(152\) 13.5264 1.09714
\(153\) 1.00000 0.0808452
\(154\) −21.2316 −1.71089
\(155\) −1.57376 −0.126407
\(156\) −0.678147 −0.0542952
\(157\) −1.00000 −0.0798087
\(158\) 7.96264 0.633474
\(159\) 4.78052 0.379120
\(160\) 1.88597 0.149099
\(161\) 12.1001 0.953625
\(162\) −1.62615 −0.127762
\(163\) 14.6184 1.14500 0.572502 0.819903i \(-0.305973\pi\)
0.572502 + 0.819903i \(0.305973\pi\)
\(164\) 0.166539 0.0130045
\(165\) −1.54363 −0.120171
\(166\) −3.46192 −0.268697
\(167\) −0.252002 −0.0195005 −0.00975025 0.999952i \(-0.503104\pi\)
−0.00975025 + 0.999952i \(0.503104\pi\)
\(168\) −10.0012 −0.771607
\(169\) −11.8924 −0.914800
\(170\) −0.872225 −0.0668966
\(171\) 6.13593 0.469226
\(172\) 0.383094 0.0292107
\(173\) 15.8601 1.20582 0.602909 0.797810i \(-0.294008\pi\)
0.602909 + 0.797810i \(0.294008\pi\)
\(174\) 6.73235 0.510378
\(175\) −21.3787 −1.61607
\(176\) −14.0255 −1.05721
\(177\) 2.88225 0.216643
\(178\) 16.7007 1.25177
\(179\) 20.2145 1.51091 0.755453 0.655203i \(-0.227417\pi\)
0.755453 + 0.655203i \(0.227417\pi\)
\(180\) 0.345621 0.0257611
\(181\) 0.965690 0.0717791 0.0358896 0.999356i \(-0.488574\pi\)
0.0358896 + 0.999356i \(0.488574\pi\)
\(182\) −7.76425 −0.575525
\(183\) −10.4506 −0.772528
\(184\) 5.87959 0.433449
\(185\) −2.79420 −0.205434
\(186\) −4.77124 −0.349844
\(187\) 2.87790 0.210453
\(188\) 2.98012 0.217347
\(189\) −4.53678 −0.330002
\(190\) −5.35191 −0.388268
\(191\) −17.6222 −1.27510 −0.637550 0.770409i \(-0.720052\pi\)
−0.637550 + 0.770409i \(0.720052\pi\)
\(192\) −4.02926 −0.290786
\(193\) −14.3544 −1.03325 −0.516625 0.856212i \(-0.672812\pi\)
−0.516625 + 0.856212i \(0.672812\pi\)
\(194\) −19.3671 −1.39048
\(195\) −0.564494 −0.0404242
\(196\) 8.75199 0.625142
\(197\) 6.30328 0.449090 0.224545 0.974464i \(-0.427910\pi\)
0.224545 + 0.974464i \(0.427910\pi\)
\(198\) −4.67990 −0.332586
\(199\) −22.9260 −1.62518 −0.812592 0.582833i \(-0.801944\pi\)
−0.812592 + 0.582833i \(0.801944\pi\)
\(200\) −10.3881 −0.734550
\(201\) −16.2149 −1.14371
\(202\) 22.5087 1.58371
\(203\) 18.7825 1.31827
\(204\) −0.644366 −0.0451146
\(205\) 0.138628 0.00968221
\(206\) −24.7994 −1.72786
\(207\) 2.66713 0.185378
\(208\) −5.12902 −0.355634
\(209\) 17.6586 1.22147
\(210\) 3.95709 0.273065
\(211\) −28.1637 −1.93887 −0.969433 0.245357i \(-0.921095\pi\)
−0.969433 + 0.245357i \(0.921095\pi\)
\(212\) −3.08040 −0.211563
\(213\) −9.88860 −0.677556
\(214\) 22.7209 1.55317
\(215\) 0.318890 0.0217481
\(216\) −2.20447 −0.149995
\(217\) −13.3112 −0.903624
\(218\) 10.1953 0.690516
\(219\) −2.83517 −0.191583
\(220\) 0.994662 0.0670601
\(221\) 1.05243 0.0707938
\(222\) −8.47132 −0.568558
\(223\) −12.3845 −0.829328 −0.414664 0.909975i \(-0.636101\pi\)
−0.414664 + 0.909975i \(0.636101\pi\)
\(224\) 15.9520 1.06584
\(225\) −4.71230 −0.314154
\(226\) 6.21971 0.413729
\(227\) −11.2981 −0.749878 −0.374939 0.927049i \(-0.622336\pi\)
−0.374939 + 0.927049i \(0.622336\pi\)
\(228\) −3.95378 −0.261846
\(229\) 7.65246 0.505689 0.252844 0.967507i \(-0.418634\pi\)
0.252844 + 0.967507i \(0.418634\pi\)
\(230\) −2.32633 −0.153394
\(231\) −13.0564 −0.859047
\(232\) 9.12661 0.599191
\(233\) −3.81049 −0.249634 −0.124817 0.992180i \(-0.539834\pi\)
−0.124817 + 0.992180i \(0.539834\pi\)
\(234\) −1.71140 −0.111878
\(235\) 2.48067 0.161821
\(236\) −1.85722 −0.120895
\(237\) 4.89662 0.318070
\(238\) −7.37748 −0.478211
\(239\) −12.0878 −0.781897 −0.390948 0.920413i \(-0.627853\pi\)
−0.390948 + 0.920413i \(0.627853\pi\)
\(240\) 2.61403 0.168735
\(241\) −6.32255 −0.407271 −0.203636 0.979047i \(-0.565276\pi\)
−0.203636 + 0.979047i \(0.565276\pi\)
\(242\) 4.41939 0.284089
\(243\) −1.00000 −0.0641500
\(244\) 6.73398 0.431099
\(245\) 7.28521 0.465435
\(246\) 0.420286 0.0267964
\(247\) 6.45761 0.410888
\(248\) −6.46805 −0.410722
\(249\) −2.12890 −0.134914
\(250\) 8.47131 0.535773
\(251\) 0.350954 0.0221520 0.0110760 0.999939i \(-0.496474\pi\)
0.0110760 + 0.999939i \(0.496474\pi\)
\(252\) 2.92334 0.184153
\(253\) 7.67572 0.482568
\(254\) −18.7456 −1.17620
\(255\) −0.536374 −0.0335890
