Properties

Label 8011.2.a.b.1.16
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 1.16
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59714 q^{2} -2.89463 q^{3} +4.74512 q^{4} +2.71586 q^{5} +7.51774 q^{6} -3.02593 q^{7} -7.12945 q^{8} +5.37887 q^{9} +O(q^{10})\) \(q-2.59714 q^{2} -2.89463 q^{3} +4.74512 q^{4} +2.71586 q^{5} +7.51774 q^{6} -3.02593 q^{7} -7.12945 q^{8} +5.37887 q^{9} -7.05346 q^{10} +6.06893 q^{11} -13.7354 q^{12} -0.0981225 q^{13} +7.85875 q^{14} -7.86141 q^{15} +9.02592 q^{16} +1.66842 q^{17} -13.9697 q^{18} +1.73026 q^{19} +12.8871 q^{20} +8.75894 q^{21} -15.7618 q^{22} +0.496599 q^{23} +20.6371 q^{24} +2.37590 q^{25} +0.254838 q^{26} -6.88595 q^{27} -14.3584 q^{28} -3.28894 q^{29} +20.4171 q^{30} +4.68386 q^{31} -9.18265 q^{32} -17.5673 q^{33} -4.33311 q^{34} -8.21800 q^{35} +25.5234 q^{36} +8.03219 q^{37} -4.49371 q^{38} +0.284028 q^{39} -19.3626 q^{40} +1.40866 q^{41} -22.7482 q^{42} +9.32188 q^{43} +28.7978 q^{44} +14.6083 q^{45} -1.28974 q^{46} -4.83030 q^{47} -26.1267 q^{48} +2.15625 q^{49} -6.17054 q^{50} -4.82944 q^{51} -0.465603 q^{52} -8.62023 q^{53} +17.8837 q^{54} +16.4824 q^{55} +21.5732 q^{56} -5.00845 q^{57} +8.54183 q^{58} +10.5661 q^{59} -37.3033 q^{60} +9.06527 q^{61} -12.1646 q^{62} -16.2761 q^{63} +5.79675 q^{64} -0.266487 q^{65} +45.6247 q^{66} -9.24343 q^{67} +7.91683 q^{68} -1.43747 q^{69} +21.3433 q^{70} -5.78055 q^{71} -38.3484 q^{72} +10.7832 q^{73} -20.8607 q^{74} -6.87735 q^{75} +8.21027 q^{76} -18.3642 q^{77} -0.737660 q^{78} -7.18491 q^{79} +24.5131 q^{80} +3.79564 q^{81} -3.65849 q^{82} -5.11825 q^{83} +41.5622 q^{84} +4.53119 q^{85} -24.2102 q^{86} +9.52026 q^{87} -43.2681 q^{88} +13.8596 q^{89} -37.9397 q^{90} +0.296912 q^{91} +2.35642 q^{92} -13.5580 q^{93} +12.5449 q^{94} +4.69913 q^{95} +26.5803 q^{96} +6.33446 q^{97} -5.60007 q^{98} +32.6440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + O(q^{10}) \) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + 21q^{10} + 70q^{11} + 20q^{12} + 53q^{13} + 69q^{14} + 28q^{15} + 449q^{16} + 88q^{17} + 86q^{18} + 44q^{19} + 136q^{20} + 125q^{21} + 17q^{22} + 104q^{23} + 84q^{24} + 444q^{25} + 100q^{26} + 32q^{27} + 46q^{28} + 373q^{29} + 99q^{30} + 30q^{31} + 221q^{32} + 56q^{33} + 26q^{34} + 164q^{35} + 599q^{36} + 81q^{37} + 66q^{38} + 143q^{39} + 42q^{40} + 182q^{41} + 32q^{42} + 40q^{43} + 184q^{44} + 198q^{45} + 54q^{46} + 66q^{47} + 5q^{48} + 479q^{49} + 184q^{50} + 123q^{51} + 64q^{52} + 221q^{53} + 67q^{54} + 38q^{55} + 174q^{56} + 84q^{57} + 44q^{58} + 127q^{59} + 29q^{60} + 174q^{61} + 86q^{62} + 48q^{63} + 549q^{64} + 202q^{65} + 32q^{66} + 29q^{67} + 172q^{68} + 249q^{69} + 12q^{70} + 185q^{71} + 218q^{72} + 57q^{73} + 272q^{74} + 24q^{75} + 84q^{76} + 384q^{77} + 12q^{78} + 93q^{79} + 215q^{80} + 702q^{81} + 48q^{82} + 121q^{83} + 179q^{84} + 177q^{85} + 209q^{86} + 91q^{87} + 36q^{88} + 186q^{89} + 66q^{90} + 32q^{91} + 272q^{92} + 220q^{93} + 60q^{94} + 170q^{95} + 162q^{96} + 22q^{97} + 196q^{98} + 152q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59714 −1.83645 −0.918227 0.396056i \(-0.870379\pi\)
−0.918227 + 0.396056i \(0.870379\pi\)
\(3\) −2.89463 −1.67121 −0.835607 0.549328i \(-0.814884\pi\)
−0.835607 + 0.549328i \(0.814884\pi\)
\(4\) 4.74512 2.37256
\(5\) 2.71586 1.21457 0.607285 0.794484i \(-0.292259\pi\)
0.607285 + 0.794484i \(0.292259\pi\)
\(6\) 7.51774 3.06911
\(7\) −3.02593 −1.14369 −0.571847 0.820360i \(-0.693773\pi\)
−0.571847 + 0.820360i \(0.693773\pi\)
\(8\) −7.12945 −2.52064
\(9\) 5.37887 1.79296
\(10\) −7.05346 −2.23050
\(11\) 6.06893 1.82985 0.914926 0.403622i \(-0.132249\pi\)
0.914926 + 0.403622i \(0.132249\pi\)
\(12\) −13.7354 −3.96506
\(13\) −0.0981225 −0.0272143 −0.0136071 0.999907i \(-0.504331\pi\)
−0.0136071 + 0.999907i \(0.504331\pi\)
\(14\) 7.85875 2.10034
\(15\) −7.86141 −2.02981
\(16\) 9.02592 2.25648
\(17\) 1.66842 0.404650 0.202325 0.979318i \(-0.435150\pi\)
0.202325 + 0.979318i \(0.435150\pi\)
\(18\) −13.9697 −3.29268
\(19\) 1.73026 0.396948 0.198474 0.980106i \(-0.436401\pi\)
0.198474 + 0.980106i \(0.436401\pi\)
\(20\) 12.8871 2.88164
\(21\) 8.75894 1.91136
\(22\) −15.7618 −3.36044
\(23\) 0.496599 0.103548 0.0517741 0.998659i \(-0.483512\pi\)
0.0517741 + 0.998659i \(0.483512\pi\)
\(24\) 20.6371 4.21253
\(25\) 2.37590 0.475180
\(26\) 0.254838 0.0499778
\(27\) −6.88595 −1.32520
\(28\) −14.3584 −2.71348
\(29\) −3.28894 −0.610741 −0.305370 0.952234i \(-0.598780\pi\)
−0.305370 + 0.952234i \(0.598780\pi\)
\(30\) 20.4171 3.72764
\(31\) 4.68386 0.841246 0.420623 0.907235i \(-0.361811\pi\)
0.420623 + 0.907235i \(0.361811\pi\)
\(32\) −9.18265 −1.62328
\(33\) −17.5673 −3.05807
\(34\) −4.33311 −0.743121
\(35\) −8.21800 −1.38910
\(36\) 25.5234 4.25390
\(37\) 8.03219 1.32048 0.660242 0.751053i \(-0.270454\pi\)
0.660242 + 0.751053i \(0.270454\pi\)
\(38\) −4.49371 −0.728976
\(39\) 0.284028 0.0454809
\(40\) −19.3626 −3.06150
\(41\) 1.40866 0.219996 0.109998 0.993932i \(-0.464916\pi\)
0.109998 + 0.993932i \(0.464916\pi\)
\(42\) −22.7482 −3.51012
\(43\) 9.32188 1.42157 0.710787 0.703408i \(-0.248339\pi\)
0.710787 + 0.703408i \(0.248339\pi\)
\(44\) 28.7978 4.34143
\(45\) 14.6083 2.17767
