Properties

Label 6027.2.a.bm.1.16
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 1.16
Root \(-2.14627\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.14627 q^{2} +1.00000 q^{3} +2.60647 q^{4} -2.36369 q^{5} +2.14627 q^{6} +1.30166 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.14627 q^{2} +1.00000 q^{3} +2.60647 q^{4} -2.36369 q^{5} +2.14627 q^{6} +1.30166 q^{8} +1.00000 q^{9} -5.07312 q^{10} -2.70007 q^{11} +2.60647 q^{12} -3.97235 q^{13} -2.36369 q^{15} -2.41924 q^{16} +6.48870 q^{17} +2.14627 q^{18} +7.54442 q^{19} -6.16090 q^{20} -5.79507 q^{22} -1.03945 q^{23} +1.30166 q^{24} +0.587030 q^{25} -8.52574 q^{26} +1.00000 q^{27} -8.83199 q^{29} -5.07312 q^{30} -2.51706 q^{31} -7.79566 q^{32} -2.70007 q^{33} +13.9265 q^{34} +2.60647 q^{36} -6.41148 q^{37} +16.1924 q^{38} -3.97235 q^{39} -3.07671 q^{40} +1.00000 q^{41} -0.547170 q^{43} -7.03765 q^{44} -2.36369 q^{45} -2.23094 q^{46} -3.62288 q^{47} -2.41924 q^{48} +1.25992 q^{50} +6.48870 q^{51} -10.3538 q^{52} -8.41749 q^{53} +2.14627 q^{54} +6.38212 q^{55} +7.54442 q^{57} -18.9558 q^{58} -12.6629 q^{59} -6.16090 q^{60} -4.26490 q^{61} -5.40229 q^{62} -11.8931 q^{64} +9.38941 q^{65} -5.79507 q^{66} -9.56262 q^{67} +16.9126 q^{68} -1.03945 q^{69} -6.72417 q^{71} +1.30166 q^{72} +7.72007 q^{73} -13.7608 q^{74} +0.587030 q^{75} +19.6643 q^{76} -8.52574 q^{78} +14.0058 q^{79} +5.71834 q^{80} +1.00000 q^{81} +2.14627 q^{82} +8.73964 q^{83} -15.3373 q^{85} -1.17437 q^{86} -8.83199 q^{87} -3.51456 q^{88} -16.8526 q^{89} -5.07312 q^{90} -2.70930 q^{92} -2.51706 q^{93} -7.77568 q^{94} -17.8327 q^{95} -7.79566 q^{96} +7.45775 q^{97} -2.70007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.14627 1.51764 0.758821 0.651299i \(-0.225776\pi\)
0.758821 + 0.651299i \(0.225776\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.60647 1.30324
\(5\) −2.36369 −1.05707 −0.528537 0.848910i \(-0.677259\pi\)
−0.528537 + 0.848910i \(0.677259\pi\)
\(6\) 2.14627 0.876211
\(7\) 0 0
\(8\) 1.30166 0.460205
\(9\) 1.00000 0.333333
\(10\) −5.07312 −1.60426
\(11\) −2.70007 −0.814101 −0.407050 0.913406i \(-0.633443\pi\)
−0.407050 + 0.913406i \(0.633443\pi\)
\(12\) 2.60647 0.752424
\(13\) −3.97235 −1.10173 −0.550866 0.834593i \(-0.685703\pi\)
−0.550866 + 0.834593i \(0.685703\pi\)
\(14\) 0 0
\(15\) −2.36369 −0.610302
\(16\) −2.41924 −0.604810
\(17\) 6.48870 1.57374 0.786871 0.617118i \(-0.211700\pi\)
0.786871 + 0.617118i \(0.211700\pi\)
\(18\) 2.14627 0.505881
\(19\) 7.54442 1.73081 0.865405 0.501073i \(-0.167061\pi\)
0.865405 + 0.501073i \(0.167061\pi\)
\(20\) −6.16090 −1.37762
\(21\) 0 0
\(22\) −5.79507 −1.23551
\(23\) −1.03945 −0.216740 −0.108370 0.994111i \(-0.534563\pi\)
−0.108370 + 0.994111i \(0.534563\pi\)
\(24\) 1.30166 0.265699
\(25\) 0.587030 0.117406
\(26\) −8.52574 −1.67204
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.83199 −1.64006 −0.820030 0.572321i \(-0.806043\pi\)
−0.820030 + 0.572321i \(0.806043\pi\)
\(30\) −5.07312 −0.926220
\(31\) −2.51706 −0.452077 −0.226038 0.974118i \(-0.572578\pi\)
−0.226038 + 0.974118i \(0.572578\pi\)
\(32\) −7.79566 −1.37809
\(33\) −2.70007 −0.470021
\(34\) 13.9265 2.38838
\(35\) 0 0
\(36\) 2.60647 0.434412
\(37\) −6.41148 −1.05404 −0.527020 0.849853i \(-0.676691\pi\)
−0.527020 + 0.849853i \(0.676691\pi\)
\(38\) 16.1924 2.62675
\(39\) −3.97235 −0.636086
\(40\) −3.07671 −0.486471
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −0.547170 −0.0834426 −0.0417213 0.999129i \(-0.513284\pi\)
−0.0417213 + 0.999129i \(0.513284\pi\)
\(44\) −7.03765 −1.06097
\(45\) −2.36369 −0.352358
\(46\) −2.23094 −0.328934
\(47\) −3.62288 −0.528451 −0.264226 0.964461i \(-0.585116\pi\)
−0.264226 + 0.964461i \(0.585116\pi\)
\(48\) −2.41924 −0.349188
\(49\) 0 0
\(50\) 1.25992 0.178180
\(51\) 6.48870 0.908600
\(52\) −10.3538 −1.43582
\(53\) −8.41749 −1.15623 −0.578116 0.815955i \(-0.696212\pi\)
−0.578116 + 0.815955i \(0.696212\pi\)
\(54\) 2.14627 0.292070
\(55\) 6.38212 0.860565
\(56\) 0 0
\(57\) 7.54442 0.999283
\(58\) −18.9558 −2.48902
\(59\) −12.6629 −1.64857 −0.824283 0.566178i \(-0.808421\pi\)
−0.824283 + 0.566178i \(0.808421\pi\)
\(60\) −6.16090 −0.795368
\(61\) −4.26490 −0.546065 −0.273032 0.962005i \(-0.588027\pi\)
−0.273032 + 0.962005i \(0.588027\pi\)
\(62\) −5.40229 −0.686091
\(63\) 0 0
\(64\) −11.8931 −1.48664
\(65\) 9.38941 1.16461
\(66\) −5.79507 −0.713324
\(67\) −9.56262 −1.16826 −0.584130 0.811660i \(-0.698564\pi\)
−0.584130 + 0.811660i \(0.698564\pi\)
\(68\) 16.9126 2.05096
\(69\) −1.03945 −0.125135
\(70\) 0 0
\(71\) −6.72417 −0.798012 −0.399006 0.916948i \(-0.630645\pi\)
−0.399006 + 0.916948i \(0.630645\pi\)
\(72\) 1.30166 0.153402
\(73\) 7.72007 0.903566 0.451783 0.892128i \(-0.350788\pi\)
0.451783 + 0.892128i \(0.350788\pi\)
\(74\) −13.7608 −1.59966