\(256\) 14.0319 0.876994
\(257\) −20.1141 −1.25469 −0.627343 0.778743i \(-0.715858\pi\)
−0.627343 + 0.778743i \(0.715858\pi\)
\(258\) 0.966794 0.0601900
\(259\) −23.6340 −1.46855
\(260\) 0.363740 0.0225582
\(261\) 4.14006 0.256263
\(262\) −14.3119 −0.884195
\(263\) −15.3035 −0.943653 −0.471826 0.881691i \(-0.656405\pi\)
−0.471826 + 0.881691i \(0.656405\pi\)
\(264\) −6.34423 −0.390460
\(265\) −2.56414 −0.157514
\(266\) −45.2677 −2.77554
\(267\) 10.2701 0.628519
\(268\) 10.4483 0.638232
\(269\) 20.3913 1.24328 0.621641 0.783302i \(-0.286466\pi\)
0.621641 + 0.783302i \(0.286466\pi\)
\(270\) 0.872225 0.0530819
\(271\) 25.8269 1.56887 0.784435 0.620211i \(-0.212953\pi\)
0.784435 + 0.620211i \(0.212953\pi\)
\(272\) −4.87352 −0.295501
\(273\) −4.77462 −0.288973
\(274\) 24.8593 1.50180
\(275\) −13.5615 −0.817791
\(276\) −1.71860 −0.103448
\(277\) −20.2293 −1.21546 −0.607731 0.794143i \(-0.707920\pi\)
−0.607731 + 0.794143i \(0.707920\pi\)
\(278\) −22.3491 −1.34041
\(279\) −2.93407 −0.175658
\(280\) 5.36436 0.320582
\(281\) 5.07183 0.302560 0.151280 0.988491i \(-0.451661\pi\)
0.151280 + 0.988491i \(0.451661\pi\)
\(282\) 7.52076 0.447855
\(283\) 11.7889 0.700778 0.350389 0.936604i \(-0.386049\pi\)
0.350389 + 0.936604i \(0.386049\pi\)
\(284\) 6.37187 0.378101
\(285\) −3.29115 −0.194951
\(286\) −4.92524 −0.291236
\(287\) 1.17255 0.0692134
\(288\) 3.51615 0.207191
\(289\) 1.00000 0.0588235
\(290\) −3.61106 −0.212049
\(291\) −11.9098 −0.698164
\(292\) 1.82688 0.106910
\(293\) −13.3955 −0.782574 −0.391287 0.920269i \(-0.627970\pi\)
−0.391287 + 0.920269i \(0.627970\pi\)
\(294\) 22.0869 1.28814
\(295\) −1.54596 −0.0900094
\(296\) −11.4840 −0.667494
\(297\) −2.87790 −0.166993
\(298\) −4.85843 −0.281441
\(299\) 2.80695 0.162330
\(300\) 3.03645 0.175309
\(301\) 2.69725 0.155467
\(302\) −37.4054 −2.15244
\(303\) 13.8417 0.795186
\(304\) −29.9036 −1.71509
\(305\) 5.60541 0.320965
\(306\) −1.62615 −0.0929608
\(307\) −5.92232 −0.338005 −0.169002 0.985616i \(-0.554055\pi\)
−0.169002 + 0.985616i \(0.554055\pi\)
\(308\) 8.41308 0.479380
\(309\) −15.2504 −0.867565
\(310\) 2.55917 0.145351
\(311\) 13.1833 0.747554 0.373777 0.927519i \(-0.378063\pi\)
0.373777 + 0.927519i \(0.378063\pi\)
\(312\) −2.32004 −0.131346
\(313\) 15.1808 0.858069 0.429035 0.903288i \(-0.358854\pi\)
0.429035 + 0.903288i \(0.358854\pi\)
\(314\) 1.62615 0.0917690
\(315\) 2.43341 0.137107
\(316\) −3.15521 −0.177495
\(317\) −18.2857 −1.02702 −0.513512 0.858082i \(-0.671656\pi\)
−0.513512 + 0.858082i \(0.671656\pi\)
\(318\) −7.77384 −0.435935
\(319\) 11.9147 0.667093
\(320\) 2.16119 0.120814
\(321\) 13.9722 0.779852
\(322\) −19.6767 −1.09654
\(323\) 6.13593 0.341412
\(324\) 0.644366 0.0357981
\(325\) −4.95935 −0.275095
\(326\) −23.7718 −1.31660
\(327\) 6.26962 0.346711
\(328\) 0.569754 0.0314594
\(329\) 20.9821 1.15678
\(330\) 2.51017 0.138181
\(331\) 5.35412 0.294289 0.147145 0.989115i \(-0.452992\pi\)
0.147145 + 0.989115i \(0.452992\pi\)
\(332\) 1.37179 0.0752869
\(333\) −5.20943 −0.285475
\(334\) 0.409793 0.0224229
\(335\) 8.69724 0.475181
\(336\) 22.1101 1.20620
\(337\) 28.5799 1.55685 0.778423 0.627740i \(-0.216020\pi\)
0.778423 + 0.627740i \(0.216020\pi\)
\(338\) 19.3388 1.05189
\(339\) 3.82481 0.207735
\(340\) 0.345621 0.0187439
\(341\) −8.44395 −0.457266
\(342\) −9.97794 −0.539545
\(343\) 29.8626 1.61243
\(344\) 1.31062 0.0706639
\(345\) −1.43058 −0.0770197
\(346\) −25.7909 −1.38652
\(347\) −31.9705 −1.71627 −0.858134 0.513425i \(-0.828376\pi\)
−0.858134 + 0.513425i \(0.828376\pi\)
\(348\) −2.66771 −0.143004
\(349\) −1.57124 −0.0841065 −0.0420533 0.999115i \(-0.513390\pi\)
−0.0420533 + 0.999115i \(0.513390\pi\)
\(350\) 34.7649 1.85826
\(351\) −1.05243 −0.0561743
\(352\) 10.1191 0.539351
\(353\) −10.1771 −0.541674 −0.270837 0.962625i \(-0.587300\pi\)
−0.270837 + 0.962625i \(0.587300\pi\)
\(354\) −4.68697 −0.249110
\(355\) 5.30399 0.281506
\(356\) −6.61769 −0.350737
\(357\) −4.53678 −0.240112
\(358\) −32.8719 −1.73733
\(359\) 23.4680 1.23859 0.619297 0.785157i \(-0.287418\pi\)