\(46\) −1.28974 −0.190161
\(47\) −4.83030 −0.704572 −0.352286 0.935892i \(-0.614595\pi\)
−0.352286 + 0.935892i \(0.614595\pi\)
\(48\) −26.1267 −3.77106
\(49\) 2.15625 0.308035
\(50\) −6.17054 −0.872646
\(51\) −4.82944 −0.676257
\(52\) −0.465603 −0.0645675
\(53\) −8.62023 −1.18408 −0.592040 0.805909i \(-0.701677\pi\)
−0.592040 + 0.805909i \(0.701677\pi\)
\(54\) 17.8837 2.43367
\(55\) 16.4824 2.22248
\(56\) 21.5732 2.88284
\(57\) −5.00845 −0.663385
\(58\) 8.54183 1.12160
\(59\) 10.5661 1.37558 0.687792 0.725907i \(-0.258580\pi\)
0.687792 + 0.725907i \(0.258580\pi\)
\(60\) −37.3033 −4.81584
\(61\) 9.06527 1.16069 0.580344 0.814371i \(-0.302918\pi\)
0.580344 + 0.814371i \(0.302918\pi\)
\(62\) −12.1646 −1.54491
\(63\) −16.2761 −2.05059
\(64\) 5.79675 0.724594
\(65\) −0.266487 −0.0330537
\(66\) 45.6247 5.61601
\(67\) −9.24343 −1.12926 −0.564632 0.825343i \(-0.690982\pi\)
−0.564632 + 0.825343i \(0.690982\pi\)
\(68\) 7.91683 0.960057
\(69\) −1.43747 −0.173051
\(70\) 21.3433 2.55101
\(71\) −5.78055 −0.686025 −0.343013 0.939331i \(-0.611447\pi\)
−0.343013 + 0.939331i \(0.611447\pi\)
\(72\) −38.3484 −4.51940
\(73\) 10.7832 1.26207 0.631036 0.775753i \(-0.282630\pi\)
0.631036 + 0.775753i \(0.282630\pi\)
\(74\) −20.8607 −2.42501
\(75\) −6.87735 −0.794127
\(76\) 8.21027 0.941783
\(77\) −18.3642 −2.09279
\(78\) −0.737660 −0.0835236
\(79\) −7.18491 −0.808366 −0.404183 0.914678i \(-0.632444\pi\)
−0.404183 + 0.914678i \(0.632444\pi\)
\(80\) 24.5131 2.74065
\(81\) 3.79564 0.421738
\(82\) −3.65849 −0.404013
\(83\) −5.11825 −0.561801 −0.280900 0.959737i \(-0.590633\pi\)
−0.280900 + 0.959737i \(0.590633\pi\)
\(84\) 41.5622 4.53481
\(85\) 4.53119 0.491476
\(86\) −24.2102 −2.61065
\(87\) 9.52026 1.02068
\(88\) −43.2681 −4.61240
\(89\) 13.8596 1.46911 0.734557 0.678547i \(-0.237390\pi\)
0.734557 + 0.678547i \(0.237390\pi\)
\(90\) −37.9397 −3.99919
\(91\) 0.296912 0.0311248
\(92\) 2.35642 0.245674
\(93\) −13.5580 −1.40590
\(94\) 12.5449 1.29391
\(95\) 4.69913 0.482121
\(96\) 26.5803 2.71284
\(97\) 6.33446 0.643167 0.321583 0.946881i \(-0.395785\pi\)
0.321583 + 0.946881i \(0.395785\pi\)
\(98\) −5.60007 −0.565692
\(99\) 32.6440 3.28084
\(100\) 11.2739 1.12739
\(101\) 11.2066 1.11510 0.557548 0.830144i \(-0.311742\pi\)
0.557548 + 0.830144i \(0.311742\pi\)
\(102\) 12.5427 1.24192
\(103\) 0.458394 0.0451669 0.0225835 0.999745i \(-0.492811\pi\)
0.0225835 + 0.999745i \(0.492811\pi\)
\(104\) 0.699560 0.0685975
\(105\) 23.7881 2.32148
\(106\) 22.3879 2.17451
\(107\) −4.29940 −0.415639 −0.207820 0.978167i \(-0.566637\pi\)
−0.207820 + 0.978167i \(0.566637\pi\)
\(108\) −32.6746 −3.14412
\(109\) 10.0608 0.963645 0.481823 0.876269i \(-0.339975\pi\)
0.481823 + 0.876269i \(0.339975\pi\)
\(110\) −42.8070 −4.08148
\(111\) −23.2502 −2.20681
\(112\) −27.3118 −2.58072
\(113\) 3.18818 0.299919 0.149959 0.988692i \(-0.452086\pi\)
0.149959 + 0.988692i \(0.452086\pi\)
\(114\) 13.0076 1.21828
\(115\) 1.34869 0.125766
\(116\) −15.6064 −1.44902
\(117\) −0.527788 −0.0487941
\(118\) −27.4415 −2.52620
\(119\) −5.04851 −0.462796
\(120\) 56.0475 5.11641
\(121\) 25.8319 2.34836
\(122\) −23.5437 −2.13155
\(123\) −4.07756 −0.367661
\(124\) 22.2255 1.99591
\(125\) −7.12669 −0.637431
\(126\) 42.2712 3.76582
\(127\) −3.53871 −0.314009 −0.157005 0.987598i \(-0.550184\pi\)
−0.157005 + 0.987598i \(0.550184\pi\)
\(128\) 3.31034 0.292596
\(129\) −26.9834 −2.37575
\(130\) 0.692104 0.0607015
\(131\) 11.8037 1.03130 0.515648 0.856801i \(-0.327551\pi\)
0.515648 + 0.856801i \(0.327551\pi\)
\(132\) −83.3589 −7.25546
\(133\) −5.23563 −0.453987
\(134\) 24.0064 2.07384
\(135\) −18.7013 −1.60955
\(136\) −11.8949 −1.01998
\(137\) 19.6492 1.67874 0.839372 0.543558i \(-0.182923\pi\)
0.839372 + 0.543558i \(0.182923\pi\)
\(138\) 3.73331 0.317800
\(139\) −6.58463 −0.558501 −0.279251 0.960218i \(-0.590086\pi\)
−0.279251 + 0.960218i \(0.590086\pi\)
\(140\) −38.9954 −3.29571
\(141\) 13.9819 1.17749
\(142\) 15.0129 1.25985
\(143\) −0.595499 −0.0497981
\(144\) 48.5493 4.04577
\(145\) −8.93231 −0.741788
\(146\) −28.0053 −2.31774
\(147\) −6.24153 −0.514793
\(148\) 38.1137 3.13293
\(149\) −1.94877 −0.159650 −0.0798248 0.996809i \(-0.525436\pi\)
−0.0798248 + 0.996809i \(0.525436\pi\)
\(150\) 17.8614 1.45838
\(151\) −1.22636 −0.0997997 −0.0498999 0.998754i \(-0.515890\pi\)
−0.0498999 + 0.998754i \(0.515890\pi\)
\(152\) −12.3358 −1.00056
\(153\) 8.97420 0.725521
\(154\) 47.6942 3.84331
\(155\) 12.7207 1.02175
\(156\) 1.34775 0.107906
\(157\) −0.822846 −0.0656703 −0.0328351 0.999461i \(-0.510454\pi\)
−0.0328351 + 0.999461i \(0.510454\pi\)
\(158\) 18.6602 1.48453
\(159\) 24.9524 1.97885
\(160\) −24.9388 −1.97158
\(161\) −1.50267 −0.118427
\(162\) −9.85779 −0.774501
\(163\) 17.1774 1.34544 0.672719 0.739898i \(-0.265126\pi\)
0.672719 + 0.739898i \(0.265126\pi\)
\(164\) 6.68427 0.521954
\(165\) −47.7103 −3.71424
\(166\) 13.2928 1.03172
\(167\) 12.1266 0.938383 0.469192 0.883096i \(-0.344545\pi\)
0.469192 + 0.883096i \(0.344545\pi\)
\(168\) −62.4464 −4.81785
\(169\) −12.9904 −0.999259
\(170\) −11.7681 −0.902573
\(171\) 9.30682 0.711711
\(172\) 44.2334 3.37277
\(173\) 12.4508 0.946620 0.473310 0.880896i \(-0.343059\pi\)
