Properties

Label 4003.2.a.b.1.4
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71591 q^{2} -1.21901 q^{3} +5.37616 q^{4} +2.34595 q^{5} +3.31073 q^{6} +3.38769 q^{7} -9.16936 q^{8} -1.51401 q^{9} +O(q^{10})\) \(q-2.71591 q^{2} -1.21901 q^{3} +5.37616 q^{4} +2.34595 q^{5} +3.31073 q^{6} +3.38769 q^{7} -9.16936 q^{8} -1.51401 q^{9} -6.37139 q^{10} -0.811481 q^{11} -6.55362 q^{12} -2.55732 q^{13} -9.20065 q^{14} -2.85974 q^{15} +14.1508 q^{16} -3.94346 q^{17} +4.11191 q^{18} -3.34018 q^{19} +12.6122 q^{20} -4.12964 q^{21} +2.20391 q^{22} -3.85630 q^{23} +11.1776 q^{24} +0.503476 q^{25} +6.94546 q^{26} +5.50263 q^{27} +18.2128 q^{28} +4.22183 q^{29} +7.76680 q^{30} +6.07512 q^{31} -20.0936 q^{32} +0.989206 q^{33} +10.7101 q^{34} +7.94734 q^{35} -8.13955 q^{36} +1.41221 q^{37} +9.07163 q^{38} +3.11741 q^{39} -21.5108 q^{40} +2.27396 q^{41} +11.2157 q^{42} +5.23352 q^{43} -4.36265 q^{44} -3.55178 q^{45} +10.4734 q^{46} -6.02476 q^{47} -17.2500 q^{48} +4.47643 q^{49} -1.36740 q^{50} +4.80713 q^{51} -13.7486 q^{52} +3.81772 q^{53} -14.9447 q^{54} -1.90369 q^{55} -31.0629 q^{56} +4.07172 q^{57} -11.4661 q^{58} -6.50570 q^{59} -15.3744 q^{60} +12.0368 q^{61} -16.4995 q^{62} -5.12898 q^{63} +26.2708 q^{64} -5.99935 q^{65} -2.68659 q^{66} +1.82591 q^{67} -21.2007 q^{68} +4.70088 q^{69} -21.5843 q^{70} +0.823990 q^{71} +13.8825 q^{72} -8.93057 q^{73} -3.83543 q^{74} -0.613744 q^{75} -17.9574 q^{76} -2.74904 q^{77} -8.46661 q^{78} -9.23686 q^{79} +33.1971 q^{80} -2.16576 q^{81} -6.17586 q^{82} +2.44747 q^{83} -22.2016 q^{84} -9.25115 q^{85} -14.2138 q^{86} -5.14646 q^{87} +7.44076 q^{88} +0.485918 q^{89} +9.64632 q^{90} -8.66342 q^{91} -20.7321 q^{92} -7.40565 q^{93} +16.3627 q^{94} -7.83589 q^{95} +24.4944 q^{96} +12.0833 q^{97} -12.1576 q^{98} +1.22859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71591 −1.92044 −0.960219 0.279248i \(-0.909915\pi\)
−0.960219 + 0.279248i \(0.909915\pi\)
\(3\) −1.21901 −0.703798 −0.351899 0.936038i \(-0.614464\pi\)
−0.351899 + 0.936038i \(0.614464\pi\)
\(4\) 5.37616 2.68808
\(5\) 2.34595 1.04914 0.524570 0.851367i \(-0.324226\pi\)
0.524570 + 0.851367i \(0.324226\pi\)
\(6\) 3.31073 1.35160
\(7\) 3.38769 1.28043 0.640213 0.768198i \(-0.278846\pi\)
0.640213 + 0.768198i \(0.278846\pi\)
\(8\) −9.16936 −3.24186
\(9\) −1.51401 −0.504669
\(10\) −6.37139 −2.01481
\(11\) −0.811481 −0.244671 −0.122335 0.992489i \(-0.539038\pi\)
−0.122335 + 0.992489i \(0.539038\pi\)
\(12\) −6.55362 −1.89187
\(13\) −2.55732 −0.709274 −0.354637 0.935004i \(-0.615396\pi\)
−0.354637 + 0.935004i \(0.615396\pi\)
\(14\) −9.20065 −2.45898
\(15\) −2.85974 −0.738382
\(16\) 14.1508 3.53770
\(17\) −3.94346 −0.956429 −0.478215 0.878243i \(-0.658716\pi\)
−0.478215 + 0.878243i \(0.658716\pi\)
\(18\) 4.11191 0.969186
\(19\) −3.34018 −0.766290 −0.383145 0.923688i \(-0.625159\pi\)
−0.383145 + 0.923688i \(0.625159\pi\)
\(20\) 12.6122 2.82018
\(21\) −4.12964 −0.901160
\(22\) 2.20391 0.469875
\(23\) −3.85630 −0.804094 −0.402047 0.915619i \(-0.631701\pi\)
−0.402047 + 0.915619i \(0.631701\pi\)
\(24\) 11.1776 2.28161
\(25\) 0.503476 0.100695
\(26\) 6.94546 1.36212
\(27\) 5.50263 1.05898
\(28\) 18.2128 3.44189
\(29\) 4.22183 0.783973 0.391987 0.919971i \(-0.371788\pi\)
0.391987 + 0.919971i \(0.371788\pi\)
\(30\) 7.76680 1.41802
\(31\) 6.07512 1.09112 0.545561 0.838071i \(-0.316316\pi\)
0.545561 + 0.838071i \(0.316316\pi\)
\(32\) −20.0936 −3.55209
\(33\) 0.989206 0.172199
\(34\) 10.7101 1.83676
\(35\) 7.94734 1.34335
\(36\) −8.13955 −1.35659
\(37\) 1.41221 0.232165 0.116083 0.993240i \(-0.462966\pi\)
0.116083 + 0.993240i \(0.462966\pi\)
\(38\) 9.07163 1.47161
\(39\) 3.11741 0.499185
\(40\) −21.5108 −3.40116
\(41\) 2.27396 0.355132 0.177566 0.984109i \(-0.443178\pi\)
0.177566 + 0.984109i \(0.443178\pi\)
\(42\) 11.2157 1.73062
\(43\) 5.23352 0.798105 0.399052 0.916928i \(-0.369339\pi\)
0.399052 + 0.916928i \(0.369339\pi\)
\(44\) −4.36265 −0.657695
\(45\) −3.55178 −0.529469
\(46\) 10.4734 1.54421
\(47\) −6.02476 −0.878801 −0.439400 0.898291i \(-0.644809\pi\)
−0.439400 + 0.898291i \(0.644809\pi\)
\(48\) −17.2500 −2.48983
\(49\) 4.47643 0.639490
\(50\) −1.36740 −0.193379
\(51\) 4.80713 0.673133
\(52\) −13.7486 −1.90659
\(53\) 3.81772 0.524404 0.262202 0.965013i \(-0.415551\pi\)
0.262202 + 0.965013i \(0.415551\pi\)
\(54\) −14.9447 −2.03371
\(55\) −1.90369 −0.256694
\(56\) −31.0629 −4.15096
\(57\) 4.07172 0.539313
\(58\) −11.4661 −1.50557
\(59\) −6.50570 −0.846970 −0.423485 0.905903i \(-0.639193\pi\)
−0.423485 + 0.905903i \(0.639193\pi\)
\(60\) −15.3744 −1.98483
\(61\) 12.0368 1.54116 0.770579 0.637344i \(-0.219967\pi\)
0.770579 + 0.637344i \(0.219967\pi\)
\(62\) −16.4995 −2.09543
\(63\) −5.12898 −0.646191
\(64\) 26.2708 3.28386
\(65\) −5.99935 −0.744128
\(66\) −2.68659 −0.330697
\(67\) 1.82591 0.223070 0.111535 0.993761i \(-0.464423\pi\)
0.111535 + 0.993761i \(0.464423\pi\)
\(68\) −21.2007 −2.57096
\(69\) 4.70088 0.565919
\(70\) −21.5843 −2.57981
\(71\) 0.823990 0.0977897 0.0488948 0.998804i \(-0.484430\pi\)