0.619297 + 0.785157i \(0.287418\pi\)
\(360\) 1.18242 0.0623189
\(361\) 18.6496 0.981559
\(362\) −1.57036 −0.0825361
\(363\) 2.71770 0.142642
\(364\) 3.07660 0.161258
\(365\) 1.52071 0.0795976
\(366\) 16.9942 0.888300
\(367\) −24.7603 −1.29248 −0.646239 0.763135i \(-0.723659\pi\)
−0.646239 + 0.763135i \(0.723659\pi\)
\(368\) −12.9983 −0.677583
\(369\) 0.258454 0.0134546
\(370\) 4.54379 0.236221
\(371\) −21.6881 −1.12599
\(372\) 1.89061 0.0980237
\(373\) 2.41072 0.124822 0.0624111 0.998051i \(-0.480121\pi\)
0.0624111 + 0.998051i \(0.480121\pi\)
\(374\) −4.67990 −0.241992
\(375\) 5.20943 0.269014
\(376\) 10.1954 0.525788
\(377\) 4.35710 0.224402
\(378\) 7.37748 0.379457
\(379\) 6.38995 0.328230 0.164115 0.986441i \(-0.447523\pi\)
0.164115 + 0.986441i \(0.447523\pi\)
\(380\) 2.12071 0.108790
\(381\) −11.5276 −0.590577
\(382\) 28.6564 1.46619
\(383\) −14.6608 −0.749132 −0.374566 0.927200i \(-0.622208\pi\)
−0.374566 + 0.927200i \(0.622208\pi\)
\(384\) 13.5845 0.693230
\(385\) 7.00310 0.356911
\(386\) 23.3423 1.18809
\(387\) 0.594529 0.0302216
\(388\) 7.67425 0.389601
\(389\) 20.7383 1.05147 0.525736 0.850648i \(-0.323790\pi\)
0.525736 + 0.850648i \(0.323790\pi\)
\(390\) 0.917952 0.0464823
\(391\) 2.66713 0.134882
\(392\) 29.9418 1.51229
\(393\) −8.80112 −0.443958
\(394\) −10.2501 −0.516392
\(395\) −2.62642 −0.132149
\(396\) 1.85442 0.0931881
\(397\) −31.1806 −1.56491 −0.782455 0.622707i \(-0.786033\pi\)
−0.782455 + 0.622707i \(0.786033\pi\)
\(398\) 37.2812 1.86874
\(399\) −27.8373 −1.39361
\(400\) 22.9655 1.14828
\(401\) −39.3277 −1.96393 −0.981965 0.189064i \(-0.939455\pi\)
−0.981965 + 0.189064i \(0.939455\pi\)
\(402\) 26.3678 1.31511
\(403\) −3.08789 −0.153819
\(404\) −8.91912 −0.443743
\(405\) 0.536374 0.0266526
\(406\) −30.5432 −1.51583
\(407\) −14.9922 −0.743136
\(408\) −2.20447 −0.109137
\(409\) 10.1598 0.502368 0.251184 0.967939i \(-0.419180\pi\)
0.251184 + 0.967939i \(0.419180\pi\)
\(410\) −0.225430 −0.0111332
\(411\) 15.2872 0.754062
\(412\) 9.82683 0.484133
\(413\) −13.0761 −0.643433
\(414\) −4.33715 −0.213159
\(415\) 1.14189 0.0560531
\(416\) 3.70049 0.181431
\(417\) −13.7436 −0.673026
\(418\) −28.7155 −1.40452
\(419\) 3.04043 0.148535 0.0742674 0.997238i \(-0.476338\pi\)
0.0742674 + 0.997238i \(0.476338\pi\)
\(420\) −1.56800 −0.0765108
\(421\) −27.7553 −1.35271 −0.676355 0.736575i \(-0.736442\pi\)
−0.676355 + 0.736575i \(0.736442\pi\)
\(422\) 45.7983 2.22943
\(423\) 4.62488 0.224870
\(424\) −10.5385 −0.511794
\(425\) −4.71230 −0.228580
\(426\) 16.0803 0.779095
\(427\) 47.4118 2.29442
\(428\) −9.00320 −0.435186
\(429\) −3.02878 −0.146231
\(430\) −0.518563 −0.0250073
\(431\) −27.5938 −1.32915 −0.664573 0.747223i \(-0.731387\pi\)
−0.664573 + 0.747223i \(0.731387\pi\)
\(432\) 4.87352 0.234478
\(433\) −13.3618 −0.642126 −0.321063 0.947058i \(-0.604040\pi\)
−0.321063 + 0.947058i \(0.604040\pi\)
\(434\) 21.6460 1.03904
\(435\) −2.22062 −0.106470
\(436\) −4.03993 −0.193477
\(437\) 16.3653 0.782858
\(438\) 4.61041 0.220294
\(439\) −4.65570 −0.222205 −0.111102 0.993809i \(-0.535438\pi\)
−0.111102 + 0.993809i \(0.535438\pi\)
\(440\) 3.40288 0.162226
\(441\) 13.5823 0.646778
\(442\) −1.71140 −0.0814031
\(443\) −16.4031 −0.779337 −0.389668 0.920955i \(-0.627410\pi\)
−0.389668 + 0.920955i \(0.627410\pi\)
\(444\) 3.35678 0.159306
\(445\) −5.50860 −0.261133
\(446\) 20.1391 0.953613
\(447\) −2.98768 −0.141313
\(448\) 18.2798 0.863641
\(449\) −2.98737 −0.140983 −0.0704915 0.997512i \(-0.522457\pi\)
−0.0704915 + 0.997512i \(0.522457\pi\)
\(450\) 7.66291 0.361233
\(451\) 0.743805 0.0350244
\(452\) −2.46458 −0.115924
\(453\) −23.0024 −1.08075
\(454\) 18.3723 0.862256
\(455\) 2.56098 0.120061
\(456\) −13.5264 −0.633434
\(457\) 37.8455 1.77034 0.885168 0.465272i \(-0.154043\pi\)
0.885168 + 0.465272i \(0.154043\pi\)
\(458\) −12.4441 −0.581472
\(459\) −1.00000 −0.0466760
\(460\) 0.921814 0.0429798
\(461\) −5.61583 −0.261556 −0.130778 0.991412i \(-0.541747\pi\)
−0.130778 + 0.991412i \(0.541747\pi\)
\(462\) 21.2316 0.987785