\(75\) 0.587030 0.0677844
\(76\) 19.6643 2.25566
\(77\) 0 0
\(78\) −8.52574 −0.965350
\(79\) 14.0058 1.57577 0.787887 0.615820i \(-0.211175\pi\)
0.787887 + 0.615820i \(0.211175\pi\)
\(80\) 5.71834 0.639330
\(81\) 1.00000 0.111111
\(82\) 2.14627 0.237016
\(83\) 8.73964 0.959301 0.479650 0.877460i \(-0.340764\pi\)
0.479650 + 0.877460i \(0.340764\pi\)
\(84\) 0 0
\(85\) −15.3373 −1.66356
\(86\) −1.17437 −0.126636
\(87\) −8.83199 −0.946889
\(88\) −3.51456 −0.374653
\(89\) −16.8526 −1.78637 −0.893185 0.449688i \(-0.851535\pi\)
−0.893185 + 0.449688i \(0.851535\pi\)
\(90\) −5.07312 −0.534753
\(91\) 0 0
\(92\) −2.70930 −0.282464
\(93\) −2.51706 −0.261007
\(94\) −7.77568 −0.802000
\(95\) −17.8327 −1.82959
\(96\) −7.79566 −0.795641
\(97\) 7.45775 0.757220 0.378610 0.925556i \(-0.376402\pi\)
0.378610 + 0.925556i \(0.376402\pi\)
\(98\) 0 0
\(99\) −2.70007 −0.271367
\(100\) 1.53008 0.153008
\(101\) −5.04947 −0.502441 −0.251221 0.967930i \(-0.580832\pi\)
−0.251221 + 0.967930i \(0.580832\pi\)
\(102\) 13.9265 1.37893
\(103\) −10.1965 −1.00469 −0.502347 0.864666i \(-0.667530\pi\)
−0.502347 + 0.864666i \(0.667530\pi\)
\(104\) −5.17064 −0.507023
\(105\) 0 0
\(106\) −18.0662 −1.75475
\(107\) 17.2088 1.66364 0.831818 0.555049i \(-0.187300\pi\)
0.831818 + 0.555049i \(0.187300\pi\)
\(108\) 2.60647 0.250808
\(109\) −1.53956 −0.147463 −0.0737316 0.997278i \(-0.523491\pi\)
−0.0737316 + 0.997278i \(0.523491\pi\)
\(110\) 13.6978 1.30603
\(111\) −6.41148 −0.608551
\(112\) 0 0
\(113\) 8.66798 0.815415 0.407708 0.913113i \(-0.366328\pi\)
0.407708 + 0.913113i \(0.366328\pi\)
\(114\) 16.1924 1.51655
\(115\) 2.45694 0.229111
\(116\) −23.0203 −2.13739
\(117\) −3.97235 −0.367244
\(118\) −27.1779 −2.50193
\(119\) 0 0
\(120\) −3.07671 −0.280864
\(121\) −3.70964 −0.337240
\(122\) −9.15363 −0.828731
\(123\) 1.00000 0.0901670
\(124\) −6.56065 −0.589163
\(125\) 10.4309 0.932967
\(126\) 0 0
\(127\) −0.809245 −0.0718088 −0.0359044 0.999355i \(-0.511431\pi\)
−0.0359044 + 0.999355i \(0.511431\pi\)
\(128\) −9.93449 −0.878093
\(129\) −0.547170 −0.0481756
\(130\) 20.1522 1.76747
\(131\) −22.1985 −1.93949 −0.969746 0.244118i \(-0.921502\pi\)
−0.969746 + 0.244118i \(0.921502\pi\)
\(132\) −7.03765 −0.612549
\(133\) 0 0
\(134\) −20.5240 −1.77300
\(135\) −2.36369 −0.203434
\(136\) 8.44606 0.724244
\(137\) 14.3569 1.22660 0.613298 0.789851i \(-0.289842\pi\)
0.613298 + 0.789851i \(0.289842\pi\)
\(138\) −2.23094 −0.189910
\(139\) −14.6198 −1.24004 −0.620018 0.784587i \(-0.712875\pi\)
−0.620018 + 0.784587i \(0.712875\pi\)
\(140\) 0 0
\(141\) −3.62288 −0.305101
\(142\) −14.4319 −1.21110
\(143\) 10.7256 0.896921
\(144\) −2.41924 −0.201603
\(145\) 20.8761 1.73366
\(146\) 16.5694 1.37129
\(147\) 0 0
\(148\) −16.7114 −1.37366
\(149\) −20.7890 −1.70310 −0.851551 0.524272i \(-0.824337\pi\)
−0.851551 + 0.524272i \(0.824337\pi\)
\(150\) 1.25992 0.102872
\(151\) −9.41227 −0.765960 −0.382980 0.923757i \(-0.625102\pi\)
−0.382980 + 0.923757i \(0.625102\pi\)
\(152\) 9.82025 0.796527
\(153\) 6.48870 0.524581
\(154\) 0 0
\(155\) 5.94954 0.477879
\(156\) −10.3538 −0.828970
\(157\) 16.2722 1.29866 0.649331 0.760506i \(-0.275049\pi\)
0.649331 + 0.760506i \(0.275049\pi\)
\(158\) 30.0602 2.39146
\(159\) −8.41749 −0.667551
\(160\) 18.4265 1.45674
\(161\) 0 0
\(162\) 2.14627 0.168627
\(163\) −4.56932 −0.357897 −0.178948 0.983858i \(-0.557269\pi\)
−0.178948 + 0.983858i \(0.557269\pi\)
\(164\) 2.60647 0.203531
\(165\) 6.38212 0.496847
\(166\) 18.7576 1.45587
\(167\) −2.84726 −0.220327 −0.110164 0.993913i \(-0.535137\pi\)
−0.110164 + 0.993913i \(0.535137\pi\)
\(168\) 0 0
\(169\) 2.77959 0.213815
\(170\) −32.9179 −2.52469
\(171\) 7.54442 0.576937
\(172\) −1.42618 −0.108746
\(173\) 14.2178 1.08096 0.540479 0.841357i \(-0.318243\pi\)
0.540479 + 0.841357i \(0.318243\pi\)
\(174\) −18.9558 −1.43704
\(175\) 0 0
\(176\) 6.53211 0.492377
\(177\) −12.6629 −0.951800
\(178\) −36.1702 −2.71107
\(179\) −0.557078 −0.0416379 −0.0208190 0.999783i \(-0.506627\pi\)
−0.0208190 + 0.999783i \(0.506627\pi\)
\(180\) −6.16090 −0.459206
\(181\) 4.64100 0.344963 0.172481 0.985013i \(-0.444822\pi\)
0.172481 + 0.985013i \(0.444822\pi\)
\(182\) 0 0
\(183\) −4.26490 −0.315271
\(184\) −1.35301 −0.0997450
\(185\) 15.1547 1.11420
\(186\) −5.40229 −0.396115
\(187\) −17.5199 −1.28118
\(188\) −9.44294 −0.688697
\(189\) 0 0
\(190\) −38.2737 −2.77667
\(191\) 13.5352 0.979371 0.489686 0.871899i \(-0.337112\pi\)
0.489686 + 0.871899i \(0.337112\pi\)
\(192\) −11.8931 −0.858311
\(193\) −1.23342 −0.0887838 −0.0443919 0.999014i \(-0.514135\pi\)
−0.0443919 + 0.999014i \(0.514135\pi\)
\(194\) 16.0063 1.14919
\(195\) 9.38941 0.672390
\(196\) 0 0
\(197\) 8.98219 0.639955 0.319977 0.947425i \(-0.396325\pi\)
0.319977 + 0.947425i \(0.396325\pi\)
\(198\) −5.79507 −0.411838