0.0488948 + 0.998804i \(0.484430\pi\)
\(72\) 13.8825 1.63607
\(73\) −8.93057 −1.04524 −0.522622 0.852564i \(-0.675046\pi\)
−0.522622 + 0.852564i \(0.675046\pi\)
\(74\) −3.83543 −0.445859
\(75\) −0.613744 −0.0708690
\(76\) −17.9574 −2.05985
\(77\) −2.74904 −0.313283
\(78\) −8.46661 −0.958655
\(79\) −9.23686 −1.03923 −0.519614 0.854401i \(-0.673924\pi\)
−0.519614 + 0.854401i \(0.673924\pi\)
\(80\) 33.1971 3.71155
\(81\) −2.16576 −0.240640
\(82\) −6.17586 −0.682009
\(83\) 2.44747 0.268644 0.134322 0.990938i \(-0.457114\pi\)
0.134322 + 0.990938i \(0.457114\pi\)
\(84\) −22.2016 −2.42239
\(85\) −9.25115 −1.00343
\(86\) −14.2138 −1.53271
\(87\) −5.14646 −0.551759
\(88\) 7.44076 0.793188
\(89\) 0.485918 0.0515072 0.0257536 0.999668i \(-0.491801\pi\)
0.0257536 + 0.999668i \(0.491801\pi\)
\(90\) 9.64632 1.01681
\(91\) −8.66342 −0.908173
\(92\) −20.7321 −2.16147
\(93\) −7.40565 −0.767930
\(94\) 16.3627 1.68768
\(95\) −7.83589 −0.803945
\(96\) 24.4944 2.49995
\(97\) 12.0833 1.22688 0.613439 0.789742i \(-0.289786\pi\)
0.613439 + 0.789742i \(0.289786\pi\)
\(98\) −12.1576 −1.22810
\(99\) 1.22859 0.123478
\(100\) 2.70677 0.270677
\(101\) −7.46651 −0.742946 −0.371473 0.928444i \(-0.621147\pi\)
−0.371473 + 0.928444i \(0.621147\pi\)
\(102\) −13.0557 −1.29271
\(103\) −16.9914 −1.67421 −0.837105 0.547043i \(-0.815754\pi\)
−0.837105 + 0.547043i \(0.815754\pi\)
\(104\) 23.4490 2.29937
\(105\) −9.68791 −0.945444
\(106\) −10.3686 −1.00708
\(107\) −8.41114 −0.813136 −0.406568 0.913621i \(-0.633275\pi\)
−0.406568 + 0.913621i \(0.633275\pi\)
\(108\) 29.5831 2.84663
\(109\) 12.3949 1.18722 0.593609 0.804753i \(-0.297702\pi\)
0.593609 + 0.804753i \(0.297702\pi\)
\(110\) 5.17026 0.492965
\(111\) −1.72150 −0.163397
\(112\) 47.9386 4.52977
\(113\) −13.7058 −1.28934 −0.644668 0.764462i \(-0.723005\pi\)
−0.644668 + 0.764462i \(0.723005\pi\)
\(114\) −11.0584 −1.03572
\(115\) −9.04668 −0.843608
\(116\) 22.6972 2.10739
\(117\) 3.87181 0.357949
\(118\) 17.6689 1.62655
\(119\) −13.3592 −1.22464
\(120\) 26.2220 2.39373
\(121\) −10.3415 −0.940136
\(122\) −32.6909 −2.95970
\(123\) −2.77198 −0.249941
\(124\) 32.6608 2.93303
\(125\) −10.5486 −0.943497
\(126\) 13.9299 1.24097
\(127\) 11.4285 1.01411 0.507056 0.861913i \(-0.330734\pi\)
0.507056 + 0.861913i \(0.330734\pi\)
\(128\) −31.1620 −2.75436
\(129\) −6.37973 −0.561704
\(130\) 16.2937 1.42905
\(131\) 11.4683 1.00199 0.500993 0.865451i \(-0.332968\pi\)
0.500993 + 0.865451i \(0.332968\pi\)
\(132\) 5.31813 0.462884
\(133\) −11.3155 −0.981177
\(134\) −4.95900 −0.428392
\(135\) 12.9089 1.11102
\(136\) 36.1590 3.10061
\(137\) −1.42455 −0.121708 −0.0608539 0.998147i \(-0.519382\pi\)
−0.0608539 + 0.998147i \(0.519382\pi\)
\(138\) −12.7672 −1.08681
\(139\) −3.89077 −0.330010 −0.165005 0.986293i \(-0.552764\pi\)
−0.165005 + 0.986293i \(0.552764\pi\)
\(140\) 42.7262 3.61102
\(141\) 7.34426 0.618498
\(142\) −2.23788 −0.187799
\(143\) 2.07522 0.173539
\(144\) −21.4244 −1.78537
\(145\) 9.90419 0.822498
\(146\) 24.2546 2.00733
\(147\) −5.45682 −0.450071
\(148\) 7.59226 0.624080
\(149\) −8.64459 −0.708192 −0.354096 0.935209i \(-0.615211\pi\)
−0.354096 + 0.935209i \(0.615211\pi\)
\(150\) 1.66687 0.136100
\(151\) 1.33471 0.108617 0.0543087 0.998524i \(-0.482705\pi\)
0.0543087 + 0.998524i \(0.482705\pi\)
\(152\) 30.6273 2.48420
\(153\) 5.97043 0.482680
\(154\) 7.46615 0.601640
\(155\) 14.2519 1.14474
\(156\) 16.7597 1.34185
\(157\) −13.8722 −1.10712 −0.553560 0.832809i \(-0.686731\pi\)
−0.553560 + 0.832809i \(0.686731\pi\)
\(158\) 25.0865 1.99577
\(159\) −4.65385 −0.369074
\(160\) −47.1386 −3.72664
\(161\) −13.0639 −1.02958
\(162\) 5.88201 0.462135
\(163\) −7.18081 −0.562444 −0.281222 0.959643i \(-0.590740\pi\)
−0.281222 + 0.959643i \(0.590740\pi\)
\(164\) 12.2252 0.954625
\(165\) 2.32063 0.180660
\(166\) −6.64710 −0.515915
\(167\) −8.26957 −0.639918 −0.319959 0.947431i \(-0.603669\pi\)
−0.319959 + 0.947431i \(0.603669\pi\)
\(168\) 37.8661 2.92143
\(169\) −6.46009 −0.496930
\(170\) 25.1253 1.92702
\(171\) 5.05706 0.386723
\(172\) 28.1363 2.14537
\(173\) −6.38589 −0.485510 −0.242755 0.970088i \(-0.578051\pi\)
−0.242755 + 0.970088i \(0.578051\pi\)
\(174\) 13.9773 1.05962
\(175\) 1.70562 0.128933
\(176\) −11.4831 −0.865573
\(177\) 7.93054 0.596096
\(178\) −1.31971 −0.0989163
\(179\) −16.6674 −1.24578 −0.622891 0.782309i \(-0.714042\pi\)
−0.622891 + 0.782309i \(0.714042\pi\)
\(180\) −19.0950 −1.42326
\(181\) 8.77818 0.652477 0.326238 0.945288i \(-0.394219\pi\)
0.326238 + 0.945288i \(0.394219\pi\)
\(182\) 23.5291 1.74409
\(183\) −14.6731 −1.08466
\(184\) 35.3598 2.60676
\(185\) 3.31296 0.243574
\(186\) 20.1131 1.47476
\(187\) 3.20004 0.234010
\(188\) −32.3901 −2.36229
\(189\) 18.6412 1.35595
\(190\) 21.2816 1.54393
\(191\) 2.77339 0.200675 0.100338 0.994953i \(-0.468008\pi\)
0.100338 + 0.994953i \(0.468008\pi\)
\(192\) −32.0245 −2.31117
\(193\) −3.19788 −0.230189 −0.115094 0.993355i \(-0.536717\pi\)
−0.115094 + 0.993355i \(0.536717\pi\)
\(194\) −32.8173 −2.35614
\(195\) 7.31329 0.523715
\(196\) 24.0660 1.71900