\(463\) 16.2899 0.757056 0.378528 0.925590i \(-0.376430\pi\)
0.378528 + 0.925590i \(0.376430\pi\)
\(464\) −20.1767 −0.936678
\(465\) 1.57376 0.0729813
\(466\) 6.19643 0.287044
\(467\) 25.0009 1.15691 0.578453 0.815716i \(-0.303657\pi\)
0.578453 + 0.815716i \(0.303657\pi\)
\(468\) 0.678147 0.0313474
\(469\) 73.5633 3.39684
\(470\) −4.03394 −0.186072
\(471\) 1.00000 0.0460776
\(472\) −6.35382 −0.292458
\(473\) 1.71100 0.0786716
\(474\) −7.96264 −0.365736
\(475\) −28.9144 −1.32668
\(476\) 2.92334 0.133991
\(477\) −4.78052 −0.218885
\(478\) 19.6566 0.899073
\(479\) 18.2803 0.835247 0.417624 0.908620i \(-0.362863\pi\)
0.417624 + 0.908620i \(0.362863\pi\)
\(480\) −1.88597 −0.0860825
\(481\) −5.48254 −0.249982
\(482\) 10.2814 0.468306
\(483\) −12.1001 −0.550576
\(484\) −1.75119 −0.0795996
\(485\) 6.38809 0.290068
\(486\) 1.62615 0.0737637
\(487\) 11.9082 0.539611 0.269805 0.962915i \(-0.413041\pi\)
0.269805 + 0.962915i \(0.413041\pi\)
\(488\) 23.0379 1.04288
\(489\) −14.6184 −0.661068
\(490\) −11.8468 −0.535186
\(491\) 10.9479 0.494070 0.247035 0.969007i \(-0.420544\pi\)
0.247035 + 0.969007i \(0.420544\pi\)
\(492\) −0.166539 −0.00750816
\(493\) 4.14006 0.186459
\(494\) −10.5010 −0.472464
\(495\) 1.54363 0.0693810
\(496\) 14.2993 0.642056
\(497\) 44.8623 2.01235
\(498\) 3.46192 0.155132
\(499\) 1.98410 0.0888206 0.0444103 0.999013i \(-0.485859\pi\)
0.0444103 + 0.999013i \(0.485859\pi\)
\(500\) −3.35677 −0.150120
\(501\) 0.252002 0.0112586
\(502\) −0.570703 −0.0254717
\(503\) 38.8310 1.73139 0.865695 0.500571i \(-0.166877\pi\)
0.865695 + 0.500571i \(0.166877\pi\)
\(504\) 10.0012 0.445487
\(505\) −7.42433 −0.330379
\(506\) −12.4819 −0.554887
\(507\) 11.8924 0.528160
\(508\) 7.42799 0.329564
\(509\) 1.53769 0.0681567 0.0340784 0.999419i \(-0.489150\pi\)
0.0340784 + 0.999419i \(0.489150\pi\)
\(510\) 0.872225 0.0386228
\(511\) 12.8625 0.569004
\(512\) 4.35098 0.192288
\(513\) −6.13593 −0.270908
\(514\) 32.7086 1.44272
\(515\) 8.17992 0.360450
\(516\) −0.383094 −0.0168648
\(517\) 13.3099 0.585371
\(518\) 38.4325 1.68863
\(519\) −15.8601 −0.696180
\(520\) 1.24441 0.0545709
\(521\) 0.0367612 0.00161054 0.000805269 1.00000i \(-0.499744\pi\)
0.000805269 1.00000i \(0.499744\pi\)
\(522\) −6.73235 −0.294667
\(523\) −17.1989 −0.752054 −0.376027 0.926609i \(-0.622710\pi\)
−0.376027 + 0.926609i \(0.622710\pi\)
\(524\) 5.67114 0.247745
\(525\) 21.3787 0.933041
\(526\) 24.8858 1.08507
\(527\) −2.93407 −0.127810
\(528\) 14.0255 0.610382
\(529\) −15.8864 −0.690715
\(530\) 4.16968 0.181119
\(531\) −2.88225 −0.125079
\(532\) 17.9374 0.777686
\(533\) 0.272004 0.0117818
\(534\) −16.7007 −0.722710
\(535\) −7.49432 −0.324008
\(536\) 35.7451 1.54395
\(537\) −20.2145 −0.872322
\(538\) −33.1594 −1.42960
\(539\) 39.0886 1.68366
\(540\) −0.345621 −0.0148732
\(541\) 25.0584 1.07734 0.538672 0.842515i \(-0.318926\pi\)
0.538672 + 0.842515i \(0.318926\pi\)
\(542\) −41.9984 −1.80398
\(543\) −0.965690 −0.0414417
\(544\) 3.51615 0.150754
\(545\) −3.36286 −0.144049
\(546\) 7.76425 0.332279
\(547\) 43.4640 1.85839 0.929193 0.369595i \(-0.120504\pi\)
0.929193 + 0.369595i \(0.120504\pi\)
\(548\) −9.85055 −0.420794
\(549\) 10.4506 0.446019
\(550\) 22.0531 0.940347
\(551\) 25.4031 1.08221
\(552\) −5.87959 −0.250252
\(553\) −22.2149 −0.944672
\(554\) 32.8959 1.39761
\(555\) 2.79420 0.118607
\(556\) 8.85590 0.375574
\(557\) −42.2867 −1.79174 −0.895872 0.444312i \(-0.853448\pi\)
−0.895872 + 0.444312i \(0.853448\pi\)
\(558\) 4.77124 0.201983
\(559\) 0.625698 0.0264642
\(560\) −11.8593 −0.501146
\(561\) −2.87790 −0.121505
\(562\) −8.24756 −0.347902
\(563\) 7.91695 0.333660 0.166830 0.985986i \(-0.446647\pi\)
0.166830 + 0.985986i \(0.446647\pi\)
\(564\) −2.98012 −0.125486
\(565\) −2.05153 −0.0863084
\(566\) −19.1705 −0.805798
\(567\) 4.53678 0.190527
\(568\) 21.7991 0.914669
\(569\) −29.0022 −1.21584 −0.607918 0.794000i \(-0.707995\pi\)
−0.607918 + 0.794000i \(0.707995\pi\)
\(570\) 5.35191 0.224167
\(571\) 35.6894 1.49356 0.746778 0.665073i \(-0.231600\pi\)