0.473310 + 0.880896i \(0.343059\pi\)
\(174\) −24.7254 −1.87443
\(175\) −7.18930 −0.543460
\(176\) 54.7777 4.12902
\(177\) −30.5848 −2.29890
\(178\) −35.9952 −2.69796
\(179\) −13.3545 −0.998160 −0.499080 0.866556i \(-0.666329\pi\)
−0.499080 + 0.866556i \(0.666329\pi\)
\(180\) 69.3180 5.16666
\(181\) 14.6248 1.08705 0.543527 0.839392i \(-0.317088\pi\)
0.543527 + 0.839392i \(0.317088\pi\)
\(182\) −0.771121 −0.0571593
\(183\) −26.2406 −1.93976
\(184\) −3.54048 −0.261008
\(185\) 21.8143 1.60382
\(186\) 35.2121 2.58187
\(187\) 10.1255 0.740450
\(188\) −22.9203 −1.67164
\(189\) 20.8364 1.51562
\(190\) −12.2043 −0.885393
\(191\) 2.79999 0.202600 0.101300 0.994856i \(-0.467700\pi\)
0.101300 + 0.994856i \(0.467700\pi\)
\(192\) −16.7794 −1.21095
\(193\) 1.56415 0.112590 0.0562949 0.998414i \(-0.482071\pi\)
0.0562949 + 0.998414i \(0.482071\pi\)
\(194\) −16.4515 −1.18115
\(195\) 0.771381 0.0552398
\(196\) 10.2317 0.730832
\(197\) 27.4718 1.95728 0.978641 0.205575i \(-0.0659066\pi\)
0.978641 + 0.205575i \(0.0659066\pi\)
\(198\) −84.7809 −6.02512
\(199\) −9.83964 −0.697513 −0.348757 0.937213i \(-0.613396\pi\)
−0.348757 + 0.937213i \(0.613396\pi\)
\(200\) −16.9389 −1.19776
\(201\) 26.7563 1.88724
\(202\) −29.1050 −2.04782
\(203\) 9.95210 0.698501
\(204\) −22.9163 −1.60446
\(205\) 3.82573 0.267201
\(206\) −1.19051 −0.0829469
\(207\) 2.67114 0.185657
\(208\) −0.885646 −0.0614085
\(209\) 10.5008 0.726356
\(210\) −61.7808 −4.26328
\(211\) −24.3900 −1.67908 −0.839540 0.543299i \(-0.817175\pi\)
−0.839540 + 0.543299i \(0.817175\pi\)
\(212\) −40.9040 −2.80930
\(213\) 16.7325 1.14650
\(214\) 11.1661 0.763302
\(215\) 25.3169 1.72660
\(216\) 49.0930 3.34036
\(217\) −14.1730 −0.962128
\(218\) −26.1292 −1.76969
\(219\) −31.2132 −2.10919
\(220\) 78.2108 5.27297
\(221\) −0.163709 −0.0110123
\(222\) 60.3839 4.05270
\(223\) 4.27847 0.286508 0.143254 0.989686i \(-0.454243\pi\)
0.143254 + 0.989686i \(0.454243\pi\)
\(224\) 27.7860 1.85653
\(225\) 12.7797 0.851977
\(226\) −8.28014 −0.550787
\(227\) −8.16005 −0.541601 −0.270801 0.962635i \(-0.587288\pi\)
−0.270801 + 0.962635i \(0.587288\pi\)
\(228\) −23.7657 −1.57392
\(229\) 13.9408 0.921231 0.460616 0.887600i \(-0.347629\pi\)
0.460616 + 0.887600i \(0.347629\pi\)
\(230\) −3.50274 −0.230964
\(231\) 53.1574 3.49750
\(232\) 23.4483 1.53946
\(233\) 11.9464 0.782635 0.391317 0.920256i \(-0.372019\pi\)
0.391317 + 0.920256i \(0.372019\pi\)
\(234\) 1.37074 0.0896080
\(235\) −13.1184 −0.855751
\(236\) 50.1373 3.26366
\(237\) 20.7977 1.35095
\(238\) 13.1117 0.849903
\(239\) 0.176706 0.0114302 0.00571508 0.999984i \(-0.498181\pi\)
0.00571508 + 0.999984i \(0.498181\pi\)
\(240\) −70.9564 −4.58022
\(241\) −8.02085 −0.516669 −0.258334 0.966056i \(-0.583174\pi\)
−0.258334 + 0.966056i \(0.583174\pi\)
\(242\) −67.0890 −4.31265
\(243\) 9.67088 0.620387
\(244\) 43.0158 2.75380
\(245\) 5.85607 0.374130
\(246\) 10.5900 0.675192
\(247\) −0.169777 −0.0108027
\(248\) −33.3934 −2.12048
\(249\) 14.8154 0.938890
\(250\) 18.5090 1.17061
\(251\) −20.2483 −1.27806 −0.639030 0.769182i \(-0.720664\pi\)
−0.639030 + 0.769182i \(0.720664\pi\)
\(252\) −77.2320 −4.86516
\(253\) 3.01383 0.189478
\(254\) 9.19050 0.576663
\(255\) −13.1161 −0.821362
\(256\) −20.1909 −1.26193
\(257\) −25.7707 −1.60753 −0.803765 0.594947i \(-0.797173\pi\)
−0.803765 + 0.594947i \(0.797173\pi\)
\(258\) 70.0795 4.36296
\(259\) −24.3048 −1.51023
\(260\) −1.26451 −0.0784218
\(261\) −17.6908 −1.09503
\(262\) −30.6559 −1.89393
\(263\) 0.484360 0.0298669 0.0149335 0.999888i \(-0.495246\pi\)
0.0149335 + 0.999888i \(0.495246\pi\)
\(264\) 125.245 7.70831
\(265\) −23.4114 −1.43815
\(266\) 13.5977 0.833726
\(267\) −40.1184 −2.45520
\(268\) −43.8612 −2.67925
\(269\) −26.4394 −1.61204 −0.806020 0.591888i \(-0.798383\pi\)
−0.806020 + 0.591888i \(0.798383\pi\)
\(270\) 48.5698 2.95586
\(271\) 15.9879 0.971198 0.485599 0.874182i \(-0.338602\pi\)
0.485599 + 0.874182i \(0.338602\pi\)
\(272\) 15.0590 0.913085
\(273\) −0.859449 −0.0520162
\(274\) −51.0316 −3.08293
\(275\) 14.4192 0.869509
\(276\) −6.82097 −0.410574
\(277\) 22.8402 1.37233 0.686167 0.727444i \(-0.259292\pi\)
0.686167 + 0.727444i \(0.259292\pi\)
\(278\) 17.1012 1.02566
\(279\) 25.1939 1.50832
\(280\) 58.5898 3.50141
\(281\) −16.0046 −0.954755 −0.477378 0.878698i \(-0.658413\pi\)
−0.477378 + 0.878698i \(0.658413\pi\)
\(282\) −36.3130 −2.16241
\(283\) −11.7723 −0.699792 −0.349896 0.936789i \(-0.613783\pi\)
−0.349896 + 0.936789i \(0.613783\pi\)
\(284\) −27.4294 −1.62764
\(285\) −13.6022 −0.805728
\(286\) 1.54659 0.0914519
\(287\) −4.26251 −0.251608
\(288\) −49.3923 −2.91047
\(289\) −14.2164 −0.836258
\(290\) 23.1984 1.36226
\(291\) −18.3359 −1.07487
\(292\) 51.1673 2.99434
\(293\) −8.54120 −0.498982 −0.249491 0.968377i \(-0.580263\pi\)
−0.249491 + 0.968377i \(0.580263\pi\)
\(294\) 16.2101 0.945393
\(295\) 28.6960 1.67074
\(296\) −57.2651 −3.32846
\(297\) −41.7903 −2.42492
\(298\) 5.06123 0.293189
\(299\) −0.0487276 −0.00281799
\(300\) −32.6338 −1.88411
\(301\) −28.2074 −1.62584
\(302\) 3.18502 0.183278
\(303\) −32.4389 −1.86357
\(304\) 15.6172 0.895705
\(305\) 24.6200 1.40974
\(306\) −23.3072 −1.33238
\(307\) −23.6764 −1.35128 −0.675641 0.737231i \(-0.736133\pi\)