\(197\) −7.75246 −0.552340 −0.276170 0.961109i \(-0.589065\pi\)
−0.276170 + 0.961109i \(0.589065\pi\)
\(198\) −3.33673 −0.237131
\(199\) −7.25874 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(200\) −4.61655 −0.326440
\(201\) −2.22580 −0.156996
\(202\) 20.2784 1.42678
\(203\) 14.3022 1.00382
\(204\) 25.8439 1.80944
\(205\) 5.33458 0.372583
\(206\) 46.1470 3.21522
\(207\) 5.83847 0.405801
\(208\) −36.1882 −2.50920
\(209\) 2.71049 0.187489
\(210\) 26.3115 1.81567
\(211\) 8.38241 0.577069 0.288534 0.957470i \(-0.406832\pi\)
0.288534 + 0.957470i \(0.406832\pi\)
\(212\) 20.5247 1.40964
\(213\) −1.00446 −0.0688241
\(214\) 22.8439 1.56158
\(215\) 12.2776 0.837324
\(216\) −50.4556 −3.43307
\(217\) 20.5806 1.39710
\(218\) −33.6635 −2.27998
\(219\) 10.8865 0.735640
\(220\) −10.2346 −0.690014
\(221\) 10.0847 0.678371
\(222\) 4.67543 0.313795
\(223\) 3.98109 0.266594 0.133297 0.991076i \(-0.457444\pi\)
0.133297 + 0.991076i \(0.457444\pi\)
\(224\) −68.0709 −4.54818
\(225\) −0.762266 −0.0508178
\(226\) 37.2238 2.47609
\(227\) −15.4613 −1.02620 −0.513101 0.858328i \(-0.671503\pi\)
−0.513101 + 0.858328i \(0.671503\pi\)
\(228\) 21.8903 1.44972
\(229\) 9.60886 0.634971 0.317486 0.948263i \(-0.397161\pi\)
0.317486 + 0.948263i \(0.397161\pi\)
\(230\) 24.5700 1.62010
\(231\) 3.35112 0.220488
\(232\) −38.7114 −2.54153
\(233\) 23.2996 1.52641 0.763203 0.646158i \(-0.223625\pi\)
0.763203 + 0.646158i \(0.223625\pi\)
\(234\) −10.5155 −0.687418
\(235\) −14.1338 −0.921985
\(236\) −34.9757 −2.27673
\(237\) 11.2599 0.731406
\(238\) 36.2824 2.35184
\(239\) −29.9454 −1.93700 −0.968502 0.249005i \(-0.919896\pi\)
−0.968502 + 0.249005i \(0.919896\pi\)
\(240\) −40.4677 −2.61218
\(241\) 9.68595 0.623927 0.311964 0.950094i \(-0.399013\pi\)
0.311964 + 0.950094i \(0.399013\pi\)
\(242\) 28.0866 1.80547
\(243\) −13.8678 −0.889620
\(244\) 64.7120 4.14276
\(245\) 10.5015 0.670914
\(246\) 7.52845 0.479997
\(247\) 8.54192 0.543509
\(248\) −55.7049 −3.53727
\(249\) −2.98349 −0.189071
\(250\) 28.6491 1.81193
\(251\) 10.5555 0.666255 0.333128 0.942882i \(-0.391896\pi\)
0.333128 + 0.942882i \(0.391896\pi\)
\(252\) −27.5743 −1.73701
\(253\) 3.12931 0.196738
\(254\) −31.0387 −1.94754
\(255\) 11.2773 0.706211
\(256\) 32.0914 2.00571
\(257\) −16.2583 −1.01417 −0.507084 0.861897i \(-0.669277\pi\)
−0.507084 + 0.861897i \(0.669277\pi\)
\(258\) 17.3268 1.07872
\(259\) 4.78411 0.297270
\(260\) −32.2535 −2.00028
\(261\) −6.39187 −0.395647
\(262\) −31.1468 −1.92425
\(263\) 8.35083 0.514934 0.257467 0.966287i \(-0.417112\pi\)
0.257467 + 0.966287i \(0.417112\pi\)
\(264\) −9.07038 −0.558243
\(265\) 8.95617 0.550173
\(266\) 30.7318 1.88429
\(267\) −0.592340 −0.0362506
\(268\) 9.81638 0.599631
\(269\) −3.76939 −0.229824 −0.114912 0.993376i \(-0.536659\pi\)
−0.114912 + 0.993376i \(0.536659\pi\)
\(270\) −35.0594 −2.13365
\(271\) −25.1946 −1.53046 −0.765231 0.643756i \(-0.777375\pi\)
−0.765231 + 0.643756i \(0.777375\pi\)
\(272\) −55.8032 −3.38357
\(273\) 10.5608 0.639170
\(274\) 3.86896 0.233732
\(275\) −0.408561 −0.0246372
\(276\) 25.2727 1.52124
\(277\) 0.668286 0.0401534 0.0200767 0.999798i \(-0.493609\pi\)
0.0200767 + 0.999798i \(0.493609\pi\)
\(278\) 10.5670 0.633765
\(279\) −9.19777 −0.550656
\(280\) −72.8720 −4.35494
\(281\) −18.2233 −1.08711 −0.543556 0.839373i \(-0.682922\pi\)
−0.543556 + 0.839373i \(0.682922\pi\)
\(282\) −19.9463 −1.18779
\(283\) −25.1313 −1.49390 −0.746949 0.664881i \(-0.768482\pi\)
−0.746949 + 0.664881i \(0.768482\pi\)
\(284\) 4.42991 0.262867
\(285\) 9.55205 0.565815
\(286\) −5.63611 −0.333270
\(287\) 7.70345 0.454720
\(288\) 30.4219 1.79263
\(289\) −1.44913 −0.0852427
\(290\) −26.8989 −1.57956
\(291\) −14.7298 −0.863474
\(292\) −48.0122 −2.80970
\(293\) −8.18796 −0.478346 −0.239173 0.970977i \(-0.576876\pi\)
−0.239173 + 0.970977i \(0.576876\pi\)
\(294\) 14.8202 0.864334
\(295\) −15.2620 −0.888591
\(296\) −12.9490 −0.752647
\(297\) −4.46528 −0.259102
\(298\) 23.4779 1.36004
\(299\) 9.86181 0.570323
\(300\) −3.29959 −0.190502
\(301\) 17.7295 1.02191
\(302\) −3.62496 −0.208593
\(303\) 9.10178 0.522884
\(304\) −47.2663 −2.71091
\(305\) 28.2378 1.61689
\(306\) −16.2151 −0.926958
\(307\) 22.3341 1.27468 0.637338 0.770585i \(-0.280036\pi\)
0.637338 + 0.770585i \(0.280036\pi\)
\(308\) −14.7793 −0.842129
\(309\) 20.7127 1.17830
\(310\) −38.7069 −2.19840
\(311\) 32.7851 1.85907 0.929536 0.368731i \(-0.120208\pi\)
0.929536 + 0.368731i \(0.120208\pi\)
\(312\) −28.5847 −1.61829
\(313\) −20.3797 −1.15193 −0.575964 0.817475i \(-0.695373\pi\)
−0.575964 + 0.817475i \(0.695373\pi\)
\(314\) 37.6756 2.12616
\(315\) −12.0323 −0.677945
\(316\) −49.6589 −2.79353
\(317\) −28.8608 −1.62099 −0.810493 0.585748i \(-0.800801\pi\)
−0.810493 + 0.585748i \(0.800801\pi\)
\(318\) 12.6394 0.708784
\(319\) −3.42593 −0.191815
\(320\) 61.6301 3.44522
\(321\) 10.2533 0.572283
\(322\) 35.4805 1.97725
\(323\) 13.1719 0.732902
\(324\) −11.6435 −0.646861
\(325\) −1.28755 −0.0714205
\(326\) 19.5024 1.08014
\(327\) −15.1096 −0.835562