0.746778 + 0.665073i \(0.231600\pi\)
\(572\) 1.95164 0.0816021
\(573\) 17.6222 0.736180
\(574\) −1.90674 −0.0795858
\(575\) −12.5683 −0.524134
\(576\) 4.02926 0.167886
\(577\) 23.5907 0.982093 0.491046 0.871133i \(-0.336615\pi\)
0.491046 + 0.871133i \(0.336615\pi\)
\(578\) −1.62615 −0.0676389
\(579\) 14.3544 0.596547
\(580\) 1.43089 0.0594145
\(581\) 9.65836 0.400696
\(582\) 19.3671 0.802792
\(583\) −13.7578 −0.569791
\(584\) 6.25003 0.258628
\(585\) 0.564494 0.0233389
\(586\) 21.7831 0.899852
\(587\) −34.7455 −1.43410 −0.717049 0.697022i \(-0.754508\pi\)
−0.717049 + 0.697022i \(0.754508\pi\)
\(588\) −8.75199 −0.360926
\(589\) −18.0032 −0.741811
\(590\) 2.51397 0.103498
\(591\) −6.30328 −0.259282
\(592\) 25.3883 1.04345
\(593\) −25.9954 −1.06751 −0.533753 0.845641i \(-0.679219\pi\)
−0.533753 + 0.845641i \(0.679219\pi\)
\(594\) 4.67990 0.192018
\(595\) 2.43341 0.0997600
\(596\) 1.92516 0.0788577
\(597\) 22.9260 0.938300
\(598\) −4.56453 −0.186657
\(599\) 36.7339 1.50091 0.750453 0.660924i \(-0.229836\pi\)
0.750453 + 0.660924i \(0.229836\pi\)
\(600\) 10.3881 0.424093
\(601\) 1.49323 0.0609103 0.0304552 0.999536i \(-0.490304\pi\)
0.0304552 + 0.999536i \(0.490304\pi\)
\(602\) −4.38613 −0.178765
\(603\) 16.2149 0.660321
\(604\) 14.8220 0.603097
\(605\) −1.45770 −0.0592640
\(606\) −22.5087 −0.914354
\(607\) −12.0497 −0.489082 −0.244541 0.969639i \(-0.578637\pi\)
−0.244541 + 0.969639i \(0.578637\pi\)
\(608\) 21.5749 0.874976
\(609\) −18.7825 −0.761106
\(610\) −9.11524 −0.369065
\(611\) 4.86735 0.196912
\(612\) 0.644366 0.0260469
\(613\) −28.2428 −1.14072 −0.570359 0.821396i \(-0.693196\pi\)
−0.570359 + 0.821396i \(0.693196\pi\)
\(614\) 9.63058 0.388659
\(615\) −0.138628 −0.00559003
\(616\) 28.7823 1.15967
\(617\) −42.3589 −1.70530 −0.852652 0.522479i \(-0.825007\pi\)
−0.852652 + 0.522479i \(0.825007\pi\)
\(618\) 24.7994 0.997580
\(619\) −32.6557 −1.31254 −0.656271 0.754525i \(-0.727867\pi\)
−0.656271 + 0.754525i \(0.727867\pi\)
\(620\) −1.01408 −0.0407263
\(621\) −2.66713 −0.107028
\(622\) −21.4380 −0.859584
\(623\) −46.5930 −1.86671
\(624\) 5.12902 0.205325
\(625\) 20.7673 0.830693
\(626\) −24.6863 −0.986662
\(627\) −17.6586 −0.705216
\(628\) −0.644366 −0.0257130
\(629\) −5.20943 −0.207714
\(630\) −3.95709 −0.157654
\(631\) 36.0897 1.43671 0.718355 0.695677i \(-0.244896\pi\)
0.718355 + 0.695677i \(0.244896\pi\)
\(632\) −10.7944 −0.429379
\(633\) 28.1637 1.11940
\(634\) 29.7352 1.18094
\(635\) 6.18311 0.245369
\(636\) 3.08040 0.122146
\(637\) 14.2944 0.566365
\(638\) −19.3750 −0.767065
\(639\) 9.88860 0.391187
\(640\) −7.28636 −0.288019
\(641\) 45.2127 1.78579 0.892897 0.450262i \(-0.148669\pi\)
0.892897 + 0.450262i \(0.148669\pi\)
\(642\) −22.7209 −0.896722
\(643\) 18.8719 0.744234 0.372117 0.928186i \(-0.378632\pi\)
0.372117 + 0.928186i \(0.378632\pi\)
\(644\) 7.79692 0.307242
\(645\) −0.318890 −0.0125563
\(646\) −9.97794 −0.392577
\(647\) 47.7355 1.87668 0.938338 0.345718i \(-0.112365\pi\)
0.938338 + 0.345718i \(0.112365\pi\)
\(648\) 2.20447 0.0865996
\(649\) −8.29482 −0.325600
\(650\) 8.06465 0.316322
\(651\) 13.3112 0.521708
\(652\) 9.41961 0.368901
\(653\) 45.2808 1.77198 0.885988 0.463708i \(-0.153481\pi\)
0.885988 + 0.463708i \(0.153481\pi\)
\(654\) −10.1953 −0.398669
\(655\) 4.72069 0.184453
\(656\) −1.25958 −0.0491785
\(657\) 2.83517 0.110610
\(658\) −34.1200 −1.33014
\(659\) −1.61714 −0.0629950 −0.0314975 0.999504i \(-0.510028\pi\)
−0.0314975 + 0.999504i \(0.510028\pi\)
\(660\) −0.994662 −0.0387172
\(661\) −50.1186 −1.94939 −0.974695 0.223540i \(-0.928239\pi\)
−0.974695 + 0.223540i \(0.928239\pi\)
\(662\) −8.70661 −0.338392
\(663\) −1.05243 −0.0408728
\(664\) 4.69310 0.182128
\(665\) 14.9312 0.579008
\(666\) 8.47132 0.328257
\(667\) 11.0420 0.427550
\(668\) −0.162381 −0.00628272
\(669\) 12.3845 0.478813
\(670\) −14.1430 −0.546392
\(671\) 30.0757 1.16106
\(672\) −15.9520 −0.615362
\(673\) 33.3422 1.28525 0.642623 0.766182i \(-0.277846\pi\)
0.642623 + 0.766182i \(0.277846\pi\)
\(674\) −46.4752 −1.79016
