Properties

Label 6027.2.a.bm.1.14
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.14
Root \(-1.87592\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.87592 q^{2} +1.00000 q^{3} +1.51907 q^{4} -1.33107 q^{5} +1.87592 q^{6} -0.902182 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.87592 q^{2} +1.00000 q^{3} +1.51907 q^{4} -1.33107 q^{5} +1.87592 q^{6} -0.902182 q^{8} +1.00000 q^{9} -2.49697 q^{10} +1.19223 q^{11} +1.51907 q^{12} +0.956777 q^{13} -1.33107 q^{15} -4.73056 q^{16} +3.26275 q^{17} +1.87592 q^{18} -6.16735 q^{19} -2.02199 q^{20} +2.23653 q^{22} -6.99354 q^{23} -0.902182 q^{24} -3.22826 q^{25} +1.79484 q^{26} +1.00000 q^{27} -2.28683 q^{29} -2.49697 q^{30} -1.84740 q^{31} -7.06979 q^{32} +1.19223 q^{33} +6.12065 q^{34} +1.51907 q^{36} -6.15612 q^{37} -11.5695 q^{38} +0.956777 q^{39} +1.20086 q^{40} +1.00000 q^{41} -5.98160 q^{43} +1.81108 q^{44} -1.33107 q^{45} -13.1193 q^{46} +6.24381 q^{47} -4.73056 q^{48} -6.05596 q^{50} +3.26275 q^{51} +1.45341 q^{52} +11.8675 q^{53} +1.87592 q^{54} -1.58694 q^{55} -6.16735 q^{57} -4.28990 q^{58} -4.26878 q^{59} -2.02199 q^{60} +4.85206 q^{61} -3.46558 q^{62} -3.80123 q^{64} -1.27353 q^{65} +2.23653 q^{66} +3.76060 q^{67} +4.95635 q^{68} -6.99354 q^{69} -11.3437 q^{71} -0.902182 q^{72} -6.06858 q^{73} -11.5484 q^{74} -3.22826 q^{75} -9.36866 q^{76} +1.79484 q^{78} -14.1656 q^{79} +6.29670 q^{80} +1.00000 q^{81} +1.87592 q^{82} +2.10474 q^{83} -4.34294 q^{85} -11.2210 q^{86} -2.28683 q^{87} -1.07561 q^{88} -9.71613 q^{89} -2.49697 q^{90} -10.6237 q^{92} -1.84740 q^{93} +11.7129 q^{94} +8.20916 q^{95} -7.06979 q^{96} +0.622368 q^{97} +1.19223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87592 1.32648 0.663238 0.748409i \(-0.269182\pi\)
0.663238 + 0.748409i \(0.269182\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.51907 0.759536
\(5\) −1.33107 −0.595271 −0.297636 0.954680i \(-0.596198\pi\)
−0.297636 + 0.954680i \(0.596198\pi\)
\(6\) 1.87592 0.765841
\(7\) 0 0
\(8\) −0.902182 −0.318969
\(9\) 1.00000 0.333333
\(10\) −2.49697 −0.789612
\(11\) 1.19223 0.359471 0.179736 0.983715i \(-0.442476\pi\)
0.179736 + 0.983715i \(0.442476\pi\)
\(12\) 1.51907 0.438518
\(13\) 0.956777 0.265362 0.132681 0.991159i \(-0.457641\pi\)
0.132681 + 0.991159i \(0.457641\pi\)
\(14\) 0 0
\(15\) −1.33107 −0.343680
\(16\) −4.73056 −1.18264
\(17\) 3.26275 0.791333 0.395666 0.918394i \(-0.370514\pi\)
0.395666 + 0.918394i \(0.370514\pi\)
\(18\) 1.87592 0.442158
\(19\) −6.16735 −1.41489 −0.707444 0.706769i \(-0.750152\pi\)
−0.707444 + 0.706769i \(0.750152\pi\)
\(20\) −2.02199 −0.452130
\(21\) 0 0
\(22\) 2.23653 0.476830
\(23\) −6.99354 −1.45825 −0.729127 0.684378i \(-0.760074\pi\)
−0.729127 + 0.684378i \(0.760074\pi\)
\(24\) −0.902182 −0.184157
\(25\) −3.22826 −0.645652
\(26\) 1.79484 0.351996
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.28683 −0.424653 −0.212327 0.977199i \(-0.568104\pi\)
−0.212327 + 0.977199i \(0.568104\pi\)
\(30\) −2.49697 −0.455883
\(31\) −1.84740 −0.331804 −0.165902 0.986142i \(-0.553053\pi\)
−0.165902 + 0.986142i \(0.553053\pi\)
\(32\) −7.06979 −1.24977
\(33\) 1.19223 0.207541
\(34\) 6.12065 1.04968
\(35\) 0 0
\(36\) 1.51907 0.253179
\(37\) −6.15612 −1.01206 −0.506030 0.862516i \(-0.668888\pi\)
−0.506030 + 0.862516i \(0.668888\pi\)
\(38\) −11.5695 −1.87681
\(39\) 0.956777 0.153207
\(40\) 1.20086 0.189873
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −5.98160 −0.912186 −0.456093 0.889932i \(-0.650752\pi\)
−0.456093 + 0.889932i \(0.650752\pi\)
\(44\) 1.81108 0.273031
\(45\) −1.33107 −0.198424
\(46\) −13.1193 −1.93434
\(47\) 6.24381 0.910754 0.455377 0.890299i \(-0.349505\pi\)
0.455377 + 0.890299i \(0.349505\pi\)
\(48\) −4.73056 −0.682798
\(49\) 0 0
\(50\) −6.05596 −0.856442
\(51\) 3.26275 0.456876
\(52\) 1.45341 0.201552
\(53\) 11.8675 1.63012 0.815060 0.579377i \(-0.196704\pi\)
0.815060 + 0.579377i \(0.196704\pi\)
\(54\) 1.87592 0.255280
\(55\) −1.58694 −0.213983
\(56\) 0 0
\(57\) −6.16735 −0.816886
\(58\) −4.28990 −0.563292
\(59\) −4.26878 −0.555748 −0.277874 0.960618i \(-0.589630\pi\)
−0.277874 + 0.960618i \(0.589630\pi\)
\(60\) −2.02199 −0.261037
\(61\) 4.85206 0.621242 0.310621 0.950534i \(-0.399463\pi\)
0.310621 + 0.950534i \(0.399463\pi\)
\(62\) −3.46558 −0.440129
\(63\) 0 0
\(64\) −3.80123 −0.475153
\(65\) −1.27353 −0.157962
\(66\) 2.23653 0.275298
\(67\) 3.76060 0.459430 0.229715 0.973258i \(-0.426221\pi\)
0.229715 + 0.973258i \(0.426221\pi\)
\(68\) 4.95635 0.601046
\(69\) −6.99354 −0.841923
\(70\) 0 0
\(71\) −11.3437 −1.34625 −0.673124 0.739530i \(-0.735048\pi\)
−0.673124 + 0.739530i \(0.735048\pi\)
\(72\) −0.902182 −0.106323
\(73\) −6.06858 −0.710273 −0.355137 0.934814i \(-0.615566\pi\)
−0.355137 + 0.934814i \(0.615566\pi\)
\(74\) −11.5484 −1.34247