−0.675641 + 0.737231i \(0.736133\pi\)
\(308\) −87.1401 −4.96527
\(309\) −1.32688 −0.0754836
\(310\) −33.0374 −1.87640
\(311\) −20.6475 −1.17081 −0.585407 0.810739i \(-0.699065\pi\)
−0.585407 + 0.810739i \(0.699065\pi\)
\(312\) −2.02497 −0.114641
\(313\) 4.35880 0.246374 0.123187 0.992383i \(-0.460689\pi\)
0.123187 + 0.992383i \(0.460689\pi\)
\(314\) 2.13704 0.120600
\(315\) −44.2036 −2.49059
\(316\) −34.0933 −1.91790
\(317\) −6.06362 −0.340567 −0.170283 0.985395i \(-0.554468\pi\)
−0.170283 + 0.985395i \(0.554468\pi\)
\(318\) −64.8047 −3.63407
\(319\) −19.9604 −1.11757
\(320\) 15.7432 0.880070
\(321\) 12.4452 0.694622
\(322\) 3.90265 0.217486
\(323\) 2.88679 0.160625
\(324\) 18.0108 1.00060
\(325\) −0.233129 −0.0129317
\(326\) −44.6120 −2.47083
\(327\) −29.1221 −1.61046
\(328\) −10.0430 −0.554532
\(329\) 14.6161 0.805814
\(330\) 123.910 6.82103
\(331\) −20.5564 −1.12988 −0.564941 0.825131i \(-0.691101\pi\)
−0.564941 + 0.825131i \(0.691101\pi\)
\(332\) −24.2867 −1.33291
\(333\) 43.2041 2.36757
\(334\) −31.4944 −1.72330
\(335\) −25.1039 −1.37157
\(336\) 79.0575 4.31294
\(337\) −4.34845 −0.236875 −0.118438 0.992962i \(-0.537789\pi\)
−0.118438 + 0.992962i \(0.537789\pi\)
\(338\) 33.7378 1.83509
\(339\) −9.22860 −0.501229
\(340\) 21.5010 1.16606
\(341\) 28.4260 1.53936
\(342\) −24.1711 −1.30702
\(343\) 14.6569 0.791396
\(344\) −66.4599 −3.58328
\(345\) −3.90397 −0.210183
\(346\) −32.3366 −1.73842
\(347\) 2.72968 0.146537 0.0732684 0.997312i \(-0.476657\pi\)
0.0732684 + 0.997312i \(0.476657\pi\)
\(348\) 45.1748 2.42162
\(349\) −32.7936 −1.75540 −0.877701 0.479209i \(-0.840924\pi\)
−0.877701 + 0.479209i \(0.840924\pi\)
\(350\) 18.6716 0.998039
\(351\) 0.675666 0.0360644
\(352\) −55.7288 −2.97036
\(353\) 27.2244 1.44901 0.724503 0.689271i \(-0.242069\pi\)
0.724503 + 0.689271i \(0.242069\pi\)
\(354\) 79.4330 4.22182
\(355\) −15.6992 −0.833226
\(356\) 65.7654 3.48556
\(357\) 14.6136 0.773431
\(358\) 34.6834 1.83307
\(359\) 1.33938 0.0706900 0.0353450 0.999375i \(-0.488747\pi\)
0.0353450 + 0.999375i \(0.488747\pi\)
\(360\) −104.149 −5.48913
\(361\) −16.0062 −0.842432
\(362\) −37.9827 −1.99632
\(363\) −74.7738 −3.92461
\(364\) 1.40888 0.0738455
\(365\) 29.2855 1.53288
\(366\) 68.1504 3.56228
\(367\) −9.84862 −0.514094 −0.257047 0.966399i \(-0.582750\pi\)
−0.257047 + 0.966399i \(0.582750\pi\)
\(368\) 4.48227 0.233654
\(369\) 7.57702 0.394444
\(370\) −56.6547 −2.94534
\(371\) 26.0842 1.35423
\(372\) −64.3345 −3.33559
\(373\) −23.0121 −1.19152 −0.595761 0.803162i \(-0.703149\pi\)
−0.595761 + 0.803162i \(0.703149\pi\)
\(374\) −26.2973 −1.35980
\(375\) 20.6291 1.06528
\(376\) 34.4374 1.77597
\(377\) 0.322719 0.0166209
\(378\) −54.1149 −2.78337
\(379\) 9.17747 0.471415 0.235708 0.971824i \(-0.424259\pi\)
0.235708 + 0.971824i \(0.424259\pi\)
\(380\) 22.2980 1.14386
\(381\) 10.2432 0.524777
\(382\) −7.27196 −0.372066
\(383\) −31.9832 −1.63427 −0.817133 0.576449i \(-0.804438\pi\)
−0.817133 + 0.576449i \(0.804438\pi\)
\(384\) −9.58221 −0.488990
\(385\) −49.8745 −2.54184
\(386\) −4.06231 −0.206766
\(387\) 50.1412 2.54882
\(388\) 30.0578 1.52595
\(389\) −3.12544 −0.158466 −0.0792331 0.996856i \(-0.525247\pi\)
−0.0792331 + 0.996856i \(0.525247\pi\)
\(390\) −2.00338 −0.101445
\(391\) 0.828534 0.0419008
\(392\) −15.3729 −0.776447
\(393\) −34.1674 −1.72352
\(394\) −71.3479 −3.59446
\(395\) −19.5132 −0.981817
\(396\) 154.900 7.78400
\(397\) −10.6864 −0.536333 −0.268167 0.963373i \(-0.586418\pi\)
−0.268167 + 0.963373i \(0.586418\pi\)
\(398\) 25.5549 1.28095
\(399\) 15.1552 0.758709
\(400\) 21.4447 1.07223
\(401\) −0.332411 −0.0165998 −0.00829991 0.999966i \(-0.502642\pi\)
−0.00829991 + 0.999966i \(0.502642\pi\)
\(402\) −69.4897 −3.46583
\(403\) −0.459592 −0.0228939
\(404\) 53.1766 2.64563
\(405\) 10.3084 0.512230
\(406\) −25.8470 −1.28276
\(407\) 48.7468 2.41629
\(408\) 34.4313 1.70460
\(409\) 30.4365 1.50499 0.752494 0.658599i \(-0.228850\pi\)
0.752494 + 0.658599i \(0.228850\pi\)
\(410\) −9.93595 −0.490702
\(411\) −56.8771 −2.80554
\(412\) 2.17513 0.107161
\(413\) −31.9722 −1.57325
\(414\) −6.93733 −0.340951
\(415\) −13.9005 −0.682346
\(416\) 0.901025 0.0441764
\(417\) 19.0601 0.933375
\(418\) −27.2720 −1.33392
\(419\) 23.6660 1.15616 0.578081 0.815979i \(-0.303802\pi\)
0.578081 + 0.815979i \(0.303802\pi\)
\(420\) 112.877 5.50784
\(421\) −20.1969 −0.984336 −0.492168 0.870500i \(-0.663795\pi\)
−0.492168 + 0.870500i \(0.663795\pi\)
\(422\) 63.3443 3.08355
\(423\) −25.9816 −1.26327
\(424\) 61.4575 2.98464
\(425\) 3.96399 0.192282
\(426\) −43.4567 −2.10548
\(427\) −27.4309 −1.32747
\(428\) −20.4012 −0.986129
\(429\) 1.72375 0.0832233
\(430\) −65.7515 −3.17082
\(431\) 22.0200 1.06067 0.530333 0.847790i \(-0.322067\pi\)
0.530333 + 0.847790i \(0.322067\pi\)
\(432\) −62.1520 −2.99029
\(433\) −0.379633 −0.0182440 −0.00912200 0.999958i \(-0.502904\pi\)
−0.00912200 + 0.999958i \(0.502904\pi\)
\(434\) 36.8093 1.76690
\(435\) 25.8557 1.23969
\(436\) 47.7395 2.28631
\(437\) 0.859244 0.0411032
\(438\) 81.0650 3.87343
\(439\) 14.0233 0.669295 0.334648 0.942343i \(-0.391383\pi\)
0.334648 + 0.942343i \(0.391383\pi\)
\(440\) −117.510 −5.60208
