Properties

Label 6027.2.a.bn.1.16
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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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: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.50751 q^{2} -1.00000 q^{3} +0.272577 q^{4} -1.10903 q^{5} -1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.50751 q^{2} -1.00000 q^{3} +0.272577 q^{4} -1.10903 q^{5} -1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} -1.67187 q^{10} +3.74096 q^{11} -0.272577 q^{12} -4.04957 q^{13} +1.10903 q^{15} -4.47086 q^{16} +1.28562 q^{17} +1.50751 q^{18} -2.77400 q^{19} -0.302296 q^{20} +5.63953 q^{22} +8.14553 q^{23} +2.60410 q^{24} -3.77005 q^{25} -6.10476 q^{26} -1.00000 q^{27} -1.13225 q^{29} +1.67187 q^{30} -3.06661 q^{31} -1.53164 q^{32} -3.74096 q^{33} +1.93807 q^{34} +0.272577 q^{36} -8.99346 q^{37} -4.18183 q^{38} +4.04957 q^{39} +2.88803 q^{40} +1.00000 q^{41} +5.07578 q^{43} +1.01970 q^{44} -1.10903 q^{45} +12.2794 q^{46} +1.77524 q^{47} +4.47086 q^{48} -5.68338 q^{50} -1.28562 q^{51} -1.10382 q^{52} -1.43908 q^{53} -1.50751 q^{54} -4.14884 q^{55} +2.77400 q^{57} -1.70688 q^{58} +11.8133 q^{59} +0.302296 q^{60} -6.29435 q^{61} -4.62294 q^{62} +6.63275 q^{64} +4.49110 q^{65} -5.63953 q^{66} +1.53411 q^{67} +0.350429 q^{68} -8.14553 q^{69} +12.4191 q^{71} -2.60410 q^{72} -7.32700 q^{73} -13.5577 q^{74} +3.77005 q^{75} -0.756129 q^{76} +6.10476 q^{78} +3.06259 q^{79} +4.95832 q^{80} +1.00000 q^{81} +1.50751 q^{82} +10.5895 q^{83} -1.42579 q^{85} +7.65178 q^{86} +1.13225 q^{87} -9.74185 q^{88} +0.862204 q^{89} -1.67187 q^{90} +2.22028 q^{92} +3.06661 q^{93} +2.67619 q^{94} +3.07645 q^{95} +1.53164 q^{96} +2.95888 q^{97} +3.74096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50751 1.06597 0.532984 0.846125i \(-0.321071\pi\)
0.532984 + 0.846125i \(0.321071\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.272577 0.136288
\(5\) −1.10903 −0.495973 −0.247987 0.968763i \(-0.579769\pi\)
−0.247987 + 0.968763i \(0.579769\pi\)
\(6\) −1.50751 −0.615437
\(7\) 0 0
\(8\) −2.60410 −0.920689
\(9\) 1.00000 0.333333
\(10\) −1.67187 −0.528692
\(11\) 3.74096 1.12794 0.563971 0.825794i \(-0.309273\pi\)
0.563971 + 0.825794i \(0.309273\pi\)
\(12\) −0.272577 −0.0786862
\(13\) −4.04957 −1.12315 −0.561575 0.827426i \(-0.689804\pi\)
−0.561575 + 0.827426i \(0.689804\pi\)
\(14\) 0 0
\(15\) 1.10903 0.286350
\(16\) −4.47086 −1.11771
\(17\) 1.28562 0.311808 0.155904 0.987772i \(-0.450171\pi\)
0.155904 + 0.987772i \(0.450171\pi\)
\(18\) 1.50751 0.355323
\(19\) −2.77400 −0.636400 −0.318200 0.948024i \(-0.603078\pi\)
−0.318200 + 0.948024i \(0.603078\pi\)
\(20\) −0.302296 −0.0675955
\(21\) 0 0
\(22\) 5.63953 1.20235
\(23\) 8.14553 1.69846 0.849230 0.528023i \(-0.177067\pi\)
0.849230 + 0.528023i \(0.177067\pi\)
\(24\) 2.60410 0.531560
\(25\) −3.77005 −0.754010
\(26\) −6.10476 −1.19724
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.13225 −0.210254 −0.105127 0.994459i \(-0.533525\pi\)
−0.105127 + 0.994459i \(0.533525\pi\)
\(30\) 1.67187 0.305240
\(31\) −3.06661 −0.550779 −0.275390 0.961333i \(-0.588807\pi\)
−0.275390 + 0.961333i \(0.588807\pi\)
\(32\) −1.53164 −0.270758
\(33\) −3.74096 −0.651218
\(34\) 1.93807 0.332377
\(35\) 0 0
\(36\) 0.272577 0.0454295
\(37\) −8.99346 −1.47852 −0.739258 0.673423i \(-0.764823\pi\)
−0.739258 + 0.673423i \(0.764823\pi\)
\(38\) −4.18183 −0.678382
\(39\) 4.04957 0.648450
\(40\) 2.88803 0.456637
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 5.07578 0.774050 0.387025 0.922069i \(-0.373503\pi\)
0.387025 + 0.922069i \(0.373503\pi\)
\(44\) 1.01970 0.153726
\(45\) −1.10903 −0.165324
\(46\) 12.2794 1.81050
\(47\) 1.77524 0.258946 0.129473 0.991583i \(-0.458671\pi\)
0.129473 + 0.991583i \(0.458671\pi\)
\(48\) 4.47086 0.645312
\(49\) 0 0
\(50\) −5.68338 −0.803751
\(51\) −1.28562 −0.180022
\(52\) −1.10382 −0.153072
\(53\) −1.43908 −0.197673 −0.0988365 0.995104i \(-0.531512\pi\)
−0.0988365 + 0.995104i \(0.531512\pi\)
\(54\) −1.50751 −0.205146
\(55\) −4.14884 −0.559430
\(56\) 0 0
\(57\) 2.77400 0.367425
\(58\) −1.70688 −0.224124
\(59\) 11.8133 1.53796 0.768980 0.639273i \(-0.220765\pi\)
0.768980 + 0.639273i \(0.220765\pi\)
\(60\) 0.302296 0.0390263
\(61\) −6.29435 −0.805908 −0.402954 0.915220i \(-0.632017\pi\)
−0.402954 + 0.915220i \(0.632017\pi\)
\(62\) −4.62294 −0.587113
\(63\) 0 0
\(64\) 6.63275 0.829094
\(65\) 4.49110 0.557052
\(66\) −5.63953 −0.694178
\(67\) 1.53411 0.187421 0.0937107 0.995599i \(-0.470127\pi\)
0.0937107 + 0.995599i \(0.470127\pi\)
\(68\) 0.350429 0.0424958
\(69\) −8.14553 −0.980606
\(70\) 0 0
\(71\) 12.4191 1.47388 0.736938 0.675960i \(-0.236271\pi\)