\(75\) −3.22826 −0.372768
\(76\) −9.36866 −1.07466
\(77\) 0 0
\(78\) 1.79484 0.203225
\(79\) −14.1656 −1.59376 −0.796878 0.604140i \(-0.793517\pi\)
−0.796878 + 0.604140i \(0.793517\pi\)
\(80\) 6.29670 0.703992
\(81\) 1.00000 0.111111
\(82\) 1.87592 0.207161
\(83\) 2.10474 0.231025 0.115512 0.993306i \(-0.463149\pi\)
0.115512 + 0.993306i \(0.463149\pi\)
\(84\) 0 0
\(85\) −4.34294 −0.471058
\(86\) −11.2210 −1.20999
\(87\) −2.28683 −0.245174
\(88\) −1.07561 −0.114660
\(89\) −9.71613 −1.02991 −0.514954 0.857218i \(-0.672191\pi\)
−0.514954 + 0.857218i \(0.672191\pi\)
\(90\) −2.49697 −0.263204
\(91\) 0 0
\(92\) −10.6237 −1.10760
\(93\) −1.84740 −0.191567
\(94\) 11.7129 1.20809
\(95\) 8.20916 0.842242
\(96\) −7.06979 −0.721558
\(97\) 0.622368 0.0631919 0.0315960 0.999501i \(-0.489941\pi\)
0.0315960 + 0.999501i \(0.489941\pi\)
\(98\) 0 0
\(99\) 1.19223 0.119824
\(100\) −4.90396 −0.490396
\(101\) −7.06334 −0.702829 −0.351415 0.936220i \(-0.614299\pi\)
−0.351415 + 0.936220i \(0.614299\pi\)
\(102\) 6.12065 0.606035
\(103\) 17.8241 1.75626 0.878132 0.478418i \(-0.158790\pi\)
0.878132 + 0.478418i \(0.158790\pi\)
\(104\) −0.863187 −0.0846425
\(105\) 0 0
\(106\) 22.2624 2.16231
\(107\) 10.7720 1.04137 0.520684 0.853749i \(-0.325677\pi\)
0.520684 + 0.853749i \(0.325677\pi\)
\(108\) 1.51907 0.146173
\(109\) −9.04356 −0.866216 −0.433108 0.901342i \(-0.642583\pi\)
−0.433108 + 0.901342i \(0.642583\pi\)
\(110\) −2.97697 −0.283843
\(111\) −6.15612 −0.584313
\(112\) 0 0
\(113\) −5.09784 −0.479565 −0.239782 0.970827i \(-0.577076\pi\)
−0.239782 + 0.970827i \(0.577076\pi\)
\(114\) −11.5695 −1.08358
\(115\) 9.30887 0.868057
\(116\) −3.47386 −0.322540
\(117\) 0.956777 0.0884541
\(118\) −8.00789 −0.737186
\(119\) 0 0
\(120\) 1.20086 0.109623
\(121\) −9.57858 −0.870780
\(122\) 9.10207 0.824062
\(123\) 1.00000 0.0901670
\(124\) −2.80634 −0.252017
\(125\) 10.9524 0.979609
\(126\) 0 0
\(127\) 9.16734 0.813470 0.406735 0.913546i \(-0.366667\pi\)
0.406735 + 0.913546i \(0.366667\pi\)
\(128\) 7.00879 0.619495
\(129\) −5.98160 −0.526651
\(130\) −2.38905 −0.209533
\(131\) 4.49020 0.392311 0.196155 0.980573i \(-0.437154\pi\)
0.196155 + 0.980573i \(0.437154\pi\)
\(132\) 1.81108 0.157635
\(133\) 0 0
\(134\) 7.05457 0.609422
\(135\) −1.33107 −0.114560
\(136\) −2.94359 −0.252411
\(137\) −7.16553 −0.612192 −0.306096 0.952001i \(-0.599023\pi\)
−0.306096 + 0.952001i \(0.599023\pi\)
\(138\) −13.1193 −1.11679
\(139\) −10.8857 −0.923310 −0.461655 0.887060i \(-0.652744\pi\)
−0.461655 + 0.887060i \(0.652744\pi\)
\(140\) 0 0
\(141\) 6.24381 0.525824
\(142\) −21.2798 −1.78576
\(143\) 1.14070 0.0953901
\(144\) −4.73056 −0.394214
\(145\) 3.04392 0.252784
\(146\) −11.3842 −0.942160
\(147\) 0 0
\(148\) −9.35160 −0.768696
\(149\) −10.1880 −0.834633 −0.417317 0.908761i \(-0.637029\pi\)
−0.417317 + 0.908761i \(0.637029\pi\)
\(150\) −6.05596 −0.494467
\(151\) −17.1572 −1.39623 −0.698116 0.715985i \(-0.745978\pi\)
−0.698116 + 0.715985i \(0.745978\pi\)
\(152\) 5.56408 0.451306
\(153\) 3.26275 0.263778
\(154\) 0 0
\(155\) 2.45902 0.197513
\(156\) 1.45341 0.116366
\(157\) 17.1453 1.36834 0.684172 0.729320i \(-0.260164\pi\)
0.684172 + 0.729320i \(0.260164\pi\)
\(158\) −26.5735 −2.11408
\(159\) 11.8675 0.941150
\(160\) 9.41036 0.743955
\(161\) 0 0
\(162\) 1.87592 0.147386
\(163\) 9.69691 0.759520 0.379760 0.925085i \(-0.376007\pi\)
0.379760 + 0.925085i \(0.376007\pi\)
\(164\) 1.51907 0.118620
\(165\) −1.58694 −0.123543
\(166\) 3.94832 0.306449
\(167\) 1.78167 0.137869 0.0689347 0.997621i \(-0.478040\pi\)
0.0689347 + 0.997621i \(0.478040\pi\)
\(168\) 0 0
\(169\) −12.0846 −0.929583
\(170\) −8.14700 −0.624846
\(171\) −6.16735 −0.471629
\(172\) −9.08649 −0.692838
\(173\) −7.95559 −0.604853 −0.302426 0.953173i \(-0.597797\pi\)
−0.302426 + 0.953173i \(0.597797\pi\)
\(174\) −4.28990 −0.325217
\(175\) 0 0
\(176\) −5.63993 −0.425125
\(177\) −4.26878 −0.320861
\(178\) −18.2267 −1.36615
\(179\) 6.55130 0.489667 0.244833 0.969565i \(-0.421267\pi\)
0.244833 + 0.969565i \(0.421267\pi\)
\(180\) −2.02199 −0.150710
\(181\) −16.4764 −1.22468 −0.612341 0.790593i \(-0.709772\pi\)
−0.612341 + 0.790593i \(0.709772\pi\)
\(182\) 0 0
\(183\) 4.85206 0.358674
\(184\) 6.30945 0.465139
\(185\) 8.19421 0.602450
\(186\) −3.46558 −0.254109
\(187\) 3.88995 0.284461
\(188\) 9.48480 0.691750
\(189\) 0 0
\(190\) 15.3997 1.11721
\(191\) −22.5981 −1.63514 −0.817570 0.575829i \(-0.804679\pi\)
−0.817570 + 0.575829i \(0.804679\pi\)
\(192\) −3.80123 −0.274330
\(193\) −2.60607 −0.187589 −0.0937943 0.995592i \(-0.529900\pi\)
−0.0937943 + 0.995592i \(0.529900\pi\)
\(194\) 1.16751 0.0838225
\(195\) −1.27353 −0.0911997
\(196\) 0 0
\(197\) −16.3863 −1.16747 −0.583737 0.811942i \(-0.698410\pi\)
−0.583737 + 0.811942i \(0.698410\pi\)
\(198\) 2.23653 0.158943