\(199\) −8.55964 −0.606777 −0.303389 0.952867i \(-0.598118\pi\)
−0.303389 + 0.952867i \(0.598118\pi\)
\(200\) 0.764111 0.0540308
\(201\) −9.56262 −0.674495
\(202\) −10.8375 −0.762526
\(203\) 0 0
\(204\) 16.9126 1.18412
\(205\) −2.36369 −0.165087
\(206\) −21.8845 −1.52477
\(207\) −1.03945 −0.0722468
\(208\) 9.61008 0.666339
\(209\) −20.3705 −1.40905
\(210\) 0 0
\(211\) −14.7292 −1.01400 −0.507000 0.861946i \(-0.669245\pi\)
−0.507000 + 0.861946i \(0.669245\pi\)
\(212\) −21.9400 −1.50684
\(213\) −6.72417 −0.460732
\(214\) 36.9347 2.52480
\(215\) 1.29334 0.0882051
\(216\) 1.30166 0.0885665
\(217\) 0 0
\(218\) −3.30431 −0.223796
\(219\) 7.72007 0.521674
\(220\) 16.6348 1.12152
\(221\) −25.7754 −1.73384
\(222\) −13.7608 −0.923562
\(223\) 13.2746 0.888934 0.444467 0.895795i \(-0.353393\pi\)
0.444467 + 0.895795i \(0.353393\pi\)
\(224\) 0 0
\(225\) 0.587030 0.0391353
\(226\) 18.6038 1.23751
\(227\) −17.4048 −1.15520 −0.577600 0.816320i \(-0.696011\pi\)
−0.577600 + 0.816320i \(0.696011\pi\)
\(228\) 19.6643 1.30230
\(229\) −3.08034 −0.203555 −0.101777 0.994807i \(-0.532453\pi\)
−0.101777 + 0.994807i \(0.532453\pi\)
\(230\) 5.27325 0.347708
\(231\) 0 0
\(232\) −11.4962 −0.754763
\(233\) −18.9481 −1.24133 −0.620665 0.784076i \(-0.713137\pi\)
−0.620665 + 0.784076i \(0.713137\pi\)
\(234\) −8.52574 −0.557345
\(235\) 8.56336 0.558612
\(236\) −33.0054 −2.14847
\(237\) 14.0058 0.909773
\(238\) 0 0
\(239\) 9.97167 0.645014 0.322507 0.946567i \(-0.395474\pi\)
0.322507 + 0.946567i \(0.395474\pi\)
\(240\) 5.71834 0.369117
\(241\) 23.0166 1.48263 0.741314 0.671158i \(-0.234203\pi\)
0.741314 + 0.671158i \(0.234203\pi\)
\(242\) −7.96189 −0.511809
\(243\) 1.00000 0.0641500
\(244\) −11.1164 −0.711652
\(245\) 0 0
\(246\) 2.14627 0.136841
\(247\) −29.9691 −1.90689
\(248\) −3.27634 −0.208048
\(249\) 8.73964 0.553852
\(250\) 22.3875 1.41591
\(251\) 30.1597 1.90366 0.951832 0.306619i \(-0.0991977\pi\)
0.951832 + 0.306619i \(0.0991977\pi\)
\(252\) 0 0
\(253\) 2.80659 0.176449
\(254\) −1.73686 −0.108980
\(255\) −15.3373 −0.960458
\(256\) 2.46411 0.154007
\(257\) −6.59194 −0.411194 −0.205597 0.978637i \(-0.565914\pi\)
−0.205597 + 0.978637i \(0.565914\pi\)
\(258\) −1.17437 −0.0731134
\(259\) 0 0
\(260\) 24.4733 1.51777
\(261\) −8.83199 −0.546686
\(262\) −47.6440 −2.94345
\(263\) 16.3547 1.00847 0.504237 0.863565i \(-0.331774\pi\)
0.504237 + 0.863565i \(0.331774\pi\)
\(264\) −3.51456 −0.216306
\(265\) 19.8963 1.22222
\(266\) 0 0
\(267\) −16.8526 −1.03136
\(268\) −24.9247 −1.52252
\(269\) −21.2223 −1.29395 −0.646973 0.762513i \(-0.723965\pi\)
−0.646973 + 0.762513i \(0.723965\pi\)
\(270\) −5.07312 −0.308740
\(271\) −1.96725 −0.119502 −0.0597509 0.998213i \(-0.519031\pi\)
−0.0597509 + 0.998213i \(0.519031\pi\)
\(272\) −15.6977 −0.951815
\(273\) 0 0
\(274\) 30.8139 1.86153
\(275\) −1.58502 −0.0955803
\(276\) −2.70930 −0.163081
\(277\) 10.1496 0.609827 0.304914 0.952380i \(-0.401372\pi\)
0.304914 + 0.952380i \(0.401372\pi\)
\(278\) −31.3781 −1.88193
\(279\) −2.51706 −0.150692
\(280\) 0 0
\(281\) 26.3025 1.56907 0.784537 0.620082i \(-0.212901\pi\)
0.784537 + 0.620082i \(0.212901\pi\)
\(282\) −7.77568 −0.463035
\(283\) 23.4341 1.39301 0.696506 0.717551i \(-0.254737\pi\)
0.696506 + 0.717551i \(0.254737\pi\)
\(284\) −17.5264 −1.04000
\(285\) −17.8327 −1.05632
\(286\) 23.0201 1.36121
\(287\) 0 0
\(288\) −7.79566 −0.459364
\(289\) 25.1033 1.47666
\(290\) 44.8057 2.63108
\(291\) 7.45775 0.437181
\(292\) 20.1222 1.17756
\(293\) 11.0295 0.644352 0.322176 0.946680i \(-0.395586\pi\)
0.322176 + 0.946680i \(0.395586\pi\)
\(294\) 0 0
\(295\) 29.9311 1.74266
\(296\) −8.34554 −0.485075
\(297\) −2.70007 −0.156674
\(298\) −44.6188 −2.58470
\(299\) 4.12907 0.238790
\(300\) 1.53008 0.0883391
\(301\) 0 0
\(302\) −20.2013 −1.16245
\(303\) −5.04947 −0.290085
\(304\) −18.2518 −1.04681
\(305\) 10.0809 0.577231
\(306\) 13.9265 0.796125
\(307\) 19.8917 1.13528 0.567639 0.823278i \(-0.307857\pi\)
0.567639 + 0.823278i \(0.307857\pi\)
\(308\) 0 0
\(309\) −10.1965 −0.580060
\(310\) 12.7693 0.725249
\(311\) 16.8715 0.956696 0.478348 0.878170i \(-0.341236\pi\)
0.478348 + 0.878170i \(0.341236\pi\)
\(312\) −5.17064 −0.292730
\(313\) 20.8946 1.18104 0.590518 0.807025i \(-0.298924\pi\)
0.590518 + 0.807025i \(0.298924\pi\)
\(314\) 34.9245 1.97090
\(315\) 0 0
\(316\) 36.5057 2.05361
\(317\) −32.5637 −1.82896 −0.914479 0.404634i \(-0.867399\pi\)
−0.914479 + 0.404634i \(0.867399\pi\)
\(318\) −18.0662 −1.01310
\(319\) 23.8470 1.33517
\(320\) 28.1116 1.57149
\(321\) 17.2088 0.960501
\(322\) 0 0
\(323\) 48.9535 2.72385
\(324\) 2.60647 0.144804
\(325\) −2.33189 −0.129350
\(326\) −9.80699 −0.543159
\(327\) −1.53956 −0.0851379
\(328\) 1.30166 0.0718719
\(329\) 0 0
\(330\) 13.6978 0.754036
