Properties

Label 6027.2.a.bm.1.10
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.404293\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.404293 q^{2} +1.00000 q^{3} -1.83655 q^{4} -3.62653 q^{5} +0.404293 q^{6} -1.55109 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.404293 q^{2} +1.00000 q^{3} -1.83655 q^{4} -3.62653 q^{5} +0.404293 q^{6} -1.55109 q^{8} +1.00000 q^{9} -1.46618 q^{10} -5.64899 q^{11} -1.83655 q^{12} +4.03783 q^{13} -3.62653 q^{15} +3.04600 q^{16} +2.00918 q^{17} +0.404293 q^{18} -1.50889 q^{19} +6.66029 q^{20} -2.28385 q^{22} +7.05059 q^{23} -1.55109 q^{24} +8.15172 q^{25} +1.63246 q^{26} +1.00000 q^{27} +5.14414 q^{29} -1.46618 q^{30} -3.25825 q^{31} +4.33365 q^{32} -5.64899 q^{33} +0.812296 q^{34} -1.83655 q^{36} +0.612983 q^{37} -0.610033 q^{38} +4.03783 q^{39} +5.62507 q^{40} +1.00000 q^{41} +1.57300 q^{43} +10.3746 q^{44} -3.62653 q^{45} +2.85050 q^{46} +0.256386 q^{47} +3.04600 q^{48} +3.29568 q^{50} +2.00918 q^{51} -7.41566 q^{52} -7.87725 q^{53} +0.404293 q^{54} +20.4862 q^{55} -1.50889 q^{57} +2.07974 q^{58} -4.32499 q^{59} +6.66029 q^{60} +2.81546 q^{61} -1.31729 q^{62} -4.33993 q^{64} -14.6433 q^{65} -2.28385 q^{66} -13.3202 q^{67} -3.68995 q^{68} +7.05059 q^{69} +2.92409 q^{71} -1.55109 q^{72} +5.90098 q^{73} +0.247825 q^{74} +8.15172 q^{75} +2.77114 q^{76} +1.63246 q^{78} -1.04645 q^{79} -11.0464 q^{80} +1.00000 q^{81} +0.404293 q^{82} -10.3790 q^{83} -7.28634 q^{85} +0.635955 q^{86} +5.14414 q^{87} +8.76208 q^{88} +9.74008 q^{89} -1.46618 q^{90} -12.9487 q^{92} -3.25825 q^{93} +0.103655 q^{94} +5.47203 q^{95} +4.33365 q^{96} -8.22998 q^{97} -5.64899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.404293 0.285878 0.142939 0.989731i \(-0.454345\pi\)
0.142939 + 0.989731i \(0.454345\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.83655 −0.918274
\(5\) −3.62653 −1.62183 −0.810917 0.585162i \(-0.801031\pi\)
−0.810917 + 0.585162i \(0.801031\pi\)
\(6\) 0.404293 0.165052
\(7\) 0 0
\(8\) −1.55109 −0.548393
\(9\) 1.00000 0.333333
\(10\) −1.46618 −0.463647
\(11\) −5.64899 −1.70323 −0.851617 0.524165i \(-0.824377\pi\)
−0.851617 + 0.524165i \(0.824377\pi\)
\(12\) −1.83655 −0.530166
\(13\) 4.03783 1.11989 0.559946 0.828529i \(-0.310822\pi\)
0.559946 + 0.828529i \(0.310822\pi\)
\(14\) 0 0
\(15\) −3.62653 −0.936366
\(16\) 3.04600 0.761500
\(17\) 2.00918 0.487297 0.243649 0.969864i \(-0.421656\pi\)
0.243649 + 0.969864i \(0.421656\pi\)
\(18\) 0.404293 0.0952928
\(19\) −1.50889 −0.346163 −0.173081 0.984908i \(-0.555372\pi\)
−0.173081 + 0.984908i \(0.555372\pi\)
\(20\) 6.66029 1.48929
\(21\) 0 0
\(22\) −2.28385 −0.486917
\(23\) 7.05059 1.47015 0.735075 0.677986i \(-0.237147\pi\)
0.735075 + 0.677986i \(0.237147\pi\)
\(24\) −1.55109 −0.316615
\(25\) 8.15172 1.63034
\(26\) 1.63246 0.320153
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 5.14414 0.955242 0.477621 0.878566i \(-0.341499\pi\)
0.477621 + 0.878566i \(0.341499\pi\)
\(30\) −1.46618 −0.267687
\(31\) −3.25825 −0.585199 −0.292600 0.956235i \(-0.594520\pi\)
−0.292600 + 0.956235i \(0.594520\pi\)
\(32\) 4.33365 0.766089
\(33\) −5.64899 −0.983362
\(34\) 0.812296 0.139308
\(35\) 0 0
\(36\) −1.83655 −0.306091
\(37\) 0.612983 0.100774 0.0503869 0.998730i \(-0.483955\pi\)
0.0503869 + 0.998730i \(0.483955\pi\)
\(38\) −0.610033 −0.0989604
\(39\) 4.03783 0.646570
\(40\) 5.62507 0.889402
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 1.57300 0.239881 0.119940 0.992781i \(-0.461730\pi\)
0.119940 + 0.992781i \(0.461730\pi\)
\(44\) 10.3746 1.56403
\(45\) −3.62653 −0.540611
\(46\) 2.85050 0.420284
\(47\) 0.256386 0.0373977 0.0186989 0.999825i \(-0.494048\pi\)
0.0186989 + 0.999825i \(0.494048\pi\)
\(48\) 3.04600 0.439652
\(49\) 0 0
\(50\) 3.29568 0.466080
\(51\) 2.00918 0.281341
\(52\) −7.41566 −1.02837
\(53\) −7.87725 −1.08202 −0.541012 0.841015i \(-0.681959\pi\)
−0.541012 + 0.841015i \(0.681959\pi\)
\(54\) 0.404293 0.0550173
\(55\) 20.4862 2.76236
\(56\) 0 0
\(57\) −1.50889 −0.199857
\(58\) 2.07974 0.273083
\(59\) −4.32499 −0.563066 −0.281533 0.959552i \(-0.590843\pi\)
−0.281533 + 0.959552i \(0.590843\pi\)
\(60\) 6.66029 0.859840
\(61\) 2.81546 0.360483 0.180242 0.983622i \(-0.442312\pi\)
0.180242 + 0.983622i \(0.442312\pi\)
\(62\) −1.31729 −0.167296
\(63\) 0 0
\(64\) −4.33993 −0.542492
\(65\) −14.6433 −1.81628
\(66\) −2.28385 −0.281122
\(67\) −13.3202 −1.62732 −0.813659 0.581342i \(-0.802528\pi\)
−0.813659 + 0.581342i \(0.802528\pi\)
\(68\) −3.68995 −0.447472
\(69\) 7.05059 0.848791
\(70\) 0 0
\(71\) 2.92409 0.347026 0.173513 0.984832i \(-0.444488\pi\)
0.173513 + 0.984832i \(0.444488\pi\)
\(72\) −1.55109 −0.182798
\(73\) 5.90098 0.690657 0.345329 0.938482i \(-0.387767\pi\)
0.345329 + 0.938482i \(0.387767\pi\)
\(74\) 0.247825 0.0288090
\(75\) 8.15172 0.941280
