Properties

Label 8011.2.a.b.1.13
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61876 q^{2} -0.901244 q^{3} +4.85788 q^{4} -1.31265 q^{5} +2.36014 q^{6} -2.24388 q^{7} -7.48409 q^{8} -2.18776 q^{9} +O(q^{10})\) \(q-2.61876 q^{2} -0.901244 q^{3} +4.85788 q^{4} -1.31265 q^{5} +2.36014 q^{6} -2.24388 q^{7} -7.48409 q^{8} -2.18776 q^{9} +3.43751 q^{10} +5.25836 q^{11} -4.37814 q^{12} -1.46998 q^{13} +5.87617 q^{14} +1.18302 q^{15} +9.88325 q^{16} -0.0584840 q^{17} +5.72921 q^{18} +1.09397 q^{19} -6.37669 q^{20} +2.02228 q^{21} -13.7704 q^{22} -6.84838 q^{23} +6.74499 q^{24} -3.27695 q^{25} +3.84952 q^{26} +4.67544 q^{27} -10.9005 q^{28} -4.73669 q^{29} -3.09803 q^{30} +7.80265 q^{31} -10.9136 q^{32} -4.73907 q^{33} +0.153155 q^{34} +2.94542 q^{35} -10.6279 q^{36} -8.81218 q^{37} -2.86484 q^{38} +1.32481 q^{39} +9.82398 q^{40} -5.59712 q^{41} -5.29586 q^{42} -3.28836 q^{43} +25.5445 q^{44} +2.87176 q^{45} +17.9342 q^{46} +2.16311 q^{47} -8.90722 q^{48} -1.96501 q^{49} +8.58154 q^{50} +0.0527083 q^{51} -7.14100 q^{52} +7.06719 q^{53} -12.2438 q^{54} -6.90238 q^{55} +16.7934 q^{56} -0.985934 q^{57} +12.4042 q^{58} +2.06153 q^{59} +5.74695 q^{60} +4.33875 q^{61} -20.4332 q^{62} +4.90907 q^{63} +8.81363 q^{64} +1.92957 q^{65} +12.4105 q^{66} -0.888835 q^{67} -0.284108 q^{68} +6.17206 q^{69} -7.71334 q^{70} +2.46324 q^{71} +16.3734 q^{72} -3.08122 q^{73} +23.0769 q^{74} +2.95334 q^{75} +5.31438 q^{76} -11.7991 q^{77} -3.46936 q^{78} +0.809398 q^{79} -12.9732 q^{80} +2.34957 q^{81} +14.6575 q^{82} +0.294813 q^{83} +9.82401 q^{84} +0.0767689 q^{85} +8.61140 q^{86} +4.26892 q^{87} -39.3541 q^{88} +4.84930 q^{89} -7.52043 q^{90} +3.29846 q^{91} -33.2686 q^{92} -7.03209 q^{93} -5.66465 q^{94} -1.43600 q^{95} +9.83584 q^{96} -8.32931 q^{97} +5.14588 q^{98} -11.5040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + O(q^{10}) \) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + 21q^{10} + 70q^{11} + 20q^{12} + 53q^{13} + 69q^{14} + 28q^{15} + 449q^{16} + 88q^{17} + 86q^{18} + 44q^{19} + 136q^{20} + 125q^{21} + 17q^{22} + 104q^{23} + 84q^{24} + 444q^{25} + 100q^{26} + 32q^{27} + 46q^{28} + 373q^{29} + 99q^{30} + 30q^{31} + 221q^{32} + 56q^{33} + 26q^{34} + 164q^{35} + 599q^{36} + 81q^{37} + 66q^{38} + 143q^{39} + 42q^{40} + 182q^{41} + 32q^{42} + 40q^{43} + 184q^{44} + 198q^{45} + 54q^{46} + 66q^{47} + 5q^{48} + 479q^{49} + 184q^{50} + 123q^{51} + 64q^{52} + 221q^{53} + 67q^{54} + 38q^{55} + 174q^{56} + 84q^{57} + 44q^{58} + 127q^{59} + 29q^{60} + 174q^{61} + 86q^{62} + 48q^{63} + 549q^{64} + 202q^{65} + 32q^{66} + 29q^{67} + 172q^{68} + 249q^{69} + 12q^{70} + 185q^{71} + 218q^{72} + 57q^{73} + 272q^{74} + 24q^{75} + 84q^{76} + 384q^{77} + 12q^{78} + 93q^{79} + 215q^{80} + 702q^{81} + 48q^{82} + 121q^{83} + 179q^{84} + 177q^{85} + 209q^{86} + 91q^{87} + 36q^{88} + 186q^{89} + 66q^{90} + 32q^{91} + 272q^{92} + 220q^{93} + 60q^{94} + 170q^{95} + 162q^{96} + 22q^{97} + 196q^{98} + 152q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61876 −1.85174 −0.925870 0.377842i \(-0.876666\pi\)
−0.925870 + 0.377842i \(0.876666\pi\)
\(3\) −0.901244 −0.520333 −0.260167 0.965564i \(-0.583778\pi\)
−0.260167 + 0.965564i \(0.583778\pi\)
\(4\) 4.85788 2.42894
\(5\) −1.31265 −0.587034 −0.293517 0.955954i \(-0.594826\pi\)
−0.293517 + 0.955954i \(0.594826\pi\)
\(6\) 2.36014 0.963522
\(7\) −2.24388 −0.848106 −0.424053 0.905637i \(-0.639393\pi\)
−0.424053 + 0.905637i \(0.639393\pi\)
\(8\) −7.48409 −2.64603
\(9\) −2.18776 −0.729253
\(10\) 3.43751 1.08703
\(11\) 5.25836 1.58546 0.792728 0.609576i \(-0.208660\pi\)
0.792728 + 0.609576i \(0.208660\pi\)
\(12\) −4.37814 −1.26386
\(13\) −1.46998 −0.407700 −0.203850 0.979002i \(-0.565345\pi\)
−0.203850 + 0.979002i \(0.565345\pi\)
\(14\) 5.87617 1.57047
\(15\) 1.18302 0.305454
\(16\) 9.88325 2.47081
\(17\) −0.0584840 −0.0141844 −0.00709222 0.999975i \(-0.502258\pi\)
−0.00709222 + 0.999975i \(0.502258\pi\)
\(18\) 5.72921 1.35039
\(19\) 1.09397 0.250974 0.125487 0.992095i \(-0.459951\pi\)
0.125487 + 0.992095i \(0.459951\pi\)
\(20\) −6.37669 −1.42587
\(21\) 2.02228 0.441298
\(22\) −13.7704 −2.93585
\(23\) −6.84838 −1.42799 −0.713993 0.700152i \(-0.753115\pi\)
−0.713993 + 0.700152i \(0.753115\pi\)
\(24\) 6.74499 1.37682
\(25\) −3.27695 −0.655391
\(26\) 3.84952 0.754954
\(27\) 4.67544 0.899788
\(28\) −10.9005 −2.06000
\(29\) −4.73669 −0.879582 −0.439791 0.898100i \(-0.644947\pi\)
−0.439791 + 0.898100i \(0.644947\pi\)
\(30\) −3.09803 −0.565620
\(31\) 7.80265 1.40140 0.700699 0.713457i \(-0.252872\pi\)
0.700699 + 0.713457i \(0.252872\pi\)
\(32\) −10.9136 −1.92928
\(33\) −4.73907 −0.824966
\(34\) 0.153155 0.0262659
\(35\) 2.94542 0.497867
\(36\) −10.6279 −1.77131
\(37\) −8.81218 −1.44871 −0.724356 0.689426i \(-0.757863\pi\)
−0.724356 + 0.689426i \(0.757863\pi\)
\(38\) −2.86484 −0.464739
\(39\) 1.32481 0.212140
\(40\) 9.82398 1.55331
\(41\) −5.59712 −0.874123 −0.437062 0.899432i \(-0.643981\pi\)
−0.437062 + 0.899432i \(0.643981\pi\)
\(42\) −5.29586 −0.817169
\(43\) −3.28836 −0.501470 −0.250735 0.968056i \(-0.580672\pi\)
−0.250735 + 0.968056i \(0.580672\pi\)
\(44\) 25.5445 3.85098
\(45\) 2.87176 0.428096
\(46\) 17.9342 2.64426