0.736938 + 0.675960i \(0.236271\pi\)
\(72\) −2.60410 −0.306896
\(73\) −7.32700 −0.857561 −0.428780 0.903409i \(-0.641057\pi\)
−0.428780 + 0.903409i \(0.641057\pi\)
\(74\) −13.5577 −1.57605
\(75\) 3.77005 0.435328
\(76\) −0.756129 −0.0867339
\(77\) 0 0
\(78\) 6.10476 0.691228
\(79\) 3.06259 0.344568 0.172284 0.985047i \(-0.444885\pi\)
0.172284 + 0.985047i \(0.444885\pi\)
\(80\) 4.95832 0.554356
\(81\) 1.00000 0.111111
\(82\) 1.50751 0.166476
\(83\) 10.5895 1.16235 0.581175 0.813778i \(-0.302593\pi\)
0.581175 + 0.813778i \(0.302593\pi\)
\(84\) 0 0
\(85\) −1.42579 −0.154648
\(86\) 7.65178 0.825112
\(87\) 1.13225 0.121390
\(88\) −9.74185 −1.03848
\(89\) 0.862204 0.0913935 0.0456967 0.998955i \(-0.485449\pi\)
0.0456967 + 0.998955i \(0.485449\pi\)
\(90\) −1.67187 −0.176231
\(91\) 0 0
\(92\) 2.22028 0.231480
\(93\) 3.06661 0.317993
\(94\) 2.67619 0.276028
\(95\) 3.07645 0.315637
\(96\) 1.53164 0.156322
\(97\) 2.95888 0.300428 0.150214 0.988653i \(-0.452004\pi\)
0.150214 + 0.988653i \(0.452004\pi\)
\(98\) 0 0
\(99\) 3.74096 0.375981
\(100\) −1.02763 −0.102763
\(101\) −9.78581 −0.973724 −0.486862 0.873479i \(-0.661859\pi\)
−0.486862 + 0.873479i \(0.661859\pi\)
\(102\) −1.93807 −0.191898
\(103\) −5.64685 −0.556400 −0.278200 0.960523i \(-0.589738\pi\)
−0.278200 + 0.960523i \(0.589738\pi\)
\(104\) 10.5455 1.03407
\(105\) 0 0
\(106\) −2.16942 −0.210713
\(107\) 14.2514 1.37773 0.688866 0.724889i \(-0.258109\pi\)
0.688866 + 0.724889i \(0.258109\pi\)
\(108\) −0.272577 −0.0262287
\(109\) −1.98301 −0.189938 −0.0949689 0.995480i \(-0.530275\pi\)
−0.0949689 + 0.995480i \(0.530275\pi\)
\(110\) −6.25441 −0.596334
\(111\) 8.99346 0.853621
\(112\) 0 0
\(113\) 1.92257 0.180860 0.0904302 0.995903i \(-0.471176\pi\)
0.0904302 + 0.995903i \(0.471176\pi\)
\(114\) 4.18183 0.391664
\(115\) −9.03364 −0.842391
\(116\) −0.308626 −0.0286552
\(117\) −4.04957 −0.374383
\(118\) 17.8086 1.63942
\(119\) 0 0
\(120\) −2.88803 −0.263640
\(121\) 2.99480 0.272255
\(122\) −9.48877 −0.859073
\(123\) −1.00000 −0.0901670
\(124\) −0.835887 −0.0750649
\(125\) 9.72625 0.869943
\(126\) 0 0
\(127\) 6.05248 0.537071 0.268536 0.963270i \(-0.413460\pi\)
0.268536 + 0.963270i \(0.413460\pi\)
\(128\) 13.0622 1.15455
\(129\) −5.07578 −0.446898
\(130\) 6.77036 0.593800
\(131\) −10.1642 −0.888055 −0.444027 0.896013i \(-0.646451\pi\)
−0.444027 + 0.896013i \(0.646451\pi\)
\(132\) −1.01970 −0.0887535
\(133\) 0 0
\(134\) 2.31268 0.199785
\(135\) 1.10903 0.0954501
\(136\) −3.34788 −0.287078
\(137\) 10.4749 0.894928 0.447464 0.894302i \(-0.352327\pi\)
0.447464 + 0.894302i \(0.352327\pi\)
\(138\) −12.2794 −1.04530
\(139\) 5.03683 0.427219 0.213609 0.976919i \(-0.431478\pi\)
0.213609 + 0.976919i \(0.431478\pi\)
\(140\) 0 0
\(141\) −1.77524 −0.149503
\(142\) 18.7219 1.57110
\(143\) −15.1493 −1.26685
\(144\) −4.47086 −0.372571
\(145\) 1.25570 0.104280
\(146\) −11.0455 −0.914132
\(147\) 0 0
\(148\) −2.45141 −0.201505
\(149\) 12.4511 1.02003 0.510016 0.860165i \(-0.329640\pi\)
0.510016 + 0.860165i \(0.329640\pi\)
\(150\) 5.68338 0.464046
\(151\) 1.01228 0.0823779 0.0411889 0.999151i \(-0.486885\pi\)
0.0411889 + 0.999151i \(0.486885\pi\)
\(152\) 7.22378 0.585926
\(153\) 1.28562 0.103936
\(154\) 0 0
\(155\) 3.40096 0.273172
\(156\) 1.10382 0.0883763
\(157\) 3.97214 0.317011 0.158506 0.987358i \(-0.449332\pi\)
0.158506 + 0.987358i \(0.449332\pi\)
\(158\) 4.61688 0.367299
\(159\) 1.43908 0.114127
\(160\) 1.69864 0.134289
\(161\) 0 0
\(162\) 1.50751 0.118441
\(163\) 22.6056 1.77061 0.885304 0.465013i \(-0.153950\pi\)
0.885304 + 0.465013i \(0.153950\pi\)
\(164\) 0.272577 0.0212847
\(165\) 4.14884 0.322987
\(166\) 15.9638 1.23903
\(167\) 10.2870 0.796035 0.398017 0.917378i \(-0.369698\pi\)
0.398017 + 0.917378i \(0.369698\pi\)
\(168\) 0 0
\(169\) 3.39903 0.261464
\(170\) −2.14938 −0.164850
\(171\) −2.77400 −0.212133
\(172\) 1.38354 0.105494
\(173\) 8.31332 0.632050 0.316025 0.948751i \(-0.397652\pi\)
0.316025 + 0.948751i \(0.397652\pi\)
\(174\) 1.70688 0.129398
\(175\) 0 0
\(176\) −16.7253 −1.26072
\(177\) −11.8133 −0.887942
\(178\) 1.29978 0.0974225
\(179\) 5.82288 0.435222 0.217611 0.976036i \(-0.430174\pi\)
0.217611 + 0.976036i \(0.430174\pi\)
\(180\) −0.302296 −0.0225318
\(181\) 16.9447 1.25949 0.629746 0.776801i \(-0.283159\pi\)
0.629746 + 0.776801i \(0.283159\pi\)
\(182\) 0 0
\(183\) 6.29435 0.465291
\(184\) −21.2118 −1.56375
\(185\) 9.97402 0.733304
\(186\) 4.62294 0.338970
\(187\) 4.80944 0.351701
\(188\) 0.483891 0.0352913
\(189\) 0 0
\(190\) 4.63777 0.336459
\(191\) 12.9496 0.937001 0.468501 0.883463i \(-0.344794\pi\)
0.468501 + 0.883463i \(0.344794\pi\)
\(192\) −6.63275 −0.478678