\(328\) −20.8507 −1.15129
\(329\) −20.4100 −1.12524
\(330\) −6.30261 −0.346947
\(331\) 24.9883 1.37348 0.686741 0.726902i \(-0.259041\pi\)
0.686741 + 0.726902i \(0.259041\pi\)
\(332\) 13.1580 0.722138
\(333\) −2.13809 −0.117167
\(334\) 22.4594 1.22892
\(335\) 4.28348 0.234032
\(336\) −58.4377 −3.18804
\(337\) −25.5893 −1.39394 −0.696970 0.717101i \(-0.745469\pi\)
−0.696970 + 0.717101i \(0.745469\pi\)
\(338\) 17.5450 0.954324
\(339\) 16.7076 0.907432
\(340\) −49.7357 −2.69730
\(341\) −4.92984 −0.266966
\(342\) −13.7345 −0.742677
\(343\) −8.54908 −0.461607
\(344\) −47.9881 −2.58734
\(345\) 11.0280 0.593729
\(346\) 17.3435 0.932392
\(347\) −7.41665 −0.398146 −0.199073 0.979985i \(-0.563793\pi\)
−0.199073 + 0.979985i \(0.563793\pi\)
\(348\) −27.6682 −1.48317
\(349\) −26.1150 −1.39790 −0.698951 0.715170i \(-0.746349\pi\)
−0.698951 + 0.715170i \(0.746349\pi\)
\(350\) −4.63231 −0.247607
\(351\) −14.0720 −0.751109
\(352\) 16.3056 0.869091
\(353\) −9.23587 −0.491576 −0.245788 0.969324i \(-0.579047\pi\)
−0.245788 + 0.969324i \(0.579047\pi\)
\(354\) −21.5386 −1.14476
\(355\) 1.93304 0.102595
\(356\) 2.61237 0.138456
\(357\) 16.2851 0.861896
\(358\) 45.2672 2.39245
\(359\) −7.16788 −0.378306 −0.189153 0.981948i \(-0.560574\pi\)
−0.189153 + 0.981948i \(0.560574\pi\)
\(360\) 32.5676 1.71646
\(361\) −7.84320 −0.412800
\(362\) −23.8407 −1.25304
\(363\) 12.6064 0.661666
\(364\) −46.5760 −2.44124
\(365\) −20.9507 −1.09661
\(366\) 39.8507 2.08303
\(367\) −16.6788 −0.870627 −0.435314 0.900279i \(-0.643363\pi\)
−0.435314 + 0.900279i \(0.643363\pi\)
\(368\) −54.5698 −2.84465
\(369\) −3.44278 −0.179224
\(370\) −8.99771 −0.467769
\(371\) 12.9332 0.671460
\(372\) −39.8140 −2.06426
\(373\) 1.81236 0.0938404 0.0469202 0.998899i \(-0.485059\pi\)
0.0469202 + 0.998899i \(0.485059\pi\)
\(374\) −8.69102 −0.449402
\(375\) 12.8589 0.664031
\(376\) 55.2431 2.84895
\(377\) −10.7966 −0.556052
\(378\) −50.6278 −2.60401
\(379\) 25.4938 1.30953 0.654766 0.755832i \(-0.272767\pi\)
0.654766 + 0.755832i \(0.272767\pi\)
\(380\) −42.1270 −2.16107
\(381\) −13.9314 −0.713729
\(382\) −7.53227 −0.385384
\(383\) −6.27741 −0.320761 −0.160380 0.987055i \(-0.551272\pi\)
−0.160380 + 0.987055i \(0.551272\pi\)
\(384\) 37.9869 1.93851
\(385\) −6.44912 −0.328677
\(386\) 8.68516 0.442063
\(387\) −7.92359 −0.402779
\(388\) 64.9621 3.29795
\(389\) −12.0484 −0.610876 −0.305438 0.952212i \(-0.598803\pi\)
−0.305438 + 0.952212i \(0.598803\pi\)
\(390\) −19.8622 −1.00576
\(391\) 15.2072 0.769059
\(392\) −41.0460 −2.07313
\(393\) −13.9800 −0.705196
\(394\) 21.0550 1.06074
\(395\) −21.6692 −1.09030
\(396\) 6.60509 0.331918
\(397\) −11.8731 −0.595891 −0.297946 0.954583i \(-0.596301\pi\)
−0.297946 + 0.954583i \(0.596301\pi\)
\(398\) 19.7141 0.988177
\(399\) 13.7937 0.690550
\(400\) 7.12460 0.356230
\(401\) −17.8025 −0.889015 −0.444507 0.895775i \(-0.646621\pi\)
−0.444507 + 0.895775i \(0.646621\pi\)
\(402\) 6.04508 0.301501
\(403\) −15.5360 −0.773905
\(404\) −40.1412 −1.99710
\(405\) −5.08077 −0.252465
\(406\) −38.8436 −1.92777
\(407\) −1.14598 −0.0568041
\(408\) −44.0783 −2.18220
\(409\) −1.46512 −0.0724455 −0.0362227 0.999344i \(-0.511533\pi\)
−0.0362227 + 0.999344i \(0.511533\pi\)
\(410\) −14.4882 −0.715523
\(411\) 1.73655 0.0856576
\(412\) −91.3484 −4.50041
\(413\) −22.0393 −1.08448
\(414\) −15.8567 −0.779316
\(415\) 5.74163 0.281846
\(416\) 51.3859 2.51940
\(417\) 4.74290 0.232261
\(418\) −7.36145 −0.360060
\(419\) 8.61860 0.421046 0.210523 0.977589i \(-0.432483\pi\)
0.210523 + 0.977589i \(0.432483\pi\)
\(420\) −52.0838 −2.54143
\(421\) −25.3563 −1.23579 −0.617896 0.786260i \(-0.712015\pi\)
−0.617896 + 0.786260i \(0.712015\pi\)
\(422\) −22.7659 −1.10822
\(423\) 9.12152 0.443504
\(424\) −35.0060 −1.70004
\(425\) −1.98544 −0.0963079
\(426\) 2.72801 0.132172
\(427\) 40.7770 1.97334
\(428\) −45.2197 −2.18578
\(429\) −2.52972 −0.122136
\(430\) −33.3448 −1.60803
\(431\) 25.5312 1.22980 0.614898 0.788607i \(-0.289197\pi\)
0.614898 + 0.788607i \(0.289197\pi\)
\(432\) 77.8668 3.74637
\(433\) −19.5854 −0.941213 −0.470606 0.882343i \(-0.655965\pi\)
−0.470606 + 0.882343i \(0.655965\pi\)
\(434\) −55.8950 −2.68305
\(435\) −12.0733 −0.578872
\(436\) 66.6372 3.19134
\(437\) 12.8807 0.616169
\(438\) −29.5667 −1.41275
\(439\) 24.5900 1.17362 0.586808 0.809726i \(-0.300384\pi\)
0.586808 + 0.809726i \(0.300384\pi\)
\(440\) 17.4556 0.832165
\(441\) −6.77734 −0.322731
\(442\) −27.3891 −1.30277
\(443\) −36.7053 −1.74392 −0.871960 0.489578i \(-0.837151\pi\)
−0.871960 + 0.489578i \(0.837151\pi\)
\(444\) −9.25506 −0.439226
\(445\) 1.13994 0.0540382
\(446\) −10.8123 −0.511977
\(447\) 10.5379 0.498424
\(448\) 88.9974 4.20473
\(449\) −6.66992 −0.314773 −0.157387 0.987537i \(-0.550307\pi\)
−0.157387 + 0.987537i \(0.550307\pi\)
\(450\) 2.07025 0.0975924
\(451\) −1.84527 −0.0868904
\(452\) −73.6849 −3.46584
\(453\) −1.62703 −0.0764446
\(454\) 41.9915 1.97076
\(455\) −20.3239 −0.952801
\(456\) −37.3351 −1.74838
\(457\) 4.35542 0.203738 0.101869 0.994798i \(-0.467518\pi\)
0.101869 + 0.994798i \(0.467518\pi\)