\(47\) 2.16311 0.315521 0.157761 0.987477i \(-0.449573\pi\)
0.157761 + 0.987477i \(0.449573\pi\)
\(48\) −8.90722 −1.28565
\(49\) −1.96501 −0.280715
\(50\) 8.58154 1.21361
\(51\) 0.0527083 0.00738064
\(52\) −7.14100 −0.990278
\(53\) 7.06719 0.970753 0.485377 0.874305i \(-0.338682\pi\)
0.485377 + 0.874305i \(0.338682\pi\)
\(54\) −12.2438 −1.66617
\(55\) −6.90238 −0.930717
\(56\) 16.7934 2.24411
\(57\) −0.985934 −0.130590
\(58\) 12.4042 1.62876
\(59\) 2.06153 0.268389 0.134194 0.990955i \(-0.457155\pi\)
0.134194 + 0.990955i \(0.457155\pi\)
\(60\) 5.74695 0.741928
\(61\) 4.33875 0.555521 0.277760 0.960650i \(-0.410408\pi\)
0.277760 + 0.960650i \(0.410408\pi\)
\(62\) −20.4332 −2.59502
\(63\) 4.90907 0.618484
\(64\) 8.81363 1.10170
\(65\) 1.92957 0.239334
\(66\) 12.4105 1.52762
\(67\) −0.888835 −0.108589 −0.0542943 0.998525i \(-0.517291\pi\)
−0.0542943 + 0.998525i \(0.517291\pi\)
\(68\) −0.284108 −0.0344532
\(69\) 6.17206 0.743029
\(70\) −7.71334 −0.921921
\(71\) 2.46324 0.292332 0.146166 0.989260i \(-0.453307\pi\)
0.146166 + 0.989260i \(0.453307\pi\)
\(72\) 16.3734 1.92962
\(73\) −3.08122 −0.360629 −0.180315 0.983609i \(-0.557712\pi\)
−0.180315 + 0.983609i \(0.557712\pi\)
\(74\) 23.0769 2.68264
\(75\) 2.95334 0.341022
\(76\) 5.31438 0.609601
\(77\) −11.7991 −1.34464
\(78\) −3.46936 −0.392828
\(79\) 0.809398 0.0910644 0.0455322 0.998963i \(-0.485502\pi\)
0.0455322 + 0.998963i \(0.485502\pi\)
\(80\) −12.9732 −1.45045
\(81\) 2.34957 0.261063
\(82\) 14.6575 1.61865
\(83\) 0.294813 0.0323599 0.0161800 0.999869i \(-0.494850\pi\)
0.0161800 + 0.999869i \(0.494850\pi\)
\(84\) 9.82401 1.07189
\(85\) 0.0767689 0.00832675
\(86\) 8.61140 0.928592
\(87\) 4.26892 0.457676
\(88\) −39.3541 −4.19516
\(89\) 4.84930 0.514025 0.257013 0.966408i \(-0.417262\pi\)
0.257013 + 0.966408i \(0.417262\pi\)
\(90\) −7.52043 −0.792723
\(91\) 3.29846 0.345773
\(92\) −33.2686 −3.46850
\(93\) −7.03209 −0.729194
\(94\) −5.66465 −0.584264
\(95\) −1.43600 −0.147330
\(96\) 9.83584 1.00387
\(97\) −8.32931 −0.845714 −0.422857 0.906197i \(-0.638973\pi\)
−0.422857 + 0.906197i \(0.638973\pi\)
\(98\) 5.14588 0.519812
\(99\) −11.5040 −1.15620
\(100\) −15.9191 −1.59191
\(101\) −2.58697 −0.257413 −0.128706 0.991683i \(-0.541082\pi\)
−0.128706 + 0.991683i \(0.541082\pi\)
\(102\) −0.138030 −0.0136670
\(103\) −0.273875 −0.0269857 −0.0134929 0.999909i \(-0.504295\pi\)
−0.0134929 + 0.999909i \(0.504295\pi\)
\(104\) 11.0015 1.07878
\(105\) −2.65455 −0.259057
\(106\) −18.5072 −1.79758
\(107\) 1.33036 0.128611 0.0643056 0.997930i \(-0.479517\pi\)
0.0643056 + 0.997930i \(0.479517\pi\)
\(108\) 22.7127 2.18553
\(109\) −15.4832 −1.48302 −0.741512 0.670940i \(-0.765891\pi\)
−0.741512 + 0.670940i \(0.765891\pi\)
\(110\) 18.0756 1.72345
\(111\) 7.94192 0.753814
\(112\) −22.1768 −2.09551
\(113\) −14.9630 −1.40760 −0.703802 0.710396i \(-0.748516\pi\)
−0.703802 + 0.710396i \(0.748516\pi\)
\(114\) 2.58192 0.241819
\(115\) 8.98952 0.838277
\(116\) −23.0103 −2.13645
\(117\) 3.21597 0.297316
\(118\) −5.39865 −0.496986
\(119\) 0.131231 0.0120299
\(120\) −8.85380 −0.808238
\(121\) 16.6504 1.51367
\(122\) −11.3621 −1.02868
\(123\) 5.04437 0.454836
\(124\) 37.9044 3.40391
\(125\) 10.8647 0.971771
\(126\) −12.8556 −1.14527
\(127\) −0.830429 −0.0736887 −0.0368443 0.999321i \(-0.511731\pi\)
−0.0368443 + 0.999321i \(0.511731\pi\)
\(128\) −1.25348 −0.110793
\(129\) 2.96361 0.260932
\(130\) −5.05307 −0.443184
\(131\) 9.17248 0.801404 0.400702 0.916209i \(-0.368766\pi\)
0.400702 + 0.916209i \(0.368766\pi\)
\(132\) −23.0218 −2.00379
\(133\) −2.45474 −0.212853
\(134\) 2.32764 0.201078
\(135\) −6.13720 −0.528206
\(136\) 0.437699 0.0375324
\(137\) −12.5284 −1.07037 −0.535186 0.844734i \(-0.679758\pi\)
−0.535186 + 0.844734i \(0.679758\pi\)
\(138\) −16.1631 −1.37590
\(139\) −17.6971 −1.50105 −0.750524 0.660843i \(-0.770199\pi\)
−0.750524 + 0.660843i \(0.770199\pi\)
\(140\) 14.3085 1.20929
\(141\) −1.94949 −0.164176
\(142\) −6.45061 −0.541323
\(143\) −7.72970 −0.646390
\(144\) −21.6222 −1.80185
\(145\) 6.21761 0.516345
\(146\) 8.06895 0.667791
\(147\) 1.77095 0.146066
\(148\) −42.8085 −3.51884
\(149\) −16.0671 −1.31627 −0.658133 0.752902i \(-0.728653\pi\)
−0.658133 + 0.752902i \(0.728653\pi\)
\(150\) −7.73406 −0.631484
\(151\) 8.18383 0.665991 0.332995 0.942928i \(-0.391941\pi\)
0.332995 + 0.942928i \(0.391941\pi\)
\(152\) −8.18738 −0.664084
\(153\) 0.127949 0.0103440
\(154\) 30.8990 2.48991
\(155\) −10.2421 −0.822668
\(156\) 6.43578 0.515275
\(157\) 1.48627 0.118617 0.0593085 0.998240i \(-0.481110\pi\)
0.0593085 + 0.998240i \(0.481110\pi\)
\(158\) −2.11962 −0.168628
\(159\) −6.36926 −0.505115
\(160\) 14.3258 1.13255
\(161\) 15.3669 1.21108
\(162\) −6.15295 −0.483421
\(163\) −7.00634 −0.548779 −0.274390 0.961619i \(-0.588476\pi\)
−0.274390 + 0.961619i \(0.588476\pi\)
\(164\) −27.1901 −2.12319
\(165\) 6.22073 0.484283
\(166\) −0.772043 −0.0599221
\(167\) −5.34483 −0.413595 −0.206798 0.978384i \(-0.566304\pi\)
−0.206798 + 0.978384i \(0.566304\pi\)
\(168\) −15.1349 −1.16769
\(169\) −10.8392 −0.833781
\(170\) −0.201039 −0.0154190
\(171\) −2.39334 −0.183024
\(172\) −15.9744 −1.21804
\(173\) 12.3255 0.937087 0.468543 0.883440i \(-0.344779\pi\)
0.468543 + 0.883440i \(0.344779\pi\)