\(199\) −8.52046 −0.604000 −0.302000 0.953308i \(-0.597654\pi\)
−0.302000 + 0.953308i \(0.597654\pi\)
\(200\) 2.91248 0.205943
\(201\) 3.76060 0.265252
\(202\) −13.2503 −0.932285
\(203\) 0 0
\(204\) 4.95635 0.347014
\(205\) −1.33107 −0.0929657
\(206\) 33.4366 2.32964
\(207\) −6.99354 −0.486085
\(208\) −4.52610 −0.313828
\(209\) −7.35291 −0.508612
\(210\) 0 0
\(211\) 23.0347 1.58577 0.792886 0.609369i \(-0.208577\pi\)
0.792886 + 0.609369i \(0.208577\pi\)
\(212\) 18.0275 1.23813
\(213\) −11.3437 −0.777256
\(214\) 20.2074 1.38135
\(215\) 7.96191 0.542998
\(216\) −0.902182 −0.0613857
\(217\) 0 0
\(218\) −16.9650 −1.14901
\(219\) −6.06858 −0.410076
\(220\) −2.41067 −0.162528
\(221\) 3.12172 0.209990
\(222\) −11.5484 −0.775077
\(223\) 9.56418 0.640465 0.320232 0.947339i \(-0.396239\pi\)
0.320232 + 0.947339i \(0.396239\pi\)
\(224\) 0 0
\(225\) −3.22826 −0.215217
\(226\) −9.56314 −0.636131
\(227\) 24.7536 1.64296 0.821478 0.570241i \(-0.193150\pi\)
0.821478 + 0.570241i \(0.193150\pi\)
\(228\) −9.36866 −0.620454
\(229\) 3.35230 0.221526 0.110763 0.993847i \(-0.464671\pi\)
0.110763 + 0.993847i \(0.464671\pi\)
\(230\) 17.4627 1.15146
\(231\) 0 0
\(232\) 2.06314 0.135451
\(233\) −1.02338 −0.0670440 −0.0335220 0.999438i \(-0.510672\pi\)
−0.0335220 + 0.999438i \(0.510672\pi\)
\(234\) 1.79484 0.117332
\(235\) −8.31093 −0.542145
\(236\) −6.48459 −0.422111
\(237\) −14.1656 −0.920155
\(238\) 0 0
\(239\) −26.4140 −1.70858 −0.854290 0.519796i \(-0.826008\pi\)
−0.854290 + 0.519796i \(0.826008\pi\)
\(240\) 6.29670 0.406450
\(241\) 22.1097 1.42421 0.712105 0.702073i \(-0.247742\pi\)
0.712105 + 0.702073i \(0.247742\pi\)
\(242\) −17.9686 −1.15507
\(243\) 1.00000 0.0641500
\(244\) 7.37062 0.471856
\(245\) 0 0
\(246\) 1.87592 0.119604
\(247\) −5.90078 −0.375458
\(248\) 1.66669 0.105835
\(249\) 2.10474 0.133382
\(250\) 20.5457 1.29943
\(251\) −19.7611 −1.24731 −0.623656 0.781699i \(-0.714353\pi\)
−0.623656 + 0.781699i \(0.714353\pi\)
\(252\) 0 0
\(253\) −8.33792 −0.524200
\(254\) 17.1972 1.07905
\(255\) −4.34294 −0.271965
\(256\) 20.7504 1.29690
\(257\) −17.4492 −1.08845 −0.544224 0.838940i \(-0.683176\pi\)
−0.544224 + 0.838940i \(0.683176\pi\)
\(258\) −11.2210 −0.698589
\(259\) 0 0
\(260\) −1.93459 −0.119978
\(261\) −2.28683 −0.141551
\(262\) 8.42325 0.520390
\(263\) 21.4392 1.32200 0.660998 0.750387i \(-0.270133\pi\)
0.660998 + 0.750387i \(0.270133\pi\)
\(264\) −1.07561 −0.0661992
\(265\) −15.7964 −0.970363
\(266\) 0 0
\(267\) −9.71613 −0.594618
\(268\) 5.71262 0.348954
\(269\) 2.02049 0.123192 0.0615959 0.998101i \(-0.480381\pi\)
0.0615959 + 0.998101i \(0.480381\pi\)
\(270\) −2.49697 −0.151961
\(271\) 11.0931 0.673861 0.336930 0.941530i \(-0.390611\pi\)
0.336930 + 0.941530i \(0.390611\pi\)
\(272\) −15.4346 −0.935863
\(273\) 0 0
\(274\) −13.4420 −0.812058
\(275\) −3.84883 −0.232093
\(276\) −10.6237 −0.639471
\(277\) 13.9305 0.837002 0.418501 0.908216i \(-0.362556\pi\)
0.418501 + 0.908216i \(0.362556\pi\)
\(278\) −20.4206 −1.22475
\(279\) −1.84740 −0.110601
\(280\) 0 0
\(281\) −1.20264 −0.0717434 −0.0358717 0.999356i \(-0.511421\pi\)
−0.0358717 + 0.999356i \(0.511421\pi\)
\(282\) 11.7129 0.697492
\(283\) −5.10533 −0.303480 −0.151740 0.988420i \(-0.548488\pi\)
−0.151740 + 0.988420i \(0.548488\pi\)
\(284\) −17.2319 −1.02252
\(285\) 8.20916 0.486269
\(286\) 2.13986 0.126533
\(287\) 0 0
\(288\) −7.06979 −0.416591
\(289\) −6.35447 −0.373792
\(290\) 5.71015 0.335311
\(291\) 0.622368 0.0364839
\(292\) −9.21860 −0.539478
\(293\) −28.2532 −1.65057 −0.825286 0.564715i \(-0.808986\pi\)
−0.825286 + 0.564715i \(0.808986\pi\)
\(294\) 0 0
\(295\) 5.68203 0.330821
\(296\) 5.55394 0.322816
\(297\) 1.19223 0.0691803
\(298\) −19.1119 −1.10712
\(299\) −6.69126 −0.386966
\(300\) −4.90396 −0.283130
\(301\) 0 0
\(302\) −32.1855 −1.85207
\(303\) −7.06334 −0.405779
\(304\) 29.1751 1.67330
\(305\) −6.45841 −0.369808
\(306\) 6.12065 0.349894
\(307\) 1.22364 0.0698370 0.0349185 0.999390i \(-0.488883\pi\)
0.0349185 + 0.999390i \(0.488883\pi\)
\(308\) 0 0
\(309\) 17.8241 1.01398
\(310\) 4.61292 0.261996
\(311\) −7.70437 −0.436875 −0.218437 0.975851i \(-0.570096\pi\)
−0.218437 + 0.975851i \(0.570096\pi\)
\(312\) −0.863187 −0.0488683
\(313\) 2.06116 0.116504 0.0582518 0.998302i \(-0.481447\pi\)
0.0582518 + 0.998302i \(0.481447\pi\)
\(314\) 32.1632 1.81508
\(315\) 0 0
\(316\) −21.5186 −1.21051
\(317\) −10.8641 −0.610187 −0.305093 0.952322i \(-0.598688\pi\)
−0.305093 + 0.952322i \(0.598688\pi\)
\(318\) 22.2624 1.24841
\(319\) −2.72643 −0.152651
\(320\) 5.05969 0.282845
\(321\) 10.7720 0.601234
\(322\) 0 0
\(323\) −20.1225 −1.11965
\(324\) 1.51907 0.0843929
\(325\) −3.08873 −0.171332
\(326\) 18.1906 1.00748
\(327\) −9.04356 −0.500110
\(328\) −0.902182 −0.0498147
\(329\) 0 0
\(330\) −2.97697 −0.163877