\(458\) −26.0968 −1.21942
\(459\) −21.6994 −1.01284
\(460\) −48.6365 −2.26769
\(461\) 14.8966 0.693806 0.346903 0.937901i \(-0.387233\pi\)
0.346903 + 0.937901i \(0.387233\pi\)
\(462\) −9.10134 −0.423433
\(463\) 13.6012 0.632103 0.316052 0.948742i \(-0.397643\pi\)
0.316052 + 0.948742i \(0.397643\pi\)
\(464\) 59.7423 2.77347
\(465\) −17.3733 −0.805666
\(466\) −63.2796 −2.93137
\(467\) −30.9495 −1.43217 −0.716087 0.698011i \(-0.754069\pi\)
−0.716087 + 0.698011i \(0.754069\pi\)
\(468\) 20.8155 0.962196
\(469\) 6.18560 0.285625
\(470\) 38.3860 1.77062
\(471\) 16.9104 0.779189
\(472\) 59.6531 2.74576
\(473\) −4.24690 −0.195273
\(474\) −30.5808 −1.40462
\(475\) −1.68170 −0.0771617
\(476\) −71.8213 −3.29192
\(477\) −5.78005 −0.264650
\(478\) 81.3289 3.71990
\(479\) −2.77895 −0.126974 −0.0634868 0.997983i \(-0.520222\pi\)
−0.0634868 + 0.997983i \(0.520222\pi\)
\(480\) 57.4626 2.62280
\(481\) −3.61147 −0.164669
\(482\) −26.3062 −1.19821
\(483\) 15.9251 0.724618
\(484\) −55.5976 −2.52716
\(485\) 28.3469 1.28717
\(486\) 37.6637 1.70846
\(487\) 3.88132 0.175880 0.0879398 0.996126i \(-0.471972\pi\)
0.0879398 + 0.996126i \(0.471972\pi\)
\(488\) −110.370 −4.99622
\(489\) 8.75350 0.395847
\(490\) −28.5210 −1.28845
\(491\) 14.4734 0.653174 0.326587 0.945167i \(-0.394101\pi\)
0.326587 + 0.945167i \(0.394101\pi\)
\(492\) −14.9026 −0.671862
\(493\) −16.6486 −0.749815
\(494\) −23.1991 −1.04378
\(495\) 2.88220 0.129545
\(496\) 85.9679 3.86007
\(497\) 2.79142 0.125212
\(498\) 8.10290 0.363100
\(499\) −8.48380 −0.379787 −0.189894 0.981805i \(-0.560814\pi\)
−0.189894 + 0.981805i \(0.560814\pi\)
\(500\) −56.7111 −2.53620
\(501\) 10.0807 0.450373
\(502\) −28.6677 −1.27950
\(503\) 20.1722 0.899432 0.449716 0.893172i \(-0.351525\pi\)
0.449716 + 0.893172i \(0.351525\pi\)
\(504\) 47.0295 2.09486
\(505\) −17.5161 −0.779455
\(506\) −8.49893 −0.377824
\(507\) 7.87494 0.349738
\(508\) 61.4413 2.72602
\(509\) 44.6181 1.97766 0.988832 0.149035i \(-0.0476167\pi\)
0.988832 + 0.149035i \(0.0476167\pi\)
\(510\) −30.6281 −1.35623
\(511\) −30.2540 −1.33836
\(512\) −24.8334 −1.09749
\(513\) −18.3798 −0.811487
\(514\) 44.1562 1.94765
\(515\) −39.8609 −1.75648
\(516\) −34.2985 −1.50991
\(517\) 4.88897 0.215017
\(518\) −12.9932 −0.570889
\(519\) 7.78448 0.341701
\(520\) 55.0102 2.41236
\(521\) 12.6560 0.554469 0.277234 0.960802i \(-0.410582\pi\)
0.277234 + 0.960802i \(0.410582\pi\)
\(522\) 17.3598 0.759816
\(523\) 36.0828 1.57779 0.788896 0.614527i \(-0.210653\pi\)
0.788896 + 0.614527i \(0.210653\pi\)
\(524\) 61.6553 2.69342
\(525\) −2.07917 −0.0907425
\(526\) −22.6801 −0.988899
\(527\) −23.9570 −1.04358
\(528\) 13.9981 0.609188
\(529\) −8.12895 −0.353433
\(530\) −24.3241 −1.05657
\(531\) 9.84968 0.427440
\(532\) −60.8339 −2.63748
\(533\) −5.81524 −0.251886
\(534\) 1.60874 0.0696171
\(535\) −19.7321 −0.853093
\(536\) −16.7424 −0.723161
\(537\) 20.3178 0.876778
\(538\) 10.2373 0.441362
\(539\) −3.63253 −0.156464
\(540\) 69.4004 2.98652
\(541\) 23.3384 1.00339 0.501697 0.865043i \(-0.332709\pi\)
0.501697 + 0.865043i \(0.332709\pi\)
\(542\) 68.4262 2.93916
\(543\) −10.7007 −0.459212
\(544\) 79.2384 3.39732
\(545\) 29.0779 1.24556
\(546\) −28.6822 −1.22749
\(547\) 1.81438 0.0775772 0.0387886 0.999247i \(-0.487650\pi\)
0.0387886 + 0.999247i \(0.487650\pi\)
\(548\) −7.65863 −0.327160
\(549\) −18.2238 −0.777775
\(550\) 1.10962 0.0473142
\(551\) −14.1017 −0.600751
\(552\) −43.1041 −1.83463
\(553\) −31.2916 −1.33065
\(554\) −1.81500 −0.0771121
\(555\) −4.03855 −0.171427
\(556\) −20.9174 −0.887095
\(557\) −24.1043 −1.02133 −0.510666 0.859779i \(-0.670601\pi\)
−0.510666 + 0.859779i \(0.670601\pi\)
\(558\) 24.9803 1.05750
\(559\) −13.3838 −0.566075
\(560\) 112.461 4.75236
\(561\) −3.90089 −0.164696
\(562\) 49.4929 2.08773
\(563\) 25.3282 1.06746 0.533729 0.845655i \(-0.320790\pi\)
0.533729 + 0.845655i \(0.320790\pi\)
\(564\) 39.4839 1.66257
\(565\) −32.1532 −1.35270
\(566\) 68.2542 2.86894
\(567\) −7.33692 −0.308122
\(568\) −7.55546 −0.317020
\(569\) 32.5865 1.36610 0.683048 0.730373i \(-0.260654\pi\)
0.683048 + 0.730373i \(0.260654\pi\)
\(570\) −25.9425 −1.08661
\(571\) 31.9431 1.33678 0.668388 0.743813i \(-0.266984\pi\)
0.668388 + 0.743813i \(0.266984\pi\)
\(572\) 11.1567 0.466486
\(573\) −3.38080 −0.141235
\(574\) −20.9219 −0.873262
\(575\) −1.94155 −0.0809684
\(576\) −39.7742 −1.65726
\(577\) −17.2713 −0.719015 −0.359507 0.933142i \(-0.617055\pi\)
−0.359507 + 0.933142i \(0.617055\pi\)
\(578\) 3.93569 0.163703
\(579\) 3.89826 0.162006
\(580\) 53.2466 2.21094
\(581\) 8.29125 0.343979
\(582\) 40.0047 1.65825
\(583\) −3.09800 −0.128306
\(584\) 81.8876 3.38853
\(585\) 9.08306 0.375538
\(586\) 22.2378 0.918634
\(587\) 14.1067 0.582247 0.291124 0.956685i \(-0.405971\pi\)
0.291124 + 0.956685i \(0.405971\pi\)
\(588\) −29.3368 −1.20983
\(589\) −20.2920 −0.836116
\(590\) 41.4503 1.70648
\(591\) 9.45035 0.388736
\(592\) 19.9839 0.821332
\(593\) 0.125965 0.00517275 0.00258638 0.999997i \(-0.499177\pi\)
0.00258638 + 0.999997i \(0.499177\pi\)