\(76\) 2.77114 0.317872
\(77\) 0 0
\(78\) 1.63246 0.184840
\(79\) −1.04645 −0.117735 −0.0588674 0.998266i \(-0.518749\pi\)
−0.0588674 + 0.998266i \(0.518749\pi\)
\(80\) −11.0464 −1.23503
\(81\) 1.00000 0.111111
\(82\) 0.404293 0.0446467
\(83\) −10.3790 −1.13925 −0.569623 0.821906i \(-0.692911\pi\)
−0.569623 + 0.821906i \(0.692911\pi\)
\(84\) 0 0
\(85\) −7.28634 −0.790315
\(86\) 0.635955 0.0685767
\(87\) 5.14414 0.551509
\(88\) 8.76208 0.934041
\(89\) 9.74008 1.03245 0.516223 0.856454i \(-0.327338\pi\)
0.516223 + 0.856454i \(0.327338\pi\)
\(90\) −1.46618 −0.154549
\(91\) 0 0
\(92\) −12.9487 −1.35000
\(93\) −3.25825 −0.337865
\(94\) 0.103655 0.0106912
\(95\) 5.47203 0.561418
\(96\) 4.33365 0.442302
\(97\) −8.22998 −0.835628 −0.417814 0.908533i \(-0.637204\pi\)
−0.417814 + 0.908533i \(0.637204\pi\)
\(98\) 0 0
\(99\) −5.64899 −0.567744
\(100\) −14.9710 −1.49710
\(101\) 13.1011 1.30361 0.651806 0.758386i \(-0.274012\pi\)
0.651806 + 0.758386i \(0.274012\pi\)
\(102\) 0.812296 0.0804293
\(103\) 12.0801 1.19029 0.595143 0.803620i \(-0.297095\pi\)
0.595143 + 0.803620i \(0.297095\pi\)
\(104\) −6.26303 −0.614140
\(105\) 0 0
\(106\) −3.18472 −0.309327
\(107\) −10.0504 −0.971613 −0.485806 0.874066i \(-0.661474\pi\)
−0.485806 + 0.874066i \(0.661474\pi\)
\(108\) −1.83655 −0.176722
\(109\) −11.8153 −1.13170 −0.565849 0.824509i \(-0.691451\pi\)
−0.565849 + 0.824509i \(0.691451\pi\)
\(110\) 8.28243 0.789699
\(111\) 0.612983 0.0581818
\(112\) 0 0
\(113\) −18.5214 −1.74235 −0.871173 0.490976i \(-0.836640\pi\)
−0.871173 + 0.490976i \(0.836640\pi\)
\(114\) −0.610033 −0.0571348
\(115\) −25.5692 −2.38434
\(116\) −9.44745 −0.877174
\(117\) 4.03783 0.373297
\(118\) −1.74856 −0.160968
\(119\) 0 0
\(120\) 5.62507 0.513496
\(121\) 20.9110 1.90100
\(122\) 1.13827 0.103054
\(123\) 1.00000 0.0901670
\(124\) 5.98393 0.537373
\(125\) −11.4298 −1.02231
\(126\) 0 0
\(127\) 8.16826 0.724816 0.362408 0.932020i \(-0.381955\pi\)
0.362408 + 0.932020i \(0.381955\pi\)
\(128\) −10.4219 −0.921176
\(129\) 1.57300 0.138495
\(130\) −5.92018 −0.519234
\(131\) −13.2261 −1.15557 −0.577786 0.816188i \(-0.696083\pi\)
−0.577786 + 0.816188i \(0.696083\pi\)
\(132\) 10.3746 0.902996
\(133\) 0 0
\(134\) −5.38525 −0.465215
\(135\) −3.62653 −0.312122
\(136\) −3.11641 −0.267230
\(137\) −17.1227 −1.46289 −0.731447 0.681898i \(-0.761155\pi\)
−0.731447 + 0.681898i \(0.761155\pi\)
\(138\) 2.85050 0.242651
\(139\) 18.7120 1.58713 0.793565 0.608485i \(-0.208223\pi\)
0.793565 + 0.608485i \(0.208223\pi\)
\(140\) 0 0
\(141\) 0.256386 0.0215916
\(142\) 1.18219 0.0992071
\(143\) −22.8096 −1.90744
\(144\) 3.04600 0.253833
\(145\) −18.6554 −1.54924
\(146\) 2.38572 0.197444
\(147\) 0 0
\(148\) −1.12577 −0.0925379
\(149\) −14.4114 −1.18063 −0.590313 0.807175i \(-0.700996\pi\)
−0.590313 + 0.807175i \(0.700996\pi\)
\(150\) 3.29568 0.269091
\(151\) −7.70354 −0.626905 −0.313452 0.949604i \(-0.601486\pi\)
−0.313452 + 0.949604i \(0.601486\pi\)
\(152\) 2.34042 0.189833
\(153\) 2.00918 0.162432
\(154\) 0 0
\(155\) 11.8161 0.949096
\(156\) −7.41566 −0.593728
\(157\) 0.429607 0.0342864 0.0171432 0.999853i \(-0.494543\pi\)
0.0171432 + 0.999853i \(0.494543\pi\)
\(158\) −0.423072 −0.0336578
\(159\) −7.87725 −0.624707
\(160\) −15.7161 −1.24247
\(161\) 0 0
\(162\) 0.404293 0.0317643
\(163\) 20.8708 1.63472 0.817362 0.576125i \(-0.195436\pi\)
0.817362 + 0.576125i \(0.195436\pi\)
\(164\) −1.83655 −0.143410
\(165\) 20.4862 1.59485
\(166\) −4.19617 −0.325686
\(167\) −15.9352 −1.23310 −0.616552 0.787314i \(-0.711471\pi\)
−0.616552 + 0.787314i \(0.711471\pi\)
\(168\) 0 0
\(169\) 3.30404 0.254157
\(170\) −2.94582 −0.225934
\(171\) −1.50889 −0.115388
\(172\) −2.88890 −0.220276
\(173\) −5.12594 −0.389718 −0.194859 0.980831i \(-0.562425\pi\)
−0.194859 + 0.980831i \(0.562425\pi\)
\(174\) 2.07974 0.157665
\(175\) 0 0
\(176\) −17.2068 −1.29701
\(177\) −4.32499 −0.325086
\(178\) 3.93785 0.295154
\(179\) −5.22886 −0.390823 −0.195412 0.980721i \(-0.562604\pi\)
−0.195412 + 0.980721i \(0.562604\pi\)
\(180\) 6.66029 0.496429
\(181\) 1.60946 0.119630 0.0598150 0.998209i \(-0.480949\pi\)
0.0598150 + 0.998209i \(0.480949\pi\)
\(182\) 0 0
\(183\) 2.81546 0.208125
\(184\) −10.9361 −0.806219
\(185\) −2.22300 −0.163438
\(186\) −1.31729 −0.0965883
\(187\) −11.3498 −0.829981
\(188\) −0.470865 −0.0343413
\(189\) 0 0
\(190\) 2.21230 0.160497
\(191\) −25.0344 −1.81142 −0.905712 0.423893i \(-0.860663\pi\)
−0.905712 + 0.423893i \(0.860663\pi\)
\(192\) −4.33993 −0.313208
\(193\) −2.83996 −0.204425 −0.102212 0.994763i \(-0.532592\pi\)
−0.102212 + 0.994763i \(0.532592\pi\)
\(194\) −3.32732 −0.238888
\(195\) −14.6433 −1.04863
\(196\) 0 0
\(197\) −26.8159 −1.91056 −0.955278 0.295709i \(-0.904444\pi\)
−0.955278 + 0.295709i \(0.904444\pi\)
\(198\) −2.28385 −0.162306