\(193\) −1.53674 −0.110617 −0.0553084 0.998469i \(-0.517614\pi\)
−0.0553084 + 0.998469i \(0.517614\pi\)
\(194\) 4.46053 0.320247
\(195\) −4.49110 −0.321614
\(196\) 0 0
\(197\) 14.6537 1.04403 0.522017 0.852935i \(-0.325180\pi\)
0.522017 + 0.852935i \(0.325180\pi\)
\(198\) 5.63953 0.400784
\(199\) 15.9626 1.13156 0.565780 0.824556i \(-0.308575\pi\)
0.565780 + 0.824556i \(0.308575\pi\)
\(200\) 9.81760 0.694209
\(201\) −1.53411 −0.108208
\(202\) −14.7522 −1.03796
\(203\) 0 0
\(204\) −0.350429 −0.0245350
\(205\) −1.10903 −0.0774580
\(206\) −8.51266 −0.593105
\(207\) 8.14553 0.566153
\(208\) 18.1050 1.25536
\(209\) −10.3774 −0.717822
\(210\) 0 0
\(211\) 23.5174 1.61901 0.809503 0.587116i \(-0.199737\pi\)
0.809503 + 0.587116i \(0.199737\pi\)
\(212\) −0.392260 −0.0269405
\(213\) −12.4191 −0.850943
\(214\) 21.4840 1.46862
\(215\) −5.62920 −0.383908
\(216\) 2.60410 0.177187
\(217\) 0 0
\(218\) −2.98940 −0.202468
\(219\) 7.32700 0.495113
\(220\) −1.13088 −0.0762438
\(221\) −5.20619 −0.350206
\(222\) 13.5577 0.909933
\(223\) 22.1230 1.48146 0.740732 0.671801i \(-0.234479\pi\)
0.740732 + 0.671801i \(0.234479\pi\)
\(224\) 0 0
\(225\) −3.77005 −0.251337
\(226\) 2.89829 0.192791
\(227\) −21.8654 −1.45126 −0.725630 0.688085i \(-0.758451\pi\)
−0.725630 + 0.688085i \(0.758451\pi\)
\(228\) 0.756129 0.0500758
\(229\) 14.7855 0.977054 0.488527 0.872549i \(-0.337534\pi\)
0.488527 + 0.872549i \(0.337534\pi\)
\(230\) −13.6183 −0.897962
\(231\) 0 0
\(232\) 2.94850 0.193578
\(233\) −27.2105 −1.78262 −0.891310 0.453394i \(-0.850213\pi\)
−0.891310 + 0.453394i \(0.850213\pi\)
\(234\) −6.10476 −0.399080
\(235\) −1.96880 −0.128430
\(236\) 3.22003 0.209606
\(237\) −3.06259 −0.198937
\(238\) 0 0
\(239\) −23.9634 −1.55006 −0.775031 0.631924i \(-0.782266\pi\)
−0.775031 + 0.631924i \(0.782266\pi\)
\(240\) −4.95832 −0.320058
\(241\) −12.9104 −0.831632 −0.415816 0.909449i \(-0.636504\pi\)
−0.415816 + 0.909449i \(0.636504\pi\)
\(242\) 4.51468 0.290215
\(243\) −1.00000 −0.0641500
\(244\) −1.71569 −0.109836
\(245\) 0 0
\(246\) −1.50751 −0.0961151
\(247\) 11.2335 0.714772
\(248\) 7.98577 0.507097
\(249\) −10.5895 −0.671083
\(250\) 14.6624 0.927331
\(251\) 13.4903 0.851497 0.425749 0.904841i \(-0.360011\pi\)
0.425749 + 0.904841i \(0.360011\pi\)
\(252\) 0 0
\(253\) 30.4721 1.91577
\(254\) 9.12416 0.572501
\(255\) 1.42579 0.0892863
\(256\) 6.42585 0.401616
\(257\) 4.35831 0.271864 0.135932 0.990718i \(-0.456597\pi\)
0.135932 + 0.990718i \(0.456597\pi\)
\(258\) −7.65178 −0.476379
\(259\) 0 0
\(260\) 1.22417 0.0759198
\(261\) −1.13225 −0.0700846
\(262\) −15.3227 −0.946638
\(263\) −14.2904 −0.881182 −0.440591 0.897708i \(-0.645231\pi\)
−0.440591 + 0.897708i \(0.645231\pi\)
\(264\) 9.74185 0.599569
\(265\) 1.59598 0.0980405
\(266\) 0 0
\(267\) −0.862204 −0.0527660
\(268\) 0.418163 0.0255434
\(269\) 20.3295 1.23951 0.619755 0.784795i \(-0.287232\pi\)
0.619755 + 0.784795i \(0.287232\pi\)
\(270\) 1.67187 0.101747
\(271\) −21.1831 −1.28678 −0.643392 0.765537i \(-0.722473\pi\)
−0.643392 + 0.765537i \(0.722473\pi\)
\(272\) −5.74780 −0.348512
\(273\) 0 0
\(274\) 15.7909 0.953965
\(275\) −14.1036 −0.850480
\(276\) −2.22028 −0.133645
\(277\) 3.20291 0.192444 0.0962221 0.995360i \(-0.469324\pi\)
0.0962221 + 0.995360i \(0.469324\pi\)
\(278\) 7.59306 0.455401
\(279\) −3.06661 −0.183593
\(280\) 0 0
\(281\) −16.8668 −1.00619 −0.503094 0.864231i \(-0.667805\pi\)
−0.503094 + 0.864231i \(0.667805\pi\)
\(282\) −2.67619 −0.159365
\(283\) −29.0207 −1.72510 −0.862551 0.505971i \(-0.831134\pi\)
−0.862551 + 0.505971i \(0.831134\pi\)
\(284\) 3.38516 0.200872
\(285\) −3.07645 −0.182233
\(286\) −22.8377 −1.35042
\(287\) 0 0
\(288\) −1.53164 −0.0902528
\(289\) −15.3472 −0.902776
\(290\) 1.89298 0.111160
\(291\) −2.95888 −0.173452
\(292\) −1.99717 −0.116876
\(293\) 33.4645 1.95502 0.977509 0.210896i \(-0.0676380\pi\)
0.977509 + 0.210896i \(0.0676380\pi\)
\(294\) 0 0
\(295\) −13.1013 −0.762787
\(296\) 23.4199 1.36125
\(297\) −3.74096 −0.217073
\(298\) 18.7701 1.08732
\(299\) −32.9859 −1.90762
\(300\) 1.02763 0.0593302
\(301\) 0 0
\(302\) 1.52601 0.0878122
\(303\) 9.78581 0.562180
\(304\) 12.4022 0.711313
\(305\) 6.98062 0.399709
\(306\) 1.93807 0.110792
\(307\) 12.0971 0.690419 0.345209 0.938526i \(-0.387808\pi\)
0.345209 + 0.938526i \(0.387808\pi\)
\(308\) 0 0
\(309\) 5.64685 0.321238
\(310\) 5.12698 0.291193
\(311\) 4.23825 0.240329 0.120165 0.992754i \(-0.461658\pi\)
0.120165 + 0.992754i \(0.461658\pi\)
\(312\) −10.5455 −0.597021
\(313\) −23.4002 −1.32266 −0.661329 0.750096i \(-0.730007\pi\)
−0.661329 + 0.750096i \(0.730007\pi\)
\(314\) 5.98802 0.337924
\(315\) 0 0
\(316\) 0.834792 0.0469607