\(174\) −11.1793 −0.847497
\(175\) 7.35309 0.555841
\(176\) 51.9697 3.91736
\(177\) −1.85794 −0.139652
\(178\) −12.6991 −0.951841
\(179\) 18.8803 1.41118 0.705589 0.708621i \(-0.250683\pi\)
0.705589 + 0.708621i \(0.250683\pi\)
\(180\) 13.9507 1.03982
\(181\) −8.94589 −0.664943 −0.332472 0.943113i \(-0.607883\pi\)
−0.332472 + 0.943113i \(0.607883\pi\)
\(182\) −8.63787 −0.640281
\(183\) −3.91028 −0.289056
\(184\) 51.2539 3.77849
\(185\) 11.5673 0.850444
\(186\) 18.4153 1.35028
\(187\) −0.307530 −0.0224888
\(188\) 10.5081 0.766383
\(189\) −10.4911 −0.763116
\(190\) 3.76053 0.272817
\(191\) −2.48542 −0.179839 −0.0899195 0.995949i \(-0.528661\pi\)
−0.0899195 + 0.995949i \(0.528661\pi\)
\(192\) −7.94323 −0.573253
\(193\) −5.86390 −0.422093 −0.211046 0.977476i \(-0.567687\pi\)
−0.211046 + 0.977476i \(0.567687\pi\)
\(194\) 21.8124 1.56604
\(195\) −1.73901 −0.124533
\(196\) −9.54578 −0.681841
\(197\) −10.2518 −0.730409 −0.365204 0.930927i \(-0.619001\pi\)
−0.365204 + 0.930927i \(0.619001\pi\)
\(198\) 30.1262 2.14098
\(199\) −22.2605 −1.57800 −0.789001 0.614392i \(-0.789401\pi\)
−0.789001 + 0.614392i \(0.789401\pi\)
\(200\) 24.5250 1.73418
\(201\) 0.801058 0.0565022
\(202\) 6.77463 0.476661
\(203\) 10.6286 0.745979
\(204\) 0.256051 0.0179271
\(205\) 7.34705 0.513140
\(206\) 0.717212 0.0499706
\(207\) 14.9826 1.04136
\(208\) −14.5282 −1.00735
\(209\) 5.75249 0.397908
\(210\) 6.95161 0.479706
\(211\) 0.289562 0.0199343 0.00996714 0.999950i \(-0.496827\pi\)
0.00996714 + 0.999950i \(0.496827\pi\)
\(212\) 34.3316 2.35790
\(213\) −2.21998 −0.152110
\(214\) −3.48390 −0.238154
\(215\) 4.31646 0.294380
\(216\) −34.9914 −2.38086
\(217\) −17.5082 −1.18853
\(218\) 40.5468 2.74617
\(219\) 2.77693 0.187647
\(220\) −33.5309 −2.26066
\(221\) 0.0859704 0.00578299
\(222\) −20.7979 −1.39587
\(223\) 22.8791 1.53210 0.766049 0.642783i \(-0.222220\pi\)
0.766049 + 0.642783i \(0.222220\pi\)
\(224\) 24.4889 1.63623
\(225\) 7.16919 0.477946
\(226\) 39.1846 2.60652
\(227\) 25.1983 1.67247 0.836234 0.548373i \(-0.184753\pi\)
0.836234 + 0.548373i \(0.184753\pi\)
\(228\) −4.78955 −0.317196
\(229\) 7.13969 0.471804 0.235902 0.971777i \(-0.424196\pi\)
0.235902 + 0.971777i \(0.424196\pi\)
\(230\) −23.5414 −1.55227
\(231\) 10.6339 0.699659
\(232\) 35.4499 2.32740
\(233\) −15.3423 −1.00510 −0.502552 0.864547i \(-0.667606\pi\)
−0.502552 + 0.864547i \(0.667606\pi\)
\(234\) −8.42183 −0.550552
\(235\) −2.83940 −0.185222
\(236\) 10.0147 0.651901
\(237\) −0.729465 −0.0473838
\(238\) −0.343662 −0.0222763
\(239\) 26.6429 1.72339 0.861693 0.507430i \(-0.169404\pi\)
0.861693 + 0.507430i \(0.169404\pi\)
\(240\) 11.6920 0.754718
\(241\) −3.32320 −0.214066 −0.107033 0.994255i \(-0.534135\pi\)
−0.107033 + 0.994255i \(0.534135\pi\)
\(242\) −43.6032 −2.80292
\(243\) −16.1438 −1.03563
\(244\) 21.0772 1.34933
\(245\) 2.57936 0.164790
\(246\) −13.2100 −0.842237
\(247\) −1.60812 −0.102322
\(248\) −58.3958 −3.70814
\(249\) −0.265698 −0.0168379
\(250\) −28.4521 −1.79947
\(251\) 0.495028 0.0312459 0.0156229 0.999878i \(-0.495027\pi\)
0.0156229 + 0.999878i \(0.495027\pi\)
\(252\) 23.8477 1.50226
\(253\) −36.0113 −2.26401
\(254\) 2.17469 0.136452
\(255\) −0.0691875 −0.00433269
\(256\) −14.3447 −0.896543
\(257\) −0.936392 −0.0584105 −0.0292053 0.999573i \(-0.509298\pi\)
−0.0292053 + 0.999573i \(0.509298\pi\)
\(258\) −7.76098 −0.483177
\(259\) 19.7735 1.22866
\(260\) 9.37362 0.581327
\(261\) 10.3627 0.641438
\(262\) −24.0205 −1.48399
\(263\) −7.05732 −0.435173 −0.217586 0.976041i \(-0.569818\pi\)
−0.217586 + 0.976041i \(0.569818\pi\)
\(264\) 35.4676 2.18288
\(265\) −9.27674 −0.569865
\(266\) 6.42836 0.394148
\(267\) −4.37041 −0.267465
\(268\) −4.31786 −0.263755
\(269\) −22.9255 −1.39780 −0.698898 0.715222i \(-0.746326\pi\)
−0.698898 + 0.715222i \(0.746326\pi\)
\(270\) 16.0718 0.978101
\(271\) 20.1635 1.22484 0.612422 0.790531i \(-0.290195\pi\)
0.612422 + 0.790531i \(0.290195\pi\)
\(272\) −0.578011 −0.0350471
\(273\) −2.97272 −0.179917
\(274\) 32.8088 1.98205
\(275\) −17.2314 −1.03909
\(276\) 29.9832 1.80477
\(277\) −6.68451 −0.401634 −0.200817 0.979629i \(-0.564360\pi\)
−0.200817 + 0.979629i \(0.564360\pi\)
\(278\) 46.3444 2.77955
\(279\) −17.0703 −1.02197
\(280\) −22.0438 −1.31737
\(281\) 4.30473 0.256798 0.128399 0.991723i \(-0.459016\pi\)
0.128399 + 0.991723i \(0.459016\pi\)
\(282\) 5.10523 0.304012
\(283\) −13.8808 −0.825126 −0.412563 0.910929i \(-0.635366\pi\)
−0.412563 + 0.910929i \(0.635366\pi\)
\(284\) 11.9661 0.710058
\(285\) 1.29419 0.0766609
\(286\) 20.2422 1.19695
\(287\) 12.5593 0.741350
\(288\) 23.8764 1.40693
\(289\) −16.9966 −0.999799
\(290\) −16.2824 −0.956136
\(291\) 7.50674 0.440053
\(292\) −14.9682 −0.875947
\(293\) 18.1249 1.05887 0.529434 0.848351i \(-0.322404\pi\)
0.529434 + 0.848351i \(0.322404\pi\)
\(294\) −4.63769 −0.270476
\(295\) −2.70607 −0.157553
\(296\) 65.9511 3.83333
\(297\) 24.5851 1.42657
\(298\) 42.0757 2.43738
\(299\) 10.0670 0.582190
\(300\) 14.3470 0.828322
\(301\) 7.37867 0.425300
\(302\) −21.4315 −1.23324
\(303\) 2.33149 0.133940
\(304\) 10.8120 0.620110
\(305\) −5.69526 −0.326110
\(306\) −0.335067 −0.0191545
\(307\) −13.9760 −0.797654 −0.398827 0.917026i \(-0.630583\pi\)