\(199\) −7.39204 −0.524008 −0.262004 0.965067i \(-0.584383\pi\)
−0.262004 + 0.965067i \(0.584383\pi\)
\(200\) −12.6440 −0.894069
\(201\) −13.3202 −0.939533
\(202\) 5.29670 0.372674
\(203\) 0 0
\(204\) −3.68995 −0.258348
\(205\) −3.62653 −0.253288
\(206\) 4.88389 0.340277
\(207\) 7.05059 0.490050
\(208\) 12.2992 0.852797
\(209\) 8.52369 0.589596
\(210\) 0 0
\(211\) 22.3498 1.53862 0.769311 0.638875i \(-0.220600\pi\)
0.769311 + 0.638875i \(0.220600\pi\)
\(212\) 14.4669 0.993594
\(213\) 2.92409 0.200355
\(214\) −4.06332 −0.277763
\(215\) −5.70455 −0.389047
\(216\) −1.55109 −0.105538
\(217\) 0 0
\(218\) −4.77683 −0.323528
\(219\) 5.90098 0.398751
\(220\) −37.6239 −2.53660
\(221\) 8.11271 0.545720
\(222\) 0.247825 0.0166329
\(223\) 28.5254 1.91020 0.955102 0.296276i \(-0.0957449\pi\)
0.955102 + 0.296276i \(0.0957449\pi\)
\(224\) 0 0
\(225\) 8.15172 0.543448
\(226\) −7.48807 −0.498099
\(227\) 23.9051 1.58664 0.793319 0.608807i \(-0.208351\pi\)
0.793319 + 0.608807i \(0.208351\pi\)
\(228\) 2.77114 0.183524
\(229\) −5.21232 −0.344440 −0.172220 0.985059i \(-0.555094\pi\)
−0.172220 + 0.985059i \(0.555094\pi\)
\(230\) −10.3374 −0.681630
\(231\) 0 0
\(232\) −7.97902 −0.523848
\(233\) −22.9871 −1.50594 −0.752969 0.658056i \(-0.771379\pi\)
−0.752969 + 0.658056i \(0.771379\pi\)
\(234\) 1.63246 0.106718
\(235\) −0.929791 −0.0606529
\(236\) 7.94305 0.517049
\(237\) −1.04645 −0.0679742
\(238\) 0 0
\(239\) 30.5972 1.97917 0.989584 0.143959i \(-0.0459832\pi\)
0.989584 + 0.143959i \(0.0459832\pi\)
\(240\) −11.0464 −0.713043
\(241\) −14.3324 −0.923232 −0.461616 0.887080i \(-0.652730\pi\)
−0.461616 + 0.887080i \(0.652730\pi\)
\(242\) 8.45419 0.543456
\(243\) 1.00000 0.0641500
\(244\) −5.17073 −0.331022
\(245\) 0 0
\(246\) 0.404293 0.0257768
\(247\) −6.09263 −0.387665
\(248\) 5.05384 0.320919
\(249\) −10.3790 −0.657744
\(250\) −4.62099 −0.292257
\(251\) −13.7477 −0.867746 −0.433873 0.900974i \(-0.642853\pi\)
−0.433873 + 0.900974i \(0.642853\pi\)
\(252\) 0 0
\(253\) −39.8287 −2.50401
\(254\) 3.30237 0.207209
\(255\) −7.28634 −0.456289
\(256\) 4.46636 0.279148
\(257\) 12.4136 0.774340 0.387170 0.922008i \(-0.373453\pi\)
0.387170 + 0.922008i \(0.373453\pi\)
\(258\) 0.635955 0.0395928
\(259\) 0 0
\(260\) 26.8931 1.66784
\(261\) 5.14414 0.318414
\(262\) −5.34723 −0.330353
\(263\) 21.1795 1.30599 0.652993 0.757364i \(-0.273513\pi\)
0.652993 + 0.757364i \(0.273513\pi\)
\(264\) 8.76208 0.539269
\(265\) 28.5671 1.75486
\(266\) 0 0
\(267\) 9.74008 0.596083
\(268\) 24.4631 1.49432
\(269\) 5.56435 0.339264 0.169632 0.985507i \(-0.445742\pi\)
0.169632 + 0.985507i \(0.445742\pi\)
\(270\) −1.46618 −0.0892289
\(271\) 11.2067 0.680762 0.340381 0.940288i \(-0.389444\pi\)
0.340381 + 0.940288i \(0.389444\pi\)
\(272\) 6.11996 0.371077
\(273\) 0 0
\(274\) −6.92260 −0.418210
\(275\) −46.0489 −2.77686
\(276\) −12.9487 −0.779422
\(277\) 9.16881 0.550900 0.275450 0.961315i \(-0.411173\pi\)
0.275450 + 0.961315i \(0.411173\pi\)
\(278\) 7.56513 0.453726
\(279\) −3.25825 −0.195066
\(280\) 0 0
\(281\) 21.2196 1.26585 0.632927 0.774212i \(-0.281853\pi\)
0.632927 + 0.774212i \(0.281853\pi\)
\(282\) 0.103655 0.00617256
\(283\) 4.61530 0.274351 0.137176 0.990547i \(-0.456198\pi\)
0.137176 + 0.990547i \(0.456198\pi\)
\(284\) −5.37023 −0.318665
\(285\) 5.47203 0.324135
\(286\) −9.22177 −0.545295
\(287\) 0 0
\(288\) 4.33365 0.255363
\(289\) −12.9632 −0.762541
\(290\) −7.54223 −0.442895
\(291\) −8.22998 −0.482450
\(292\) −10.8374 −0.634212
\(293\) −4.86448 −0.284186 −0.142093 0.989853i \(-0.545383\pi\)
−0.142093 + 0.989853i \(0.545383\pi\)
\(294\) 0 0
\(295\) 15.6847 0.913199
\(296\) −0.950791 −0.0552636
\(297\) −5.64899 −0.327787
\(298\) −5.82642 −0.337515
\(299\) 28.4691 1.64641
\(300\) −14.9710 −0.864352
\(301\) 0 0
\(302\) −3.11449 −0.179219
\(303\) 13.1011 0.752641
\(304\) −4.59607 −0.263603
\(305\) −10.2104 −0.584644
\(306\) 0.812296 0.0464359
\(307\) −5.00629 −0.285724 −0.142862 0.989743i \(-0.545631\pi\)
−0.142862 + 0.989743i \(0.545631\pi\)
\(308\) 0 0
\(309\) 12.0801 0.687212
\(310\) 4.77719 0.271326
\(311\) −13.3816 −0.758804 −0.379402 0.925232i \(-0.623870\pi\)
−0.379402 + 0.925232i \(0.623870\pi\)
\(312\) −6.26303 −0.354574
\(313\) −14.0907 −0.796451 −0.398225 0.917288i \(-0.630374\pi\)
−0.398225 + 0.917288i \(0.630374\pi\)
\(314\) 0.173687 0.00980173
\(315\) 0 0
\(316\) 1.92185 0.108113
\(317\) −0.790011 −0.0443714 −0.0221857 0.999754i \(-0.507063\pi\)
−0.0221857 + 0.999754i \(0.507063\pi\)
\(318\) −3.18472 −0.178590
\(319\) −29.0592 −1.62700
\(320\) 15.7389 0.879831
\(321\) −10.0504 −0.560961
\(322\) 0 0
\(323\) −3.03162 −0.168684
\(324\) −1.83655 −0.102030
\(325\) 32.9152 1.82581
\(326\) 8.43790 0.467332
\(327\) −11.8153 −0.653386
\(328\) −1.55109 −0.0856446
\(329\) 0 0
\(330\) 8.28243 0.455933