\(317\) 7.71467 0.433299 0.216650 0.976249i \(-0.430487\pi\)
0.216650 + 0.976249i \(0.430487\pi\)
\(318\) 2.16942 0.121655
\(319\) −4.23571 −0.237154
\(320\) −7.35592 −0.411209
\(321\) −14.2514 −0.795434
\(322\) 0 0
\(323\) −3.56630 −0.198434
\(324\) 0.272577 0.0151432
\(325\) 15.2671 0.846866
\(326\) 34.0781 1.88741
\(327\) 1.98301 0.109661
\(328\) −2.60410 −0.143787
\(329\) 0 0
\(330\) 6.25441 0.344294
\(331\) 0.784765 0.0431346 0.0215673 0.999767i \(-0.493134\pi\)
0.0215673 + 0.999767i \(0.493134\pi\)
\(332\) 2.88646 0.158415
\(333\) −8.99346 −0.492838
\(334\) 15.5078 0.848548
\(335\) −1.70138 −0.0929561
\(336\) 0 0
\(337\) −11.6836 −0.636447 −0.318224 0.948016i \(-0.603086\pi\)
−0.318224 + 0.948016i \(0.603086\pi\)
\(338\) 5.12406 0.278712
\(339\) −1.92257 −0.104420
\(340\) −0.388637 −0.0210768
\(341\) −11.4721 −0.621248
\(342\) −4.18183 −0.226127
\(343\) 0 0
\(344\) −13.2179 −0.712659
\(345\) 9.03364 0.486355
\(346\) 12.5324 0.673745
\(347\) 1.28541 0.0690042 0.0345021 0.999405i \(-0.489015\pi\)
0.0345021 + 0.999405i \(0.489015\pi\)
\(348\) 0.308626 0.0165441
\(349\) 30.6569 1.64103 0.820513 0.571628i \(-0.193688\pi\)
0.820513 + 0.571628i \(0.193688\pi\)
\(350\) 0 0
\(351\) 4.04957 0.216150
\(352\) −5.72981 −0.305400
\(353\) 0.656222 0.0349271 0.0174636 0.999848i \(-0.494441\pi\)
0.0174636 + 0.999848i \(0.494441\pi\)
\(354\) −17.8086 −0.946518
\(355\) −13.7732 −0.731003
\(356\) 0.235017 0.0124559
\(357\) 0 0
\(358\) 8.77803 0.463933
\(359\) −0.670115 −0.0353673 −0.0176837 0.999844i \(-0.505629\pi\)
−0.0176837 + 0.999844i \(0.505629\pi\)
\(360\) 2.88803 0.152212
\(361\) −11.3049 −0.594996
\(362\) 25.5443 1.34258
\(363\) −2.99480 −0.157186
\(364\) 0 0
\(365\) 8.12587 0.425327
\(366\) 9.48877 0.495986
\(367\) 24.0081 1.25321 0.626607 0.779335i \(-0.284443\pi\)
0.626607 + 0.779335i \(0.284443\pi\)
\(368\) −36.4175 −1.89839
\(369\) 1.00000 0.0520579
\(370\) 15.0359 0.781679
\(371\) 0 0
\(372\) 0.835887 0.0433387
\(373\) −3.48977 −0.180694 −0.0903468 0.995910i \(-0.528798\pi\)
−0.0903468 + 0.995910i \(0.528798\pi\)
\(374\) 7.25027 0.374902
\(375\) −9.72625 −0.502262
\(376\) −4.62292 −0.238409
\(377\) 4.58513 0.236146
\(378\) 0 0
\(379\) 29.7705 1.52921 0.764603 0.644501i \(-0.222935\pi\)
0.764603 + 0.644501i \(0.222935\pi\)
\(380\) 0.838570 0.0430177
\(381\) −6.05248 −0.310078
\(382\) 19.5216 0.998814
\(383\) 9.44326 0.482528 0.241264 0.970460i \(-0.422438\pi\)
0.241264 + 0.970460i \(0.422438\pi\)
\(384\) −13.0622 −0.666578
\(385\) 0 0
\(386\) −2.31664 −0.117914
\(387\) 5.07578 0.258017
\(388\) 0.806521 0.0409449
\(389\) 31.9855 1.62173 0.810864 0.585235i \(-0.198998\pi\)
0.810864 + 0.585235i \(0.198998\pi\)
\(390\) −6.77036 −0.342831
\(391\) 10.4720 0.529593
\(392\) 0 0
\(393\) 10.1642 0.512719
\(394\) 22.0906 1.11291
\(395\) −3.39651 −0.170897
\(396\) 1.01970 0.0512419
\(397\) 21.0779 1.05787 0.528934 0.848663i \(-0.322592\pi\)
0.528934 + 0.848663i \(0.322592\pi\)
\(398\) 24.0638 1.20621
\(399\) 0 0
\(400\) 16.8554 0.842768
\(401\) −21.5312 −1.07522 −0.537609 0.843194i \(-0.680672\pi\)
−0.537609 + 0.843194i \(0.680672\pi\)
\(402\) −2.31268 −0.115346
\(403\) 12.4185 0.618607
\(404\) −2.66739 −0.132707
\(405\) −1.10903 −0.0551082
\(406\) 0 0
\(407\) −33.6442 −1.66768
\(408\) 3.34788 0.165745
\(409\) −35.8518 −1.77276 −0.886379 0.462961i \(-0.846787\pi\)
−0.886379 + 0.462961i \(0.846787\pi\)
\(410\) −1.67187 −0.0825678
\(411\) −10.4749 −0.516687
\(412\) −1.53920 −0.0758310
\(413\) 0 0
\(414\) 12.2794 0.603501
\(415\) −11.7441 −0.576495
\(416\) 6.20249 0.304102
\(417\) −5.03683 −0.246655
\(418\) −15.6441 −0.765176
\(419\) 9.75270 0.476451 0.238225 0.971210i \(-0.423434\pi\)
0.238225 + 0.971210i \(0.423434\pi\)
\(420\) 0 0
\(421\) 0.117163 0.00571015 0.00285508 0.999996i \(-0.499091\pi\)
0.00285508 + 0.999996i \(0.499091\pi\)
\(422\) 35.4527 1.72581
\(423\) 1.77524 0.0863153
\(424\) 3.74751 0.181995
\(425\) −4.84684 −0.235106
\(426\) −18.7219 −0.907078
\(427\) 0 0
\(428\) 3.88459 0.187769
\(429\) 15.1493 0.731415
\(430\) −8.48605 −0.409234
\(431\) 21.1818 1.02029 0.510146 0.860088i \(-0.329591\pi\)
0.510146 + 0.860088i \(0.329591\pi\)
\(432\) 4.47086 0.215104
\(433\) 23.6911 1.13852 0.569260 0.822157i \(-0.307230\pi\)
0.569260 + 0.822157i \(0.307230\pi\)
\(434\) 0 0
\(435\) −1.25570 −0.0602063
\(436\) −0.540523 −0.0258863
\(437\) −22.5957 −1.08090
\(438\) 11.0455 0.527775
\(439\) 17.5444 0.837349 0.418675 0.908136i \(-0.362495\pi\)
0.418675 + 0.908136i \(0.362495\pi\)
\(440\) 10.8040 0.515061
\(441\) 0 0
\(442\) −7.84837 −0.373309
\(443\) 4.89678 0.232653 0.116327 0.993211i \(-0.462888\pi\)
0.116327 + 0.993211i \(0.462888\pi\)
\(444\) 2.45141 0.116339