\(331\) 13.7235 0.754314 0.377157 0.926149i \(-0.376902\pi\)
0.377157 + 0.926149i \(0.376902\pi\)
\(332\) 22.7797 1.25020
\(333\) −6.41148 −0.351347
\(334\) −6.11098 −0.334378
\(335\) 22.6031 1.23494
\(336\) 0 0
\(337\) 16.8326 0.916928 0.458464 0.888713i \(-0.348400\pi\)
0.458464 + 0.888713i \(0.348400\pi\)
\(338\) 5.96576 0.324495
\(339\) 8.66798 0.470780
\(340\) −39.9762 −2.16802
\(341\) 6.79622 0.368036
\(342\) 16.1924 0.875583
\(343\) 0 0
\(344\) −0.712227 −0.0384007
\(345\) 2.45694 0.132277
\(346\) 30.5152 1.64051
\(347\) −30.4692 −1.63567 −0.817837 0.575450i \(-0.804827\pi\)
−0.817837 + 0.575450i \(0.804827\pi\)
\(348\) −23.0203 −1.23402
\(349\) 28.7979 1.54151 0.770757 0.637129i \(-0.219878\pi\)
0.770757 + 0.637129i \(0.219878\pi\)
\(350\) 0 0
\(351\) −3.97235 −0.212029
\(352\) 21.0488 1.12190
\(353\) 15.7831 0.840049 0.420025 0.907513i \(-0.362021\pi\)
0.420025 + 0.907513i \(0.362021\pi\)
\(354\) −27.1779 −1.44449
\(355\) 15.8938 0.843558
\(356\) −43.9258 −2.32806
\(357\) 0 0
\(358\) −1.19564 −0.0631915
\(359\) −22.2166 −1.17255 −0.586273 0.810114i \(-0.699405\pi\)
−0.586273 + 0.810114i \(0.699405\pi\)
\(360\) −3.07671 −0.162157
\(361\) 37.9183 1.99570
\(362\) 9.96084 0.523530
\(363\) −3.70964 −0.194706
\(364\) 0 0
\(365\) −18.2478 −0.955136
\(366\) −9.15363 −0.478468
\(367\) −5.65678 −0.295282 −0.147641 0.989041i \(-0.547168\pi\)
−0.147641 + 0.989041i \(0.547168\pi\)
\(368\) 2.51468 0.131087
\(369\) 1.00000 0.0520579
\(370\) 32.5262 1.69096
\(371\) 0 0
\(372\) −6.56065 −0.340154
\(373\) 16.1337 0.835370 0.417685 0.908592i \(-0.362842\pi\)
0.417685 + 0.908592i \(0.362842\pi\)
\(374\) −37.6025 −1.94438
\(375\) 10.4309 0.538649
\(376\) −4.71574 −0.243196
\(377\) 35.0838 1.80691
\(378\) 0 0
\(379\) −3.92347 −0.201535 −0.100768 0.994910i \(-0.532130\pi\)
−0.100768 + 0.994910i \(0.532130\pi\)
\(380\) −46.4804 −2.38440
\(381\) −0.809245 −0.0414589
\(382\) 29.0501 1.48633
\(383\) −4.82783 −0.246691 −0.123345 0.992364i \(-0.539362\pi\)
−0.123345 + 0.992364i \(0.539362\pi\)
\(384\) −9.93449 −0.506967
\(385\) 0 0
\(386\) −2.64726 −0.134742
\(387\) −0.547170 −0.0278142
\(388\) 19.4384 0.986836
\(389\) −18.7165 −0.948966 −0.474483 0.880265i \(-0.657365\pi\)
−0.474483 + 0.880265i \(0.657365\pi\)
\(390\) 20.1522 1.02045
\(391\) −6.74469 −0.341093
\(392\) 0 0
\(393\) −22.1985 −1.11977
\(394\) 19.2782 0.971222
\(395\) −33.1053 −1.66571
\(396\) −7.03765 −0.353655
\(397\) −21.8834 −1.09830 −0.549149 0.835725i \(-0.685048\pi\)
−0.549149 + 0.835725i \(0.685048\pi\)
\(398\) −18.3713 −0.920870
\(399\) 0 0
\(400\) −1.42017 −0.0710084
\(401\) −31.3215 −1.56412 −0.782060 0.623203i \(-0.785831\pi\)
−0.782060 + 0.623203i \(0.785831\pi\)
\(402\) −20.5240 −1.02364
\(403\) 9.99864 0.498068
\(404\) −13.1613 −0.654800
\(405\) −2.36369 −0.117453
\(406\) 0 0
\(407\) 17.3114 0.858095
\(408\) 8.44606 0.418142
\(409\) −17.6392 −0.872200 −0.436100 0.899898i \(-0.643641\pi\)
−0.436100 + 0.899898i \(0.643641\pi\)
\(410\) −5.07312 −0.250543
\(411\) 14.3569 0.708176
\(412\) −26.5770 −1.30935
\(413\) 0 0
\(414\) −2.23094 −0.109645
\(415\) −20.6578 −1.01405
\(416\) 30.9671 1.51829
\(417\) −14.6198 −0.715935
\(418\) −43.7205 −2.13844
\(419\) 7.89174 0.385537 0.192768 0.981244i \(-0.438253\pi\)
0.192768 + 0.981244i \(0.438253\pi\)
\(420\) 0 0
\(421\) −13.7342 −0.669364 −0.334682 0.942331i \(-0.608629\pi\)
−0.334682 + 0.942331i \(0.608629\pi\)
\(422\) −31.6128 −1.53889
\(423\) −3.62288 −0.176150
\(424\) −10.9567 −0.532104
\(425\) 3.80906 0.184767
\(426\) −14.4319 −0.699227
\(427\) 0 0
\(428\) 44.8542 2.16811
\(429\) 10.7256 0.517838
\(430\) 2.77586 0.133864
\(431\) −3.47384 −0.167329 −0.0836646 0.996494i \(-0.526662\pi\)
−0.0836646 + 0.996494i \(0.526662\pi\)
\(432\) −2.41924 −0.116396
\(433\) −13.4315 −0.645476 −0.322738 0.946488i \(-0.604603\pi\)
−0.322738 + 0.946488i \(0.604603\pi\)
\(434\) 0 0
\(435\) 20.8761 1.00093
\(436\) −4.01282 −0.192179
\(437\) −7.84206 −0.375136
\(438\) 16.5694 0.791714
\(439\) 16.1538 0.770980 0.385490 0.922712i \(-0.374032\pi\)
0.385490 + 0.922712i \(0.374032\pi\)
\(440\) 8.30733 0.396036
\(441\) 0 0
\(442\) −55.3210 −2.63135
\(443\) 30.6303 1.45529 0.727645 0.685954i \(-0.240615\pi\)
0.727645 + 0.685954i \(0.240615\pi\)
\(444\) −16.7114 −0.793086
\(445\) 39.8343 1.88833
\(446\) 28.4909 1.34908
\(447\) −20.7890 −0.983286
\(448\) 0 0
\(449\) −19.0932 −0.901063 −0.450531 0.892761i \(-0.648765\pi\)
−0.450531 + 0.892761i \(0.648765\pi\)
\(450\) 1.25992 0.0593934
\(451\) −2.70007 −0.127141
\(452\) 22.5929 1.06268
\(453\) −9.41227 −0.442227
\(454\) −37.3555 −1.75318
\(455\) 0 0
\(456\) 9.82025 0.459875
\(457\) 23.5772 1.10290 0.551448 0.834209i \(-0.314076\pi\)
0.551448 + 0.834209i \(0.314076\pi\)
\(458\) −6.61125 −0.308923
\(459\) 6.48870 0.302867
\(460\) 6.40395 0.298586