\(675\) 4.71230 0.181377
\(676\) −7.66305 −0.294733
\(677\) −33.5004 −1.28753 −0.643763 0.765225i \(-0.722628\pi\)
−0.643763 + 0.765225i \(0.722628\pi\)
\(678\) −6.21971 −0.238867
\(679\) 54.0320 2.07356
\(680\) 1.18242 0.0453437
\(681\) 11.2981 0.432942
\(682\) 13.7311 0.525793
\(683\) −29.2586 −1.11955 −0.559775 0.828644i \(-0.689113\pi\)
−0.559775 + 0.828644i \(0.689113\pi\)
\(684\) 3.95378 0.151177
\(685\) −8.19966 −0.313293
\(686\) −48.5610 −1.85407
\(687\) −7.65246 −0.291960
\(688\) −2.89745 −0.110464
\(689\) −5.03114 −0.191671
\(690\) 2.32633 0.0885620
\(691\) 25.4297 0.967392 0.483696 0.875236i \(-0.339294\pi\)
0.483696 + 0.875236i \(0.339294\pi\)
\(692\) 10.2197 0.388494
\(693\) 13.0564 0.495971
\(694\) 51.9889 1.97347
\(695\) 7.37170 0.279625
\(696\) −9.12661 −0.345943
\(697\) 0.258454 0.00978965
\(698\) 2.55507 0.0967109
\(699\) 3.81049 0.144126
\(700\) −13.7757 −0.520671
\(701\) −28.3858 −1.07212 −0.536058 0.844181i \(-0.680087\pi\)
−0.536058 + 0.844181i \(0.680087\pi\)
\(702\) 1.71140 0.0645927
\(703\) −31.9647 −1.20557
\(704\) 11.5958 0.437033
\(705\) −2.48067 −0.0934273
\(706\) 16.5495 0.622850
\(707\) −62.7967 −2.36171
\(708\) 1.85722 0.0697986
\(709\) −9.70194 −0.364364 −0.182182 0.983265i \(-0.558316\pi\)
−0.182182 + 0.983265i \(0.558316\pi\)
\(710\) −8.62508 −0.323693
\(711\) −4.89662 −0.183638
\(712\) −22.6400 −0.848471
\(713\) −7.82553 −0.293068
\(714\) 7.37748 0.276095
\(715\) 1.62456 0.0607550
\(716\) 13.0256 0.486788
\(717\) 12.0878 0.451428
\(718\) −38.1625 −1.42421
\(719\) 9.74472 0.363417 0.181708 0.983352i \(-0.441837\pi\)
0.181708 + 0.983352i \(0.441837\pi\)
\(720\) −2.61403 −0.0974192
\(721\) 69.1876 2.57668
\(722\) −30.3271 −1.12866
\(723\) 6.32255 0.235138
\(724\) 0.622257 0.0231260
\(725\) −19.5092 −0.724553
\(726\) −4.41939 −0.164019
\(727\) 15.3997 0.571144 0.285572 0.958357i \(-0.407816\pi\)
0.285572 + 0.958357i \(0.407816\pi\)
\(728\) 10.5255 0.390101
\(729\) 1.00000 0.0370370
\(730\) −2.47290 −0.0915263
\(731\) 0.594529 0.0219895
\(732\) −6.73398 −0.248895
\(733\) 27.3353 1.00965 0.504827 0.863221i \(-0.331556\pi\)
0.504827 + 0.863221i \(0.331556\pi\)
\(734\) 40.2640 1.48617
\(735\) −7.28521 −0.268719
\(736\) 9.37802 0.345678
\(737\) 46.6648 1.71892
\(738\) −0.420286 −0.0154709
\(739\) −45.5885 −1.67700 −0.838499 0.544903i \(-0.816567\pi\)
−0.838499 + 0.544903i \(0.816567\pi\)
\(740\) −1.80049 −0.0661872
\(741\) −6.45761 −0.237226
\(742\) 35.2682 1.29473
\(743\) 40.5650 1.48819 0.744093 0.668076i \(-0.232882\pi\)
0.744093 + 0.668076i \(0.232882\pi\)
\(744\) 6.46805 0.237130
\(745\) 1.60252 0.0587117
\(746\) −3.92019 −0.143528
\(747\) 2.12890 0.0778926
\(748\) 1.85442 0.0678043
\(749\) −63.3887 −2.31617
\(750\) −8.47131 −0.309329
\(751\) −20.1819 −0.736450 −0.368225 0.929737i \(-0.620034\pi\)
−0.368225 + 0.929737i \(0.620034\pi\)
\(752\) −22.5395 −0.821931
\(753\) −0.350954 −0.0127895
\(754\) −7.08531 −0.258032
\(755\) 12.3379 0.449022
\(756\) −2.92334 −0.106321
\(757\) 14.4041 0.523526 0.261763 0.965132i \(-0.415696\pi\)
0.261763 + 0.965132i \(0.415696\pi\)
\(758\) −10.3910 −0.377419
\(759\) −7.67572 −0.278611
\(760\) 7.25523 0.263175
\(761\) 0.929157 0.0336819 0.0168410 0.999858i \(-0.494639\pi\)
0.0168410 + 0.999858i \(0.494639\pi\)
\(762\) 18.7456 0.679082
\(763\) −28.4438 −1.02974
\(764\) −11.3552 −0.410815
\(765\) 0.536374 0.0193926
\(766\) 23.8407 0.861398
\(767\) −3.03335 −0.109528
\(768\) −14.0319 −0.506333
\(769\) 14.8258 0.534631 0.267316 0.963609i \(-0.413863\pi\)
0.267316 + 0.963609i \(0.413863\pi\)
\(770\) −11.3881 −0.410399
\(771\) 20.1141 0.724393
\(772\) −9.24945 −0.332895
\(773\) −10.7624 −0.387097 −0.193549 0.981091i \(-0.562000\pi\)
−0.193549 + 0.981091i \(0.562000\pi\)
\(774\) −0.966794 −0.0347507
\(775\) 13.8262 0.496653
\(776\) 26.2547 0.942489
\(777\) 23.6340 0.847865
\(778\) −33.7236 −1.20905
\(779\) 1.58586 0.0568192
\(780\) −0.363740 −0.0130240
\(781\) 28.4584 1.01832
\(782\) −4.33715 −0.155096
\(783\) −4.14006 −0.147954
\(784\) −66.1938 −2.36407