\(441\) 11.5982 0.552294
\(442\) 0.425175 0.0202235
\(443\) 20.4338 0.970838 0.485419 0.874282i \(-0.338667\pi\)
0.485419 + 0.874282i \(0.338667\pi\)
\(444\) −110.325 −5.23579
\(445\) 37.6407 1.78434
\(446\) −11.1118 −0.526158
\(447\) 5.64097 0.266809
\(448\) −17.5406 −0.828713
\(449\) 13.4696 0.635671 0.317836 0.948146i \(-0.397044\pi\)
0.317836 + 0.948146i \(0.397044\pi\)
\(450\) −33.1905 −1.56462
\(451\) 8.54908 0.402560
\(452\) 15.1283 0.711575
\(453\) 3.54985 0.166787
\(454\) 21.1928 0.994626
\(455\) 0.806371 0.0378033
\(456\) 35.7075 1.67216
\(457\) −30.2430 −1.41471 −0.707354 0.706859i \(-0.750111\pi\)
−0.707354 + 0.706859i \(0.750111\pi\)
\(458\) −36.2061 −1.69180
\(459\) −11.4886 −0.536243
\(460\) 6.39972 0.298388
\(461\) 6.73713 0.313779 0.156890 0.987616i \(-0.449853\pi\)
0.156890 + 0.987616i \(0.449853\pi\)
\(462\) −138.057 −6.42299
\(463\) 22.8093 1.06004 0.530019 0.847986i \(-0.322185\pi\)
0.530019 + 0.847986i \(0.322185\pi\)
\(464\) −29.6857 −1.37812
\(465\) −36.8217 −1.70757
\(466\) −31.0264 −1.43727
\(467\) 8.37717 0.387649 0.193825 0.981036i \(-0.437911\pi\)
0.193825 + 0.981036i \(0.437911\pi\)
\(468\) −2.50442 −0.115767
\(469\) 27.9700 1.29153
\(470\) 34.0703 1.57155
\(471\) 2.38183 0.109749
\(472\) −75.3303 −3.46736
\(473\) 56.5738 2.60127
\(474\) −54.0143 −2.48096
\(475\) 4.11092 0.188622
\(476\) −23.9558 −1.09801
\(477\) −46.3671 −2.12300
\(478\) −0.458929 −0.0209909
\(479\) 12.1559 0.555415 0.277708 0.960666i \(-0.410425\pi\)
0.277708 + 0.960666i \(0.410425\pi\)
\(480\) 72.1885 3.29494
\(481\) −0.788138 −0.0359360
\(482\) 20.8313 0.948838
\(483\) 4.34968 0.197917
\(484\) 122.576 5.57161
\(485\) 17.2035 0.781171
\(486\) −25.1166 −1.13931
\(487\) 7.52557 0.341016 0.170508 0.985356i \(-0.445459\pi\)
0.170508 + 0.985356i \(0.445459\pi\)
\(488\) −64.6304 −2.92568
\(489\) −49.7222 −2.24851
\(490\) −15.2090 −0.687073
\(491\) −39.2892 −1.77310 −0.886548 0.462637i \(-0.846903\pi\)
−0.886548 + 0.462637i \(0.846903\pi\)
\(492\) −19.3485 −0.872297
\(493\) −5.48732 −0.247137
\(494\) 0.440934 0.0198386
\(495\) 88.6565 3.98481
\(496\) 42.2761 1.89826
\(497\) 17.4915 0.784603
\(498\) −38.4777 −1.72423
\(499\) −5.45682 −0.244281 −0.122140 0.992513i \(-0.538976\pi\)
−0.122140 + 0.992513i \(0.538976\pi\)
\(500\) −33.8170 −1.51234
\(501\) −35.1020 −1.56824
\(502\) 52.5875 2.34710
\(503\) 18.7083 0.834164 0.417082 0.908869i \(-0.363053\pi\)
0.417082 + 0.908869i \(0.363053\pi\)
\(504\) 116.040 5.16881
\(505\) 30.4355 1.35436
\(506\) −7.82732 −0.347967
\(507\) 37.6023 1.66998
\(508\) −16.7916 −0.745006
\(509\) 3.60880 0.159957 0.0799786 0.996797i \(-0.474515\pi\)
0.0799786 + 0.996797i \(0.474515\pi\)
\(510\) 34.0643 1.50839
\(511\) −32.6291 −1.44342
\(512\) 45.8179 2.02488
\(513\) −11.9144 −0.526036
\(514\) 66.9299 2.95215
\(515\) 1.24493 0.0548584
\(516\) −128.039 −5.63662
\(517\) −29.3147 −1.28926
\(518\) 63.1230 2.77346
\(519\) −36.0406 −1.58201
\(520\) 1.89991 0.0833164
\(521\) 39.7585 1.74185 0.870926 0.491414i \(-0.163520\pi\)
0.870926 + 0.491414i \(0.163520\pi\)
\(522\) 45.9454 2.01098
\(523\) −30.3451 −1.32690 −0.663450 0.748221i \(-0.730908\pi\)
−0.663450 + 0.748221i \(0.730908\pi\)
\(524\) 56.0101 2.44681
\(525\) 20.8104 0.908239
\(526\) −1.25795 −0.0548492
\(527\) 7.81463 0.340411
\(528\) −158.561 −6.90048
\(529\) −22.7534 −0.989278
\(530\) 60.8025 2.64109
\(531\) 56.8335 2.46636
\(532\) −24.8437 −1.07711
\(533\) −0.138222 −0.00598704
\(534\) 104.193 4.50887
\(535\) −11.6766 −0.504823
\(536\) 65.9006 2.84647
\(537\) 38.6562 1.66814
\(538\) 68.6668 2.96044
\(539\) 13.0861 0.563659
\(540\) −88.7398 −3.81875
\(541\) −23.3703 −1.00477 −0.502383 0.864645i \(-0.667543\pi\)
−0.502383 + 0.864645i \(0.667543\pi\)
\(542\) −41.5228 −1.78356
\(543\) −42.3334 −1.81670
\(544\) −15.3205 −0.656860
\(545\) 27.3236 1.17041
\(546\) 2.23211 0.0955254
\(547\) −23.7302 −1.01463 −0.507315 0.861761i \(-0.669362\pi\)
−0.507315 + 0.861761i \(0.669362\pi\)
\(548\) 93.2377 3.98292
\(549\) 48.7609 2.08106
\(550\) −37.4486 −1.59681
\(551\) −5.69071 −0.242432
\(552\) 10.2484 0.436200
\(553\) 21.7410 0.924523
\(554\) −59.3191 −2.52023
\(555\) −63.1443 −2.68033
\(556\) −31.2449 −1.32508
\(557\) 8.58077 0.363579 0.181789 0.983337i \(-0.441811\pi\)
0.181789 + 0.983337i \(0.441811\pi\)
\(558\) −65.4320 −2.76996
\(559\) −0.914687 −0.0386871
\(560\) −74.1750 −3.13447
\(561\) −29.3096 −1.23745
\(562\) 41.5662 1.75336
\(563\) −11.3497 −0.478334 −0.239167 0.970978i \(-0.576874\pi\)
−0.239167 + 0.970978i \(0.576874\pi\)
\(564\) 66.3459 2.79367
\(565\) 8.65866 0.364272
\(566\) 30.5743 1.28514
\(567\) −11.4853 −0.482339
\(568\) 41.2122 1.72922
\(569\) 23.5185 0.985948 0.492974 0.870044i \(-0.335910\pi\)
0.492974 + 0.870044i \(0.335910\pi\)
\(570\) 35.3269 1.47968
\(571\) 10.1200 0.423508 0.211754 0.977323i \(-0.432082\pi\)
0.211754 + 0.977323i \(0.432082\pi\)
\(572\) −2.82571 −0.118149
\(573\) −8.10493 −0.338588
\(574\) 11.0703 0.462067
\(575\) 1.17987 0.0492040
\(576\) 31.1800 1.29917
\(577\) −13.1026 −0.545468 −0.272734 0.962089i \(-0.587928\pi\)
−0.272734 + 0.962089i \(0.587928\pi\)
\(578\) 36.9219 1.53575
\(579\) −4.52763 −0.188162
\(580\) −42.3849 −1.75994