−0.398827 + 0.917026i \(0.630583\pi\)
\(308\) −57.3188 −3.26604
\(309\) 0.246828 0.0140416
\(310\) 26.8217 1.52337
\(311\) 1.31078 0.0743274 0.0371637 0.999309i \(-0.488168\pi\)
0.0371637 + 0.999309i \(0.488168\pi\)
\(312\) −9.91502 −0.561328
\(313\) −20.4467 −1.15572 −0.577858 0.816137i \(-0.696111\pi\)
−0.577858 + 0.816137i \(0.696111\pi\)
\(314\) −3.89217 −0.219648
\(315\) −6.44388 −0.363071
\(316\) 3.93196 0.221190
\(317\) −24.4394 −1.37266 −0.686328 0.727292i \(-0.740778\pi\)
−0.686328 + 0.727292i \(0.740778\pi\)
\(318\) 16.6795 0.935342
\(319\) −24.9072 −1.39454
\(320\) −11.5692 −0.646738
\(321\) −1.19898 −0.0669207
\(322\) −40.2423 −2.24261
\(323\) −0.0639797 −0.00355993
\(324\) 11.4139 0.634107
\(325\) 4.81706 0.267203
\(326\) 18.3479 1.01620
\(327\) 13.9542 0.771667
\(328\) 41.8894 2.31295
\(329\) −4.85375 −0.267596
\(330\) −16.2906 −0.896766
\(331\) −2.15567 −0.118486 −0.0592431 0.998244i \(-0.518869\pi\)
−0.0592431 + 0.998244i \(0.518869\pi\)
\(332\) 1.43217 0.0786003
\(333\) 19.2789 1.05648
\(334\) 13.9968 0.765871
\(335\) 1.16673 0.0637452
\(336\) 19.9867 1.09036
\(337\) −5.23249 −0.285032 −0.142516 0.989792i \(-0.545519\pi\)
−0.142516 + 0.989792i \(0.545519\pi\)
\(338\) 28.3851 1.54395
\(339\) 13.4854 0.732424
\(340\) 0.372934 0.0202252
\(341\) 41.0292 2.22185
\(342\) 6.26758 0.338912
\(343\) 20.1164 1.08618
\(344\) 24.6104 1.32690
\(345\) −8.10175 −0.436184
\(346\) −32.2773 −1.73524
\(347\) −1.45563 −0.0781424 −0.0390712 0.999236i \(-0.512440\pi\)
−0.0390712 + 0.999236i \(0.512440\pi\)
\(348\) 20.7379 1.11167
\(349\) −0.812222 −0.0434773 −0.0217386 0.999764i \(-0.506920\pi\)
−0.0217386 + 0.999764i \(0.506920\pi\)
\(350\) −19.2559 −1.02927
\(351\) −6.87281 −0.366843
\(352\) −57.3878 −3.05878
\(353\) 10.6193 0.565209 0.282605 0.959236i \(-0.408802\pi\)
0.282605 + 0.959236i \(0.408802\pi\)
\(354\) 4.86550 0.258599
\(355\) −3.23336 −0.171609
\(356\) 23.5573 1.24854
\(357\) −0.118271 −0.00625957
\(358\) −49.4428 −2.61313
\(359\) 22.5915 1.19233 0.596166 0.802861i \(-0.296690\pi\)
0.596166 + 0.802861i \(0.296690\pi\)
\(360\) −21.4925 −1.13275
\(361\) −17.8032 −0.937012
\(362\) 23.4271 1.23130
\(363\) −15.0060 −0.787613
\(364\) 16.0235 0.839861
\(365\) 4.04455 0.211702
\(366\) 10.2401 0.535256
\(367\) 18.7786 0.980237 0.490118 0.871656i \(-0.336954\pi\)
0.490118 + 0.871656i \(0.336954\pi\)
\(368\) −67.6843 −3.52829
\(369\) 12.2452 0.637457
\(370\) −30.2919 −1.57480
\(371\) −15.8579 −0.823302
\(372\) −34.1611 −1.77117
\(373\) −19.7564 −1.02295 −0.511473 0.859300i \(-0.670900\pi\)
−0.511473 + 0.859300i \(0.670900\pi\)
\(374\) 0.805345 0.0416434
\(375\) −9.79177 −0.505645
\(376\) −16.1889 −0.834878
\(377\) 6.96286 0.358605
\(378\) 27.4737 1.41309
\(379\) −6.31261 −0.324257 −0.162128 0.986770i \(-0.551836\pi\)
−0.162128 + 0.986770i \(0.551836\pi\)
\(380\) −6.97591 −0.357857
\(381\) 0.748419 0.0383427
\(382\) 6.50872 0.333015
\(383\) 12.9466 0.661538 0.330769 0.943712i \(-0.392692\pi\)
0.330769 + 0.943712i \(0.392692\pi\)
\(384\) 1.12970 0.0576495
\(385\) 15.4881 0.789347
\(386\) 15.3561 0.781606
\(387\) 7.19413 0.365698
\(388\) −40.4628 −2.05419
\(389\) −7.44001 −0.377224 −0.188612 0.982052i \(-0.560399\pi\)
−0.188612 + 0.982052i \(0.560399\pi\)
\(390\) 4.55405 0.230603
\(391\) 0.400521 0.0202552
\(392\) 14.7063 0.742781
\(393\) −8.26664 −0.416997
\(394\) 26.8469 1.35253
\(395\) −1.06245 −0.0534579
\(396\) −55.8852 −2.80834
\(397\) −23.5160 −1.18023 −0.590117 0.807318i \(-0.700918\pi\)
−0.590117 + 0.807318i \(0.700918\pi\)
\(398\) 58.2947 2.92205
\(399\) 2.21232 0.110754
\(400\) −32.3870 −1.61935
\(401\) −14.4370 −0.720950 −0.360475 0.932769i \(-0.617385\pi\)
−0.360475 + 0.932769i \(0.617385\pi\)
\(402\) −2.09777 −0.104627
\(403\) −11.4698 −0.571349
\(404\) −12.5672 −0.625240
\(405\) −3.08416 −0.153253
\(406\) −27.8336 −1.38136
\(407\) −46.3376 −2.29687
\(408\) −0.394474 −0.0195294
\(409\) −5.62839 −0.278306 −0.139153 0.990271i \(-0.544438\pi\)
−0.139153 + 0.990271i \(0.544438\pi\)
\(410\) −19.2401 −0.950202
\(411\) 11.2911 0.556950
\(412\) −1.33045 −0.0655467
\(413\) −4.62583 −0.227622
\(414\) −39.2358 −1.92833
\(415\) −0.386985 −0.0189964
\(416\) 16.0428 0.786565
\(417\) 15.9494 0.781046
\(418\) −15.0644 −0.736823
\(419\) −21.2788 −1.03954 −0.519769 0.854307i \(-0.673982\pi\)
−0.519769 + 0.854307i \(0.673982\pi\)
\(420\) −12.8955 −0.629234
\(421\) −0.291480 −0.0142059 −0.00710294 0.999975i \(-0.502261\pi\)
−0.00710294 + 0.999975i \(0.502261\pi\)
\(422\) −0.758292 −0.0369131
\(423\) −4.73236 −0.230095
\(424\) −52.8915 −2.56864
\(425\) 0.191649 0.00929635
\(426\) 5.81357 0.281669
\(427\) −9.73564 −0.471141
\(428\) 6.46275 0.312389
\(429\) 6.96634 0.336338
\(430\) −11.3037 −0.545115
\(431\) 10.8396 0.522123 0.261062 0.965322i \(-0.415927\pi\)
0.261062 + 0.965322i \(0.415927\pi\)
\(432\) 46.2085 2.22321
\(433\) 19.2482 0.925010 0.462505 0.886617i \(-0.346951\pi\)
0.462505 + 0.886617i \(0.346951\pi\)
\(434\) 45.8497 2.20086
\(435\) −5.60359 −0.268671
\(436\) −75.2157 −3.60218
\(437\) −7.49193 −0.358388
\(438\) −7.27210 −0.347474
\(439\) 24.1607 1.15313 0.576563 0.817053i \(-0.304394\pi\)
0.576563 + 0.817053i \(0.304394\pi\)
\(440\) 51.6581 2.46270
\(441\) 4.29896 0.204713