\(331\) 4.79253 0.263421 0.131711 0.991288i \(-0.457953\pi\)
0.131711 + 0.991288i \(0.457953\pi\)
\(332\) 19.0616 1.04614
\(333\) 0.612983 0.0335913
\(334\) −6.44250 −0.352518
\(335\) 48.3060 2.63924
\(336\) 0 0
\(337\) −4.66846 −0.254307 −0.127153 0.991883i \(-0.540584\pi\)
−0.127153 + 0.991883i \(0.540584\pi\)
\(338\) 1.33580 0.0726580
\(339\) −18.5214 −1.00594
\(340\) 13.3817 0.725725
\(341\) 18.4058 0.996731
\(342\) −0.610033 −0.0329868
\(343\) 0 0
\(344\) −2.43987 −0.131549
\(345\) −25.5692 −1.37660
\(346\) −2.07238 −0.111412
\(347\) −24.1667 −1.29734 −0.648668 0.761072i \(-0.724673\pi\)
−0.648668 + 0.761072i \(0.724673\pi\)
\(348\) −9.44745 −0.506437
\(349\) −23.7131 −1.26933 −0.634665 0.772787i \(-0.718862\pi\)
−0.634665 + 0.772787i \(0.718862\pi\)
\(350\) 0 0
\(351\) 4.03783 0.215523
\(352\) −24.4808 −1.30483
\(353\) −8.89299 −0.473326 −0.236663 0.971592i \(-0.576054\pi\)
−0.236663 + 0.971592i \(0.576054\pi\)
\(354\) −1.74856 −0.0929351
\(355\) −10.6043 −0.562818
\(356\) −17.8881 −0.948068
\(357\) 0 0
\(358\) −2.11399 −0.111728
\(359\) −21.1936 −1.11856 −0.559278 0.828980i \(-0.688922\pi\)
−0.559278 + 0.828980i \(0.688922\pi\)
\(360\) 5.62507 0.296467
\(361\) −16.7233 −0.880171
\(362\) 0.650692 0.0341996
\(363\) 20.9110 1.09754
\(364\) 0 0
\(365\) −21.4001 −1.12013
\(366\) 1.13827 0.0594984
\(367\) 21.4776 1.12112 0.560560 0.828114i \(-0.310586\pi\)
0.560560 + 0.828114i \(0.310586\pi\)
\(368\) 21.4761 1.11952
\(369\) 1.00000 0.0520579
\(370\) −0.898743 −0.0467234
\(371\) 0 0
\(372\) 5.98393 0.310253
\(373\) −37.7164 −1.95288 −0.976442 0.215781i \(-0.930770\pi\)
−0.976442 + 0.215781i \(0.930770\pi\)
\(374\) −4.58865 −0.237273
\(375\) −11.4298 −0.590233
\(376\) −0.397677 −0.0205086
\(377\) 20.7711 1.06977
\(378\) 0 0
\(379\) −15.8102 −0.812115 −0.406057 0.913848i \(-0.633097\pi\)
−0.406057 + 0.913848i \(0.633097\pi\)
\(380\) −10.0496 −0.515536
\(381\) 8.16826 0.418472
\(382\) −10.1212 −0.517847
\(383\) 17.8178 0.910449 0.455225 0.890377i \(-0.349559\pi\)
0.455225 + 0.890377i \(0.349559\pi\)
\(384\) −10.4219 −0.531841
\(385\) 0 0
\(386\) −1.14818 −0.0584406
\(387\) 1.57300 0.0799603
\(388\) 15.1147 0.767335
\(389\) −35.3148 −1.79053 −0.895265 0.445534i \(-0.853014\pi\)
−0.895265 + 0.445534i \(0.853014\pi\)
\(390\) −5.92018 −0.299780
\(391\) 14.1659 0.716400
\(392\) 0 0
\(393\) −13.2261 −0.667170
\(394\) −10.8415 −0.546186
\(395\) 3.79498 0.190946
\(396\) 10.3746 0.521345
\(397\) −5.29392 −0.265694 −0.132847 0.991137i \(-0.542412\pi\)
−0.132847 + 0.991137i \(0.542412\pi\)
\(398\) −2.98855 −0.149802
\(399\) 0 0
\(400\) 24.8301 1.24151
\(401\) −29.3969 −1.46801 −0.734005 0.679144i \(-0.762351\pi\)
−0.734005 + 0.679144i \(0.762351\pi\)
\(402\) −5.38525 −0.268592
\(403\) −13.1563 −0.655360
\(404\) −24.0609 −1.19707
\(405\) −3.62653 −0.180204
\(406\) 0 0
\(407\) −3.46273 −0.171641
\(408\) −3.11641 −0.154285
\(409\) −21.6968 −1.07284 −0.536419 0.843952i \(-0.680223\pi\)
−0.536419 + 0.843952i \(0.680223\pi\)
\(410\) −1.46618 −0.0724095
\(411\) −17.1227 −0.844602
\(412\) −22.1856 −1.09301
\(413\) 0 0
\(414\) 2.85050 0.140095
\(415\) 37.6398 1.84767
\(416\) 17.4985 0.857937
\(417\) 18.7120 0.916330
\(418\) 3.44607 0.168553
\(419\) 1.07735 0.0526321 0.0263161 0.999654i \(-0.491622\pi\)
0.0263161 + 0.999654i \(0.491622\pi\)
\(420\) 0 0
\(421\) −18.8444 −0.918418 −0.459209 0.888328i \(-0.651867\pi\)
−0.459209 + 0.888328i \(0.651867\pi\)
\(422\) 9.03586 0.439859
\(423\) 0.256386 0.0124659
\(424\) 12.2183 0.593374
\(425\) 16.3783 0.794462
\(426\) 1.18219 0.0572773
\(427\) 0 0
\(428\) 18.4581 0.892206
\(429\) −22.8096 −1.10126
\(430\) −2.30631 −0.111220
\(431\) 21.2760 1.02483 0.512414 0.858739i \(-0.328751\pi\)
0.512414 + 0.858739i \(0.328751\pi\)
\(432\) 3.04600 0.146551
\(433\) 36.1242 1.73602 0.868010 0.496546i \(-0.165399\pi\)
0.868010 + 0.496546i \(0.165399\pi\)
\(434\) 0 0
\(435\) −18.6554 −0.894457
\(436\) 21.6993 1.03921
\(437\) −10.6385 −0.508911
\(438\) 2.38572 0.113994
\(439\) 24.0930 1.14989 0.574947 0.818191i \(-0.305023\pi\)
0.574947 + 0.818191i \(0.305023\pi\)
\(440\) −31.7759 −1.51486
\(441\) 0 0
\(442\) 3.27991 0.156010
\(443\) 18.9748 0.901519 0.450759 0.892645i \(-0.351153\pi\)
0.450759 + 0.892645i \(0.351153\pi\)
\(444\) −1.12577 −0.0534268
\(445\) −35.3227 −1.67446
\(446\) 11.5326 0.546086
\(447\) −14.4114 −0.681635
\(448\) 0 0
\(449\) 14.3690 0.678115 0.339058 0.940766i \(-0.389892\pi\)
0.339058 + 0.940766i \(0.389892\pi\)
\(450\) 3.29568 0.155360
\(451\) −5.64899 −0.266000
\(452\) 34.0154 1.59995
\(453\) −7.70354 −0.361944
\(454\) 9.66466 0.453585
\(455\) 0 0
\(456\) 2.34042 0.109600
\(457\) 8.51958 0.398529 0.199265 0.979946i \(-0.436145\pi\)
0.199265 + 0.979946i \(0.436145\pi\)
\(458\) −2.10730 −0.0984679
\(459\) 2.00918 0.0937804
\(460\) 46.9590 2.18947