\(594\) 12.1273 0.497589
\(595\) −31.3400 −1.28482
\(596\) −46.4747 −1.90368
\(597\) 8.84850 0.362145
\(598\) −26.7838 −1.09527
\(599\) −8.70627 −0.355728 −0.177864 0.984055i \(-0.556919\pi\)
−0.177864 + 0.984055i \(0.556919\pi\)
\(600\) 5.62764 0.229747
\(601\) 45.0940 1.83942 0.919712 0.392594i \(-0.128422\pi\)
0.919712 + 0.392594i \(0.128422\pi\)
\(602\) −48.1518 −1.96252
\(603\) −2.76444 −0.112577
\(604\) 7.17563 0.291972
\(605\) −24.2606 −0.986335
\(606\) −24.7196 −1.00417
\(607\) 39.5949 1.60711 0.803555 0.595231i \(-0.202939\pi\)
0.803555 + 0.595231i \(0.202939\pi\)
\(608\) 67.1163 2.72193
\(609\) −17.4346 −0.706486
\(610\) −76.6913 −3.10514
\(611\) 15.4073 0.623311
\(612\) 32.0980 1.29748
\(613\) −45.7881 −1.84937 −0.924683 0.380738i \(-0.875670\pi\)
−0.924683 + 0.380738i \(0.875670\pi\)
\(614\) −60.6574 −2.44793
\(615\) −6.50293 −0.262223
\(616\) 25.2070 1.01562
\(617\) −31.0597 −1.25042 −0.625209 0.780458i \(-0.714986\pi\)
−0.625209 + 0.780458i \(0.714986\pi\)
\(618\) −56.2538 −2.26286
\(619\) −37.0714 −1.49003 −0.745013 0.667050i \(-0.767557\pi\)
−0.745013 + 0.667050i \(0.767557\pi\)
\(620\) 76.6206 3.07716
\(621\) −21.2198 −0.851522
\(622\) −89.0413 −3.57023
\(623\) 1.64614 0.0659511
\(624\) 44.1139 1.76597
\(625\) −27.2639 −1.09056
\(626\) 55.3494 2.21221
\(627\) −3.30412 −0.131954
\(628\) −74.5791 −2.97603
\(629\) −5.56898 −0.222050
\(630\) 32.6787 1.30195
\(631\) 29.9595 1.19267 0.596334 0.802737i \(-0.296624\pi\)
0.596334 + 0.802737i \(0.296624\pi\)
\(632\) 84.6961 3.36903
\(633\) −10.2183 −0.406139
\(634\) 78.3834 3.11300
\(635\) 26.8106 1.06395
\(636\) −25.0198 −0.992101
\(637\) −11.4477 −0.453573
\(638\) 9.30452 0.368369
\(639\) −1.24753 −0.0493514
\(640\) −73.1044 −2.88970
\(641\) 24.9439 0.985225 0.492612 0.870249i \(-0.336042\pi\)
0.492612 + 0.870249i \(0.336042\pi\)
\(642\) −27.8470 −1.09903
\(643\) 7.70102 0.303699 0.151849 0.988404i \(-0.451477\pi\)
0.151849 + 0.988404i \(0.451477\pi\)
\(644\) −70.2339 −2.76760
\(645\) −14.9665 −0.589307
\(646\) −35.7736 −1.40749
\(647\) −14.5983 −0.573918 −0.286959 0.957943i \(-0.592644\pi\)
−0.286959 + 0.957943i \(0.592644\pi\)
\(648\) 19.8586 0.780121
\(649\) 5.27925 0.207229
\(650\) 3.49687 0.137159
\(651\) −25.0880 −0.983277
\(652\) −38.6052 −1.51190
\(653\) 35.9508 1.40686 0.703431 0.710764i \(-0.251650\pi\)
0.703431 + 0.710764i \(0.251650\pi\)
\(654\) 41.0362 1.60464
\(655\) 26.9040 1.05122
\(656\) 32.1783 1.25635
\(657\) 13.5209 0.527502
\(658\) 55.4317 2.16095
\(659\) −23.4272 −0.912596 −0.456298 0.889827i \(-0.650825\pi\)
−0.456298 + 0.889827i \(0.650825\pi\)
\(660\) 12.4761 0.485630
\(661\) −17.0585 −0.663499 −0.331749 0.943368i \(-0.607639\pi\)
−0.331749 + 0.943368i \(0.607639\pi\)
\(662\) −67.8660 −2.63769
\(663\) −12.2934 −0.477436
\(664\) −22.4417 −0.870907
\(665\) −26.5455 −1.02939
\(666\) 5.80686 0.225011
\(667\) −16.2806 −0.630388
\(668\) −44.4586 −1.72015
\(669\) −4.85300 −0.187628
\(670\) −11.6336 −0.449444
\(671\) −9.76766 −0.377076
\(672\) 82.9794 3.20100
\(673\) 46.6597 1.79860 0.899300 0.437332i \(-0.144077\pi\)
0.899300 + 0.437332i \(0.144077\pi\)
\(674\) 69.4983 2.67697
\(675\) 2.77044 0.106634
\(676\) −34.7305 −1.33579
\(677\) −27.9266 −1.07331 −0.536653 0.843803i \(-0.680311\pi\)
−0.536653 + 0.843803i \(0.680311\pi\)
\(678\) −45.3763 −1.74267
\(679\) 40.9346 1.57093
\(680\) 84.8272 3.25297
\(681\) 18.8475 0.722239
\(682\) 13.3890 0.512691
\(683\) −38.5106 −1.47357 −0.736783 0.676129i \(-0.763656\pi\)
−0.736783 + 0.676129i \(0.763656\pi\)
\(684\) 27.1876 1.03954
\(685\) −3.34193 −0.127688
\(686\) 23.2185 0.886487
\(687\) −11.7133 −0.446891
\(688\) 74.0587 2.82346
\(689\) −9.76314 −0.371946
\(690\) −29.9511 −1.14022
\(691\) 11.8064 0.449137 0.224569 0.974458i \(-0.427903\pi\)
0.224569 + 0.974458i \(0.427903\pi\)
\(692\) −34.3316 −1.30509
\(693\) 4.16207 0.158104
\(694\) 20.1429 0.764616
\(695\) −9.12754 −0.346227
\(696\) 47.1898 1.78872
\(697\) −8.96725 −0.339659
\(698\) 70.9259 2.68458
\(699\) −28.4025 −1.07428
\(700\) 9.16969 0.346582
\(701\) −36.4154 −1.37539 −0.687695 0.726000i \(-0.741377\pi\)
−0.687695 + 0.726000i \(0.741377\pi\)
\(702\) 38.2183 1.44246
\(703\) −4.71702 −0.177906
\(704\) −21.3183 −0.803463
\(705\) 17.2292 0.648891
\(706\) 25.0838 0.944040
\(707\) −25.2942 −0.951287
\(708\) 42.6359 1.60235
\(709\) 22.1543 0.832022 0.416011 0.909360i \(-0.363428\pi\)
0.416011 + 0.909360i \(0.363428\pi\)
\(710\) −5.24996 −0.197028
\(711\) 13.9847 0.524466
\(712\) −4.45555 −0.166979
\(713\) −23.4275 −0.877366
\(714\) −44.2287 −1.65522
\(715\) 4.86836 0.182066
\(716\) −89.6068 −3.34876
\(717\) 36.5038 1.36326
\(718\) 19.4673 0.726514
\(719\) 36.2655 1.35247 0.676237 0.736684i \(-0.263610\pi\)
0.676237 + 0.736684i \(0.263610\pi\)
\(720\) −50.2606 −1.87310
\(721\) −57.5615 −2.14370
\(722\) 21.3014 0.792757
\(723\) −11.8073 −0.439118
\(724\) 47.1929 1.75391
\(725\) 2.12559 0.0789424
\(726\) −34.2379 −1.27069
\(727\) −48.6385 −1.80390 −0.901952 0.431837i \(-0.857866\pi\)
−0.901952 + 0.431837i \(0.857866\pi\)