\(442\) −0.225135 −0.0107086
\(443\) 2.85937 0.135853 0.0679264 0.997690i \(-0.478362\pi\)
0.0679264 + 0.997690i \(0.478362\pi\)
\(444\) 38.5809 1.83097
\(445\) −6.36543 −0.301750
\(446\) −59.9147 −2.83705
\(447\) 14.4803 0.684897
\(448\) −19.7767 −0.934362
\(449\) −13.4059 −0.632662 −0.316331 0.948649i \(-0.602451\pi\)
−0.316331 + 0.948649i \(0.602451\pi\)
\(450\) −18.7744 −0.885031
\(451\) −29.4317 −1.38588
\(452\) −72.6887 −3.41899
\(453\) −7.37563 −0.346537
\(454\) −65.9881 −3.09698
\(455\) −4.32972 −0.202980
\(456\) 7.37882 0.345545
\(457\) 18.8094 0.879865 0.439933 0.898031i \(-0.355002\pi\)
0.439933 + 0.898031i \(0.355002\pi\)
\(458\) −18.6971 −0.873659
\(459\) −0.273438 −0.0127630
\(460\) 43.6700 2.03613
\(461\) 11.1609 0.519817 0.259908 0.965633i \(-0.416308\pi\)
0.259908 + 0.965633i \(0.416308\pi\)
\(462\) −27.8476 −1.29559
\(463\) −11.9519 −0.555454 −0.277727 0.960660i \(-0.589581\pi\)
−0.277727 + 0.960660i \(0.589581\pi\)
\(464\) −46.8139 −2.17328
\(465\) 9.23067 0.428062
\(466\) 40.1776 1.86119
\(467\) 23.8755 1.10483 0.552414 0.833570i \(-0.313707\pi\)
0.552414 + 0.833570i \(0.313707\pi\)
\(468\) 15.6228 0.722164
\(469\) 1.99444 0.0920946
\(470\) 7.43569 0.342983
\(471\) −1.33949 −0.0617204
\(472\) −15.4287 −0.710164
\(473\) −17.2914 −0.795058
\(474\) 1.91029 0.0877426
\(475\) −3.58489 −0.164486
\(476\) 0.637504 0.0292200
\(477\) −15.4613 −0.707925
\(478\) −69.7712 −3.19126
\(479\) −10.3133 −0.471228 −0.235614 0.971847i \(-0.575710\pi\)
−0.235614 + 0.971847i \(0.575710\pi\)
\(480\) −12.9110 −0.589304
\(481\) 12.9537 0.590640
\(482\) 8.70264 0.396394
\(483\) −13.8494 −0.630168
\(484\) 80.8855 3.67661
\(485\) 10.9335 0.496463
\(486\) 42.2768 1.91771
\(487\) −22.7203 −1.02955 −0.514777 0.857324i \(-0.672125\pi\)
−0.514777 + 0.857324i \(0.672125\pi\)
\(488\) −32.4716 −1.46992
\(489\) 6.31443 0.285548
\(490\) −6.75473 −0.305147
\(491\) −3.37996 −0.152536 −0.0762678 0.997087i \(-0.524300\pi\)
−0.0762678 + 0.997087i \(0.524300\pi\)
\(492\) 24.5050 1.10477
\(493\) 0.277021 0.0124764
\(494\) 4.21127 0.189474
\(495\) 15.1007 0.678728
\(496\) 77.1156 3.46259
\(497\) −5.52720 −0.247929
\(498\) 0.695799 0.0311795
\(499\) 2.66008 0.119082 0.0595408 0.998226i \(-0.481036\pi\)
0.0595408 + 0.998226i \(0.481036\pi\)
\(500\) 52.7796 2.36037
\(501\) 4.81699 0.215207
\(502\) −1.29636 −0.0578593
\(503\) −19.1406 −0.853438 −0.426719 0.904384i \(-0.640331\pi\)
−0.426719 + 0.904384i \(0.640331\pi\)
\(504\) −36.7399 −1.63653
\(505\) 3.39578 0.151110
\(506\) 94.3047 4.19236
\(507\) 9.76872 0.433844
\(508\) −4.03413 −0.178985
\(509\) 22.0754 0.978474 0.489237 0.872151i \(-0.337275\pi\)
0.489237 + 0.872151i \(0.337275\pi\)
\(510\) 0.181185 0.00802301
\(511\) 6.91388 0.305852
\(512\) 40.0722 1.77096
\(513\) 5.11479 0.225823
\(514\) 2.45218 0.108161
\(515\) 0.359502 0.0158415
\(516\) 14.3969 0.633787
\(517\) 11.3744 0.500245
\(518\) −51.7818 −2.27516
\(519\) −11.1082 −0.487598
\(520\) −14.4411 −0.633283
\(521\) −27.1076 −1.18761 −0.593803 0.804611i \(-0.702374\pi\)
−0.593803 + 0.804611i \(0.702374\pi\)
\(522\) −27.1375 −1.18778
\(523\) −21.3228 −0.932382 −0.466191 0.884684i \(-0.654374\pi\)
−0.466191 + 0.884684i \(0.654374\pi\)
\(524\) 44.5588 1.94656
\(525\) −6.62693 −0.289223
\(526\) 18.4814 0.805827
\(527\) −0.456330 −0.0198780
\(528\) −46.8374 −2.03834
\(529\) 23.9004 1.03915
\(530\) 24.2935 1.05524
\(531\) −4.51014 −0.195723
\(532\) −11.9248 −0.517007
\(533\) 8.22767 0.356380
\(534\) 11.4450 0.495275
\(535\) −1.74630 −0.0754991
\(536\) 6.65213 0.287328
\(537\) −17.0157 −0.734283
\(538\) 60.0364 2.58835
\(539\) −10.3327 −0.445062
\(540\) −29.8138 −1.28298
\(541\) −11.3051 −0.486044 −0.243022 0.970021i \(-0.578139\pi\)
−0.243022 + 0.970021i \(0.578139\pi\)
\(542\) −52.8032 −2.26809
\(543\) 8.06243 0.345992
\(544\) 0.638272 0.0273657
\(545\) 20.3240 0.870586
\(546\) 7.78482 0.333160
\(547\) 34.3608 1.46916 0.734580 0.678522i \(-0.237379\pi\)
0.734580 + 0.678522i \(0.237379\pi\)
\(548\) −60.8614 −2.59987
\(549\) −9.49215 −0.405115
\(550\) 45.1249 1.92413
\(551\) −5.18180 −0.220752
\(552\) −46.1923 −1.96608
\(553\) −1.81619 −0.0772323
\(554\) 17.5051 0.743721
\(555\) −10.4249 −0.442514
\(556\) −85.9704 −3.64596
\(557\) −32.7272 −1.38670 −0.693349 0.720602i \(-0.743865\pi\)
−0.693349 + 0.720602i \(0.743865\pi\)
\(558\) 44.7030 1.89243
\(559\) 4.83383 0.204449
\(560\) 29.1104 1.23014
\(561\) 0.277159 0.0117017
\(562\) −11.2730 −0.475524
\(563\) −12.0272 −0.506887 −0.253444 0.967350i \(-0.581563\pi\)
−0.253444 + 0.967350i \(0.581563\pi\)
\(564\) −9.47037 −0.398775
\(565\) 19.6412 0.826312
\(566\) 36.3503 1.52792
\(567\) −5.27215 −0.221409
\(568\) −18.4351 −0.773519
\(569\) −24.0773 −1.00937 −0.504686 0.863303i \(-0.668392\pi\)
−0.504686 + 0.863303i \(0.668392\pi\)
\(570\) −3.38915 −0.141956
\(571\) 17.2168 0.720500 0.360250 0.932856i \(-0.382691\pi\)
0.360250 + 0.932856i \(0.382691\pi\)
\(572\) −37.5500 −1.57004
\(573\) 2.23997 0.0935762
\(574\) −32.8896 −1.37279
\(575\) 22.4418 0.935890
\(576\) −19.2821 −0.803421
\(577\) 17.9542 0.747444 0.373722 0.927541i \(-0.378081\pi\)
0.373722 + 0.927541i \(0.378081\pi\)
\(578\) 44.5099 1.85137
\(579\) 5.28481 0.219629
\(580\) 30.2044 1.25417