\(331\) 28.8910 1.58799 0.793997 0.607921i \(-0.207996\pi\)
0.793997 + 0.607921i \(0.207996\pi\)
\(332\) 3.19725 0.175472
\(333\) −6.15612 −0.337353
\(334\) 3.34226 0.182880
\(335\) −5.00560 −0.273485
\(336\) 0 0
\(337\) 20.3472 1.10838 0.554192 0.832389i \(-0.313027\pi\)
0.554192 + 0.832389i \(0.313027\pi\)
\(338\) −22.6697 −1.23307
\(339\) −5.09784 −0.276877
\(340\) −6.59723 −0.357785
\(341\) −2.20253 −0.119274
\(342\) −11.5695 −0.625605
\(343\) 0 0
\(344\) 5.39649 0.290959
\(345\) 9.30887 0.501173
\(346\) −14.9241 −0.802322
\(347\) 8.70651 0.467390 0.233695 0.972310i \(-0.424918\pi\)
0.233695 + 0.972310i \(0.424918\pi\)
\(348\) −3.47386 −0.186218
\(349\) 0.668717 0.0357956 0.0178978 0.999840i \(-0.494303\pi\)
0.0178978 + 0.999840i \(0.494303\pi\)
\(350\) 0 0
\(351\) 0.956777 0.0510690
\(352\) −8.42883 −0.449258
\(353\) −11.0813 −0.589798 −0.294899 0.955528i \(-0.595286\pi\)
−0.294899 + 0.955528i \(0.595286\pi\)
\(354\) −8.00789 −0.425615
\(355\) 15.0992 0.801382
\(356\) −14.7595 −0.782252
\(357\) 0 0
\(358\) 12.2897 0.649531
\(359\) −9.64446 −0.509015 −0.254507 0.967071i \(-0.581913\pi\)
−0.254507 + 0.967071i \(0.581913\pi\)
\(360\) 1.20086 0.0632911
\(361\) 19.0363 1.00191
\(362\) −30.9084 −1.62451
\(363\) −9.57858 −0.502745
\(364\) 0 0
\(365\) 8.07768 0.422805
\(366\) 9.10207 0.475773
\(367\) 35.5344 1.85488 0.927440 0.373971i \(-0.122004\pi\)
0.927440 + 0.373971i \(0.122004\pi\)
\(368\) 33.0834 1.72459
\(369\) 1.00000 0.0520579
\(370\) 15.3717 0.799135
\(371\) 0 0
\(372\) −2.80634 −0.145502
\(373\) 0.914929 0.0473732 0.0236866 0.999719i \(-0.492460\pi\)
0.0236866 + 0.999719i \(0.492460\pi\)
\(374\) 7.29723 0.377331
\(375\) 10.9524 0.565578
\(376\) −5.63305 −0.290503
\(377\) −2.18799 −0.112687
\(378\) 0 0
\(379\) −1.54979 −0.0796071 −0.0398036 0.999208i \(-0.512673\pi\)
−0.0398036 + 0.999208i \(0.512673\pi\)
\(380\) 12.4703 0.639713
\(381\) 9.16734 0.469657
\(382\) −42.3922 −2.16897
\(383\) 38.3803 1.96114 0.980570 0.196167i \(-0.0628496\pi\)
0.980570 + 0.196167i \(0.0628496\pi\)
\(384\) 7.00879 0.357666
\(385\) 0 0
\(386\) −4.88877 −0.248832
\(387\) −5.98160 −0.304062
\(388\) 0.945422 0.0479965
\(389\) 4.21777 0.213849 0.106925 0.994267i \(-0.465900\pi\)
0.106925 + 0.994267i \(0.465900\pi\)
\(390\) −2.38905 −0.120974
\(391\) −22.8182 −1.15396
\(392\) 0 0
\(393\) 4.49020 0.226501
\(394\) −30.7394 −1.54863
\(395\) 18.8554 0.948717
\(396\) 1.81108 0.0910104
\(397\) 29.8860 1.49993 0.749967 0.661475i \(-0.230069\pi\)
0.749967 + 0.661475i \(0.230069\pi\)
\(398\) −15.9837 −0.801190
\(399\) 0 0
\(400\) 15.2715 0.763575
\(401\) 17.2699 0.862417 0.431209 0.902252i \(-0.358087\pi\)
0.431209 + 0.902252i \(0.358087\pi\)
\(402\) 7.05457 0.351850
\(403\) −1.76755 −0.0880481
\(404\) −10.7297 −0.533824
\(405\) −1.33107 −0.0661412
\(406\) 0 0
\(407\) −7.33952 −0.363807
\(408\) −2.94359 −0.145730
\(409\) 0.572746 0.0283205 0.0141602 0.999900i \(-0.495493\pi\)
0.0141602 + 0.999900i \(0.495493\pi\)
\(410\) −2.49697 −0.123317
\(411\) −7.16553 −0.353450
\(412\) 27.0761 1.33395
\(413\) 0 0
\(414\) −13.1193 −0.644779
\(415\) −2.80155 −0.137522
\(416\) −6.76421 −0.331643
\(417\) −10.8857 −0.533073
\(418\) −13.7935 −0.674661
\(419\) −9.37586 −0.458041 −0.229020 0.973422i \(-0.573552\pi\)
−0.229020 + 0.973422i \(0.573552\pi\)
\(420\) 0 0
\(421\) 0.621048 0.0302680 0.0151340 0.999885i \(-0.495183\pi\)
0.0151340 + 0.999885i \(0.495183\pi\)
\(422\) 43.2112 2.10349
\(423\) 6.24381 0.303585
\(424\) −10.7066 −0.519958
\(425\) −10.5330 −0.510926
\(426\) −21.2798 −1.03101
\(427\) 0 0
\(428\) 16.3634 0.790957
\(429\) 1.14070 0.0550735
\(430\) 14.9359 0.720273
\(431\) 39.2853 1.89231 0.946154 0.323718i \(-0.104933\pi\)
0.946154 + 0.323718i \(0.104933\pi\)
\(432\) −4.73056 −0.227599
\(433\) 6.54587 0.314575 0.157287 0.987553i \(-0.449725\pi\)
0.157287 + 0.987553i \(0.449725\pi\)
\(434\) 0 0
\(435\) 3.04392 0.145945
\(436\) −13.7378 −0.657922
\(437\) 43.1317 2.06327
\(438\) −11.3842 −0.543956
\(439\) −11.9986 −0.572664 −0.286332 0.958130i \(-0.592436\pi\)
−0.286332 + 0.958130i \(0.592436\pi\)
\(440\) 1.43171 0.0682540
\(441\) 0 0
\(442\) 5.85610 0.278546
\(443\) −4.85767 −0.230795 −0.115397 0.993319i \(-0.536814\pi\)
−0.115397 + 0.993319i \(0.536814\pi\)
\(444\) −9.35160 −0.443807
\(445\) 12.9328 0.613074
\(446\) 17.9416 0.849561
\(447\) −10.1880 −0.481876
\(448\) 0 0
\(449\) 8.35529 0.394311 0.197155 0.980372i \(-0.436830\pi\)
0.197155 + 0.980372i \(0.436830\pi\)
\(450\) −6.05596 −0.285481
\(451\) 1.19223 0.0561400
\(452\) −7.74399 −0.364247
\(453\) −17.1572 −0.806114
\(454\) 46.4358 2.17934
\(455\) 0 0
\(456\) 5.56408 0.260562
\(457\) −38.9673 −1.82281 −0.911407 0.411506i \(-0.865003\pi\)
−0.911407 + 0.411506i \(0.865003\pi\)
\(458\) 6.28864 0.293849
\(459\) 3.26275 0.152292
\(460\) 14.1408 0.659320