\(445\) −0.956211 −0.0453287
\(446\) 33.3505 1.57919
\(447\) −12.4511 −0.588915
\(448\) 0 0
\(449\) −25.8031 −1.21772 −0.608862 0.793276i \(-0.708374\pi\)
−0.608862 + 0.793276i \(0.708374\pi\)
\(450\) −5.68338 −0.267917
\(451\) 3.74096 0.176155
\(452\) 0.524049 0.0246492
\(453\) −1.01228 −0.0475609
\(454\) −32.9623 −1.54700
\(455\) 0 0
\(456\) −7.22378 −0.338285
\(457\) −10.7604 −0.503349 −0.251675 0.967812i \(-0.580981\pi\)
−0.251675 + 0.967812i \(0.580981\pi\)
\(458\) 22.2893 1.04151
\(459\) −1.28562 −0.0600074
\(460\) −2.46236 −0.114808
\(461\) −4.73851 −0.220694 −0.110347 0.993893i \(-0.535196\pi\)
−0.110347 + 0.993893i \(0.535196\pi\)
\(462\) 0 0
\(463\) −13.8446 −0.643413 −0.321707 0.946839i \(-0.604256\pi\)
−0.321707 + 0.946839i \(0.604256\pi\)
\(464\) 5.06213 0.235004
\(465\) −3.40096 −0.157716
\(466\) −41.0200 −1.90022
\(467\) −11.5666 −0.535238 −0.267619 0.963525i \(-0.586237\pi\)
−0.267619 + 0.963525i \(0.586237\pi\)
\(468\) −1.10382 −0.0510241
\(469\) 0 0
\(470\) −2.96798 −0.136903
\(471\) −3.97214 −0.183026
\(472\) −30.7630 −1.41598
\(473\) 18.9883 0.873084
\(474\) −4.61688 −0.212060
\(475\) 10.4581 0.479852
\(476\) 0 0
\(477\) −1.43908 −0.0658910
\(478\) −36.1249 −1.65232
\(479\) −11.9744 −0.547123 −0.273562 0.961854i \(-0.588202\pi\)
−0.273562 + 0.961854i \(0.588202\pi\)
\(480\) −1.69864 −0.0775318
\(481\) 36.4196 1.66059
\(482\) −19.4625 −0.886494
\(483\) 0 0
\(484\) 0.816313 0.0371052
\(485\) −3.28148 −0.149004
\(486\) −1.50751 −0.0683819
\(487\) −11.7895 −0.534235 −0.267118 0.963664i \(-0.586071\pi\)
−0.267118 + 0.963664i \(0.586071\pi\)
\(488\) 16.3911 0.741991
\(489\) −22.6056 −1.02226
\(490\) 0 0
\(491\) −41.8155 −1.88711 −0.943553 0.331222i \(-0.892539\pi\)
−0.943553 + 0.331222i \(0.892539\pi\)
\(492\) −0.272577 −0.0122887
\(493\) −1.45564 −0.0655588
\(494\) 16.9346 0.761924
\(495\) −4.14884 −0.186477
\(496\) 13.7104 0.615614
\(497\) 0 0
\(498\) −15.9638 −0.715354
\(499\) −18.7923 −0.841260 −0.420630 0.907232i \(-0.638191\pi\)
−0.420630 + 0.907232i \(0.638191\pi\)
\(500\) 2.65115 0.118563
\(501\) −10.2870 −0.459591
\(502\) 20.3367 0.907669
\(503\) −5.66329 −0.252514 −0.126257 0.991998i \(-0.540296\pi\)
−0.126257 + 0.991998i \(0.540296\pi\)
\(504\) 0 0
\(505\) 10.8528 0.482941
\(506\) 45.9369 2.04215
\(507\) −3.39903 −0.150956
\(508\) 1.64977 0.0731966
\(509\) 16.0628 0.711970 0.355985 0.934492i \(-0.384145\pi\)
0.355985 + 0.934492i \(0.384145\pi\)
\(510\) 2.14938 0.0951763
\(511\) 0 0
\(512\) −16.4374 −0.726437
\(513\) 2.77400 0.122475
\(514\) 6.57018 0.289798
\(515\) 6.26253 0.275960
\(516\) −1.38354 −0.0609070
\(517\) 6.64112 0.292076
\(518\) 0 0
\(519\) −8.31332 −0.364914
\(520\) −11.6953 −0.512872
\(521\) 29.4204 1.28893 0.644465 0.764634i \(-0.277080\pi\)
0.644465 + 0.764634i \(0.277080\pi\)
\(522\) −1.70688 −0.0747080
\(523\) −1.46912 −0.0642401 −0.0321201 0.999484i \(-0.510226\pi\)
−0.0321201 + 0.999484i \(0.510226\pi\)
\(524\) −2.77054 −0.121032
\(525\) 0 0
\(526\) −21.5428 −0.939312
\(527\) −3.94248 −0.171737
\(528\) 16.7253 0.727875
\(529\) 43.3496 1.88477
\(530\) 2.40596 0.104508
\(531\) 11.8133 0.512653
\(532\) 0 0
\(533\) −4.04957 −0.175406
\(534\) −1.29978 −0.0562469
\(535\) −15.8052 −0.683318
\(536\) −3.99498 −0.172557
\(537\) −5.82288 −0.251276
\(538\) 30.6468 1.32128
\(539\) 0 0
\(540\) 0.302296 0.0130088
\(541\) 14.1541 0.608534 0.304267 0.952587i \(-0.401588\pi\)
0.304267 + 0.952587i \(0.401588\pi\)
\(542\) −31.9337 −1.37167
\(543\) −16.9447 −0.727168
\(544\) −1.96910 −0.0844246
\(545\) 2.19922 0.0942042
\(546\) 0 0
\(547\) −36.1112 −1.54401 −0.772003 0.635619i \(-0.780745\pi\)
−0.772003 + 0.635619i \(0.780745\pi\)
\(548\) 2.85521 0.121968
\(549\) −6.29435 −0.268636
\(550\) −21.2613 −0.906585
\(551\) 3.14087 0.133805
\(552\) 21.2118 0.902834
\(553\) 0 0
\(554\) 4.82841 0.205139
\(555\) −9.97402 −0.423373
\(556\) 1.37292 0.0582250
\(557\) −28.3038 −1.19927 −0.599635 0.800274i \(-0.704687\pi\)
−0.599635 + 0.800274i \(0.704687\pi\)
\(558\) −4.62294 −0.195704
\(559\) −20.5547 −0.869373
\(560\) 0 0
\(561\) −4.80944 −0.203055
\(562\) −25.4268 −1.07257
\(563\) 28.6819 1.20880 0.604399 0.796682i \(-0.293413\pi\)
0.604399 + 0.796682i \(0.293413\pi\)
\(564\) −0.483891 −0.0203755
\(565\) −2.13219 −0.0897019
\(566\) −43.7489 −1.83890
\(567\) 0 0
\(568\) −32.3406 −1.35698
\(569\) −25.3316 −1.06195 −0.530977 0.847386i \(-0.678175\pi\)
−0.530977 + 0.847386i \(0.678175\pi\)
\(570\) −4.63777 −0.194255
\(571\) −44.5188 −1.86305 −0.931526 0.363674i \(-0.881522\pi\)
−0.931526 + 0.363674i \(0.881522\pi\)
\(572\) −4.12935 −0.172657
\(573\) −12.9496 −0.540978
\(574\) 0 0
\(575\) −30.7091 −1.28066