\(461\) −32.8708 −1.53095 −0.765473 0.643468i \(-0.777495\pi\)
−0.765473 + 0.643468i \(0.777495\pi\)
\(462\) 0 0
\(463\) 32.4709 1.50905 0.754526 0.656270i \(-0.227867\pi\)
0.754526 + 0.656270i \(0.227867\pi\)
\(464\) 15.6690 0.727417
\(465\) 11.8161 0.547961
\(466\) −9.29354 −0.430515
\(467\) −28.5450 −1.32091 −0.660453 0.750867i \(-0.729636\pi\)
−0.660453 + 0.750867i \(0.729636\pi\)
\(468\) −7.41566 −0.342789
\(469\) 0 0
\(470\) −0.375908 −0.0173393
\(471\) 0.429607 0.0197952
\(472\) 6.70845 0.308781
\(473\) −8.88588 −0.408573
\(474\) −0.423072 −0.0194323
\(475\) −12.3000 −0.564364
\(476\) 0 0
\(477\) −7.87725 −0.360675
\(478\) 12.3702 0.565801
\(479\) −22.9726 −1.04964 −0.524822 0.851212i \(-0.675868\pi\)
−0.524822 + 0.851212i \(0.675868\pi\)
\(480\) −15.7161 −0.717340
\(481\) 2.47512 0.112856
\(482\) −5.79450 −0.263932
\(483\) 0 0
\(484\) −38.4041 −1.74564
\(485\) 29.8463 1.35525
\(486\) 0.404293 0.0183391
\(487\) 10.4709 0.474483 0.237242 0.971451i \(-0.423757\pi\)
0.237242 + 0.971451i \(0.423757\pi\)
\(488\) −4.36703 −0.197686
\(489\) 20.8708 0.943808
\(490\) 0 0
\(491\) −24.5729 −1.10896 −0.554479 0.832198i \(-0.687082\pi\)
−0.554479 + 0.832198i \(0.687082\pi\)
\(492\) −1.83655 −0.0827979
\(493\) 10.3355 0.465487
\(494\) −2.46321 −0.110825
\(495\) 20.4862 0.920787
\(496\) −9.92464 −0.445629
\(497\) 0 0
\(498\) −4.19617 −0.188035
\(499\) −24.2119 −1.08387 −0.541937 0.840419i \(-0.682309\pi\)
−0.541937 + 0.840419i \(0.682309\pi\)
\(500\) 20.9914 0.938763
\(501\) −15.9352 −0.711933
\(502\) −5.55809 −0.248070
\(503\) 2.90630 0.129586 0.0647928 0.997899i \(-0.479361\pi\)
0.0647928 + 0.997899i \(0.479361\pi\)
\(504\) 0 0
\(505\) −47.5117 −2.11424
\(506\) −16.1025 −0.715841
\(507\) 3.30404 0.146738
\(508\) −15.0014 −0.665579
\(509\) −2.21101 −0.0980015 −0.0490008 0.998799i \(-0.515604\pi\)
−0.0490008 + 0.998799i \(0.515604\pi\)
\(510\) −2.94582 −0.130443
\(511\) 0 0
\(512\) 22.6495 1.00098
\(513\) −1.50889 −0.0666190
\(514\) 5.01874 0.221367
\(515\) −43.8088 −1.93045
\(516\) −2.88890 −0.127177
\(517\) −1.44832 −0.0636970
\(518\) 0 0
\(519\) −5.12594 −0.225004
\(520\) 22.7131 0.996034
\(521\) 7.75309 0.339669 0.169835 0.985473i \(-0.445677\pi\)
0.169835 + 0.985473i \(0.445677\pi\)
\(522\) 2.07974 0.0910277
\(523\) −17.8791 −0.781798 −0.390899 0.920434i \(-0.627836\pi\)
−0.390899 + 0.920434i \(0.627836\pi\)
\(524\) 24.2904 1.06113
\(525\) 0 0
\(526\) 8.56274 0.373353
\(527\) −6.54641 −0.285166
\(528\) −17.2068 −0.748830
\(529\) 26.7108 1.16134
\(530\) 11.5495 0.501677
\(531\) −4.32499 −0.187689
\(532\) 0 0
\(533\) 4.03783 0.174898
\(534\) 3.93785 0.170407
\(535\) 36.4482 1.57579
\(536\) 20.6608 0.892410
\(537\) −5.22886 −0.225642
\(538\) 2.24963 0.0969883
\(539\) 0 0
\(540\) 6.66029 0.286613
\(541\) −8.00513 −0.344167 −0.172084 0.985082i \(-0.555050\pi\)
−0.172084 + 0.985082i \(0.555050\pi\)
\(542\) 4.53081 0.194615
\(543\) 1.60946 0.0690684
\(544\) 8.70708 0.373313
\(545\) 42.8484 1.83543
\(546\) 0 0
\(547\) 17.5624 0.750915 0.375458 0.926840i \(-0.377486\pi\)
0.375458 + 0.926840i \(0.377486\pi\)
\(548\) 31.4467 1.34334
\(549\) 2.81546 0.120161
\(550\) −18.6173 −0.793843
\(551\) −7.76193 −0.330669
\(552\) −10.9361 −0.465471
\(553\) 0 0
\(554\) 3.70688 0.157490
\(555\) −2.22300 −0.0943611
\(556\) −34.3655 −1.45742
\(557\) 24.1031 1.02128 0.510640 0.859794i \(-0.329408\pi\)
0.510640 + 0.859794i \(0.329408\pi\)
\(558\) −1.31729 −0.0557653
\(559\) 6.35152 0.268641
\(560\) 0 0
\(561\) −11.3498 −0.479190
\(562\) 8.57892 0.361880
\(563\) 38.9921 1.64332 0.821662 0.569976i \(-0.193047\pi\)
0.821662 + 0.569976i \(0.193047\pi\)
\(564\) −0.470865 −0.0198270
\(565\) 67.1684 2.82580
\(566\) 1.86593 0.0784311
\(567\) 0 0
\(568\) −4.53553 −0.190306
\(569\) 10.9127 0.457485 0.228743 0.973487i \(-0.426539\pi\)
0.228743 + 0.973487i \(0.426539\pi\)
\(570\) 2.21230 0.0926631
\(571\) −33.5273 −1.40307 −0.701537 0.712633i \(-0.747503\pi\)
−0.701537 + 0.712633i \(0.747503\pi\)
\(572\) 41.8910 1.75155
\(573\) −25.0344 −1.04583
\(574\) 0 0
\(575\) 57.4744 2.39685
\(576\) −4.33993 −0.180831
\(577\) −34.2097 −1.42417 −0.712084 0.702094i \(-0.752248\pi\)
−0.712084 + 0.702094i \(0.752248\pi\)
\(578\) −5.24093 −0.217994
\(579\) −2.83996 −0.118025
\(580\) 34.2615 1.42263
\(581\) 0 0
\(582\) −3.32732 −0.137922
\(583\) 44.4985 1.84294
\(584\) −9.15294 −0.378751
\(585\) −14.6433 −0.605426
\(586\) −1.96667 −0.0812426
\(587\) 34.0227 1.40427 0.702134 0.712045i \(-0.252231\pi\)
0.702134 + 0.712045i \(0.252231\pi\)
\(588\) 0 0
\(589\) 4.91634 0.202574
\(590\) 6.34122 0.261064
\(591\) −26.8159 −1.10306
\(592\) 1.86715 0.0767392
\(593\) −35.1165 −1.44206 −0.721030 0.692904i \(-0.756331\pi\)
−0.721030 + 0.692904i \(0.756331\pi\)
\(594\) −2.28385 −0.0937073
\(595\) 0 0
\(596\) 26.4672 1.08414