\(581\) 15.4875 0.642528
\(582\) 47.6208 1.97395
\(583\) −52.3156 −2.16669
\(584\) −76.8779 −3.18123
\(585\) −1.43340 −0.0592638
\(586\) 22.1827 0.916358
\(587\) −22.3414 −0.922130 −0.461065 0.887366i \(-0.652532\pi\)
−0.461065 + 0.887366i \(0.652532\pi\)
\(588\) −29.6168 −1.22138
\(589\) 8.10428 0.333931
\(590\) −74.5274 −3.06824
\(591\) −79.5206 −3.27104
\(592\) 72.4979 2.97964
\(593\) 41.0860 1.68720 0.843600 0.536972i \(-0.180432\pi\)
0.843600 + 0.536972i \(0.180432\pi\)
\(594\) 108.535 4.45325
\(595\) −13.7110 −0.562098
\(596\) −9.24715 −0.378778
\(597\) 28.4821 1.16569
\(598\) 0.126552 0.00517511
\(599\) −44.3917 −1.81380 −0.906898 0.421350i \(-0.861556\pi\)
−0.906898 + 0.421350i \(0.861556\pi\)
\(600\) 49.0317 2.00171
\(601\) −32.8064 −1.33820 −0.669101 0.743171i \(-0.733321\pi\)
−0.669101 + 0.743171i \(0.733321\pi\)
\(602\) 73.2584 2.98579
\(603\) −49.7192 −2.02472
\(604\) −5.81922 −0.236781
\(605\) 70.1559 2.85224
\(606\) 84.2482 3.42235
\(607\) 21.4982 0.872584 0.436292 0.899805i \(-0.356291\pi\)
0.436292 + 0.899805i \(0.356291\pi\)
\(608\) −15.8883 −0.644357
\(609\) −28.8076 −1.16734
\(610\) −63.9415 −2.58892
\(611\) 0.473961 0.0191744
\(612\) 42.5836 1.72134
\(613\) −23.2765 −0.940130 −0.470065 0.882632i \(-0.655770\pi\)
−0.470065 + 0.882632i \(0.655770\pi\)
\(614\) 61.4908 2.48157
\(615\) −11.0741 −0.446550
\(616\) 130.926 5.27517
\(617\) −43.0031 −1.73124 −0.865620 0.500701i \(-0.833075\pi\)
−0.865620 + 0.500701i \(0.833075\pi\)
\(618\) 3.44609 0.138622
\(619\) 8.88564 0.357144 0.178572 0.983927i \(-0.442852\pi\)
0.178572 + 0.983927i \(0.442852\pi\)
\(620\) 60.3613 2.42417
\(621\) −3.41956 −0.137222
\(622\) 53.6245 2.15015
\(623\) −41.9381 −1.68022
\(624\) 2.56362 0.102627
\(625\) −31.2346 −1.24938
\(626\) −11.3204 −0.452454
\(627\) −30.3959 −1.21390
\(628\) −3.90450 −0.155807
\(629\) 13.4010 0.534334
\(630\) 114.803 4.57385
\(631\) 17.9842 0.715942 0.357971 0.933733i \(-0.383469\pi\)
0.357971 + 0.933733i \(0.383469\pi\)
\(632\) 51.2245 2.03760
\(633\) 70.6001 2.80610
\(634\) 15.7480 0.625435
\(635\) −9.61063 −0.381386
\(636\) 118.402 4.69494
\(637\) −0.211576 −0.00838297
\(638\) 51.8398 2.05236
\(639\) −31.0928 −1.23001
\(640\) 8.99043 0.355378
\(641\) 42.5720 1.68149 0.840746 0.541430i \(-0.182117\pi\)
0.840746 + 0.541430i \(0.182117\pi\)
\(642\) −32.3218 −1.27564
\(643\) −5.20691 −0.205341 −0.102670 0.994715i \(-0.532739\pi\)
−0.102670 + 0.994715i \(0.532739\pi\)
\(644\) −7.13037 −0.280976
\(645\) −73.2831 −2.88552
\(646\) −7.49738 −0.294981
\(647\) −14.0356 −0.551796 −0.275898 0.961187i \(-0.588975\pi\)
−0.275898 + 0.961187i \(0.588975\pi\)
\(648\) −27.0608 −1.06305
\(649\) 64.1247 2.51712
\(650\) 0.605469 0.0237484
\(651\) 41.0256 1.60792
\(652\) 81.5088 3.19213
\(653\) 22.3561 0.874861 0.437431 0.899252i \(-0.355889\pi\)
0.437431 + 0.899252i \(0.355889\pi\)
\(654\) 75.6342 2.95753
\(655\) 32.0573 1.25258
\(656\) 12.7145 0.496417
\(657\) 58.0012 2.26284
\(658\) −37.9601 −1.47984
\(659\) −9.99227 −0.389244 −0.194622 0.980878i \(-0.562348\pi\)
−0.194622 + 0.980878i \(0.562348\pi\)
\(660\) −226.391 −8.81227
\(661\) 45.9954 1.78901 0.894507 0.447055i \(-0.147527\pi\)
0.894507 + 0.447055i \(0.147527\pi\)
\(662\) 53.3878 2.07498
\(663\) 0.473877 0.0184039
\(664\) 36.4903 1.41610
\(665\) −14.2192 −0.551399
\(666\) −112.207 −4.34793
\(667\) −1.63329 −0.0632411
\(668\) 57.5421 2.22637
\(669\) −12.3846 −0.478816
\(670\) 65.1982 2.51882
\(671\) 55.0165 2.12389
\(672\) −80.4302 −3.10266
\(673\) 11.3273 0.436634 0.218317 0.975878i \(-0.429943\pi\)
0.218317 + 0.975878i \(0.429943\pi\)
\(674\) 11.2935 0.435010
\(675\) −16.3603 −0.629709
\(676\) −61.6409 −2.37080
\(677\) −21.0450 −0.808826 −0.404413 0.914576i \(-0.632524\pi\)
−0.404413 + 0.914576i \(0.632524\pi\)
\(678\) 23.9679 0.920483
\(679\) −19.1676 −0.735586
\(680\) −32.3049 −1.23884
\(681\) 23.6203 0.905132
\(682\) −73.8263 −2.82695
\(683\) −9.78428 −0.374385 −0.187193 0.982323i \(-0.559939\pi\)
−0.187193 + 0.982323i \(0.559939\pi\)
\(684\) 44.1620 1.68858
\(685\) 53.3644 2.03895
\(686\) −38.0658 −1.45336
\(687\) −40.3533 −1.53957
\(688\) 84.1385 3.20775
\(689\) 0.845839 0.0322239
\(690\) 10.1391 0.385991
\(691\) 24.7012 0.939679 0.469839 0.882752i \(-0.344312\pi\)
0.469839 + 0.882752i \(0.344312\pi\)
\(692\) 59.0808 2.24591
\(693\) −98.7784 −3.75228
\(694\) −7.08935 −0.269108
\(695\) −17.8829 −0.678339
\(696\) −67.8742 −2.57277
\(697\) 2.35024 0.0890215
\(698\) 85.1695 3.22371
\(699\) −34.5804 −1.30795
\(700\) −34.1141 −1.28939
\(701\) −1.66130 −0.0627465 −0.0313733 0.999508i \(-0.509988\pi\)
−0.0313733 + 0.999508i \(0.509988\pi\)
\(702\) −1.75480 −0.0662306
\(703\) 13.8977 0.524163
\(704\) 35.1801 1.32590
\(705\) 37.9729 1.43014
\(706\) −70.7054 −2.66103
\(707\) −33.9103 −1.27533
\(708\) −145.129 −5.45427
\(709\) 5.08840 0.191099 0.0955494 0.995425i \(-0.469539\pi\)
0.0955494 + 0.995425i \(0.469539\pi\)
\(710\) 40.7729 1.53018
\(711\) −38.6467 −1.44937
\(712\) −98.8113 −3.70311
\(713\) 2.32600 0.0871095
\(714\) −37.9534 −1.42037
\(715\) −1.61729 −0.0604833
\(716\) −63.3685 −2.36819
\(717\) −0.511498 −0.0191022
\(718\) −3.47857 −0.129819
\(719\) 3.62884 0.135333 0.0676664 0.997708i \(-0.478445\pi\)