\(461\) 23.6532 1.10164 0.550819 0.834625i \(-0.314315\pi\)
0.550819 + 0.834625i \(0.314315\pi\)
\(462\) 0 0
\(463\) −1.86553 −0.0866985 −0.0433492 0.999060i \(-0.513803\pi\)
−0.0433492 + 0.999060i \(0.513803\pi\)
\(464\) 10.8180 0.502213
\(465\) 2.45902 0.114034
\(466\) −1.91978 −0.0889322
\(467\) 5.20134 0.240689 0.120345 0.992732i \(-0.461600\pi\)
0.120345 + 0.992732i \(0.461600\pi\)
\(468\) 1.45341 0.0671841
\(469\) 0 0
\(470\) −15.5906 −0.719142
\(471\) 17.1453 0.790014
\(472\) 3.85122 0.177267
\(473\) −7.13145 −0.327905
\(474\) −26.5735 −1.22056
\(475\) 19.9098 0.913526
\(476\) 0 0
\(477\) 11.8675 0.543373
\(478\) −49.5506 −2.26639
\(479\) −2.97785 −0.136062 −0.0680308 0.997683i \(-0.521672\pi\)
−0.0680308 + 0.997683i \(0.521672\pi\)
\(480\) 9.41036 0.429522
\(481\) −5.89004 −0.268563
\(482\) 41.4760 1.88918
\(483\) 0 0
\(484\) −14.5506 −0.661389
\(485\) −0.828414 −0.0376163
\(486\) 1.87592 0.0850934
\(487\) 41.2011 1.86700 0.933500 0.358578i \(-0.116738\pi\)
0.933500 + 0.358578i \(0.116738\pi\)
\(488\) −4.37744 −0.198157
\(489\) 9.69691 0.438509
\(490\) 0 0
\(491\) −9.81187 −0.442803 −0.221402 0.975183i \(-0.571063\pi\)
−0.221402 + 0.975183i \(0.571063\pi\)
\(492\) 1.51907 0.0684851
\(493\) −7.46135 −0.336042
\(494\) −11.0694 −0.498036
\(495\) −1.58694 −0.0713276
\(496\) 8.73926 0.392404
\(497\) 0 0
\(498\) 3.94832 0.176928
\(499\) 15.2282 0.681708 0.340854 0.940116i \(-0.389284\pi\)
0.340854 + 0.940116i \(0.389284\pi\)
\(500\) 16.6374 0.744048
\(501\) 1.78167 0.0795989
\(502\) −37.0703 −1.65453
\(503\) −7.15496 −0.319024 −0.159512 0.987196i \(-0.550992\pi\)
−0.159512 + 0.987196i \(0.550992\pi\)
\(504\) 0 0
\(505\) 9.40178 0.418374
\(506\) −15.6413 −0.695339
\(507\) −12.0846 −0.536695
\(508\) 13.9258 0.617860
\(509\) −2.75329 −0.122037 −0.0610187 0.998137i \(-0.519435\pi\)
−0.0610187 + 0.998137i \(0.519435\pi\)
\(510\) −8.14700 −0.360755
\(511\) 0 0
\(512\) 24.9084 1.10081
\(513\) −6.16735 −0.272295
\(514\) −32.7332 −1.44380
\(515\) −23.7251 −1.04545
\(516\) −9.08649 −0.400010
\(517\) 7.44407 0.327390
\(518\) 0 0
\(519\) −7.95559 −0.349212
\(520\) 1.14896 0.0503852
\(521\) −21.3386 −0.934861 −0.467431 0.884030i \(-0.654820\pi\)
−0.467431 + 0.884030i \(0.654820\pi\)
\(522\) −4.28990 −0.187764
\(523\) −5.54381 −0.242414 −0.121207 0.992627i \(-0.538676\pi\)
−0.121207 + 0.992627i \(0.538676\pi\)
\(524\) 6.82094 0.297974
\(525\) 0 0
\(526\) 40.2182 1.75360
\(527\) −6.02761 −0.262567
\(528\) −5.63993 −0.245446
\(529\) 25.9096 1.12651
\(530\) −29.6327 −1.28716
\(531\) −4.26878 −0.185249
\(532\) 0 0
\(533\) 0.956777 0.0414426
\(534\) −18.2267 −0.788745
\(535\) −14.3382 −0.619896
\(536\) −3.39274 −0.146544
\(537\) 6.55130 0.282709
\(538\) 3.79028 0.163411
\(539\) 0 0
\(540\) −2.02199 −0.0870124
\(541\) 9.42177 0.405073 0.202537 0.979275i \(-0.435081\pi\)
0.202537 + 0.979275i \(0.435081\pi\)
\(542\) 20.8098 0.893859
\(543\) −16.4764 −0.707071
\(544\) −23.0670 −0.988987
\(545\) 12.0376 0.515633
\(546\) 0 0
\(547\) 24.9252 1.06573 0.532863 0.846202i \(-0.321116\pi\)
0.532863 + 0.846202i \(0.321116\pi\)
\(548\) −10.8850 −0.464982
\(549\) 4.85206 0.207081
\(550\) −7.22010 −0.307866
\(551\) 14.1037 0.600837
\(552\) 6.30945 0.268548
\(553\) 0 0
\(554\) 26.1325 1.11026
\(555\) 8.19421 0.347825
\(556\) −16.5361 −0.701287
\(557\) 7.44490 0.315451 0.157725 0.987483i \(-0.449584\pi\)
0.157725 + 0.987483i \(0.449584\pi\)
\(558\) −3.46558 −0.146710
\(559\) −5.72306 −0.242060
\(560\) 0 0
\(561\) 3.88995 0.164234
\(562\) −2.25605 −0.0951658
\(563\) 33.3241 1.40444 0.702222 0.711958i \(-0.252191\pi\)
0.702222 + 0.711958i \(0.252191\pi\)
\(564\) 9.48480 0.399382
\(565\) 6.78557 0.285471
\(566\) −9.57719 −0.402559
\(567\) 0 0
\(568\) 10.2341 0.429412
\(569\) 33.6371 1.41014 0.705071 0.709137i \(-0.250915\pi\)
0.705071 + 0.709137i \(0.250915\pi\)
\(570\) 15.3997 0.645023
\(571\) 16.5003 0.690518 0.345259 0.938507i \(-0.387791\pi\)
0.345259 + 0.938507i \(0.387791\pi\)
\(572\) 1.73280 0.0724522
\(573\) −22.5981 −0.944049
\(574\) 0 0
\(575\) 22.5770 0.941525
\(576\) −3.80123 −0.158384
\(577\) 16.8768 0.702592 0.351296 0.936265i \(-0.385741\pi\)
0.351296 + 0.936265i \(0.385741\pi\)
\(578\) −11.9205 −0.495826
\(579\) −2.60607 −0.108304
\(580\) 4.62393 0.191998
\(581\) 0 0
\(582\) 1.16751 0.0483949
\(583\) 14.1487 0.585981
\(584\) 5.47496 0.226555
\(585\) −1.27353 −0.0526542
\(586\) −53.0008 −2.18944
\(587\) −25.8123 −1.06539 −0.532694 0.846308i \(-0.678820\pi\)
−0.532694 + 0.846308i \(0.678820\pi\)
\(588\) 0 0
\(589\) 11.3936 0.469465
\(590\) 10.6590 0.438826
\(591\) −16.3863 −0.674042
\(592\) 29.1219 1.19690
\(593\) 17.2786 0.709547 0.354774 0.934952i \(-0.384558\pi\)
0.354774 + 0.934952i \(0.384558\pi\)
\(594\) 2.23653 0.0917659
\(595\) 0 0
\(596\) −15.4763 −0.633934