\(576\) 6.63275 0.276365
\(577\) −8.77810 −0.365437 −0.182718 0.983165i \(-0.558490\pi\)
−0.182718 + 0.983165i \(0.558490\pi\)
\(578\) −23.1360 −0.962331
\(579\) 1.53674 0.0638646
\(580\) 0.342275 0.0142122
\(581\) 0 0
\(582\) −4.46053 −0.184895
\(583\) −5.38355 −0.222964
\(584\) 19.0803 0.789547
\(585\) 4.49110 0.185684
\(586\) 50.4480 2.08399
\(587\) −8.35115 −0.344689 −0.172344 0.985037i \(-0.555134\pi\)
−0.172344 + 0.985037i \(0.555134\pi\)
\(588\) 0 0
\(589\) 8.50678 0.350516
\(590\) −19.7503 −0.813107
\(591\) −14.6537 −0.602773
\(592\) 40.2084 1.65256
\(593\) −6.68553 −0.274542 −0.137271 0.990534i \(-0.543833\pi\)
−0.137271 + 0.990534i \(0.543833\pi\)
\(594\) −5.63953 −0.231393
\(595\) 0 0
\(596\) 3.39387 0.139018
\(597\) −15.9626 −0.653306
\(598\) −49.7265 −2.03347
\(599\) 6.46648 0.264213 0.132107 0.991236i \(-0.457826\pi\)
0.132107 + 0.991236i \(0.457826\pi\)
\(600\) −9.81760 −0.400802
\(601\) −40.0959 −1.63554 −0.817772 0.575542i \(-0.804791\pi\)
−0.817772 + 0.575542i \(0.804791\pi\)
\(602\) 0 0
\(603\) 1.53411 0.0624738
\(604\) 0.275923 0.0112272
\(605\) −3.32132 −0.135031
\(606\) 14.7522 0.599266
\(607\) −2.40461 −0.0976000 −0.0488000 0.998809i \(-0.515540\pi\)
−0.0488000 + 0.998809i \(0.515540\pi\)
\(608\) 4.24877 0.172311
\(609\) 0 0
\(610\) 10.5233 0.426077
\(611\) −7.18898 −0.290835
\(612\) 0.350429 0.0141653
\(613\) −21.6500 −0.874435 −0.437218 0.899356i \(-0.644036\pi\)
−0.437218 + 0.899356i \(0.644036\pi\)
\(614\) 18.2365 0.735964
\(615\) 1.10903 0.0447204
\(616\) 0 0
\(617\) −5.55725 −0.223726 −0.111863 0.993724i \(-0.535682\pi\)
−0.111863 + 0.993724i \(0.535682\pi\)
\(618\) 8.51266 0.342429
\(619\) 39.3059 1.57984 0.789918 0.613212i \(-0.210123\pi\)
0.789918 + 0.613212i \(0.210123\pi\)
\(620\) 0.927024 0.0372302
\(621\) −8.14553 −0.326869
\(622\) 6.38920 0.256183
\(623\) 0 0
\(624\) −18.1050 −0.724782
\(625\) 8.06355 0.322542
\(626\) −35.2760 −1.40991
\(627\) 10.3774 0.414435
\(628\) 1.08271 0.0432049
\(629\) −11.5621 −0.461012
\(630\) 0 0
\(631\) −1.34175 −0.0534142 −0.0267071 0.999643i \(-0.508502\pi\)
−0.0267071 + 0.999643i \(0.508502\pi\)
\(632\) −7.97530 −0.317240
\(633\) −23.5174 −0.934733
\(634\) 11.6299 0.461883
\(635\) −6.71239 −0.266373
\(636\) 0.392260 0.0155541
\(637\) 0 0
\(638\) −6.38536 −0.252799
\(639\) 12.4191 0.491292
\(640\) −14.4864 −0.572624
\(641\) 21.6189 0.853894 0.426947 0.904277i \(-0.359589\pi\)
0.426947 + 0.904277i \(0.359589\pi\)
\(642\) −21.4840 −0.847907
\(643\) 24.8621 0.980465 0.490233 0.871592i \(-0.336912\pi\)
0.490233 + 0.871592i \(0.336912\pi\)
\(644\) 0 0
\(645\) 5.62920 0.221649
\(646\) −5.37622 −0.211525
\(647\) 29.3258 1.15292 0.576459 0.817126i \(-0.304434\pi\)
0.576459 + 0.817126i \(0.304434\pi\)
\(648\) −2.60410 −0.102299
\(649\) 44.1931 1.73473
\(650\) 23.0152 0.902732
\(651\) 0 0
\(652\) 6.16177 0.241313
\(653\) 40.3928 1.58069 0.790346 0.612661i \(-0.209901\pi\)
0.790346 + 0.612661i \(0.209901\pi\)
\(654\) 2.98940 0.116895
\(655\) 11.2725 0.440452
\(656\) −4.47086 −0.174558
\(657\) −7.32700 −0.285854
\(658\) 0 0
\(659\) 36.6015 1.42579 0.712895 0.701271i \(-0.247384\pi\)
0.712895 + 0.701271i \(0.247384\pi\)
\(660\) 1.13088 0.0440194
\(661\) −35.4309 −1.37810 −0.689050 0.724714i \(-0.741972\pi\)
−0.689050 + 0.724714i \(0.741972\pi\)
\(662\) 1.18304 0.0459801
\(663\) 5.20619 0.202192
\(664\) −27.5762 −1.07016
\(665\) 0 0
\(666\) −13.5577 −0.525350
\(667\) −9.22279 −0.357108
\(668\) 2.80401 0.108490
\(669\) −22.1230 −0.855323
\(670\) −2.56484 −0.0990882
\(671\) −23.5469 −0.909018
\(672\) 0 0
\(673\) 4.09653 0.157910 0.0789549 0.996878i \(-0.474842\pi\)
0.0789549 + 0.996878i \(0.474842\pi\)
\(674\) −17.6131 −0.678432
\(675\) 3.77005 0.145109
\(676\) 0.926497 0.0356345
\(677\) −46.9399 −1.80405 −0.902023 0.431687i \(-0.857919\pi\)
−0.902023 + 0.431687i \(0.857919\pi\)
\(678\) −2.89829 −0.111308
\(679\) 0 0
\(680\) 3.71290 0.142383
\(681\) 21.8654 0.837885
\(682\) −17.2942 −0.662230
\(683\) 43.8835 1.67916 0.839578 0.543239i \(-0.182802\pi\)
0.839578 + 0.543239i \(0.182802\pi\)
\(684\) −0.756129 −0.0289113
\(685\) −11.6169 −0.443861
\(686\) 0 0
\(687\) −14.7855 −0.564103
\(688\) −22.6931 −0.865166
\(689\) 5.82766 0.222016
\(690\) 13.6183 0.518439
\(691\) −13.1815 −0.501446 −0.250723 0.968059i \(-0.580668\pi\)
−0.250723 + 0.968059i \(0.580668\pi\)
\(692\) 2.26602 0.0861411
\(693\) 0 0
\(694\) 1.93776 0.0735563
\(695\) −5.58600 −0.211889
\(696\) −2.94850 −0.111763
\(697\) 1.28562 0.0486962
\(698\) 46.2155 1.74928
\(699\) 27.2105 1.02920
\(700\) 0 0
\(701\) −21.8416 −0.824945 −0.412472 0.910970i \(-0.635335\pi\)
−0.412472 + 0.910970i \(0.635335\pi\)
\(702\) 6.10476 0.230409