\(728\) 79.4380 2.94417
\(729\) 23.4023 0.866753
\(730\) 56.9001 2.10597
\(731\) −20.6382 −0.763331
\(732\) −78.8848 −2.91566
\(733\) −15.1688 −0.560271 −0.280135 0.959960i \(-0.590379\pi\)
−0.280135 + 0.959960i \(0.590379\pi\)
\(734\) 45.2982 1.67199
\(735\) −12.8014 −0.472188
\(736\) 77.4871 2.85621
\(737\) −1.48169 −0.0545787
\(738\) 9.35029 0.344189
\(739\) −31.0650 −1.14275 −0.571373 0.820691i \(-0.693589\pi\)
−0.571373 + 0.820691i \(0.693589\pi\)
\(740\) 17.8110 0.654747
\(741\) −10.4127 −0.382521
\(742\) −35.1255 −1.28950
\(743\) 53.8252 1.97465 0.987327 0.158696i \(-0.0507290\pi\)
0.987327 + 0.158696i \(0.0507290\pi\)
\(744\) 67.9050 2.48952
\(745\) −20.2798 −0.742993
\(746\) −4.92220 −0.180215
\(747\) −3.70548 −0.135577
\(748\) 17.2040 0.629039
\(749\) −28.4943 −1.04116
\(750\) −34.9236 −1.27523
\(751\) −24.3647 −0.889080 −0.444540 0.895759i \(-0.646633\pi\)
−0.444540 + 0.895759i \(0.646633\pi\)
\(752\) −85.2552 −3.10894
\(753\) −12.8673 −0.468909
\(754\) 29.3225 1.06786
\(755\) 3.13117 0.113955
\(756\) 100.218 3.64490
\(757\) −21.2877 −0.773715 −0.386857 0.922140i \(-0.626439\pi\)
−0.386857 + 0.922140i \(0.626439\pi\)
\(758\) −69.2390 −2.51487
\(759\) −3.81467 −0.138464
\(760\) 71.8501 2.60628
\(761\) 5.15064 0.186710 0.0933552 0.995633i \(-0.470241\pi\)
0.0933552 + 0.995633i \(0.470241\pi\)
\(762\) 37.8365 1.37067
\(763\) 41.9901 1.52014
\(764\) 14.9102 0.539432
\(765\) 14.0063 0.506399
\(766\) 17.0489 0.616001
\(767\) 16.6372 0.600734
\(768\) −39.1199 −1.41162
\(769\) −10.3093 −0.371762 −0.185881 0.982572i \(-0.559514\pi\)
−0.185881 + 0.982572i \(0.559514\pi\)
\(770\) 17.5152 0.631205
\(771\) 19.8191 0.713769
\(772\) −17.1923 −0.618766
\(773\) 40.4102 1.45345 0.726727 0.686927i \(-0.241041\pi\)
0.726727 + 0.686927i \(0.241041\pi\)
\(774\) 21.5198 0.773512
\(775\) 3.05868 0.109871
\(776\) −110.797 −3.97736
\(777\) −5.83190 −0.209218
\(778\) 32.7223 1.17315
\(779\) −7.59542 −0.272134
\(780\) 39.3174 1.40779
\(781\) −0.668652 −0.0239263
\(782\) −41.3013 −1.47693
\(783\) 23.2312 0.830214
\(784\) 63.3451 2.26233
\(785\) −32.5434 −1.16152
\(786\) 37.9683 1.35428
\(787\) −19.6957 −0.702075 −0.351037 0.936361i \(-0.614171\pi\)
−0.351037 + 0.936361i \(0.614171\pi\)
\(788\) −41.6785 −1.48474
\(789\) −10.1798 −0.362409
\(790\) 58.8516 2.09385
\(791\) −46.4311 −1.65090
\(792\) −11.2654 −0.400297
\(793\) −30.7821 −1.09310
\(794\) 32.2461 1.14437
\(795\) −10.9177 −0.387210
\(796\) −39.0242 −1.38318
\(797\) 3.49397 0.123763 0.0618813 0.998084i \(-0.480290\pi\)
0.0618813 + 0.998084i \(0.480290\pi\)
\(798\) −37.4625 −1.32616
\(799\) 23.7584 0.840511
\(800\) −10.1167 −0.357678
\(801\) −0.735683 −0.0259941
\(802\) 48.3500 1.70730
\(803\) 7.24699 0.255741
\(804\) −11.9663 −0.422019
\(805\) −30.6473 −1.08018
\(806\) 42.1945 1.48624
\(807\) 4.59493 0.161749
\(808\) 68.4632 2.40853
\(809\) 23.6320 0.830855 0.415428 0.909626i \(-0.363632\pi\)
0.415428 + 0.909626i \(0.363632\pi\)
\(810\) 13.7989 0.484844
\(811\) −11.2573 −0.395296 −0.197648 0.980273i \(-0.563330\pi\)
−0.197648 + 0.980273i \(0.563330\pi\)
\(812\) 76.8911 2.69835
\(813\) 30.7125 1.07713
\(814\) 3.11237 0.109089
\(815\) −16.8458 −0.590083
\(816\) 68.0248 2.38134
\(817\) −17.4809 −0.611580
\(818\) 3.97913 0.139127
\(819\) 13.1165 0.458327
\(820\) 28.6796 1.00154
\(821\) −7.41175 −0.258672 −0.129336 0.991601i \(-0.541285\pi\)
−0.129336 + 0.991601i \(0.541285\pi\)
\(822\) −4.71631 −0.164500
\(823\) −7.51069 −0.261806 −0.130903 0.991395i \(-0.541788\pi\)
−0.130903 + 0.991395i \(0.541788\pi\)
\(824\) 155.800 5.42755
\(825\) 0.498041 0.0173396
\(826\) 59.8567 2.08268
\(827\) −10.4117 −0.362050 −0.181025 0.983478i \(-0.557942\pi\)
−0.181025 + 0.983478i \(0.557942\pi\)
\(828\) 31.3886 1.09083
\(829\) −54.9525 −1.90858 −0.954290 0.298882i \(-0.903386\pi\)
−0.954290 + 0.298882i \(0.903386\pi\)
\(830\) −15.5938 −0.541267
\(831\) −0.814649 −0.0282599
\(832\) −67.1831 −2.32915
\(833\) −17.6526 −0.611627
\(834\) −12.8813 −0.446042
\(835\) −19.4000 −0.671364
\(836\) 14.5720 0.503985
\(837\) 33.4291 1.15548
\(838\) −23.4074 −0.808594
\(839\) −24.3022 −0.839005 −0.419503 0.907754i \(-0.637795\pi\)
−0.419503 + 0.907754i \(0.637795\pi\)
\(840\) 88.8320 3.06499
\(841\) −11.1762 −0.385386
\(842\) 68.8655 2.37326
\(843\) 22.2145 0.765106
\(844\) 45.0652 1.55121
\(845\) −15.1550 −0.521349
\(846\) −24.7732 −0.851721
\(847\) −35.0338 −1.20377
\(848\) 54.0238 1.85518
\(849\) 30.6353 1.05140
\(850\) 5.39227 0.184953
\(851\) −5.44589 −0.186683
\(852\) −5.40012 −0.185005
\(853\) 19.5618 0.669783 0.334891 0.942257i \(-0.391300\pi\)
0.334891 + 0.942257i \(0.391300\pi\)
\(854\) −110.747 −3.78967
\(855\) 11.8636 0.405726
\(856\) 77.1248 2.63607
\(857\) −31.5568 −1.07796 −0.538980 0.842319i \(-0.681190\pi\)
−0.538980 + 0.842319i \(0.681190\pi\)
\(858\) 6.87049 0.234555
\(859\) −9.57504 −0.326696 −0.163348 0.986569i \(-0.552229\pi\)
−0.163348 + 0.986569i \(0.552229\pi\)
\(860\) 66.0063 2.25080
\(861\) −9.39061 −0.320031
\(862\) −69.3405 −2.36175