\(597\) −8.52046 −0.348719
\(598\) −12.5523 −0.513300
\(599\) 25.0317 1.02277 0.511384 0.859352i \(-0.329133\pi\)
0.511384 + 0.859352i \(0.329133\pi\)
\(600\) 2.91248 0.118901
\(601\) 31.0336 1.26589 0.632944 0.774198i \(-0.281846\pi\)
0.632944 + 0.774198i \(0.281846\pi\)
\(602\) 0 0
\(603\) 3.76060 0.153143
\(604\) −26.0630 −1.06049
\(605\) 12.7497 0.518350
\(606\) −13.2503 −0.538255
\(607\) −8.46352 −0.343524 −0.171762 0.985138i \(-0.554946\pi\)
−0.171762 + 0.985138i \(0.554946\pi\)
\(608\) 43.6019 1.76829
\(609\) 0 0
\(610\) −12.1155 −0.490540
\(611\) 5.97394 0.241680
\(612\) 4.95635 0.200349
\(613\) −40.4704 −1.63458 −0.817291 0.576225i \(-0.804525\pi\)
−0.817291 + 0.576225i \(0.804525\pi\)
\(614\) 2.29546 0.0926370
\(615\) −1.33107 −0.0536738
\(616\) 0 0
\(617\) −32.0283 −1.28941 −0.644706 0.764430i \(-0.723020\pi\)
−0.644706 + 0.764430i \(0.723020\pi\)
\(618\) 33.4366 1.34502
\(619\) −40.1469 −1.61364 −0.806819 0.590798i \(-0.798813\pi\)
−0.806819 + 0.590798i \(0.798813\pi\)
\(620\) 3.73542 0.150018
\(621\) −6.99354 −0.280641
\(622\) −14.4528 −0.579504
\(623\) 0 0
\(624\) −4.52610 −0.181189
\(625\) 1.56298 0.0625194
\(626\) 3.86657 0.154539
\(627\) −7.35291 −0.293647
\(628\) 26.0450 1.03931
\(629\) −20.0859 −0.800877
\(630\) 0 0
\(631\) 8.26664 0.329090 0.164545 0.986370i \(-0.447384\pi\)
0.164545 + 0.986370i \(0.447384\pi\)
\(632\) 12.7800 0.508359
\(633\) 23.0347 0.915546
\(634\) −20.3801 −0.809398
\(635\) −12.2023 −0.484235
\(636\) 18.0275 0.714837
\(637\) 0 0
\(638\) −5.11456 −0.202487
\(639\) −11.3437 −0.448749
\(640\) −9.32916 −0.368768
\(641\) −10.8409 −0.428189 −0.214094 0.976813i \(-0.568680\pi\)
−0.214094 + 0.976813i \(0.568680\pi\)
\(642\) 20.2074 0.797522
\(643\) −27.7902 −1.09594 −0.547969 0.836499i \(-0.684599\pi\)
−0.547969 + 0.836499i \(0.684599\pi\)
\(644\) 0 0
\(645\) 7.96191 0.313500
\(646\) −37.7482 −1.48518
\(647\) −34.1540 −1.34273 −0.671366 0.741126i \(-0.734292\pi\)
−0.671366 + 0.741126i \(0.734292\pi\)
\(648\) −0.902182 −0.0354411
\(649\) −5.08938 −0.199775
\(650\) −5.79420 −0.227267
\(651\) 0 0
\(652\) 14.7303 0.576883
\(653\) −0.920987 −0.0360410 −0.0180205 0.999838i \(-0.505736\pi\)
−0.0180205 + 0.999838i \(0.505736\pi\)
\(654\) −16.9650 −0.663383
\(655\) −5.97675 −0.233531
\(656\) −4.73056 −0.184698
\(657\) −6.06858 −0.236758
\(658\) 0 0
\(659\) 5.06675 0.197372 0.0986862 0.995119i \(-0.468536\pi\)
0.0986862 + 0.995119i \(0.468536\pi\)
\(660\) −2.41067 −0.0938354
\(661\) −22.6196 −0.879801 −0.439901 0.898046i \(-0.644986\pi\)
−0.439901 + 0.898046i \(0.644986\pi\)
\(662\) 54.1972 2.10644
\(663\) 3.12172 0.121238
\(664\) −1.89886 −0.0736899
\(665\) 0 0
\(666\) −11.5484 −0.447491
\(667\) 15.9930 0.619253
\(668\) 2.70648 0.104717
\(669\) 9.56418 0.369773
\(670\) −9.39011 −0.362772
\(671\) 5.78477 0.223319
\(672\) 0 0
\(673\) 13.7602 0.530418 0.265209 0.964191i \(-0.414559\pi\)
0.265209 + 0.964191i \(0.414559\pi\)
\(674\) 38.1697 1.47024
\(675\) −3.22826 −0.124256
\(676\) −18.3573 −0.706052
\(677\) 0.583084 0.0224097 0.0112049 0.999937i \(-0.496433\pi\)
0.0112049 + 0.999937i \(0.496433\pi\)
\(678\) −9.56314 −0.367270
\(679\) 0 0
\(680\) 3.91812 0.150253
\(681\) 24.7536 0.948561
\(682\) −4.13177 −0.158214
\(683\) 27.6868 1.05941 0.529704 0.848183i \(-0.322303\pi\)
0.529704 + 0.848183i \(0.322303\pi\)
\(684\) −9.36866 −0.358220
\(685\) 9.53780 0.364420
\(686\) 0 0
\(687\) 3.35230 0.127898
\(688\) 28.2964 1.07879
\(689\) 11.3545 0.432572
\(690\) 17.4627 0.664793
\(691\) −14.8271 −0.564049 −0.282025 0.959407i \(-0.591006\pi\)
−0.282025 + 0.959407i \(0.591006\pi\)
\(692\) −12.0851 −0.459407
\(693\) 0 0
\(694\) 16.3327 0.619981
\(695\) 14.4895 0.549620
\(696\) 2.06314 0.0782029
\(697\) 3.26275 0.123585
\(698\) 1.25446 0.0474820
\(699\) −1.02338 −0.0387079
\(700\) 0 0
\(701\) 2.79286 0.105485 0.0527424 0.998608i \(-0.483204\pi\)
0.0527424 + 0.998608i \(0.483204\pi\)
\(702\) 1.79484 0.0677417
\(703\) 37.9670 1.43195
\(704\) −4.53194 −0.170804
\(705\) −8.31093 −0.313008
\(706\) −20.7876 −0.782353
\(707\) 0 0
\(708\) −6.48459 −0.243706
\(709\) −42.6863 −1.60312 −0.801558 0.597917i \(-0.795995\pi\)
−0.801558 + 0.597917i \(0.795995\pi\)
\(710\) 28.3249 1.06301
\(711\) −14.1656 −0.531252
\(712\) 8.76572 0.328509
\(713\) 12.9199 0.483854
\(714\) 0 0
\(715\) −1.51835 −0.0567830
\(716\) 9.95189 0.371920
\(717\) −26.4140 −0.986449
\(718\) −18.0922 −0.675196
\(719\) −44.1357 −1.64598 −0.822992 0.568053i \(-0.807697\pi\)
−0.822992 + 0.568053i \(0.807697\pi\)
\(720\) 6.29670 0.234664
\(721\) 0 0
\(722\) 35.7105 1.32901
\(723\) 22.1097 0.822268
\(724\) −25.0289 −0.930191
\(725\) 7.38248 0.274178
\(726\) −17.9686 −0.666879
\(727\) 13.6510 0.506288 0.253144 0.967429i \(-0.418535\pi\)
0.253144 + 0.967429i \(0.418535\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 15.1531 0.560840