\(461\) −9.36375 −0.436113 −0.218057 0.975936i \(-0.569972\pi\)
−0.218057 + 0.975936i \(0.569972\pi\)
\(462\) 0 0
\(463\) −7.27610 −0.338149 −0.169074 0.985603i \(-0.554078\pi\)
−0.169074 + 0.985603i \(0.554078\pi\)
\(464\) 21.3667 0.991925
\(465\) 5.94954 0.275904
\(466\) −40.6677 −1.88389
\(467\) −10.0800 −0.466445 −0.233222 0.972423i \(-0.574927\pi\)
−0.233222 + 0.972423i \(0.574927\pi\)
\(468\) −10.3538 −0.478606
\(469\) 0 0
\(470\) 18.3793 0.847773
\(471\) 16.2722 0.749783
\(472\) −16.4827 −0.758678
\(473\) 1.47740 0.0679307
\(474\) 30.0602 1.38071
\(475\) 4.42880 0.203207
\(476\) 0 0
\(477\) −8.41749 −0.385411
\(478\) 21.4019 0.978900
\(479\) −34.2087 −1.56304 −0.781518 0.623882i \(-0.785554\pi\)
−0.781518 + 0.623882i \(0.785554\pi\)
\(480\) 18.4265 0.841052
\(481\) 25.4687 1.16127
\(482\) 49.3998 2.25010
\(483\) 0 0
\(484\) −9.66908 −0.439504
\(485\) −17.6278 −0.800437
\(486\) 2.14627 0.0973568
\(487\) −7.80193 −0.353539 −0.176770 0.984252i \(-0.556565\pi\)
−0.176770 + 0.984252i \(0.556565\pi\)
\(488\) −5.55144 −0.251302
\(489\) −4.56932 −0.206632
\(490\) 0 0
\(491\) −0.678699 −0.0306292 −0.0153146 0.999883i \(-0.504875\pi\)
−0.0153146 + 0.999883i \(0.504875\pi\)
\(492\) 2.60647 0.117509
\(493\) −57.3082 −2.58103
\(494\) −64.3218 −2.89398
\(495\) 6.38212 0.286855
\(496\) 6.08937 0.273421
\(497\) 0 0
\(498\) 18.7576 0.840550
\(499\) −1.92512 −0.0861802 −0.0430901 0.999071i \(-0.513720\pi\)
−0.0430901 + 0.999071i \(0.513720\pi\)
\(500\) 27.1878 1.21588
\(501\) −2.84726 −0.127206
\(502\) 64.7309 2.88908
\(503\) 13.4830 0.601179 0.300590 0.953754i \(-0.402817\pi\)
0.300590 + 0.953754i \(0.402817\pi\)
\(504\) 0 0
\(505\) 11.9354 0.531118
\(506\) 6.02369 0.267786
\(507\) 2.77959 0.123446
\(508\) −2.10927 −0.0935839
\(509\) 42.4828 1.88302 0.941510 0.336986i \(-0.109408\pi\)
0.941510 + 0.336986i \(0.109408\pi\)
\(510\) −32.9179 −1.45763
\(511\) 0 0
\(512\) 25.1576 1.11182
\(513\) 7.54442 0.333094
\(514\) −14.1481 −0.624045
\(515\) 24.1014 1.06204
\(516\) −1.42618 −0.0627843
\(517\) 9.78202 0.430213
\(518\) 0 0
\(519\) 14.2178 0.624092
\(520\) 12.2218 0.535961
\(521\) 5.58156 0.244533 0.122266 0.992497i \(-0.460984\pi\)
0.122266 + 0.992497i \(0.460984\pi\)
\(522\) −18.9558 −0.829674
\(523\) −33.2749 −1.45501 −0.727505 0.686103i \(-0.759320\pi\)
−0.727505 + 0.686103i \(0.759320\pi\)
\(524\) −57.8598 −2.52762
\(525\) 0 0
\(526\) 35.1016 1.53050
\(527\) −16.3324 −0.711452
\(528\) 6.53211 0.284274
\(529\) −21.9195 −0.953024
\(530\) 42.7029 1.85490
\(531\) −12.6629 −0.549522
\(532\) 0 0
\(533\) −3.97235 −0.172062
\(534\) −36.1702 −1.56524
\(535\) −40.6762 −1.75859
\(536\) −12.4472 −0.537639
\(537\) −0.557078 −0.0240397
\(538\) −45.5488 −1.96375
\(539\) 0 0
\(540\) −6.16090 −0.265123
\(541\) −9.69717 −0.416914 −0.208457 0.978032i \(-0.566844\pi\)
−0.208457 + 0.978032i \(0.566844\pi\)
\(542\) −4.22225 −0.181361
\(543\) 4.64100 0.199164
\(544\) −50.5837 −2.16876
\(545\) 3.63904 0.155879
\(546\) 0 0
\(547\) −18.9270 −0.809258 −0.404629 0.914481i \(-0.632599\pi\)
−0.404629 + 0.914481i \(0.632599\pi\)
\(548\) 37.4210 1.59855
\(549\) −4.26490 −0.182022
\(550\) −3.40188 −0.145057
\(551\) −66.6323 −2.83863
\(552\) −1.35301 −0.0575878
\(553\) 0 0
\(554\) 21.7837 0.925500
\(555\) 15.1547 0.643283
\(556\) −38.1062 −1.61606
\(557\) −1.78182 −0.0754983 −0.0377491 0.999287i \(-0.512019\pi\)
−0.0377491 + 0.999287i \(0.512019\pi\)
\(558\) −5.40229 −0.228697
\(559\) 2.17355 0.0919315
\(560\) 0 0
\(561\) −17.5199 −0.739692
\(562\) 56.4522 2.38129
\(563\) −17.8823 −0.753650 −0.376825 0.926284i \(-0.622984\pi\)
−0.376825 + 0.926284i \(0.622984\pi\)
\(564\) −9.44294 −0.397620
\(565\) −20.4884 −0.861955
\(566\) 50.2959 2.11409
\(567\) 0 0
\(568\) −8.75256 −0.367249
\(569\) 0.523555 0.0219486 0.0109743 0.999940i \(-0.496507\pi\)
0.0109743 + 0.999940i \(0.496507\pi\)
\(570\) −38.2737 −1.60311
\(571\) −0.00376852 −0.000157708 0 −7.88539e−5 1.00000i \(-0.500025\pi\)
−7.88539e−5 1.00000i \(0.500025\pi\)
\(572\) 27.9560 1.16890
\(573\) 13.5352 0.565440
\(574\) 0 0
\(575\) −0.610189 −0.0254466
\(576\) −11.8931 −0.495546
\(577\) 43.4350 1.80822 0.904111 0.427297i \(-0.140534\pi\)
0.904111 + 0.427297i \(0.140534\pi\)
\(578\) 53.8784 2.24105
\(579\) −1.23342 −0.0512593
\(580\) 54.4130 2.25938
\(581\) 0 0
\(582\) 16.0063 0.663484
\(583\) 22.7278 0.941289
\(584\) 10.0489 0.415825
\(585\) 9.38941 0.388204
\(586\) 23.6724 0.977896
\(587\) −44.5640 −1.83935 −0.919677 0.392675i \(-0.871550\pi\)
−0.919677 + 0.392675i \(0.871550\pi\)
\(588\) 0 0
\(589\) −18.9898 −0.782459
\(590\) 64.2402 2.64473
\(591\) 8.98219 0.369478
\(592\) 15.5109 0.637495
\(593\) −15.3565 −0.630617 −0.315308 0.948989i \(-0.602108\pi\)
−0.315308 + 0.948989i \(0.602108\pi\)
\(594\) −5.79507 −0.237775