\(597\) −7.39204 −0.302536
\(598\) 11.5098 0.470672
\(599\) −7.10088 −0.290134 −0.145067 0.989422i \(-0.546340\pi\)
−0.145067 + 0.989422i \(0.546340\pi\)
\(600\) −12.6440 −0.516191
\(601\) −1.73551 −0.0707930 −0.0353965 0.999373i \(-0.511269\pi\)
−0.0353965 + 0.999373i \(0.511269\pi\)
\(602\) 0 0
\(603\) −13.3202 −0.542439
\(604\) 14.1479 0.575670
\(605\) −75.8345 −3.08311
\(606\) 5.29670 0.215164
\(607\) 13.3765 0.542934 0.271467 0.962448i \(-0.412491\pi\)
0.271467 + 0.962448i \(0.412491\pi\)
\(608\) −6.53900 −0.265191
\(609\) 0 0
\(610\) −4.12798 −0.167137
\(611\) 1.03524 0.0418814
\(612\) −3.68995 −0.149157
\(613\) −1.90309 −0.0768652 −0.0384326 0.999261i \(-0.512236\pi\)
−0.0384326 + 0.999261i \(0.512236\pi\)
\(614\) −2.02401 −0.0816824
\(615\) −3.62653 −0.146236
\(616\) 0 0
\(617\) −9.72463 −0.391499 −0.195749 0.980654i \(-0.562714\pi\)
−0.195749 + 0.980654i \(0.562714\pi\)
\(618\) 4.88389 0.196459
\(619\) −6.45607 −0.259491 −0.129746 0.991547i \(-0.541416\pi\)
−0.129746 + 0.991547i \(0.541416\pi\)
\(620\) −21.7009 −0.871530
\(621\) 7.05059 0.282930
\(622\) −5.41011 −0.216925
\(623\) 0 0
\(624\) 12.2992 0.492363
\(625\) 0.691937 0.0276775
\(626\) −5.69675 −0.227688
\(627\) 8.52369 0.340403
\(628\) −0.788993 −0.0314843
\(629\) 1.23159 0.0491068
\(630\) 0 0
\(631\) −34.1970 −1.36136 −0.680681 0.732580i \(-0.738316\pi\)
−0.680681 + 0.732580i \(0.738316\pi\)
\(632\) 1.62314 0.0645649
\(633\) 22.3498 0.888324
\(634\) −0.319396 −0.0126848
\(635\) −29.6224 −1.17553
\(636\) 14.4669 0.573652
\(637\) 0 0
\(638\) −11.7484 −0.465124
\(639\) 2.92409 0.115675
\(640\) 37.7954 1.49399
\(641\) 4.71311 0.186157 0.0930784 0.995659i \(-0.470329\pi\)
0.0930784 + 0.995659i \(0.470329\pi\)
\(642\) −4.06332 −0.160367
\(643\) −15.6912 −0.618800 −0.309400 0.950932i \(-0.600128\pi\)
−0.309400 + 0.950932i \(0.600128\pi\)
\(644\) 0 0
\(645\) −5.70455 −0.224616
\(646\) −1.22566 −0.0482231
\(647\) −20.5419 −0.807585 −0.403793 0.914851i \(-0.632308\pi\)
−0.403793 + 0.914851i \(0.632308\pi\)
\(648\) −1.55109 −0.0609325
\(649\) 24.4318 0.959033
\(650\) 13.3074 0.521959
\(651\) 0 0
\(652\) −38.3301 −1.50112
\(653\) −16.9600 −0.663698 −0.331849 0.943333i \(-0.607672\pi\)
−0.331849 + 0.943333i \(0.607672\pi\)
\(654\) −4.77683 −0.186789
\(655\) 47.9649 1.87414
\(656\) 3.04600 0.118926
\(657\) 5.90098 0.230219
\(658\) 0 0
\(659\) 1.00491 0.0391459 0.0195729 0.999808i \(-0.493769\pi\)
0.0195729 + 0.999808i \(0.493769\pi\)
\(660\) −37.6239 −1.46451
\(661\) −1.53402 −0.0596663 −0.0298332 0.999555i \(-0.509498\pi\)
−0.0298332 + 0.999555i \(0.509498\pi\)
\(662\) 1.93759 0.0753065
\(663\) 8.11271 0.315072
\(664\) 16.0988 0.624754
\(665\) 0 0
\(666\) 0.247825 0.00960301
\(667\) 36.2692 1.40435
\(668\) 29.2658 1.13233
\(669\) 28.5254 1.10286
\(670\) 19.5298 0.754501
\(671\) −15.9045 −0.613987
\(672\) 0 0
\(673\) −4.78993 −0.184638 −0.0923192 0.995729i \(-0.529428\pi\)
−0.0923192 + 0.995729i \(0.529428\pi\)
\(674\) −1.88742 −0.0727008
\(675\) 8.15172 0.313760
\(676\) −6.06803 −0.233386
\(677\) 34.0664 1.30928 0.654638 0.755942i \(-0.272821\pi\)
0.654638 + 0.755942i \(0.272821\pi\)
\(678\) −7.48807 −0.287578
\(679\) 0 0
\(680\) 11.3018 0.433403
\(681\) 23.9051 0.916045
\(682\) 7.44134 0.284944
\(683\) −9.63255 −0.368579 −0.184290 0.982872i \(-0.558998\pi\)
−0.184290 + 0.982872i \(0.558998\pi\)
\(684\) 2.77114 0.105957
\(685\) 62.0961 2.37257
\(686\) 0 0
\(687\) −5.21232 −0.198862
\(688\) 4.79137 0.182669
\(689\) −31.8070 −1.21175
\(690\) −10.3374 −0.393539
\(691\) 42.1141 1.60210 0.801049 0.598599i \(-0.204276\pi\)
0.801049 + 0.598599i \(0.204276\pi\)
\(692\) 9.41403 0.357868
\(693\) 0 0
\(694\) −9.77042 −0.370880
\(695\) −67.8596 −2.57406
\(696\) −7.97902 −0.302444
\(697\) 2.00918 0.0761030
\(698\) −9.58702 −0.362874
\(699\) −22.9871 −0.869453
\(700\) 0 0
\(701\) −30.5053 −1.15217 −0.576084 0.817391i \(-0.695420\pi\)
−0.576084 + 0.817391i \(0.695420\pi\)
\(702\) 1.63246 0.0616134
\(703\) −0.924922 −0.0348841
\(704\) 24.5162 0.923990
\(705\) −0.929791 −0.0350179
\(706\) −3.59537 −0.135314
\(707\) 0 0
\(708\) 7.94305 0.298518
\(709\) 46.4610 1.74488 0.872440 0.488721i \(-0.162536\pi\)
0.872440 + 0.488721i \(0.162536\pi\)
\(710\) −4.28724 −0.160897
\(711\) −1.04645 −0.0392449
\(712\) −15.1077 −0.566186
\(713\) −22.9726 −0.860330
\(714\) 0 0
\(715\) 82.7198 3.09354
\(716\) 9.60305 0.358883
\(717\) 30.5972 1.14267
\(718\) −8.56843 −0.319771
\(719\) −42.8582 −1.59834 −0.799170 0.601105i \(-0.794727\pi\)
−0.799170 + 0.601105i \(0.794727\pi\)
\(720\) −11.0464 −0.411675
\(721\) 0 0
\(722\) −6.76109 −0.251622
\(723\) −14.3324 −0.533028
\(724\) −2.95584 −0.109853
\(725\) 41.9336 1.55737
\(726\) 8.45419 0.313764
\(727\) −18.9785 −0.703874 −0.351937 0.936024i \(-0.614477\pi\)