0.0676664 + 0.997708i \(0.478445\pi\)
\(720\) 131.853 4.91387
\(721\) −1.38707 −0.0516571
\(722\) 41.5703 1.54709
\(723\) 23.2174 0.863464
\(724\) 69.3965 2.57910
\(725\) −7.81419 −0.290212
\(726\) 194.198 7.20735
\(727\) −31.0204 −1.15048 −0.575242 0.817983i \(-0.695092\pi\)
−0.575242 + 0.817983i \(0.695092\pi\)
\(728\) −2.11682 −0.0784545
\(729\) −39.3805 −1.45854
\(730\) −76.0585 −2.81505
\(731\) 15.5528 0.575240
\(732\) −124.515 −4.60219
\(733\) 5.94675 0.219648 0.109824 0.993951i \(-0.464971\pi\)
0.109824 + 0.993951i \(0.464971\pi\)
\(734\) 25.5782 0.944109
\(735\) −16.9511 −0.625252
\(736\) −4.56010 −0.168087
\(737\) −56.0977 −2.06639
\(738\) −19.6785 −0.724377
\(739\) 14.0384 0.516412 0.258206 0.966090i \(-0.416869\pi\)
0.258206 + 0.966090i \(0.416869\pi\)
\(740\) 103.511 3.80516
\(741\) 0.491442 0.0180536
\(742\) −67.7443 −2.48697
\(743\) 36.6943 1.34618 0.673092 0.739559i \(-0.264966\pi\)
0.673092 + 0.739559i \(0.264966\pi\)
\(744\) 96.6613 3.54378
\(745\) −5.29259 −0.193906
\(746\) 59.7656 2.18817
\(747\) −27.5304 −1.00728
\(748\) 48.0467 1.75676
\(749\) 13.0097 0.475364
\(750\) −53.5766 −1.95634
\(751\) 25.9446 0.946730 0.473365 0.880866i \(-0.343039\pi\)
0.473365 + 0.880866i \(0.343039\pi\)
\(752\) −43.5979 −1.58985
\(753\) 58.6112 2.13591
\(754\) −0.838146 −0.0305235
\(755\) −3.33062 −0.121214
\(756\) 98.8711 3.59591
\(757\) 4.58366 0.166596 0.0832980 0.996525i \(-0.473455\pi\)
0.0832980 + 0.996525i \(0.473455\pi\)
\(758\) −23.8352 −0.865732
\(759\) −8.72391 −0.316658
\(760\) −33.5022 −1.21525
\(761\) 44.9563 1.62967 0.814833 0.579696i \(-0.196829\pi\)
0.814833 + 0.579696i \(0.196829\pi\)
\(762\) −26.6031 −0.963728
\(763\) −30.4431 −1.10212
\(764\) 13.2863 0.480681
\(765\) 24.3727 0.881196
\(766\) 83.0648 3.00125
\(767\) −1.03677 −0.0374356
\(768\) 58.4452 2.10896
\(769\) −34.5558 −1.24611 −0.623057 0.782176i \(-0.714110\pi\)
−0.623057 + 0.782176i \(0.714110\pi\)
\(770\) 129.531 4.66797
\(771\) 74.5965 2.68653
\(772\) 7.42207 0.267126
\(773\) 39.4155 1.41768 0.708838 0.705372i \(-0.249220\pi\)
0.708838 + 0.705372i \(0.249220\pi\)
\(774\) −130.224 −4.68079
\(775\) 11.1284 0.399743
\(776\) −45.1612 −1.62119
\(777\) 70.3534 2.52392
\(778\) 8.11720 0.291016
\(779\) 2.43735 0.0873270
\(780\) 3.66030 0.131060
\(781\) −35.0818 −1.25532
\(782\) −2.15182 −0.0769488
\(783\) 22.6475 0.809354
\(784\) 19.4621 0.695076
\(785\) −2.23474 −0.0797611
\(786\) 88.7374 3.16516
\(787\) −31.9260 −1.13804 −0.569019 0.822324i \(-0.692677\pi\)
−0.569019 + 0.822324i \(0.692677\pi\)
\(788\) 130.357 4.64377
\(789\) −1.40204 −0.0499140
\(790\) 50.6785 1.80306
\(791\) −9.64721 −0.343015
\(792\) −232.734 −8.26983
\(793\) −0.889507 −0.0315873
\(794\) 27.7539 0.984951
\(795\) 67.7672 2.40345
\(796\) −46.6903 −1.65489
\(797\) 4.12973 0.146283 0.0731413 0.997322i \(-0.476698\pi\)
0.0731413 + 0.997322i \(0.476698\pi\)
\(798\) −39.3601 −1.39333
\(799\) −8.05895 −0.285105
\(800\) −21.8170 −0.771349
\(801\) 74.5489 2.63406
\(802\) 0.863317 0.0304848
\(803\) 65.4422 2.30940
\(804\) 126.962 4.47760
\(805\) −4.08105 −0.143838
\(806\) 1.19362 0.0420436
\(807\) 76.5323 2.69407
\(808\) −79.8968 −2.81076
\(809\) −26.3280 −0.925642 −0.462821 0.886452i \(-0.653163\pi\)
−0.462821 + 0.886452i \(0.653163\pi\)
\(810\) −26.7724 −0.940686
\(811\) 38.6183 1.35607 0.678036 0.735029i \(-0.262831\pi\)
0.678036 + 0.735029i \(0.262831\pi\)
\(812\) 47.2239 1.65723
\(813\) −46.2791 −1.62308
\(814\) −126.602 −4.43740
\(815\) 46.6514 1.63413
\(816\) −43.5902 −1.52596
\(817\) 16.1292 0.564291
\(818\) −79.0478 −2.76384
\(819\) 1.59705 0.0558055
\(820\) 18.1536 0.633950
\(821\) 34.6345 1.20875 0.604375 0.796700i \(-0.293423\pi\)
0.604375 + 0.796700i \(0.293423\pi\)
\(822\) 147.718 5.15224
\(823\) −0.673535 −0.0234780 −0.0117390 0.999931i \(-0.503737\pi\)
−0.0117390 + 0.999931i \(0.503737\pi\)
\(824\) −3.26810 −0.113850
\(825\) −41.7381 −1.45314
\(826\) 83.0361 2.88920
\(827\) 31.7288 1.10332 0.551660 0.834069i \(-0.313995\pi\)
0.551660 + 0.834069i \(0.313995\pi\)
\(828\) 12.6749 0.440483
\(829\) 31.9368 1.10921 0.554605 0.832114i \(-0.312869\pi\)
0.554605 + 0.832114i \(0.312869\pi\)
\(830\) 36.1014 1.25310
\(831\) −66.1139 −2.29346
\(832\) −0.568792 −0.0197193
\(833\) 3.59752 0.124647
\(834\) −49.5016 −1.71410
\(835\) 32.9341 1.13973
\(836\) 49.8276 1.72332
\(837\) −32.2528 −1.11482
\(838\) −61.4639 −2.12324
\(839\) −28.2199 −0.974259 −0.487129 0.873330i \(-0.661956\pi\)
−0.487129 + 0.873330i \(0.661956\pi\)
\(840\) −169.596 −5.85161
\(841\) −18.1829 −0.626995
\(842\) 52.4541 1.80769
\(843\) 46.3274 1.59560
\(844\) −115.734 −3.98372
\(845\) −35.2800 −1.21367
\(846\) 67.4777 2.31993
\(847\) −78.1655 −2.68580
\(848\) −77.8055 −2.67185
\(849\) 34.0765 1.16950
\(850\) −10.2950 −0.353116
\(851\) 3.98878 0.136734
\(852\) 79.3979 2.72013
\(853\) −33.3188 −1.14081 −0.570407 0.821362i \(-0.693215\pi\)
−0.570407 + 0.821362i \(0.693215\pi\)
\(854\) 71.2417 2.43784
\(855\) 25.2760 0.864422
\(856\) 30.6524 1.04768
\(857\) −15.4129 −0.526495 −0.263248 0.964728i \(-0.584794\pi\)
−0.263248 + 0.964728i \(0.584794\pi\)
\(858\) −4.47681 −0.152836
\(859\) −44.1927 −1.50783 −0.753917 0.656970i \(-0.771838\pi\)