\(595\) 0 0
\(596\) −54.1860 −2.21954
\(597\) −8.55964 −0.350323
\(598\) 8.86209 0.362398
\(599\) −29.7817 −1.21685 −0.608423 0.793613i \(-0.708198\pi\)
−0.608423 + 0.793613i \(0.708198\pi\)
\(600\) 0.764111 0.0311947
\(601\) −25.9030 −1.05660 −0.528302 0.849057i \(-0.677171\pi\)
−0.528302 + 0.849057i \(0.677171\pi\)
\(602\) 0 0
\(603\) −9.56262 −0.389420
\(604\) −24.5328 −0.998227
\(605\) 8.76844 0.356488
\(606\) −10.8375 −0.440245
\(607\) −23.4600 −0.952211 −0.476105 0.879388i \(-0.657952\pi\)
−0.476105 + 0.879388i \(0.657952\pi\)
\(608\) −58.8138 −2.38521
\(609\) 0 0
\(610\) 21.6363 0.876030
\(611\) 14.3914 0.582212
\(612\) 16.9126 0.683653
\(613\) −48.3231 −1.95175 −0.975875 0.218330i \(-0.929939\pi\)
−0.975875 + 0.218330i \(0.929939\pi\)
\(614\) 42.6929 1.72294
\(615\) −2.36369 −0.0953132
\(616\) 0 0
\(617\) 16.9455 0.682201 0.341100 0.940027i \(-0.389200\pi\)
0.341100 + 0.940027i \(0.389200\pi\)
\(618\) −21.8845 −0.880324
\(619\) 9.43946 0.379404 0.189702 0.981842i \(-0.439248\pi\)
0.189702 + 0.981842i \(0.439248\pi\)
\(620\) 15.5073 0.622789
\(621\) −1.03945 −0.0417117
\(622\) 36.2108 1.45192
\(623\) 0 0
\(624\) 9.61008 0.384711
\(625\) −27.5905 −1.10362
\(626\) 44.8455 1.79239
\(627\) −20.3705 −0.813517
\(628\) 42.4130 1.69246
\(629\) −41.6022 −1.65879
\(630\) 0 0
\(631\) 11.9744 0.476694 0.238347 0.971180i \(-0.423394\pi\)
0.238347 + 0.971180i \(0.423394\pi\)
\(632\) 18.2307 0.725179
\(633\) −14.7292 −0.585433
\(634\) −69.8904 −2.77570
\(635\) 1.91280 0.0759073
\(636\) −21.9400 −0.869977
\(637\) 0 0
\(638\) 51.1820 2.02632
\(639\) −6.72417 −0.266004
\(640\) 23.4820 0.928209
\(641\) 16.4679 0.650444 0.325222 0.945638i \(-0.394561\pi\)
0.325222 + 0.945638i \(0.394561\pi\)
\(642\) 36.9347 1.45770
\(643\) 26.1074 1.02957 0.514787 0.857318i \(-0.327871\pi\)
0.514787 + 0.857318i \(0.327871\pi\)
\(644\) 0 0
\(645\) 1.29334 0.0509252
\(646\) 105.067 4.13382
\(647\) −6.19131 −0.243405 −0.121703 0.992567i \(-0.538835\pi\)
−0.121703 + 0.992567i \(0.538835\pi\)
\(648\) 1.30166 0.0511339
\(649\) 34.1906 1.34210
\(650\) −5.00487 −0.196307
\(651\) 0 0
\(652\) −11.9098 −0.466424
\(653\) −34.9689 −1.36844 −0.684219 0.729276i \(-0.739857\pi\)
−0.684219 + 0.729276i \(0.739857\pi\)
\(654\) −3.30431 −0.129209
\(655\) 52.4704 2.05019
\(656\) −2.41924 −0.0944555
\(657\) 7.72007 0.301189
\(658\) 0 0
\(659\) −9.85808 −0.384016 −0.192008 0.981393i \(-0.561500\pi\)
−0.192008 + 0.981393i \(0.561500\pi\)
\(660\) 16.6348 0.647510
\(661\) 20.0383 0.779401 0.389700 0.920942i \(-0.372579\pi\)
0.389700 + 0.920942i \(0.372579\pi\)
\(662\) 29.4544 1.14478
\(663\) −25.7754 −1.00103
\(664\) 11.3760 0.441475
\(665\) 0 0
\(666\) −13.7608 −0.533219
\(667\) 9.18042 0.355467
\(668\) −7.42130 −0.287139
\(669\) 13.2746 0.513226
\(670\) 48.5123 1.87419
\(671\) 11.5155 0.444552
\(672\) 0 0
\(673\) 23.8533 0.919478 0.459739 0.888054i \(-0.347943\pi\)
0.459739 + 0.888054i \(0.347943\pi\)
\(674\) 36.1272 1.39157
\(675\) 0.587030 0.0225948
\(676\) 7.24494 0.278652
\(677\) −21.0909 −0.810588 −0.405294 0.914186i \(-0.632831\pi\)
−0.405294 + 0.914186i \(0.632831\pi\)
\(678\) 18.6038 0.714476
\(679\) 0 0
\(680\) −19.9639 −0.765579
\(681\) −17.4048 −0.666955
\(682\) 14.5865 0.558547
\(683\) −15.0526 −0.575970 −0.287985 0.957635i \(-0.592985\pi\)
−0.287985 + 0.957635i \(0.592985\pi\)
\(684\) 19.6643 0.751885
\(685\) −33.9354 −1.29660
\(686\) 0 0
\(687\) −3.08034 −0.117522
\(688\) 1.32374 0.0504670
\(689\) 33.4373 1.27386
\(690\) 5.27325 0.200749
\(691\) 28.1067 1.06923 0.534615 0.845096i \(-0.320457\pi\)
0.534615 + 0.845096i \(0.320457\pi\)
\(692\) 37.0583 1.40874
\(693\) 0 0
\(694\) −65.3952 −2.48237
\(695\) 34.5567 1.31081
\(696\) −11.4962 −0.435763
\(697\) 6.48870 0.245777
\(698\) 61.8080 2.33947
\(699\) −18.9481 −0.716682
\(700\) 0 0
\(701\) 19.3952 0.732545 0.366272 0.930508i \(-0.380634\pi\)
0.366272 + 0.930508i \(0.380634\pi\)
\(702\) −8.52574 −0.321783
\(703\) −48.3709 −1.82434
\(704\) 32.1122 1.21027
\(705\) 8.56336 0.322515
\(706\) 33.8748 1.27489
\(707\) 0 0
\(708\) −33.0054 −1.24042
\(709\) 16.5021 0.619749 0.309874 0.950777i \(-0.399713\pi\)
0.309874 + 0.950777i \(0.399713\pi\)
\(710\) 34.1125 1.28022
\(711\) 14.0058 0.525258
\(712\) −21.9363 −0.822097
\(713\) 2.61636 0.0979834
\(714\) 0 0
\(715\) −25.3520 −0.948113
\(716\) −1.45201 −0.0542641
\(717\) 9.97167 0.372399
\(718\) −47.6827 −1.77950
\(719\) −44.6880 −1.66658 −0.833291 0.552834i \(-0.813546\pi\)
−0.833291 + 0.552834i \(0.813546\pi\)
\(720\) 5.71834 0.213110
\(721\) 0 0
\(722\) 81.3830 3.02876
\(723\) 23.0166 0.855996
\(724\) 12.0966 0.449568
\(725\) −5.18464 −0.192553
\(726\) −7.96189 −0.295493
\(727\) 3.76452 0.139618 0.0698092 0.997560i \(-0.477761\pi\)