−0.351937 + 0.936024i \(0.614477\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −8.65190 −0.320221
\(731\) 3.16045 0.116893
\(732\) −5.17073 −0.191116
\(733\) −43.0175 −1.58889 −0.794445 0.607337i \(-0.792238\pi\)
−0.794445 + 0.607337i \(0.792238\pi\)
\(734\) 8.68323 0.320504
\(735\) 0 0
\(736\) 30.5548 1.12627
\(737\) 75.2455 2.77170
\(738\) 0.404293 0.0148822
\(739\) −16.2946 −0.599408 −0.299704 0.954032i \(-0.596888\pi\)
−0.299704 + 0.954032i \(0.596888\pi\)
\(740\) 4.08265 0.150081
\(741\) −6.09263 −0.223818
\(742\) 0 0
\(743\) −24.1083 −0.884449 −0.442224 0.896905i \(-0.645810\pi\)
−0.442224 + 0.896905i \(0.645810\pi\)
\(744\) 5.05384 0.185283
\(745\) 52.2633 1.91478
\(746\) −15.2485 −0.558287
\(747\) −10.3790 −0.379749
\(748\) 20.8445 0.762149
\(749\) 0 0
\(750\) −4.62099 −0.168735
\(751\) −39.4430 −1.43929 −0.719647 0.694340i \(-0.755697\pi\)
−0.719647 + 0.694340i \(0.755697\pi\)
\(752\) 0.780951 0.0284784
\(753\) −13.7477 −0.500994
\(754\) 8.39762 0.305823
\(755\) 27.9371 1.01674
\(756\) 0 0
\(757\) −3.32835 −0.120971 −0.0604855 0.998169i \(-0.519265\pi\)
−0.0604855 + 0.998169i \(0.519265\pi\)
\(758\) −6.39195 −0.232166
\(759\) −39.8287 −1.44569
\(760\) −8.48760 −0.307878
\(761\) −54.7231 −1.98371 −0.991856 0.127364i \(-0.959348\pi\)
−0.991856 + 0.127364i \(0.959348\pi\)
\(762\) 3.30237 0.119632
\(763\) 0 0
\(764\) 45.9768 1.66338
\(765\) −7.28634 −0.263438
\(766\) 7.20363 0.260278
\(767\) −17.4636 −0.630573
\(768\) 4.46636 0.161166
\(769\) 23.7003 0.854655 0.427328 0.904097i \(-0.359455\pi\)
0.427328 + 0.904097i \(0.359455\pi\)
\(770\) 0 0
\(771\) 12.4136 0.447065
\(772\) 5.21572 0.187718
\(773\) 32.7011 1.17618 0.588089 0.808796i \(-0.299880\pi\)
0.588089 + 0.808796i \(0.299880\pi\)
\(774\) 0.635955 0.0228589
\(775\) −26.5604 −0.954076
\(776\) 12.7654 0.458252
\(777\) 0 0
\(778\) −14.2775 −0.511874
\(779\) −1.50889 −0.0540615
\(780\) 26.8931 0.962928
\(781\) −16.5181 −0.591066
\(782\) 5.72717 0.204803
\(783\) 5.14414 0.183836
\(784\) 0 0
\(785\) −1.55798 −0.0556068
\(786\) −5.34723 −0.190729
\(787\) −18.2860 −0.651824 −0.325912 0.945400i \(-0.605671\pi\)
−0.325912 + 0.945400i \(0.605671\pi\)
\(788\) 49.2487 1.75441
\(789\) 21.1795 0.754011
\(790\) 1.53428 0.0545873
\(791\) 0 0
\(792\) 8.76208 0.311347
\(793\) 11.3684 0.403702
\(794\) −2.14030 −0.0759563
\(795\) 28.5671 1.01317
\(796\) 13.5758 0.481183
\(797\) −7.87343 −0.278891 −0.139446 0.990230i \(-0.544532\pi\)
−0.139446 + 0.990230i \(0.544532\pi\)
\(798\) 0 0
\(799\) 0.515125 0.0182238
\(800\) 35.3267 1.24899
\(801\) 9.74008 0.344149
\(802\) −11.8849 −0.419672
\(803\) −33.3345 −1.17635
\(804\) 24.4631 0.862748
\(805\) 0 0
\(806\) −5.31898 −0.187353
\(807\) 5.56435 0.195874
\(808\) −20.3210 −0.714892
\(809\) 19.0892 0.671140 0.335570 0.942015i \(-0.391071\pi\)
0.335570 + 0.942015i \(0.391071\pi\)
\(810\) −1.46618 −0.0515163
\(811\) 20.5665 0.722186 0.361093 0.932530i \(-0.382404\pi\)
0.361093 + 0.932530i \(0.382404\pi\)
\(812\) 0 0
\(813\) 11.2067 0.393038
\(814\) −1.39996 −0.0490685
\(815\) −75.6884 −2.65125
\(816\) 6.11996 0.214241
\(817\) −2.37349 −0.0830378
\(818\) −8.77186 −0.306701
\(819\) 0 0
\(820\) 6.66029 0.232588
\(821\) −2.65350 −0.0926079 −0.0463040 0.998927i \(-0.514744\pi\)
−0.0463040 + 0.998927i \(0.514744\pi\)
\(822\) −6.92260 −0.241453
\(823\) 30.8909 1.07679 0.538394 0.842693i \(-0.319031\pi\)
0.538394 + 0.842693i \(0.319031\pi\)
\(824\) −18.7373 −0.652744
\(825\) −46.0489 −1.60322
\(826\) 0 0
\(827\) 0.774423 0.0269293 0.0134647 0.999909i \(-0.495714\pi\)
0.0134647 + 0.999909i \(0.495714\pi\)
\(828\) −12.9487 −0.450000
\(829\) −15.5292 −0.539352 −0.269676 0.962951i \(-0.586917\pi\)
−0.269676 + 0.962951i \(0.586917\pi\)
\(830\) 15.2175 0.528208
\(831\) 9.16881 0.318062
\(832\) −17.5239 −0.607532
\(833\) 0 0
\(834\) 7.56513 0.261959
\(835\) 57.7896 1.99989
\(836\) −15.6542 −0.541410
\(837\) −3.25825 −0.112622
\(838\) 0.435566 0.0150464
\(839\) −2.34091 −0.0808172 −0.0404086 0.999183i \(-0.512866\pi\)
−0.0404086 + 0.999183i \(0.512866\pi\)
\(840\) 0 0
\(841\) −2.53785 −0.0875119
\(842\) −7.61864 −0.262556
\(843\) 21.2196 0.730841
\(844\) −41.0464 −1.41288
\(845\) −11.9822 −0.412201
\(846\) 0.103655 0.00356373
\(847\) 0 0
\(848\) −23.9941 −0.823961
\(849\) 4.61530 0.158397
\(850\) 6.62161 0.227119
\(851\) 4.32189 0.148152
\(852\) −5.37023 −0.183981
\(853\) 46.7682 1.60131 0.800656 0.599125i \(-0.204485\pi\)
0.800656 + 0.599125i \(0.204485\pi\)
\(854\) 0 0
\(855\) 5.47203 0.187139
\(856\) 15.5891 0.532825
\(857\) −3.78098 −0.129156 −0.0645778 0.997913i \(-0.520570\pi\)
−0.0645778 + 0.997913i \(0.520570\pi\)
\(858\) −9.22177 −0.314826
\(859\) 16.9802 0.579357 0.289679 0.957124i \(-0.406452\pi\)
0.289679 + 0.957124i \(0.406452\pi\)
\(860\) 10.4767 0.357251
\(861\) 0 0
\(862\) 8.60172 0.292976