\(703\) 24.9479 0.940926
\(704\) 24.8129 0.935170
\(705\) 1.96880 0.0741493
\(706\) 0.989258 0.0372312
\(707\) 0 0
\(708\) −3.22003 −0.121016
\(709\) −23.7312 −0.891243 −0.445622 0.895221i \(-0.647017\pi\)
−0.445622 + 0.895221i \(0.647017\pi\)
\(710\) −20.7631 −0.779226
\(711\) 3.06259 0.114856
\(712\) −2.24527 −0.0841450
\(713\) −24.9792 −0.935477
\(714\) 0 0
\(715\) 16.8010 0.628323
\(716\) 1.58718 0.0593158
\(717\) 23.9634 0.894928
\(718\) −1.01020 −0.0377005
\(719\) 14.4356 0.538358 0.269179 0.963090i \(-0.413248\pi\)
0.269179 + 0.963090i \(0.413248\pi\)
\(720\) 4.95832 0.184785
\(721\) 0 0
\(722\) −17.0422 −0.634246
\(723\) 12.9104 0.480143
\(724\) 4.61874 0.171654
\(725\) 4.26865 0.158534
\(726\) −4.51468 −0.167556
\(727\) 7.96786 0.295512 0.147756 0.989024i \(-0.452795\pi\)
0.147756 + 0.989024i \(0.452795\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 12.2498 0.453385
\(731\) 6.52551 0.241355
\(732\) 1.71569 0.0634138
\(733\) −33.3492 −1.23178 −0.615890 0.787832i \(-0.711204\pi\)
−0.615890 + 0.787832i \(0.711204\pi\)
\(734\) 36.1924 1.33589
\(735\) 0 0
\(736\) −12.4760 −0.459872
\(737\) 5.73905 0.211401
\(738\) 1.50751 0.0554921
\(739\) −14.8315 −0.545584 −0.272792 0.962073i \(-0.587947\pi\)
−0.272792 + 0.962073i \(0.587947\pi\)
\(740\) 2.71869 0.0999409
\(741\) −11.2335 −0.412674
\(742\) 0 0
\(743\) 31.1321 1.14213 0.571063 0.820906i \(-0.306531\pi\)
0.571063 + 0.820906i \(0.306531\pi\)
\(744\) −7.98577 −0.292772
\(745\) −13.8086 −0.505908
\(746\) −5.26086 −0.192614
\(747\) 10.5895 0.387450
\(748\) 1.31094 0.0479328
\(749\) 0 0
\(750\) −14.6624 −0.535395
\(751\) 3.96823 0.144803 0.0724014 0.997376i \(-0.476934\pi\)
0.0724014 + 0.997376i \(0.476934\pi\)
\(752\) −7.93686 −0.289427
\(753\) −13.4903 −0.491612
\(754\) 6.91212 0.251725
\(755\) −1.12265 −0.0408572
\(756\) 0 0
\(757\) −28.9528 −1.05231 −0.526153 0.850390i \(-0.676366\pi\)
−0.526153 + 0.850390i \(0.676366\pi\)
\(758\) 44.8792 1.63009
\(759\) −30.4721 −1.10607
\(760\) −8.01139 −0.290604
\(761\) −12.6480 −0.458490 −0.229245 0.973369i \(-0.573626\pi\)
−0.229245 + 0.973369i \(0.573626\pi\)
\(762\) −9.12416 −0.330533
\(763\) 0 0
\(764\) 3.52977 0.127702
\(765\) −1.42579 −0.0515494
\(766\) 14.2358 0.514359
\(767\) −47.8388 −1.72736
\(768\) −6.42585 −0.231873
\(769\) −22.8838 −0.825210 −0.412605 0.910910i \(-0.635381\pi\)
−0.412605 + 0.910910i \(0.635381\pi\)
\(770\) 0 0
\(771\) −4.35831 −0.156961
\(772\) −0.418879 −0.0150758
\(773\) 0.777954 0.0279811 0.0139905 0.999902i \(-0.495547\pi\)
0.0139905 + 0.999902i \(0.495547\pi\)
\(774\) 7.65178 0.275037
\(775\) 11.5613 0.415293
\(776\) −7.70521 −0.276601
\(777\) 0 0
\(778\) 48.2183 1.72871
\(779\) −2.77400 −0.0993889
\(780\) −1.22417 −0.0438323
\(781\) 46.4594 1.66245
\(782\) 15.7866 0.564529
\(783\) 1.13225 0.0404634
\(784\) 0 0
\(785\) −4.40522 −0.157229
\(786\) 15.3227 0.546542
\(787\) 29.3699 1.04692 0.523462 0.852049i \(-0.324640\pi\)
0.523462 + 0.852049i \(0.324640\pi\)
\(788\) 3.99426 0.142290
\(789\) 14.2904 0.508751
\(790\) −5.12026 −0.182171
\(791\) 0 0
\(792\) −9.74185 −0.346162
\(793\) 25.4894 0.905155
\(794\) 31.7750 1.12765
\(795\) −1.59598 −0.0566037
\(796\) 4.35104 0.154219
\(797\) 22.5919 0.800247 0.400124 0.916461i \(-0.368967\pi\)
0.400124 + 0.916461i \(0.368967\pi\)
\(798\) 0 0
\(799\) 2.28228 0.0807413
\(800\) 5.77437 0.204155
\(801\) 0.862204 0.0304645
\(802\) −32.4585 −1.14615
\(803\) −27.4100 −0.967279
\(804\) −0.418163 −0.0147475
\(805\) 0 0
\(806\) 18.7209 0.659416
\(807\) −20.3295 −0.715632
\(808\) 25.4832 0.896497
\(809\) 31.0716 1.09242 0.546209 0.837649i \(-0.316070\pi\)
0.546209 + 0.837649i \(0.316070\pi\)
\(810\) −1.67187 −0.0587436
\(811\) 32.1947 1.13051 0.565254 0.824917i \(-0.308778\pi\)
0.565254 + 0.824917i \(0.308778\pi\)
\(812\) 0 0
\(813\) 21.1831 0.742925
\(814\) −50.7188 −1.77769
\(815\) −25.0703 −0.878175
\(816\) 5.74780 0.201213
\(817\) −14.0802 −0.492605
\(818\) −54.0468 −1.88970
\(819\) 0 0
\(820\) −0.302296 −0.0105566
\(821\) −21.4757 −0.749509 −0.374754 0.927124i \(-0.622273\pi\)
−0.374754 + 0.927124i \(0.622273\pi\)
\(822\) −15.7909 −0.550772
\(823\) 27.4356 0.956345 0.478172 0.878266i \(-0.341299\pi\)
0.478172 + 0.878266i \(0.341299\pi\)
\(824\) 14.7050 0.512272
\(825\) 14.1036 0.491025
\(826\) 0 0
\(827\) 5.26418 0.183053 0.0915267 0.995803i \(-0.470825\pi\)
0.0915267 + 0.995803i \(0.470825\pi\)
\(828\) 2.22028 0.0771602
\(829\) −36.4033 −1.26434 −0.632169 0.774831i \(-0.717835\pi\)
−0.632169 + 0.774831i \(0.717835\pi\)
\(830\) −17.7043 −0.614525
\(831\) −3.20291 −0.111108
\(832\) −26.8598 −0.931196
\(833\) 0 0
\(834\) −7.59306 −0.262926
\(835\) −11.4086 −0.394812