0.0698092 + 0.997560i \(0.477761\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −39.1648 −1.44955
\(731\) −3.55042 −0.131317
\(732\) −11.1164 −0.410872
\(733\) 2.11688 0.0781888 0.0390944 0.999236i \(-0.487553\pi\)
0.0390944 + 0.999236i \(0.487553\pi\)
\(734\) −12.1410 −0.448132
\(735\) 0 0
\(736\) 8.10320 0.298688
\(737\) 25.8197 0.951081
\(738\) 2.14627 0.0790053
\(739\) −23.9700 −0.881750 −0.440875 0.897568i \(-0.645332\pi\)
−0.440875 + 0.897568i \(0.645332\pi\)
\(740\) 39.5005 1.45207
\(741\) −29.9691 −1.10094
\(742\) 0 0
\(743\) 33.2447 1.21963 0.609814 0.792544i \(-0.291244\pi\)
0.609814 + 0.792544i \(0.291244\pi\)
\(744\) −3.27634 −0.120117
\(745\) 49.1388 1.80030
\(746\) 34.6272 1.26779
\(747\) 8.73964 0.319767
\(748\) −45.6652 −1.66969
\(749\) 0 0
\(750\) 22.3875 0.817476
\(751\) 20.3773 0.743579 0.371790 0.928317i \(-0.378744\pi\)
0.371790 + 0.928317i \(0.378744\pi\)
\(752\) 8.76462 0.319613
\(753\) 30.1597 1.09908
\(754\) 75.2993 2.74224
\(755\) 22.2477 0.809676
\(756\) 0 0
\(757\) −13.4178 −0.487679 −0.243839 0.969816i \(-0.578407\pi\)
−0.243839 + 0.969816i \(0.578407\pi\)
\(758\) −8.42083 −0.305858
\(759\) 2.80659 0.101873
\(760\) −23.2120 −0.841989
\(761\) −8.17818 −0.296459 −0.148229 0.988953i \(-0.547357\pi\)
−0.148229 + 0.988953i \(0.547357\pi\)
\(762\) −1.73686 −0.0629197
\(763\) 0 0
\(764\) 35.2791 1.27635
\(765\) −15.3373 −0.554521
\(766\) −10.3618 −0.374388
\(767\) 50.3014 1.81628
\(768\) 2.46411 0.0889160
\(769\) 2.57529 0.0928673 0.0464336 0.998921i \(-0.485214\pi\)
0.0464336 + 0.998921i \(0.485214\pi\)
\(770\) 0 0
\(771\) −6.59194 −0.237403
\(772\) −3.21489 −0.115706
\(773\) 2.59611 0.0933756 0.0466878 0.998910i \(-0.485133\pi\)
0.0466878 + 0.998910i \(0.485133\pi\)
\(774\) −1.17437 −0.0422120
\(775\) −1.47759 −0.0530765
\(776\) 9.70742 0.348476
\(777\) 0 0
\(778\) −40.1707 −1.44019
\(779\) 7.54442 0.270307
\(780\) 24.4733 0.876283
\(781\) 18.1557 0.649662
\(782\) −14.4759 −0.517658
\(783\) −8.83199 −0.315630
\(784\) 0 0
\(785\) −38.4624 −1.37278
\(786\) −47.6440 −1.69940
\(787\) −1.96310 −0.0699769 −0.0349884 0.999388i \(-0.511139\pi\)
−0.0349884 + 0.999388i \(0.511139\pi\)
\(788\) 23.4118 0.834013
\(789\) 16.3547 0.582243
\(790\) −71.0530 −2.52795
\(791\) 0 0
\(792\) −3.51456 −0.124884
\(793\) 16.9417 0.601617
\(794\) −46.9677 −1.66682
\(795\) 19.8963 0.705651
\(796\) −22.3105 −0.790774
\(797\) 17.6653 0.625735 0.312868 0.949797i \(-0.398710\pi\)
0.312868 + 0.949797i \(0.398710\pi\)
\(798\) 0 0
\(799\) −23.5078 −0.831646
\(800\) −4.57629 −0.161796
\(801\) −16.8526 −0.595457
\(802\) −67.2244 −2.37377
\(803\) −20.8447 −0.735594
\(804\) −24.9247 −0.879027
\(805\) 0 0
\(806\) 21.4598 0.755889
\(807\) −21.2223 −0.747060
\(808\) −6.57268 −0.231226
\(809\) −27.2660 −0.958620 −0.479310 0.877646i \(-0.659113\pi\)
−0.479310 + 0.877646i \(0.659113\pi\)
\(810\) −5.07312 −0.178251
\(811\) −27.2425 −0.956613 −0.478306 0.878193i \(-0.658749\pi\)
−0.478306 + 0.878193i \(0.658749\pi\)
\(812\) 0 0
\(813\) −1.96725 −0.0689944
\(814\) 37.1550 1.30228
\(815\) 10.8005 0.378323
\(816\) −15.6977 −0.549531
\(817\) −4.12808 −0.144423
\(818\) −37.8584 −1.32369
\(819\) 0 0
\(820\) −6.16090 −0.215148
\(821\) 3.83844 0.133963 0.0669813 0.997754i \(-0.478663\pi\)
0.0669813 + 0.997754i \(0.478663\pi\)
\(822\) 30.8139 1.07476
\(823\) 3.75854 0.131015 0.0655073 0.997852i \(-0.479133\pi\)
0.0655073 + 0.997852i \(0.479133\pi\)
\(824\) −13.2724 −0.462365
\(825\) −1.58502 −0.0551833
\(826\) 0 0
\(827\) 22.8573 0.794826 0.397413 0.917640i \(-0.369908\pi\)
0.397413 + 0.917640i \(0.369908\pi\)
\(828\) −2.70930 −0.0941547
\(829\) −39.5690 −1.37429 −0.687144 0.726521i \(-0.741136\pi\)
−0.687144 + 0.726521i \(0.741136\pi\)
\(830\) −44.3372 −1.53897
\(831\) 10.1496 0.352084
\(832\) 47.2436 1.63788
\(833\) 0 0
\(834\) −31.3781 −1.08653
\(835\) 6.73003 0.232902
\(836\) −53.0950 −1.83633
\(837\) −2.51706 −0.0870022
\(838\) 16.9378 0.585106
\(839\) 19.9208 0.687743 0.343871 0.939017i \(-0.388262\pi\)
0.343871 + 0.939017i \(0.388262\pi\)
\(840\) 0 0
\(841\) 49.0040 1.68979
\(842\) −29.4773 −1.01585
\(843\) 26.3025 0.905906
\(844\) −38.3913 −1.32148
\(845\) −6.57010 −0.226018
\(846\) −7.77568 −0.267333
\(847\) 0 0
\(848\) 20.3640 0.699301
\(849\) 23.4341 0.804256
\(850\) 8.17528 0.280410
\(851\) 6.66442 0.228453
\(852\) −17.5264 −0.600443
\(853\) −7.90604 −0.270698 −0.135349 0.990798i \(-0.543216\pi\)
−0.135349 + 0.990798i \(0.543216\pi\)
\(854\) 0 0
\(855\) −17.8327 −0.609865
\(856\) 22.3999 0.765614
\(857\) −35.6747 −1.21863 −0.609313 0.792930i \(-0.708555\pi\)
−0.609313 + 0.792930i \(0.708555\pi\)
\(858\) 23.0201 0.785892
\(859\) 34.1715 1.16592 0.582958 0.812503i \(-0.301895\pi\)
0.582958 + 0.812503i \(0.301895\pi\)
\(860\) 3.37106 0.114952
\(861\) 0 0
\(862\) −7.45581 −0.253946