\(731\) −19.5165 −0.721843
\(732\) 7.37062 0.272426
\(733\) −15.2128 −0.561896 −0.280948 0.959723i \(-0.590649\pi\)
−0.280948 + 0.959723i \(0.590649\pi\)
\(734\) 66.6597 2.46045
\(735\) 0 0
\(736\) 49.4429 1.82249
\(737\) 4.48350 0.165152
\(738\) 1.87592 0.0690535
\(739\) 12.6595 0.465689 0.232844 0.972514i \(-0.425197\pi\)
0.232844 + 0.972514i \(0.425197\pi\)
\(740\) 12.4476 0.457583
\(741\) −5.90078 −0.216771
\(742\) 0 0
\(743\) −32.8862 −1.20648 −0.603238 0.797561i \(-0.706123\pi\)
−0.603238 + 0.797561i \(0.706123\pi\)
\(744\) 1.66669 0.0611040
\(745\) 13.5609 0.496833
\(746\) 1.71633 0.0628394
\(747\) 2.10474 0.0770083
\(748\) 5.90912 0.216059
\(749\) 0 0
\(750\) 20.5457 0.750225
\(751\) 5.59396 0.204127 0.102063 0.994778i \(-0.467456\pi\)
0.102063 + 0.994778i \(0.467456\pi\)
\(752\) −29.5368 −1.07709
\(753\) −19.7611 −0.720136
\(754\) −4.10448 −0.149476
\(755\) 22.8373 0.831136
\(756\) 0 0
\(757\) −49.2675 −1.79066 −0.895329 0.445406i \(-0.853059\pi\)
−0.895329 + 0.445406i \(0.853059\pi\)
\(758\) −2.90727 −0.105597
\(759\) −8.33792 −0.302647
\(760\) −7.40616 −0.268649
\(761\) −37.0827 −1.34425 −0.672123 0.740439i \(-0.734618\pi\)
−0.672123 + 0.740439i \(0.734618\pi\)
\(762\) 17.1972 0.622988
\(763\) 0 0
\(764\) −34.3281 −1.24195
\(765\) −4.34294 −0.157019
\(766\) 71.9983 2.60140
\(767\) −4.08427 −0.147475
\(768\) 20.7504 0.748765
\(769\) 46.4807 1.67614 0.838069 0.545564i \(-0.183684\pi\)
0.838069 + 0.545564i \(0.183684\pi\)
\(770\) 0 0
\(771\) −17.4492 −0.628416
\(772\) −3.95880 −0.142480
\(773\) 53.4446 1.92227 0.961134 0.276081i \(-0.0890360\pi\)
0.961134 + 0.276081i \(0.0890360\pi\)
\(774\) −11.2210 −0.403331
\(775\) 5.96390 0.214230
\(776\) −0.561489 −0.0201563
\(777\) 0 0
\(778\) 7.91219 0.283666
\(779\) −6.16735 −0.220968
\(780\) −1.93459 −0.0692694
\(781\) −13.5243 −0.483937
\(782\) −42.8050 −1.53071
\(783\) −2.28683 −0.0817246
\(784\) 0 0
\(785\) −22.8216 −0.814536
\(786\) 8.42325 0.300447
\(787\) 19.7132 0.702700 0.351350 0.936244i \(-0.385723\pi\)
0.351350 + 0.936244i \(0.385723\pi\)
\(788\) −24.8920 −0.886739
\(789\) 21.4392 0.763255
\(790\) 35.3711 1.25845
\(791\) 0 0
\(792\) −1.07561 −0.0382201
\(793\) 4.64234 0.164854
\(794\) 56.0637 1.98962
\(795\) −15.7964 −0.560239
\(796\) −12.9432 −0.458759
\(797\) −42.7009 −1.51254 −0.756271 0.654259i \(-0.772981\pi\)
−0.756271 + 0.654259i \(0.772981\pi\)
\(798\) 0 0
\(799\) 20.3720 0.720709
\(800\) 22.8231 0.806920
\(801\) −9.71613 −0.343303
\(802\) 32.3969 1.14397
\(803\) −7.23515 −0.255323
\(804\) 5.71262 0.201468
\(805\) 0 0
\(806\) −3.31579 −0.116794
\(807\) 2.02049 0.0711248
\(808\) 6.37242 0.224181
\(809\) −6.30079 −0.221524 −0.110762 0.993847i \(-0.535329\pi\)
−0.110762 + 0.993847i \(0.535329\pi\)
\(810\) −2.49697 −0.0877347
\(811\) −21.0846 −0.740379 −0.370189 0.928956i \(-0.620707\pi\)
−0.370189 + 0.928956i \(0.620707\pi\)
\(812\) 0 0
\(813\) 11.0931 0.389054
\(814\) −13.7683 −0.482580
\(815\) −12.9072 −0.452121
\(816\) −15.4346 −0.540321
\(817\) 36.8907 1.29064
\(818\) 1.07443 0.0375664
\(819\) 0 0
\(820\) −2.02199 −0.0706108
\(821\) −4.52453 −0.157907 −0.0789537 0.996878i \(-0.525158\pi\)
−0.0789537 + 0.996878i \(0.525158\pi\)
\(822\) −13.4420 −0.468842
\(823\) −40.2931 −1.40453 −0.702264 0.711916i \(-0.747827\pi\)
−0.702264 + 0.711916i \(0.747827\pi\)
\(824\) −16.0806 −0.560195
\(825\) −3.84883 −0.133999
\(826\) 0 0
\(827\) −11.1628 −0.388169 −0.194085 0.980985i \(-0.562174\pi\)
−0.194085 + 0.980985i \(0.562174\pi\)
\(828\) −10.6237 −0.369199
\(829\) −38.5413 −1.33859 −0.669297 0.742995i \(-0.733404\pi\)
−0.669297 + 0.742995i \(0.733404\pi\)
\(830\) −5.25547 −0.182420
\(831\) 13.9305 0.483243
\(832\) −3.63693 −0.126088
\(833\) 0 0
\(834\) −20.4206 −0.707108
\(835\) −2.37151 −0.0820697
\(836\) −11.1696 −0.386309
\(837\) −1.84740 −0.0638556
\(838\) −17.5883 −0.607579
\(839\) 0.657012 0.0226826 0.0113413 0.999936i \(-0.496390\pi\)
0.0113413 + 0.999936i \(0.496390\pi\)
\(840\) 0 0
\(841\) −23.7704 −0.819670
\(842\) 1.16504 0.0401498
\(843\) −1.20264 −0.0414211
\(844\) 34.9913 1.20445
\(845\) 16.0854 0.553354
\(846\) 11.7129 0.402697
\(847\) 0 0
\(848\) −56.1397 −1.92785
\(849\) −5.10533 −0.175214
\(850\) −19.7591 −0.677730
\(851\) 43.0531 1.47584
\(852\) −17.2319 −0.590354
\(853\) −2.29577 −0.0786058 −0.0393029 0.999227i \(-0.512514\pi\)
−0.0393029 + 0.999227i \(0.512514\pi\)
\(854\) 0 0
\(855\) 8.20916 0.280747
\(856\) −9.71830 −0.332165
\(857\) −18.9064 −0.645830 −0.322915 0.946428i \(-0.604663\pi\)
−0.322915 + 0.946428i \(0.604663\pi\)
\(858\) 2.13986 0.0730536
\(859\) −33.0093 −1.12626 −0.563131 0.826368i \(-0.690403\pi\)
−0.563131 + 0.826368i \(0.690403\pi\)
\(860\) 12.0947 0.412426
\(861\) 0 0
\(862\) 73.6961 2.51010