−0.753917 + 0.656970i \(0.771838\pi\)
\(860\) 120.132 4.09646
\(861\) 12.3384 0.420491
\(862\) −57.1889 −1.94786
\(863\) −41.6241 −1.41690 −0.708450 0.705761i \(-0.750605\pi\)
−0.708450 + 0.705761i \(0.750605\pi\)
\(864\) 63.2312 2.15117
\(865\) 33.8148 1.14974
\(866\) 0.985959 0.0335042
\(867\) 41.1512 1.39757
\(868\) −67.2527 −2.28271
\(869\) −43.6047 −1.47919
\(870\) −67.1508 −2.27662
\(871\) 0.906989 0.0307321
\(872\) −71.7276 −2.42900
\(873\) 34.0722 1.15317
\(874\) −2.23157 −0.0754841
\(875\) 21.5649 0.729025
\(876\) −148.110 −5.00419
\(877\) 52.2061 1.76287 0.881437 0.472302i \(-0.156577\pi\)
0.881437 + 0.472302i \(0.156577\pi\)
\(878\) −36.4204 −1.22913
\(879\) 24.7236 0.833906
\(880\) 148.769 5.01499
\(881\) 20.9233 0.704925 0.352463 0.935826i \(-0.385344\pi\)
0.352463 + 0.935826i \(0.385344\pi\)
\(882\) −30.1221 −1.01426
\(883\) 17.5012 0.588961 0.294480 0.955657i \(-0.404853\pi\)
0.294480 + 0.955657i \(0.404853\pi\)
\(884\) −0.776820 −0.0261273
\(885\) −83.0641 −2.79217
\(886\) −53.0693 −1.78290
\(887\) 31.3614 1.05301 0.526507 0.850171i \(-0.323501\pi\)
0.526507 + 0.850171i \(0.323501\pi\)
\(888\) 165.761 5.56258
\(889\) 10.7079 0.359130
\(890\) −97.7581 −3.27686
\(891\) 23.0355 0.771717
\(892\) 20.3019 0.679757
\(893\) −8.35766 −0.279678
\(894\) −14.6504 −0.489981
\(895\) −36.2689 −1.21233
\(896\) −10.0169 −0.334640
\(897\) 0.141048 0.00470946
\(898\) −34.9825 −1.16738
\(899\) −15.4049 −0.513784
\(900\) 60.6410 2.02137
\(901\) −14.3821 −0.479138
\(902\) −22.2031 −0.739283
\(903\) 81.6498 2.71713
\(904\) −22.7300 −0.755988
\(905\) 39.7190 1.32030
\(906\) −9.21946 −0.306296
\(907\) −6.95136 −0.230816 −0.115408 0.993318i \(-0.536818\pi\)
−0.115408 + 0.993318i \(0.536818\pi\)
\(908\) −38.7204 −1.28498
\(909\) 60.2788 1.99932
\(910\) −2.09426 −0.0694239
\(911\) −0.791263 −0.0262157 −0.0131079 0.999914i \(-0.504172\pi\)
−0.0131079 + 0.999914i \(0.504172\pi\)
\(912\) −45.2058 −1.49692
\(913\) −31.0623 −1.02801
\(914\) 78.5452 2.59805
\(915\) −71.2657 −2.35597
\(916\) 66.1506 2.18568
\(917\) −35.7172 −1.17949
\(918\) 29.8375 0.984785
\(919\) 30.8388 1.01728 0.508639 0.860980i \(-0.330149\pi\)
0.508639 + 0.860980i \(0.330149\pi\)
\(920\) −9.61545 −0.317012
\(921\) 68.5343 2.25828
\(922\) −17.4972 −0.576241
\(923\) 0.567202 0.0186697
\(924\) 252.238 8.29803
\(925\) 19.0837 0.627467
\(926\) −59.2388 −1.94671
\(927\) 2.46564 0.0809823
\(928\) 30.2012 0.991402
\(929\) −5.21718 −0.171170 −0.0855851 0.996331i \(-0.527276\pi\)
−0.0855851 + 0.996331i \(0.527276\pi\)
\(930\) 95.6311 3.13587
\(931\) 3.73086 0.122274
\(932\) 56.6871 1.85685
\(933\) 59.7670 1.95668
\(934\) −21.7567 −0.711900
\(935\) 27.4995 0.899328
\(936\) 3.76284 0.122992
\(937\) −21.7090 −0.709202 −0.354601 0.935018i \(-0.615383\pi\)
−0.354601 + 0.935018i \(0.615383\pi\)
\(938\) −72.6418 −2.37184
\(939\) −12.6171 −0.411744
\(940\) −62.2485 −2.03032
\(941\) 15.9003 0.518334 0.259167 0.965833i \(-0.416552\pi\)
0.259167 + 0.965833i \(0.416552\pi\)
\(942\) −6.18595 −0.201549
\(943\) 0.699541 0.0227802
\(944\) 95.3685 3.10398
\(945\) 56.5887 1.84083
\(946\) −146.930 −4.77711
\(947\) 7.70460 0.250366 0.125183 0.992134i \(-0.460048\pi\)
0.125183 + 0.992134i \(0.460048\pi\)
\(948\) 98.6873 3.20522
\(949\) −1.05807 −0.0343464
\(950\) −10.6766 −0.346395
\(951\) 17.5519 0.569160
\(952\) 35.9931 1.16654
\(953\) 56.5495 1.83182 0.915909 0.401385i \(-0.131471\pi\)
0.915909 + 0.401385i \(0.131471\pi\)
\(954\) 120.422 3.89880
\(955\) 7.60438 0.246072
\(956\) 0.838491 0.0271187
\(957\) 57.7778 1.86769
\(958\) −31.5704 −1.01999
\(959\) −59.4570 −1.91997
\(960\) −45.5706 −1.47078
\(961\) −9.06145 −0.292305
\(962\) 2.04690 0.0659948
\(963\) −23.1259 −0.745223
\(964\) −38.0599 −1.22583
\(965\) 4.24801 0.136748
\(966\) −11.2967 −0.363466
\(967\) 6.47417 0.208195 0.104098 0.994567i \(-0.466805\pi\)
0.104098 + 0.994567i \(0.466805\pi\)
\(968\) −184.167 −5.91936
\(969\) −8.35618 −0.268439
\(970\) −44.6799 −1.43458
\(971\) −6.52729 −0.209471 −0.104735 0.994500i \(-0.533400\pi\)
−0.104735 + 0.994500i \(0.533400\pi\)
\(972\) 45.8895 1.47191
\(973\) 19.9246 0.638754
\(974\) −19.5449 −0.626260
\(975\) 0.674823 0.0216116
\(976\) 81.8224 2.61907
\(977\) 30.8621 0.987365 0.493683 0.869642i \(-0.335650\pi\)
0.493683 + 0.869642i \(0.335650\pi\)
\(978\) 129.135 4.12929
\(979\) 84.1129 2.68826
\(980\) 27.7877 0.887647
\(981\) 54.1155 1.72777
\(982\) 102.039 3.25621
\(983\) −50.6469 −1.61538 −0.807692 0.589604i \(-0.799284\pi\)
−0.807692 + 0.589604i \(0.799284\pi\)
\(984\) 29.0707 0.926741
\(985\) 74.6095 2.37726
\(986\) 14.2513 0.453855
\(987\) −42.3083 −1.34669
\(988\) −0.805613 −0.0256300
\(989\) 4.62924 0.147201
\(990\) −230.253 −7.31793
\(991\) 1.87369 0.0595198 0.0297599 0.999557i \(-0.490526\pi\)
0.0297599 + 0.999557i \(0.490526\pi\)
\(992\) −43.0102 −1.36558
\(993\) 59.5031 1.88827
\(994\) −45.4279 −1.44089
\(995\) −26.7231 −0.847179
\(996\) 70.3010 2.22757
\(997\) −16.9000 −0.535229 −0.267614 0.963526i \(-0.586235\pi\)
−0.267614 + 0.963526i \(0.586235\pi\)
\(998\) 14.1721 0.448610
\(999\) −55.3092 −1.74991
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 \(a_p\))