\(863\) −51.5126 −1.75351 −0.876755 0.480937i \(-0.840297\pi\)
−0.876755 + 0.480937i \(0.840297\pi\)
\(864\) −7.79566 −0.265214
\(865\) −33.6064 −1.14265
\(866\) −28.8276 −0.979602
\(867\) 25.1033 0.852552
\(868\) 0 0
\(869\) −37.8166 −1.28284
\(870\) 44.8057 1.51906
\(871\) 37.9861 1.28711
\(872\) −2.00398 −0.0678633
\(873\) 7.45775 0.252407
\(874\) −16.8312 −0.569323
\(875\) 0 0
\(876\) 20.1222 0.679865
\(877\) 22.3831 0.755822 0.377911 0.925842i \(-0.376642\pi\)
0.377911 + 0.925842i \(0.376642\pi\)
\(878\) 34.6705 1.17007
\(879\) 11.0295 0.372017
\(880\) −15.4399 −0.520479
\(881\) 22.3157 0.751835 0.375918 0.926653i \(-0.377328\pi\)
0.375918 + 0.926653i \(0.377328\pi\)
\(882\) 0 0
\(883\) 27.6469 0.930392 0.465196 0.885208i \(-0.345984\pi\)
0.465196 + 0.885208i \(0.345984\pi\)
\(884\) −67.1830 −2.25961
\(885\) 29.9311 1.00612
\(886\) 65.7409 2.20861
\(887\) 9.84010 0.330398 0.165199 0.986260i \(-0.447173\pi\)
0.165199 + 0.986260i \(0.447173\pi\)
\(888\) −8.34554 −0.280058
\(889\) 0 0
\(890\) 85.4951 2.86580
\(891\) −2.70007 −0.0904556
\(892\) 34.5999 1.15849
\(893\) −27.3325 −0.914649
\(894\) −44.6188 −1.49228
\(895\) 1.31676 0.0440144
\(896\) 0 0
\(897\) 4.12907 0.137865
\(898\) −40.9791 −1.36749
\(899\) 22.2306 0.741433
\(900\) 1.53008 0.0510026
\(901\) −54.6186 −1.81961
\(902\) −5.79507 −0.192955
\(903\) 0 0
\(904\) 11.2827 0.375258
\(905\) −10.9699 −0.364651
\(906\) −20.2013 −0.671142
\(907\) 10.7705 0.357627 0.178814 0.983883i \(-0.442774\pi\)
0.178814 + 0.983883i \(0.442774\pi\)
\(908\) −45.3653 −1.50550
\(909\) −5.04947 −0.167480
\(910\) 0 0
\(911\) 42.6611 1.41343 0.706713 0.707500i \(-0.250177\pi\)
0.706713 + 0.707500i \(0.250177\pi\)
\(912\) −18.2518 −0.604377
\(913\) −23.5976 −0.780967
\(914\) 50.6031 1.67380
\(915\) 10.0809 0.333264
\(916\) −8.02884 −0.265280
\(917\) 0 0
\(918\) 13.9265 0.459643
\(919\) −33.1114 −1.09224 −0.546122 0.837706i \(-0.683896\pi\)
−0.546122 + 0.837706i \(0.683896\pi\)
\(920\) 3.19809 0.105438
\(921\) 19.8917 0.655453
\(922\) −20.0971 −0.661864
\(923\) 26.7108 0.879196
\(924\) 0 0
\(925\) −3.76373 −0.123751
\(926\) −15.6165 −0.513189
\(927\) −10.1965 −0.334898
\(928\) 68.8512 2.26015
\(929\) 36.9948 1.21376 0.606881 0.794793i \(-0.292421\pi\)
0.606881 + 0.794793i \(0.292421\pi\)
\(930\) 12.7693 0.418723
\(931\) 0 0
\(932\) −49.3877 −1.61775
\(933\) 16.8715 0.552348
\(934\) −21.6343 −0.707896
\(935\) 41.4117 1.35431
\(936\) −5.17064 −0.169008
\(937\) 10.1650 0.332076 0.166038 0.986119i \(-0.446903\pi\)
0.166038 + 0.986119i \(0.446903\pi\)
\(938\) 0 0
\(939\) 20.8946 0.681871
\(940\) 22.3202 0.728004
\(941\) 21.1350 0.688982 0.344491 0.938790i \(-0.388051\pi\)
0.344491 + 0.938790i \(0.388051\pi\)
\(942\) 34.9245 1.13790
\(943\) −1.03945 −0.0338492
\(944\) 30.6346 0.997070
\(945\) 0 0
\(946\) 3.17089 0.103095
\(947\) −33.0070 −1.07258 −0.536292 0.844032i \(-0.680176\pi\)
−0.536292 + 0.844032i \(0.680176\pi\)
\(948\) 36.5057 1.18565
\(949\) −30.6668 −0.995488
\(950\) 9.50541 0.308396
\(951\) −32.5637 −1.05595
\(952\) 0 0
\(953\) 10.9557 0.354889 0.177445 0.984131i \(-0.443217\pi\)
0.177445 + 0.984131i \(0.443217\pi\)
\(954\) −18.0662 −0.584915
\(955\) −31.9930 −1.03527
\(956\) 25.9909 0.840606
\(957\) 23.8470 0.770863
\(958\) −73.4212 −2.37213
\(959\) 0 0
\(960\) 28.1116 0.907298
\(961\) −24.6644 −0.795626
\(962\) 54.6626 1.76239
\(963\) 17.2088 0.554545
\(964\) 59.9921 1.93222
\(965\) 2.91543 0.0938510
\(966\) 0 0
\(967\) −10.4174 −0.335002 −0.167501 0.985872i \(-0.553570\pi\)
−0.167501 + 0.985872i \(0.553570\pi\)
\(968\) −4.82868 −0.155200
\(969\) 48.9535 1.57261
\(970\) −37.8340 −1.21478
\(971\) −12.6885 −0.407192 −0.203596 0.979055i \(-0.565263\pi\)
−0.203596 + 0.979055i \(0.565263\pi\)
\(972\) 2.60647 0.0836027
\(973\) 0 0
\(974\) −16.7450 −0.536546
\(975\) −2.33189 −0.0746803
\(976\) 10.3178 0.330266
\(977\) −44.9608 −1.43842 −0.719212 0.694791i \(-0.755497\pi\)
−0.719212 + 0.694791i \(0.755497\pi\)
\(978\) −9.80699 −0.313593
\(979\) 45.5031 1.45429
\(980\) 0 0
\(981\) −1.53956 −0.0491544
\(982\) −1.45667 −0.0464842
\(983\) −28.4540 −0.907543 −0.453771 0.891118i \(-0.649922\pi\)
−0.453771 + 0.891118i \(0.649922\pi\)
\(984\) 1.30166 0.0414953
\(985\) −21.2311 −0.676480
\(986\) −122.999 −3.91708
\(987\) 0 0
\(988\) −78.1137 −2.48513
\(989\) 0.568756 0.0180854
\(990\) 13.6978 0.435343
\(991\) 18.2267 0.578990 0.289495 0.957180i \(-0.406513\pi\)
0.289495 + 0.957180i \(0.406513\pi\)
\(992\) 19.6221 0.623003
\(993\) 13.7235 0.435504
\(994\) 0 0
\(995\) 20.2323 0.641408
\(996\) 22.7797 0.721801
\(997\) −50.7037 −1.60580 −0.802900 0.596113i \(-0.796711\pi\)
−0.802900 + 0.596113i \(0.796711\pi\)
\(998\) −4.13183 −0.130791
\(999\) −6.41148 −0.202850
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 \(a_p\))