\(785\) −0.536374 −0.0191440
\(786\) 14.3119 0.510490
\(787\) 21.4583 0.764904 0.382452 0.923975i \(-0.375080\pi\)
0.382452 + 0.923975i \(0.375080\pi\)
\(788\) 4.06162 0.144689
\(789\) 15.3035 0.544818
\(790\) 4.27095 0.151954
\(791\) −17.3523 −0.616977
\(792\) 6.34423 0.225432
\(793\) 10.9984 0.390566
\(794\) 50.7044 1.79943
\(795\) 2.56414 0.0909408
\(796\) −14.7727 −0.523606
\(797\) 1.32287 0.0468583 0.0234292 0.999725i \(-0.492542\pi\)
0.0234292 + 0.999725i \(0.492542\pi\)
\(798\) 45.2677 1.60246
\(799\) 4.62488 0.163617
\(800\) −16.5692 −0.585809
\(801\) −10.2701 −0.362875
\(802\) 63.9527 2.25825
\(803\) 8.15933 0.287936
\(804\) −10.4483 −0.368483
\(805\) 6.49020 0.228750
\(806\) 5.02138 0.176870
\(807\) −20.3913 −0.717809
\(808\) −30.5136 −1.07346
\(809\) 32.0313 1.12616 0.563080 0.826402i \(-0.309616\pi\)
0.563080 + 0.826402i \(0.309616\pi\)
\(810\) −0.872225 −0.0306469
\(811\) 45.0726 1.58271 0.791357 0.611354i \(-0.209375\pi\)
0.791357 + 0.611354i \(0.209375\pi\)
\(812\) 12.1028 0.424725
\(813\) −25.8269 −0.905788
\(814\) 24.3796 0.854504
\(815\) 7.84095 0.274656
\(816\) 4.87352 0.170607
\(817\) 3.64799 0.127627
\(818\) −16.5213 −0.577654
\(819\) 4.77462 0.166839
\(820\) 0.0893272 0.00311944
\(821\) −3.23973 −0.113067 −0.0565337 0.998401i \(-0.518005\pi\)
−0.0565337 + 0.998401i \(0.518005\pi\)
\(822\) −24.8593 −0.867067
\(823\) −29.2894 −1.02097 −0.510483 0.859888i \(-0.670533\pi\)
−0.510483 + 0.859888i \(0.670533\pi\)
\(824\) 33.6190 1.17117
\(825\) 13.5615 0.472152
\(826\) 21.2637 0.739860
\(827\) 35.2182 1.22466 0.612328 0.790604i \(-0.290233\pi\)
0.612328 + 0.790604i \(0.290233\pi\)
\(828\) 1.71860 0.0597256
\(829\) −0.0569368 −0.00197750 −0.000988748 1.00000i \(-0.500315\pi\)
−0.000988748 1.00000i \(0.500315\pi\)
\(830\) −1.85688 −0.0644534
\(831\) 20.2293 0.701748
\(832\) 4.24049 0.147013
\(833\) 13.5823 0.470600
\(834\) 22.3491 0.773888
\(835\) −0.135167 −0.00467766
\(836\) 11.3786 0.393537
\(837\) 2.93407 0.101416
\(838\) −4.94420 −0.170795
\(839\) −43.2435 −1.49293 −0.746466 0.665423i \(-0.768251\pi\)
−0.746466 + 0.665423i \(0.768251\pi\)
\(840\) −5.36436 −0.185088
\(841\) −11.8599 −0.408963
\(842\) 45.1343 1.55543
\(843\) −5.07183 −0.174683
\(844\) −18.1477 −0.624669
\(845\) −6.37877 −0.219436
\(846\) −7.52076 −0.258569
\(847\) −12.3296 −0.423650
\(848\) 23.2980 0.800055
\(849\) −11.7889 −0.404594
\(850\) 7.66291 0.262836
\(851\) −13.8942 −0.476287
\(852\) −6.37187 −0.218297
\(853\) 32.4019 1.10942 0.554711 0.832043i \(-0.312829\pi\)
0.554711 + 0.832043i \(0.312829\pi\)
\(854\) −77.0988 −2.63827
\(855\) 3.29115 0.112555
\(856\) −30.8012 −1.05276
\(857\) 38.6500 1.32026 0.660130 0.751152i \(-0.270501\pi\)
0.660130 + 0.751152i \(0.270501\pi\)
\(858\) 4.92524 0.168145
\(859\) −52.1116 −1.77802 −0.889012 0.457883i \(-0.848608\pi\)
−0.889012 + 0.457883i \(0.848608\pi\)
\(860\) 0.205482 0.00700687
\(861\) −1.17255 −0.0399604
\(862\) 44.8717 1.52833
\(863\) −29.6109 −1.00797 −0.503983 0.863714i \(-0.668133\pi\)
−0.503983 + 0.863714i \(0.668133\pi\)
\(864\) −3.51615 −0.119622
\(865\) 8.50693 0.289244
\(866\) 21.7282 0.738356
\(867\) −1.00000 −0.0339618
\(868\) −8.57729 −0.291132
\(869\) −14.0920 −0.478037
\(870\) 3.61106 0.122426
\(871\) 17.0650 0.578224
\(872\) −13.8212 −0.468043
\(873\) 11.9098 0.403085
\(874\) −26.6124 −0.900179
\(875\) −23.6340 −0.798975
\(876\) −1.82688 −0.0617247
\(877\) −15.6832 −0.529583 −0.264792 0.964306i \(-0.585303\pi\)
−0.264792 + 0.964306i \(0.585303\pi\)
\(878\) 7.57088 0.255505
\(879\) 13.3955 0.451819
\(880\) −7.52292 −0.253598
\(881\) −49.5529 −1.66948 −0.834740 0.550644i \(-0.814382\pi\)
−0.834740 + 0.550644i \(0.814382\pi\)
\(882\) −22.0869 −0.743705
\(883\) 13.7529 0.462821 0.231410 0.972856i \(-0.425666\pi\)
0.231410 + 0.972856i \(0.425666\pi\)
\(884\) 0.678147 0.0228086
\(885\) 1.54596 0.0519670
\(886\) 26.6740 0.896130
\(887\) 20.0163 0.672082 0.336041 0.941847i \(-0.390912\pi\)
0.336041 + 0.941847i \(0.390912\pi\)
\(888\) 11.4840 0.385378
\(889\) 52.2982 1.75402