\(581\) −0.661524 −0.0274446
\(582\) −19.6583 −0.814864
\(583\) 37.1618 1.53909
\(584\) 23.0601 0.954234
\(585\) −4.22143 −0.174535
\(586\) −47.4647 −1.96075
\(587\) 17.0435 0.703460 0.351730 0.936102i \(-0.385594\pi\)
0.351730 + 0.936102i \(0.385594\pi\)
\(588\) 8.60307 0.354785
\(589\) 8.53587 0.351714
\(590\) 7.08653 0.291748
\(591\) 9.23935 0.380056
\(592\) −87.0929 −3.57950
\(593\) 39.0129 1.60207 0.801034 0.598619i \(-0.204283\pi\)
0.801034 + 0.598619i \(0.204283\pi\)
\(594\) −64.3825 −2.64164
\(595\) −0.172260 −0.00706197
\(596\) −78.0519 −3.19713
\(597\) 20.0621 0.821087
\(598\) −26.3630 −1.07806
\(599\) 34.2148 1.39798 0.698990 0.715132i \(-0.253633\pi\)
0.698990 + 0.715132i \(0.253633\pi\)
\(600\) −22.1030 −0.902353
\(601\) 8.26767 0.337245 0.168623 0.985681i \(-0.446068\pi\)
0.168623 + 0.985681i \(0.446068\pi\)
\(602\) −19.3229 −0.787545
\(603\) 1.94456 0.0791885
\(604\) 39.7561 1.61765
\(605\) −21.8561 −0.888576
\(606\) −6.10560 −0.248023
\(607\) −44.9054 −1.82265 −0.911326 0.411685i \(-0.864940\pi\)
−0.911326 + 0.411685i \(0.864940\pi\)
\(608\) −11.9392 −0.484198
\(609\) −9.57893 −0.388158
\(610\) 14.9145 0.603870
\(611\) −3.17973 −0.128638
\(612\) 0.621560 0.0251251
\(613\) −8.11165 −0.327626 −0.163813 0.986491i \(-0.552379\pi\)
−0.163813 + 0.986491i \(0.552379\pi\)
\(614\) 36.5998 1.47705
\(615\) −6.62149 −0.267004
\(616\) 88.3058 3.55794
\(617\) 22.2908 0.897393 0.448696 0.893684i \(-0.351888\pi\)
0.448696 + 0.893684i \(0.351888\pi\)
\(618\) −0.646383 −0.0260014
\(619\) 2.00944 0.0807661 0.0403831 0.999184i \(-0.487142\pi\)
0.0403831 + 0.999184i \(0.487142\pi\)
\(620\) −49.7551 −1.99821
\(621\) −32.0192 −1.28489
\(622\) −3.43261 −0.137635
\(623\) −10.8813 −0.435948
\(624\) 13.0935 0.524158
\(625\) 2.12320 0.0849281
\(626\) 53.5449 2.14009
\(627\) −5.18440 −0.207045
\(628\) 7.22011 0.288114
\(629\) 0.515371 0.0205492
\(630\) 16.8749 0.672314
\(631\) −7.57409 −0.301520 −0.150760 0.988570i \(-0.548172\pi\)
−0.150760 + 0.988570i \(0.548172\pi\)
\(632\) −6.05761 −0.240959
\(633\) −0.260966 −0.0103725
\(634\) 64.0009 2.54180
\(635\) 1.09006 0.0432578
\(636\) −30.9411 −1.22690
\(637\) 2.88853 0.114448
\(638\) 65.2260 2.58232
\(639\) −5.38897 −0.213184
\(640\) 1.64538 0.0650395
\(641\) 45.6521 1.80315 0.901575 0.432624i \(-0.142412\pi\)
0.901575 + 0.432624i \(0.142412\pi\)
\(642\) 3.13984 0.123920
\(643\) 2.39068 0.0942793 0.0471397 0.998888i \(-0.484989\pi\)
0.0471397 + 0.998888i \(0.484989\pi\)
\(644\) 74.6508 2.94165
\(645\) −3.89018 −0.153176
\(646\) 0.167547 0.00659206
\(647\) 12.3138 0.484107 0.242053 0.970263i \(-0.422179\pi\)
0.242053 + 0.970263i \(0.422179\pi\)
\(648\) −17.5844 −0.690780
\(649\) 10.8403 0.425519
\(650\) −12.6147 −0.494790
\(651\) 15.7792 0.618434
\(652\) −34.0360 −1.33295
\(653\) 45.4456 1.77842 0.889212 0.457495i \(-0.151253\pi\)
0.889212 + 0.457495i \(0.151253\pi\)
\(654\) −36.5425 −1.42893
\(655\) −12.0402 −0.470451
\(656\) −55.3177 −2.15979
\(657\) 6.74096 0.262990
\(658\) 12.7108 0.495518
\(659\) 7.72380 0.300876 0.150438 0.988619i \(-0.451932\pi\)
0.150438 + 0.988619i \(0.451932\pi\)
\(660\) 30.2196 1.17629
\(661\) 29.9995 1.16685 0.583423 0.812169i \(-0.301713\pi\)
0.583423 + 0.812169i \(0.301713\pi\)
\(662\) 5.64517 0.219406
\(663\) −0.0774803 −0.00300908
\(664\) −2.20641 −0.0856252
\(665\) 3.22221 0.124952
\(666\) −50.4868 −1.95632
\(667\) 32.4387 1.25603
\(668\) −25.9645 −1.00460
\(669\) −20.6196 −0.797201
\(670\) −3.05538 −0.118039
\(671\) 22.8147 0.880753
\(672\) −22.0704 −0.851386
\(673\) −14.6450 −0.564524 −0.282262 0.959337i \(-0.591085\pi\)
−0.282262 + 0.959337i \(0.591085\pi\)
\(674\) 13.7026 0.527805
\(675\) −15.3212 −0.589713
\(676\) −52.6553 −2.02520
\(677\) 35.0577 1.34738 0.673688 0.739016i \(-0.264709\pi\)
0.673688 + 0.739016i \(0.264709\pi\)
\(678\) −35.3148 −1.35626
\(679\) 18.6900 0.717255
\(680\) −0.574545 −0.0220328
\(681\) −22.7098 −0.870241
\(682\) −107.445 −4.11430
\(683\) 36.1070 1.38160 0.690798 0.723047i \(-0.257259\pi\)
0.690798 + 0.723047i \(0.257259\pi\)
\(684\) −11.6266 −0.444553
\(685\) 16.4454 0.628345
\(686\) −52.6799 −2.01133
\(687\) −6.43461 −0.245496
\(688\) −32.4997 −1.23904
\(689\) −10.3886 −0.395776
\(690\) 21.2165 0.807699
\(691\) −30.8427 −1.17331 −0.586657 0.809836i \(-0.699556\pi\)
−0.586657 + 0.809836i \(0.699556\pi\)
\(692\) 59.8756 2.27613
\(693\) 25.8136 0.980579
\(694\) 3.81194 0.144699
\(695\) 23.2301 0.881167
\(696\) −31.9490 −1.21102
\(697\) 0.327342 0.0123990
\(698\) 2.12701 0.0805086
\(699\) 13.8271 0.522989
\(700\) 35.7204 1.35011
\(701\) −14.1942 −0.536106 −0.268053 0.963404i \(-0.586380\pi\)
−0.268053 + 0.963404i \(0.586380\pi\)
\(702\) 17.9982 0.679299
\(703\) −9.64026 −0.363589
\(704\) 46.3453 1.74670
\(705\) 2.55899 0.0963771
\(706\) −27.8094 −1.04662
\(707\) 5.80484 0.218313
\(708\) −9.02568 −0.339206
\(709\) −25.7519 −0.967135 −0.483567 0.875307i \(-0.660659\pi\)
−0.483567 + 0.875307i \(0.660659\pi\)
\(710\) 8.46738 0.317775
\(711\) −1.77077 −0.0664090
\(712\) −36.2927 −1.36012
\(713\) −53.4356 −2.00118
\(714\) 0.309723 0.0115911
\(715\) 10.1464 0.379453
\(716\) 91.7181 3.42767
\(717\) −24.0118 −0.896735
\(718\) −59.1616 −2.20789