\(863\) 3.59312 0.122311 0.0611557 0.998128i \(-0.480521\pi\)
0.0611557 + 0.998128i \(0.480521\pi\)
\(864\) −110.568 −3.76160
\(865\) −14.9810 −0.509368
\(866\) 53.1921 1.80754
\(867\) 1.76650 0.0599936
\(868\) 110.645 3.75552
\(869\) 7.49554 0.254269
\(870\) 32.7901 1.11169
\(871\) −4.66944 −0.158218
\(872\) −113.654 −3.84879
\(873\) −18.2943 −0.619167
\(874\) −34.9829 −1.18331
\(875\) −35.7354 −1.20808
\(876\) 58.5275 1.97746
\(877\) 22.4987 0.759727 0.379863 0.925043i \(-0.375971\pi\)
0.379863 + 0.925043i \(0.375971\pi\)
\(878\) −66.7841 −2.25386
\(879\) 9.98124 0.336659
\(880\) −26.9388 −0.908107
\(881\) −7.18161 −0.241955 −0.120977 0.992655i \(-0.538603\pi\)
−0.120977 + 0.992655i \(0.538603\pi\)
\(882\) 18.4066 0.619784
\(883\) −5.02831 −0.169216 −0.0846080 0.996414i \(-0.526964\pi\)
−0.0846080 + 0.996414i \(0.526964\pi\)
\(884\) 54.2170 1.82352
\(885\) 18.6046 0.625388
\(886\) 99.6881 3.34909
\(887\) 31.8830 1.07053 0.535263 0.844686i \(-0.320213\pi\)
0.535263 + 0.844686i \(0.320213\pi\)
\(888\) 15.7850 0.529711
\(889\) 38.7160 1.29849
\(890\) −3.09597 −0.103777
\(891\) 1.75747 0.0588776
\(892\) 21.4030 0.716626
\(893\) 20.1238 0.673416
\(894\) −28.6199 −0.957193
\(895\) −39.1009 −1.30700
\(896\) −105.567 −3.52675
\(897\) −12.0217 −0.401392
\(898\) 18.1149 0.604502
\(899\) 25.6481 0.855411
\(900\) −4.09807 −0.136602
\(901\) −15.0550 −0.501555
\(902\) 5.01159 0.166868
\(903\) −21.6125 −0.719220
\(904\) 125.674 4.17985
\(905\) 20.5932 0.684540
\(906\) 4.41887 0.146807
\(907\) 0.764286 0.0253777 0.0126889 0.999919i \(-0.495961\pi\)
0.0126889 + 0.999919i \(0.495961\pi\)
\(908\) −83.1225 −2.75852
\(909\) 11.3044 0.374942
\(910\) 55.1980 1.82979
\(911\) 42.5702 1.41041 0.705207 0.709001i \(-0.250854\pi\)
0.705207 + 0.709001i \(0.250854\pi\)
\(912\) 57.6182 1.90793
\(913\) −1.98607 −0.0657294
\(914\) −11.8289 −0.391266
\(915\) −34.4222 −1.13796
\(916\) 51.6588 1.70686
\(917\) 38.8509 1.28297
\(918\) 58.9336 1.94510
\(919\) 38.8369 1.28111 0.640556 0.767912i \(-0.278704\pi\)
0.640556 + 0.767912i \(0.278704\pi\)
\(920\) 82.9523 2.73486
\(921\) −27.2256 −0.897113
\(922\) −40.4579 −1.33241
\(923\) −2.10721 −0.0693597
\(924\) 18.0162 0.592689
\(925\) 0.711012 0.0233779
\(926\) −36.9398 −1.21392
\(927\) 25.7251 0.844922
\(928\) −84.8318 −2.78474
\(929\) −5.84638 −0.191813 −0.0959067 0.995390i \(-0.530575\pi\)
−0.0959067 + 0.995390i \(0.530575\pi\)
\(930\) 47.1842 1.54723
\(931\) −14.9521 −0.490034
\(932\) 125.262 4.10311
\(933\) −39.9655 −1.30841
\(934\) 84.0561 2.75040
\(935\) 7.50713 0.245510
\(936\) −35.5020 −1.16042
\(937\) −44.3789 −1.44980 −0.724898 0.688856i \(-0.758113\pi\)
−0.724898 + 0.688856i \(0.758113\pi\)
\(938\) −16.7995 −0.548524
\(939\) 24.8431 0.810724
\(940\) −75.9855 −2.47837
\(941\) −31.3992 −1.02359 −0.511793 0.859109i \(-0.671019\pi\)
−0.511793 + 0.859109i \(0.671019\pi\)
\(942\) −45.9270 −1.49638
\(943\) −8.76905 −0.285560
\(944\) −92.0610 −2.99633
\(945\) 43.7313 1.42258
\(946\) 11.5342 0.375009
\(947\) −0.0640227 −0.00208046 −0.00104023 0.999999i \(-0.500331\pi\)
−0.00104023 + 0.999999i \(0.500331\pi\)
\(948\) 60.5349 1.96608
\(949\) 22.8384 0.741365
\(950\) 4.56735 0.148184
\(951\) 35.1817 1.14085
\(952\) 122.495 3.97010
\(953\) 27.1203 0.878512 0.439256 0.898362i \(-0.355242\pi\)
0.439256 + 0.898362i \(0.355242\pi\)
\(954\) 15.6981 0.508244
\(955\) 6.50622 0.210536
\(956\) −160.991 −5.20683
\(957\) 4.17625 0.134999
\(958\) 7.54739 0.243845
\(959\) −4.82594 −0.155838
\(960\) −75.1278 −2.42474
\(961\) 5.90703 0.190549
\(962\) 9.80843 0.316236
\(963\) 12.7345 0.410364
\(964\) 52.0733 1.67717
\(965\) −7.50207 −0.241500
\(966\) −43.2512 −1.39158
\(967\) 17.8100 0.572731 0.286365 0.958120i \(-0.407553\pi\)
0.286365 + 0.958120i \(0.407553\pi\)
\(968\) 94.8249 3.04779
\(969\) −16.0567 −0.515815
\(970\) −76.9877 −2.47193
\(971\) 5.44421 0.174713 0.0873565 0.996177i \(-0.472158\pi\)
0.0873565 + 0.996177i \(0.472158\pi\)
\(972\) −74.5556 −2.39137
\(973\) −13.1807 −0.422554
\(974\) −10.5413 −0.337766
\(975\) 1.56954 0.0502656
\(976\) 170.331 5.45216
\(977\) −8.84834 −0.283084 −0.141542 0.989932i \(-0.545206\pi\)
−0.141542 + 0.989932i \(0.545206\pi\)
\(978\) −23.7737 −0.760200
\(979\) −0.394313 −0.0126023
\(980\) 56.4576 1.80347
\(981\) −18.7660 −0.599152
\(982\) −39.3084 −1.25438
\(983\) 46.5123 1.48351 0.741756 0.670670i \(-0.233993\pi\)
0.741756 + 0.670670i \(0.233993\pi\)
\(984\) 25.4173 0.810274
\(985\) −18.1869 −0.579482
\(986\) 45.2161 1.43997
\(987\) 24.8800 0.791941
\(988\) 45.9228 1.46100
\(989\) −20.1820 −0.641751
\(990\) −7.82781 −0.248784
\(991\) 32.6179 1.03614 0.518071 0.855337i \(-0.326650\pi\)
0.518071 + 0.855337i \(0.326650\pi\)
\(992\) −122.071 −3.87576
\(993\) −30.4611 −0.966653
\(994\) −7.58125 −0.240463
\(995\) −17.0286 −0.539844
\(996\) −16.0398 −0.508239
\(997\) 44.1410 1.39796 0.698980 0.715141i \(-0.253637\pi\)
0.698980 + 0.715141i \(0.253637\pi\)
\(998\) 23.0412 0.729358
\(999\) 7.77086 0.245859
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 \(a_p\))