\(890\) 8.95782 0.300267
\(891\) 2.87790 0.0964132
\(892\) −7.98015 −0.267195
\(893\) 28.3780 0.949632
\(894\) 4.85843 0.162490
\(895\) 10.8426 0.362426
\(896\) −61.6297 −2.05891
\(897\) −2.80695 −0.0937214
\(898\) 4.85792 0.162111
\(899\) −12.1472 −0.405132
\(900\) −3.03645 −0.101215
\(901\) −4.78052 −0.159262
\(902\) −1.20954 −0.0402733
\(903\) −2.69725 −0.0897587
\(904\) −8.43166 −0.280433
\(905\) 0.517971 0.0172179
\(906\) 37.4054 1.24271
\(907\) −45.4528 −1.50924 −0.754618 0.656164i \(-0.772178\pi\)
−0.754618 + 0.656164i \(0.772178\pi\)
\(908\) −7.28007 −0.241598
\(909\) −13.8417 −0.459101
\(910\) −4.16454 −0.138053
\(911\) −35.1316 −1.16396 −0.581980 0.813203i \(-0.697722\pi\)
−0.581980 + 0.813203i \(0.697722\pi\)
\(912\) 29.9036 0.990207
\(913\) 6.12677 0.202767
\(914\) −61.5424 −2.03564
\(915\) −5.60541 −0.185309
\(916\) 4.93098 0.162924
\(917\) 39.9287 1.31856
\(918\) 1.62615 0.0536710
\(919\) −3.92819 −0.129579 −0.0647896 0.997899i \(-0.520638\pi\)
−0.0647896 + 0.997899i \(0.520638\pi\)
\(920\) 3.15366 0.103973
\(921\) 5.92232 0.195147
\(922\) 9.13219 0.300753
\(923\) 10.4070 0.342551
\(924\) −8.41308 −0.276770
\(925\) 24.5484 0.807147
\(926\) −26.4898 −0.870510
\(927\) 15.2504 0.500889
\(928\) 14.5571 0.477859
\(929\) 4.22701 0.138684 0.0693419 0.997593i \(-0.477910\pi\)
0.0693419 + 0.997593i \(0.477910\pi\)
\(930\) −2.55917 −0.0839184
\(931\) 83.3402 2.73137
\(932\) −2.45535 −0.0804276
\(933\) −13.1833 −0.431600
\(934\) −40.6553 −1.33028
\(935\) 1.54363 0.0504821
\(936\) 2.32004 0.0758328
\(937\) 50.7125 1.65671 0.828353 0.560206i \(-0.189278\pi\)
0.828353 + 0.560206i \(0.189278\pi\)
\(938\) −119.625 −3.90589
\(939\) −15.1808 −0.495407
\(940\) 1.59846 0.0521359
\(941\) 30.3991 0.990984 0.495492 0.868613i \(-0.334988\pi\)
0.495492 + 0.868613i \(0.334988\pi\)
\(942\) −1.62615 −0.0529828
\(943\) 0.689330 0.0224477
\(944\) 14.0467 0.457181
\(945\) −2.43341 −0.0791588
\(946\) −2.78234 −0.0904615
\(947\) 16.9509 0.550830 0.275415 0.961325i \(-0.411185\pi\)
0.275415 + 0.961325i \(0.411185\pi\)
\(948\) 3.15521 0.102477
\(949\) 2.98380 0.0968584
\(950\) 47.0191 1.52550
\(951\) 18.2857 0.592953
\(952\) 10.0012 0.324140
\(953\) −4.80852 −0.155763 −0.0778815 0.996963i \(-0.524816\pi\)
−0.0778815 + 0.996963i \(0.524816\pi\)
\(954\) 7.77384 0.251687
\(955\) −9.45211 −0.305863
\(956\) −7.78898 −0.251914
\(957\) −11.9147 −0.385146
\(958\) −29.7265 −0.960419
\(959\) −69.3546 −2.23958
\(960\) −2.16119 −0.0697520
\(961\) −22.3912 −0.722298
\(962\) 8.91543 0.287445
\(963\) −13.9722 −0.450248
\(964\) −4.07404 −0.131216
\(965\) −7.69930 −0.247849
\(966\) 19.6767 0.633086
\(967\) −8.11932 −0.261100 −0.130550 0.991442i \(-0.541674\pi\)
−0.130550 + 0.991442i \(0.541674\pi\)
\(968\) −5.99107 −0.192560
\(969\) −6.13593 −0.197114
\(970\) −10.3880 −0.333539
\(971\) 7.69890 0.247069 0.123535 0.992340i \(-0.460577\pi\)
0.123535 + 0.992340i \(0.460577\pi\)
\(972\) −0.644366 −0.0206680
\(973\) 62.3516 1.99890
\(974\) −19.3645 −0.620478
\(975\) 4.95935 0.158826
\(976\) −50.9311 −1.63026
\(977\) −47.4683 −1.51865 −0.759323 0.650713i \(-0.774470\pi\)
−0.759323 + 0.650713i \(0.774470\pi\)
\(978\) 23.7718 0.760137
\(979\) −29.5563 −0.944622
\(980\) 4.69434 0.149955
\(981\) −6.26962 −0.200173
\(982\) −17.8029 −0.568112
\(983\) −17.1451 −0.546845 −0.273423 0.961894i \(-0.588156\pi\)
−0.273423 + 0.961894i \(0.588156\pi\)
\(984\) −0.569754 −0.0181631
\(985\) 3.38092 0.107725
\(986\) −6.73235 −0.214402
\(987\) −20.9821 −0.667866
\(988\) 4.16106 0.132381
\(989\) 1.58568 0.0504218
\(990\) −2.51017 −0.0797786
\(991\) 54.3776 1.72736 0.863681 0.504039i \(-0.168153\pi\)
0.863681 + 0.504039i \(0.168153\pi\)
\(992\) −10.3166 −0.327553
\(993\) −5.35412 −0.169908
\(994\) −72.9529 −2.31393
\(995\) −12.2969 −0.389839
\(996\) −1.37179 −0.0434669
\(997\) −30.7869 −0.975031 −0.487516 0.873114i \(-0.662097\pi\)
−0.487516 + 0.873114i \(0.662097\pi\)
\(998\) −3.22645 −0.102131
\(999\) 5.20943 0.164819
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 \(a_p\))