\(719\) −9.25780 −0.345258 −0.172629 0.984987i \(-0.555226\pi\)
−0.172629 + 0.984987i \(0.555226\pi\)
\(720\) 28.3823 1.05775
\(721\) 0.614543 0.0228868
\(722\) 46.6223 1.73510
\(723\) 2.99501 0.111386
\(724\) −43.4581 −1.61511
\(725\) 15.5219 0.576470
\(726\) 39.2972 1.45845
\(727\) 2.91949 0.108278 0.0541389 0.998533i \(-0.482759\pi\)
0.0541389 + 0.998533i \(0.482759\pi\)
\(728\) −24.6860 −0.914924
\(729\) 7.50084 0.277809
\(730\) −10.5917 −0.392016
\(731\) 0.192316 0.00711307
\(732\) −18.9957 −0.702100
\(733\) 25.0044 0.923558 0.461779 0.886995i \(-0.347211\pi\)
0.461779 + 0.886995i \(0.347211\pi\)
\(734\) −49.1766 −1.81514
\(735\) −2.32464 −0.0857455
\(736\) 74.7407 2.75498
\(737\) −4.67382 −0.172162
\(738\) −32.0671 −1.18040
\(739\) 24.1406 0.888028 0.444014 0.896020i \(-0.353554\pi\)
0.444014 + 0.896020i \(0.353554\pi\)
\(740\) 56.1925 2.06568
\(741\) 1.44931 0.0532416
\(742\) 41.5280 1.52454
\(743\) 41.7345 1.53109 0.765544 0.643383i \(-0.222470\pi\)
0.765544 + 0.643383i \(0.222470\pi\)
\(744\) 52.6288 1.92947
\(745\) 21.0904 0.772693
\(746\) 51.7371 1.89423
\(747\) −0.644979 −0.0235986
\(748\) −1.49394 −0.0546240
\(749\) −2.98518 −0.109076
\(750\) 25.6423 0.936323
\(751\) 38.2762 1.39672 0.698359 0.715748i \(-0.253914\pi\)
0.698359 + 0.715748i \(0.253914\pi\)
\(752\) 21.3785 0.779594
\(753\) −0.446141 −0.0162583
\(754\) −18.2340 −0.664044
\(755\) −10.7425 −0.390959
\(756\) −50.9646 −1.85356
\(757\) 44.6475 1.62274 0.811371 0.584532i \(-0.198722\pi\)
0.811371 + 0.584532i \(0.198722\pi\)
\(758\) 16.5312 0.600439
\(759\) 32.4549 1.17804
\(760\) 10.7471 0.389840
\(761\) 54.9865 1.99326 0.996629 0.0820385i \(-0.0261431\pi\)
0.996629 + 0.0820385i \(0.0261431\pi\)
\(762\) −1.95993 −0.0710007
\(763\) 34.7425 1.25776
\(764\) −12.0739 −0.436818
\(765\) −0.167952 −0.00607231
\(766\) −33.9039 −1.22500
\(767\) −3.03042 −0.109422
\(768\) 12.9281 0.466501
\(769\) 43.8665 1.58187 0.790933 0.611902i \(-0.209596\pi\)
0.790933 + 0.611902i \(0.209596\pi\)
\(770\) −40.5596 −1.46166
\(771\) 0.843917 0.0303929
\(772\) −28.4861 −1.02524
\(773\) 41.9860 1.51013 0.755066 0.655649i \(-0.227605\pi\)
0.755066 + 0.655649i \(0.227605\pi\)
\(774\) −18.8397 −0.677178
\(775\) −25.5689 −0.918463
\(776\) 62.3374 2.23778
\(777\) −17.8207 −0.639314
\(778\) 19.4836 0.698520
\(779\) −6.12308 −0.219382
\(780\) −8.44792 −0.302484
\(781\) 12.9526 0.463480
\(782\) −1.04887 −0.0375074
\(783\) −22.1461 −0.791438
\(784\) −19.4207 −0.693595
\(785\) −1.95095 −0.0696323
\(786\) 21.6483 0.772170
\(787\) 17.4984 0.623749 0.311875 0.950123i \(-0.399043\pi\)
0.311875 + 0.950123i \(0.399043\pi\)
\(788\) −49.8019 −1.77412
\(789\) 6.36037 0.226435
\(790\) 2.78231 0.0989901
\(791\) 33.5753 1.19380
\(792\) 86.0972 3.05933
\(793\) −6.37789 −0.226486
\(794\) 61.5826 2.18549
\(795\) 8.36060 0.296520
\(796\) −108.139 −3.83287
\(797\) −26.2150 −0.928584 −0.464292 0.885682i \(-0.653691\pi\)
−0.464292 + 0.885682i \(0.653691\pi\)
\(798\) −5.79352 −0.205088
\(799\) −0.126507 −0.00447550
\(800\) 35.7635 1.26443
\(801\) −10.6091 −0.374855
\(802\) 37.8070 1.33501
\(803\) −16.2022 −0.571762
\(804\) 3.89144 0.137241
\(805\) −20.1714 −0.710948
\(806\) 30.0365 1.05799
\(807\) 20.6615 0.727320
\(808\) 19.3611 0.681121
\(809\) 45.1262 1.58655 0.793276 0.608862i \(-0.208374\pi\)
0.793276 + 0.608862i \(0.208374\pi\)
\(810\) 8.07665 0.283785
\(811\) −40.2914 −1.41482 −0.707411 0.706803i \(-0.750137\pi\)
−0.707411 + 0.706803i \(0.750137\pi\)
\(812\) 51.6323 1.81194
\(813\) −18.1722 −0.637327
\(814\) 121.347 4.25321
\(815\) 9.19687 0.322152
\(816\) 0.520929 0.0182362
\(817\) −3.59737 −0.125856
\(818\) 14.7394 0.515350
\(819\) −7.21624 −0.252156
\(820\) 35.6911 1.24639
\(821\) −18.0485 −0.629896 −0.314948 0.949109i \(-0.601987\pi\)
−0.314948 + 0.949109i \(0.601987\pi\)
\(822\) −29.5687 −1.03133
\(823\) 43.8574 1.52877 0.764387 0.644758i \(-0.223042\pi\)
0.764387 + 0.644758i \(0.223042\pi\)
\(824\) 2.04971 0.0714050
\(825\) 15.5297 0.540675
\(826\) 12.1139 0.421497
\(827\) −3.22810 −0.112252 −0.0561261 0.998424i \(-0.517875\pi\)
−0.0561261 + 0.998424i \(0.517875\pi\)
\(828\) 72.7838 2.52941
\(829\) −33.7011 −1.17049 −0.585243 0.810858i \(-0.699001\pi\)
−0.585243 + 0.810858i \(0.699001\pi\)
\(830\) 1.01342 0.0351763
\(831\) 6.02438 0.208983
\(832\) −12.9559 −0.449164
\(833\) 0.114921 0.00398179
\(834\) −41.7676 −1.44629
\(835\) 7.01588 0.242794
\(836\) 27.9449 0.966496
\(837\) 36.4808 1.26096
\(838\) 55.7240 1.92495
\(839\) −53.8946 −1.86065 −0.930324 0.366738i \(-0.880475\pi\)
−0.930324 + 0.366738i \(0.880475\pi\)
\(840\) 19.8669 0.685472
\(841\) −6.56373 −0.226336
\(842\) 0.763316 0.0263056
\(843\) −3.87961 −0.133621
\(844\) 1.40666 0.0484192
\(845\) 14.2280 0.489458
\(846\) 12.3929 0.426076
\(847\) −37.3614 −1.28375
\(848\) 69.8468 2.39855
\(849\) 12.5100 0.429341
\(850\) −0.501883 −0.0172144
\(851\) 60.3492 2.06874
\(852\) −10.7844 −0.369467
\(853\) −9.47927 −0.324564 −0.162282 0.986744i \(-0.551885\pi\)
−0.162282 + 0.986744i \(0.551885\pi\)
\(854\) 25.4953 0.872430
\(855\) 3.14162 0.107441
\(856\) −9.95657 −0.340309
\(857\) 7.70389 0.263160 0.131580 0.991306i \(-0.457995\pi\)
0.131580 + 0.991306i \(0.457995\pi\)
\(858\) −18.2432 −0.622811