\(863\) −32.3940 −1.10271 −0.551353 0.834272i \(-0.685888\pi\)
−0.551353 + 0.834272i \(0.685888\pi\)
\(864\) −7.06979 −0.240519
\(865\) 10.5894 0.360051
\(866\) 12.2795 0.417275
\(867\) −6.35447 −0.215809
\(868\) 0 0
\(869\) −16.8887 −0.572909
\(870\) 5.71015 0.193592
\(871\) 3.59805 0.121915
\(872\) 8.15893 0.276296
\(873\) 0.622368 0.0210640
\(874\) 80.9115 2.73687
\(875\) 0 0
\(876\) −9.21860 −0.311468
\(877\) 2.48394 0.0838768 0.0419384 0.999120i \(-0.486647\pi\)
0.0419384 + 0.999120i \(0.486647\pi\)
\(878\) −22.5085 −0.759625
\(879\) −28.2532 −0.952958
\(880\) 7.50712 0.253065
\(881\) −4.62881 −0.155949 −0.0779744 0.996955i \(-0.524845\pi\)
−0.0779744 + 0.996955i \(0.524845\pi\)
\(882\) 0 0
\(883\) 13.8165 0.464962 0.232481 0.972601i \(-0.425316\pi\)
0.232481 + 0.972601i \(0.425316\pi\)
\(884\) 4.74212 0.159495
\(885\) 5.68203 0.190999
\(886\) −9.11260 −0.306144
\(887\) 13.3709 0.448950 0.224475 0.974480i \(-0.427933\pi\)
0.224475 + 0.974480i \(0.427933\pi\)
\(888\) 5.55394 0.186378
\(889\) 0 0
\(890\) 24.2609 0.813228
\(891\) 1.19223 0.0399412
\(892\) 14.5287 0.486456
\(893\) −38.5078 −1.28861
\(894\) −19.1119 −0.639196
\(895\) −8.72021 −0.291485
\(896\) 0 0
\(897\) −6.69126 −0.223415
\(898\) 15.6739 0.523043
\(899\) 4.22470 0.140901
\(900\) −4.90396 −0.163465
\(901\) 38.7205 1.28997
\(902\) 2.23653 0.0744683
\(903\) 0 0
\(904\) 4.59918 0.152966
\(905\) 21.9312 0.729018
\(906\) −32.1855 −1.06929
\(907\) 35.7979 1.18865 0.594325 0.804225i \(-0.297419\pi\)
0.594325 + 0.804225i \(0.297419\pi\)
\(908\) 37.6025 1.24788
\(909\) −7.06334 −0.234276
\(910\) 0 0
\(911\) 42.9779 1.42392 0.711960 0.702220i \(-0.247808\pi\)
0.711960 + 0.702220i \(0.247808\pi\)
\(912\) 29.1751 0.966083
\(913\) 2.50933 0.0830468
\(914\) −73.0995 −2.41792
\(915\) −6.45841 −0.213508
\(916\) 5.09238 0.168257
\(917\) 0 0
\(918\) 6.12065 0.202012
\(919\) 13.4263 0.442893 0.221447 0.975173i \(-0.428922\pi\)
0.221447 + 0.975173i \(0.428922\pi\)
\(920\) −8.39829 −0.276884
\(921\) 1.22364 0.0403204
\(922\) 44.3715 1.46130
\(923\) −10.8534 −0.357243
\(924\) 0 0
\(925\) 19.8736 0.653439
\(926\) −3.49958 −0.115003
\(927\) 17.8241 0.585421
\(928\) 16.1674 0.530721
\(929\) 32.5053 1.06646 0.533232 0.845969i \(-0.320977\pi\)
0.533232 + 0.845969i \(0.320977\pi\)
\(930\) 4.61292 0.151264
\(931\) 0 0
\(932\) −1.55459 −0.0509223
\(933\) −7.70437 −0.252230
\(934\) 9.75729 0.319268
\(935\) −5.17778 −0.169332
\(936\) −0.863187 −0.0282142
\(937\) 10.0847 0.329454 0.164727 0.986339i \(-0.447326\pi\)
0.164727 + 0.986339i \(0.447326\pi\)
\(938\) 0 0
\(939\) 2.06116 0.0672634
\(940\) −12.6249 −0.411779
\(941\) −45.9898 −1.49923 −0.749613 0.661876i \(-0.769760\pi\)
−0.749613 + 0.661876i \(0.769760\pi\)
\(942\) 32.1632 1.04793
\(943\) −6.99354 −0.227741
\(944\) 20.1938 0.657251
\(945\) 0 0
\(946\) −13.3780 −0.434957
\(947\) 2.76566 0.0898719 0.0449359 0.998990i \(-0.485692\pi\)
0.0449359 + 0.998990i \(0.485692\pi\)
\(948\) −21.5186 −0.698891
\(949\) −5.80628 −0.188480
\(950\) 37.3492 1.21177
\(951\) −10.8641 −0.352292
\(952\) 0 0
\(953\) 9.52118 0.308421 0.154211 0.988038i \(-0.450717\pi\)
0.154211 + 0.988038i \(0.450717\pi\)
\(954\) 22.2624 0.720771
\(955\) 30.0796 0.973352
\(956\) −40.1248 −1.29773
\(957\) −2.72643 −0.0881329
\(958\) −5.58621 −0.180482
\(959\) 0 0
\(960\) 5.05969 0.163301
\(961\) −27.5871 −0.889906
\(962\) −11.0492 −0.356242
\(963\) 10.7720 0.347123
\(964\) 33.5862 1.08174
\(965\) 3.46885 0.111666
\(966\) 0 0
\(967\) −12.5417 −0.403314 −0.201657 0.979456i \(-0.564633\pi\)
−0.201657 + 0.979456i \(0.564633\pi\)
\(968\) 8.64163 0.277752
\(969\) −20.1225 −0.646429
\(970\) −1.55404 −0.0498971
\(971\) 1.59591 0.0512153 0.0256076 0.999672i \(-0.491848\pi\)
0.0256076 + 0.999672i \(0.491848\pi\)
\(972\) 1.51907 0.0487243
\(973\) 0 0
\(974\) 77.2899 2.47653
\(975\) −3.08873 −0.0989184
\(976\) −22.9530 −0.734707
\(977\) 3.70916 0.118667 0.0593333 0.998238i \(-0.481103\pi\)
0.0593333 + 0.998238i \(0.481103\pi\)
\(978\) 18.1906 0.581672
\(979\) −11.5839 −0.370222
\(980\) 0 0
\(981\) −9.04356 −0.288739
\(982\) −18.4063 −0.587368
\(983\) 14.2656 0.455001 0.227501 0.973778i \(-0.426945\pi\)
0.227501 + 0.973778i \(0.426945\pi\)
\(984\) −0.902182 −0.0287605
\(985\) 21.8112 0.694964
\(986\) −13.9969 −0.445752
\(987\) 0 0
\(988\) −8.96372 −0.285174
\(989\) 41.8326 1.33020
\(990\) −2.97697 −0.0946143
\(991\) 57.4385 1.82459 0.912297 0.409530i \(-0.134307\pi\)
0.912297 + 0.409530i \(0.134307\pi\)
\(992\) 13.0608 0.414680
\(993\) 28.8910 0.916829
\(994\) 0 0
\(995\) 11.3413 0.359543
\(996\) 3.19725 0.101309
\(997\) −28.4978 −0.902534 −0.451267 0.892389i \(-0.649028\pi\)
−0.451267 + 0.892389i \(0.649028\pi\)
\(998\) 28.5669 0.904268
\(999\) −6.15612 −0.194771
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 \(a_p\))