\(863\) 42.9271 1.46125 0.730627 0.682776i \(-0.239228\pi\)
0.730627 + 0.682776i \(0.239228\pi\)
\(864\) 4.33365 0.147434
\(865\) 18.5894 0.632058
\(866\) 14.6048 0.496291
\(867\) −12.9632 −0.440253
\(868\) 0 0
\(869\) 5.91138 0.200530
\(870\) −7.54223 −0.255706
\(871\) −53.7846 −1.82242
\(872\) 18.3265 0.620615
\(873\) −8.22998 −0.278543
\(874\) −4.30109 −0.145487
\(875\) 0 0
\(876\) −10.8374 −0.366163
\(877\) −14.8161 −0.500303 −0.250152 0.968207i \(-0.580480\pi\)
−0.250152 + 0.968207i \(0.580480\pi\)
\(878\) 9.74061 0.328730
\(879\) −4.86448 −0.164075
\(880\) 62.4010 2.10354
\(881\) 48.7594 1.64275 0.821373 0.570391i \(-0.193208\pi\)
0.821373 + 0.570391i \(0.193208\pi\)
\(882\) 0 0
\(883\) −27.6259 −0.929687 −0.464843 0.885393i \(-0.653889\pi\)
−0.464843 + 0.885393i \(0.653889\pi\)
\(884\) −14.8994 −0.501120
\(885\) 15.6847 0.527236
\(886\) 7.67137 0.257725
\(887\) −29.6770 −0.996457 −0.498229 0.867046i \(-0.666016\pi\)
−0.498229 + 0.867046i \(0.666016\pi\)
\(888\) −0.950791 −0.0319065
\(889\) 0 0
\(890\) −14.2807 −0.478691
\(891\) −5.64899 −0.189248
\(892\) −52.3883 −1.75409
\(893\) −0.386857 −0.0129457
\(894\) −5.82642 −0.194865
\(895\) 18.9626 0.633850
\(896\) 0 0
\(897\) 28.4691 0.950554
\(898\) 5.80929 0.193858
\(899\) −16.7609 −0.559007
\(900\) −14.9710 −0.499034
\(901\) −15.8268 −0.527267
\(902\) −2.28385 −0.0760437
\(903\) 0 0
\(904\) 28.7283 0.955490
\(905\) −5.83674 −0.194020
\(906\) −3.11449 −0.103472
\(907\) 35.1406 1.16683 0.583413 0.812176i \(-0.301717\pi\)
0.583413 + 0.812176i \(0.301717\pi\)
\(908\) −43.9028 −1.45697
\(909\) 13.1011 0.434537
\(910\) 0 0
\(911\) 48.9016 1.62018 0.810091 0.586305i \(-0.199418\pi\)
0.810091 + 0.586305i \(0.199418\pi\)
\(912\) −4.59607 −0.152191
\(913\) 58.6310 1.94040
\(914\) 3.44441 0.113931
\(915\) −10.2104 −0.337544
\(916\) 9.57267 0.316290
\(917\) 0 0
\(918\) 0.812296 0.0268098
\(919\) 29.0668 0.958825 0.479412 0.877590i \(-0.340850\pi\)
0.479412 + 0.877590i \(0.340850\pi\)
\(920\) 39.6601 1.30755
\(921\) −5.00629 −0.164963
\(922\) −13.2894 −0.437664
\(923\) 11.8070 0.388631
\(924\) 0 0
\(925\) 4.99686 0.164296
\(926\) 13.1278 0.431405
\(927\) 12.0801 0.396762
\(928\) 22.2929 0.731801
\(929\) 4.60405 0.151054 0.0755271 0.997144i \(-0.475936\pi\)
0.0755271 + 0.997144i \(0.475936\pi\)
\(930\) 4.77719 0.156650
\(931\) 0 0
\(932\) 42.2170 1.38286
\(933\) −13.3816 −0.438095
\(934\) −11.5406 −0.377618
\(935\) 41.1605 1.34609
\(936\) −6.26303 −0.204713
\(937\) −9.16034 −0.299255 −0.149628 0.988742i \(-0.547807\pi\)
−0.149628 + 0.988742i \(0.547807\pi\)
\(938\) 0 0
\(939\) −14.0907 −0.459831
\(940\) 1.70760 0.0556959
\(941\) −49.9191 −1.62732 −0.813658 0.581344i \(-0.802527\pi\)
−0.813658 + 0.581344i \(0.802527\pi\)
\(942\) 0.173687 0.00565903
\(943\) 7.05059 0.229599
\(944\) −13.1739 −0.428775
\(945\) 0 0
\(946\) −3.59250 −0.116802
\(947\) 46.5491 1.51264 0.756322 0.654200i \(-0.226994\pi\)
0.756322 + 0.654200i \(0.226994\pi\)
\(948\) 1.92185 0.0624189
\(949\) 23.8271 0.773461
\(950\) −4.97282 −0.161339
\(951\) −0.790011 −0.0256179
\(952\) 0 0
\(953\) −11.7321 −0.380041 −0.190020 0.981780i \(-0.560855\pi\)
−0.190020 + 0.981780i \(0.560855\pi\)
\(954\) −3.18472 −0.103109
\(955\) 90.7880 2.93783
\(956\) −56.1932 −1.81742
\(957\) −29.0592 −0.939349
\(958\) −9.28765 −0.300070
\(959\) 0 0
\(960\) 15.7389 0.507971
\(961\) −20.3838 −0.657542
\(962\) 1.00067 0.0322630
\(963\) −10.0504 −0.323871
\(964\) 26.3222 0.847780
\(965\) 10.2992 0.331543
\(966\) 0 0
\(967\) −57.4991 −1.84905 −0.924523 0.381127i \(-0.875536\pi\)
−0.924523 + 0.381127i \(0.875536\pi\)
\(968\) −32.4349 −1.04250
\(969\) −3.03162 −0.0973898
\(970\) 12.0666 0.387436
\(971\) −48.4020 −1.55329 −0.776647 0.629936i \(-0.783081\pi\)
−0.776647 + 0.629936i \(0.783081\pi\)
\(972\) −1.83655 −0.0589073
\(973\) 0 0
\(974\) 4.23332 0.135644
\(975\) 32.9152 1.05413
\(976\) 8.57590 0.274508
\(977\) 20.1753 0.645464 0.322732 0.946490i \(-0.395399\pi\)
0.322732 + 0.946490i \(0.395399\pi\)
\(978\) 8.43790 0.269814
\(979\) −55.0216 −1.75850
\(980\) 0 0
\(981\) −11.8153 −0.377233
\(982\) −9.93463 −0.317027
\(983\) −32.6666 −1.04190 −0.520952 0.853586i \(-0.674423\pi\)
−0.520952 + 0.853586i \(0.674423\pi\)
\(984\) −1.55109 −0.0494469
\(985\) 97.2488 3.09860
\(986\) 4.17857 0.133073
\(987\) 0 0
\(988\) 11.1894 0.355982
\(989\) 11.0906 0.352661
\(990\) 8.28243 0.263233
\(991\) 35.1121 1.11537 0.557686 0.830052i \(-0.311689\pi\)
0.557686 + 0.830052i \(0.311689\pi\)
\(992\) −14.1201 −0.448315
\(993\) 4.79253 0.152086
\(994\) 0 0
\(995\) 26.8075 0.849854
\(996\) 19.0616 0.603989
\(997\) −12.4124 −0.393104 −0.196552 0.980493i \(-0.562974\pi\)
−0.196552 + 0.980493i \(0.562974\pi\)
\(998\) −9.78870 −0.309856
\(999\) 0.612983 0.0193939
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 \(a_p\))