\(859\) 33.6201 1.14710 0.573552 0.819169i \(-0.305565\pi\)
0.573552 + 0.819169i \(0.305565\pi\)
\(860\) 20.9688 0.715031
\(861\) −11.3190 −0.385749
\(862\) −28.3862 −0.966837
\(863\) 24.1626 0.822505 0.411253 0.911521i \(-0.365091\pi\)
0.411253 + 0.911521i \(0.365091\pi\)
\(864\) −51.0260 −1.73594
\(865\) −16.1790 −0.550102
\(866\) −50.4064 −1.71288
\(867\) 15.3181 0.520229
\(868\) −85.0528 −2.88688
\(869\) 4.25611 0.144379
\(870\) 14.6744 0.497510
\(871\) 1.30657 0.0442715
\(872\) 115.878 3.92412
\(873\) 18.2225 0.616739
\(874\) 19.6195 0.663641
\(875\) −24.3791 −0.824165
\(876\) 13.4900 0.455784
\(877\) −43.9049 −1.48256 −0.741282 0.671194i \(-0.765782\pi\)
−0.741282 + 0.671194i \(0.765782\pi\)
\(878\) −63.2709 −2.13529
\(879\) −16.3350 −0.550965
\(880\) −68.2179 −2.29963
\(881\) 48.8546 1.64595 0.822976 0.568076i \(-0.192312\pi\)
0.822976 + 0.568076i \(0.192312\pi\)
\(882\) −11.2579 −0.379074
\(883\) −28.7852 −0.968700 −0.484350 0.874874i \(-0.660944\pi\)
−0.484350 + 0.874874i \(0.660944\pi\)
\(884\) 0.417634 0.0140465
\(885\) 2.43883 0.0819803
\(886\) −7.48799 −0.251564
\(887\) −1.30317 −0.0437562 −0.0218781 0.999761i \(-0.506965\pi\)
−0.0218781 + 0.999761i \(0.506965\pi\)
\(888\) −59.4381 −1.99461
\(889\) 1.86338 0.0624958
\(890\) 16.6695 0.558763
\(891\) 12.3549 0.413904
\(892\) 111.144 3.72137
\(893\) 2.36637 0.0791877
\(894\) −37.9205 −1.26825
\(895\) −24.7832 −0.828410
\(896\) 2.81267 0.0939646
\(897\) −9.07283 −0.302933
\(898\) 35.1067 1.17153
\(899\) −36.9588 −1.23264
\(900\) 34.8271 1.16090
\(901\) −0.413317 −0.0137696
\(902\) 77.0744 2.56630
\(903\) −6.64999 −0.221298
\(904\) 111.985 3.72456
\(905\) 11.7428 0.390344
\(906\) 19.3150 0.641697
\(907\) 24.6075 0.817077 0.408539 0.912741i \(-0.366039\pi\)
0.408539 + 0.912741i \(0.366039\pi\)
\(908\) 122.410 4.06233
\(909\) 5.65966 0.187719
\(910\) 11.3385 0.375867
\(911\) 10.0081 0.331585 0.165792 0.986161i \(-0.446982\pi\)
0.165792 + 0.986161i \(0.446982\pi\)
\(912\) −9.74424 −0.322664
\(913\) 1.55023 0.0513052
\(914\) −49.2572 −1.62928
\(915\) 5.13282 0.169686
\(916\) 34.6838 1.14598
\(917\) −20.5819 −0.679676
\(918\) 0.716067 0.0236337
\(919\) 53.6454 1.76960 0.884800 0.465972i \(-0.154295\pi\)
0.884800 + 0.465972i \(0.154295\pi\)
\(920\) −67.2784 −2.21810
\(921\) 12.5958 0.415046
\(922\) −29.2278 −0.962566
\(923\) −3.62091 −0.119184
\(924\) 51.6582 1.69943
\(925\) 28.8771 0.949473
\(926\) 31.2992 1.02856
\(927\) 0.599173 0.0196794
\(928\) 51.6945 1.69696
\(929\) 11.9246 0.391234 0.195617 0.980680i \(-0.437329\pi\)
0.195617 + 0.980680i \(0.437329\pi\)
\(930\) −24.1729 −0.792659
\(931\) −2.14966 −0.0704523
\(932\) −74.5308 −2.44134
\(933\) −1.18133 −0.0386750
\(934\) −62.5242 −2.04585
\(935\) 0.403678 0.0132017
\(936\) −24.0686 −0.786707
\(937\) 57.5435 1.87986 0.939932 0.341362i \(-0.110888\pi\)
0.939932 + 0.341362i \(0.110888\pi\)
\(938\) −5.22295 −0.170535
\(939\) 18.4275 0.601358
\(940\) −13.7935 −0.449893
\(941\) 35.6327 1.16159 0.580796 0.814049i \(-0.302741\pi\)
0.580796 + 0.814049i \(0.302741\pi\)
\(942\) 3.50780 0.114290
\(943\) 38.3312 1.24824
\(944\) 20.3747 0.663138
\(945\) 13.7711 0.447975
\(946\) 45.2819 1.47224
\(947\) −13.4996 −0.438678 −0.219339 0.975649i \(-0.570390\pi\)
−0.219339 + 0.975649i \(0.570390\pi\)
\(948\) −3.54365 −0.115093
\(949\) 4.52933 0.147028
\(950\) 9.38796 0.304585
\(951\) 22.0259 0.714239
\(952\) −0.982144 −0.0318315
\(953\) 9.77739 0.316721 0.158360 0.987381i \(-0.449379\pi\)
0.158360 + 0.987381i \(0.449379\pi\)
\(954\) 40.4894 1.31089
\(955\) 3.26249 0.105572
\(956\) 129.428 4.18600
\(957\) 22.4475 0.725625
\(958\) 27.0081 0.872591
\(959\) 28.1122 0.907789
\(960\) 10.4267 0.336519
\(961\) 29.8814 0.963915
\(962\) −33.9227 −1.09371
\(963\) −2.91052 −0.0937901
\(964\) −16.1437 −0.519953
\(965\) 7.69724 0.247783
\(966\) 36.2681 1.16691
\(967\) 6.63701 0.213432 0.106716 0.994290i \(-0.465966\pi\)
0.106716 + 0.994290i \(0.465966\pi\)
\(968\) −124.613 −4.00521
\(969\) 0.0576613 0.00185235
\(970\) −28.6321 −0.919320
\(971\) −34.7681 −1.11576 −0.557881 0.829921i \(-0.688385\pi\)
−0.557881 + 0.829921i \(0.688385\pi\)
\(972\) −78.4249 −2.51548
\(973\) 39.7102 1.27305
\(974\) 59.4989 1.90647
\(975\) −4.34135 −0.139034
\(976\) 42.8810 1.37259
\(977\) −55.2328 −1.76705 −0.883527 0.468380i \(-0.844838\pi\)
−0.883527 + 0.468380i \(0.844838\pi\)
\(978\) −16.5359 −0.528761
\(979\) 25.4994 0.814964
\(980\) 12.5302 0.400264
\(981\) 33.8736 1.08150
\(982\) 8.85129 0.282456
\(983\) 34.8213 1.11063 0.555313 0.831641i \(-0.312598\pi\)
0.555313 + 0.831641i \(0.312598\pi\)
\(984\) −37.7525 −1.20351
\(985\) 13.4570 0.428775
\(986\) −0.725449 −0.0231030
\(987\) 4.37441 0.139239
\(988\) −7.81204 −0.248534
\(989\) 22.5199 0.716092
\(990\) −39.5452 −1.25683
\(991\) 9.66400 0.306987 0.153493 0.988150i \(-0.450948\pi\)
0.153493 + 0.988150i \(0.450948\pi\)
\(992\) −85.1553 −2.70368
\(993\) 1.94278 0.0616524
\(994\) 14.4744 0.459100
\(995\) 29.2201 0.926341
\(996\) −1.29073 −0.0408984
\(997\) −35.9193 −1.13758 −0.568788 0.822484i \(-0.692588\pi\)
−0.568788 + 0.822484i \(0.692588\pi\)
\(998\) −6.96611 −0.220508
\(999\) −41.2008 −1.30353
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 \(a_p\))