\(836\) −2.82865 −0.0978309
\(837\) 3.06661 0.105998
\(838\) 14.7023 0.507881
\(839\) −35.5047 −1.22576 −0.612880 0.790176i \(-0.709989\pi\)
−0.612880 + 0.790176i \(0.709989\pi\)
\(840\) 0 0
\(841\) −27.7180 −0.955793
\(842\) 0.176623 0.00608684
\(843\) 16.8668 0.580923
\(844\) 6.41030 0.220652
\(845\) −3.76963 −0.129679
\(846\) 2.67619 0.0920094
\(847\) 0 0
\(848\) 6.43392 0.220942
\(849\) 29.0207 0.995988
\(850\) −7.30664 −0.250616
\(851\) −73.2564 −2.51120
\(852\) −3.38516 −0.115974
\(853\) 28.0973 0.962035 0.481017 0.876711i \(-0.340267\pi\)
0.481017 + 0.876711i \(0.340267\pi\)
\(854\) 0 0
\(855\) 3.07645 0.105212
\(856\) −37.1120 −1.26846
\(857\) −45.0276 −1.53811 −0.769056 0.639181i \(-0.779273\pi\)
−0.769056 + 0.639181i \(0.779273\pi\)
\(858\) 22.8377 0.779665
\(859\) −19.7121 −0.672568 −0.336284 0.941761i \(-0.609170\pi\)
−0.336284 + 0.941761i \(0.609170\pi\)
\(860\) −1.53439 −0.0523222
\(861\) 0 0
\(862\) 31.9317 1.08760
\(863\) −8.30927 −0.282851 −0.141425 0.989949i \(-0.545169\pi\)
−0.141425 + 0.989949i \(0.545169\pi\)
\(864\) 1.53164 0.0521075
\(865\) −9.21972 −0.313480
\(866\) 35.7145 1.21363
\(867\) 15.3472 0.521218
\(868\) 0 0
\(869\) 11.4570 0.388653
\(870\) −1.89298 −0.0641780
\(871\) −6.21249 −0.210502
\(872\) 5.16396 0.174874
\(873\) 2.95888 0.100143
\(874\) −34.0632 −1.15220
\(875\) 0 0
\(876\) 1.99717 0.0674782
\(877\) 36.4096 1.22947 0.614733 0.788735i \(-0.289264\pi\)
0.614733 + 0.788735i \(0.289264\pi\)
\(878\) 26.4483 0.892588
\(879\) −33.4645 −1.12873
\(880\) 18.5489 0.625282
\(881\) 41.2925 1.39118 0.695590 0.718439i \(-0.255143\pi\)
0.695590 + 0.718439i \(0.255143\pi\)
\(882\) 0 0
\(883\) −27.7916 −0.935261 −0.467631 0.883924i \(-0.654892\pi\)
−0.467631 + 0.883924i \(0.654892\pi\)
\(884\) −1.41909 −0.0477291
\(885\) 13.1013 0.440395
\(886\) 7.38193 0.248001
\(887\) 22.4719 0.754534 0.377267 0.926105i \(-0.376864\pi\)
0.377267 + 0.926105i \(0.376864\pi\)
\(888\) −23.4199 −0.785920
\(889\) 0 0
\(890\) −1.44149 −0.0483190
\(891\) 3.74096 0.125327
\(892\) 6.03021 0.201906
\(893\) −4.92453 −0.164793
\(894\) −18.7701 −0.627765
\(895\) −6.45775 −0.215859
\(896\) 0 0
\(897\) 32.9859 1.10137
\(898\) −38.8984 −1.29806
\(899\) 3.47217 0.115803
\(900\) −1.02763 −0.0342543
\(901\) −1.85010 −0.0616359
\(902\) 5.63953 0.187776
\(903\) 0 0
\(904\) −5.00657 −0.166516
\(905\) −18.7922 −0.624675
\(906\) −1.52601 −0.0506984
\(907\) −48.2992 −1.60375 −0.801875 0.597492i \(-0.796164\pi\)
−0.801875 + 0.597492i \(0.796164\pi\)
\(908\) −5.96001 −0.197790
\(909\) −9.78581 −0.324575
\(910\) 0 0
\(911\) 37.4429 1.24054 0.620269 0.784389i \(-0.287023\pi\)
0.620269 + 0.784389i \(0.287023\pi\)
\(912\) −12.4022 −0.410677
\(913\) 39.6150 1.31106
\(914\) −16.2213 −0.536554
\(915\) −6.98062 −0.230772
\(916\) 4.03019 0.133161
\(917\) 0 0
\(918\) −1.93807 −0.0639660
\(919\) −11.5498 −0.380992 −0.190496 0.981688i \(-0.561010\pi\)
−0.190496 + 0.981688i \(0.561010\pi\)
\(920\) 23.5245 0.775580
\(921\) −12.0971 −0.398613
\(922\) −7.14334 −0.235253
\(923\) −50.2920 −1.65538
\(924\) 0 0
\(925\) 33.9058 1.11482
\(926\) −20.8708 −0.685858
\(927\) −5.64685 −0.185467
\(928\) 1.73420 0.0569280
\(929\) −2.48031 −0.0813764 −0.0406882 0.999172i \(-0.512955\pi\)
−0.0406882 + 0.999172i \(0.512955\pi\)
\(930\) −5.12698 −0.168120
\(931\) 0 0
\(932\) −7.41696 −0.242951
\(933\) −4.23825 −0.138754
\(934\) −17.4367 −0.570547
\(935\) −5.33382 −0.174434
\(936\) 10.5455 0.344690
\(937\) 20.6957 0.676098 0.338049 0.941128i \(-0.390233\pi\)
0.338049 + 0.941128i \(0.390233\pi\)
\(938\) 0 0
\(939\) 23.4002 0.763637
\(940\) −0.536649 −0.0175036
\(941\) 19.6088 0.639230 0.319615 0.947547i \(-0.396446\pi\)
0.319615 + 0.947547i \(0.396446\pi\)
\(942\) −5.98802 −0.195100
\(943\) 8.14553 0.265255
\(944\) −52.8155 −1.71900
\(945\) 0 0
\(946\) 28.6250 0.930679
\(947\) 51.2866 1.66659 0.833296 0.552828i \(-0.186451\pi\)
0.833296 + 0.552828i \(0.186451\pi\)
\(948\) −0.834792 −0.0271128
\(949\) 29.6712 0.963168
\(950\) 15.7657 0.511507
\(951\) −7.71467 −0.250165
\(952\) 0 0
\(953\) 49.5293 1.60441 0.802205 0.597048i \(-0.203660\pi\)
0.802205 + 0.597048i \(0.203660\pi\)
\(954\) −2.16942 −0.0702377
\(955\) −14.3615 −0.464728
\(956\) −6.53186 −0.211255
\(957\) 4.23571 0.136921
\(958\) −18.0515 −0.583216
\(959\) 0 0
\(960\) 7.35592 0.237411
\(961\) −21.5959 −0.696642
\(962\) 54.9029 1.77014
\(963\) 14.2514 0.459244
\(964\) −3.51908 −0.113342
\(965\) 1.70429 0.0548630
\(966\) 0 0
\(967\) −22.8164 −0.733727 −0.366863 0.930275i \(-0.619568\pi\)
−0.366863 + 0.930275i \(0.619568\pi\)
\(968\) −7.79877 −0.250662
\(969\) 3.56630 0.114566
\(970\) −4.94686 −0.158834
\(971\) −24.2347 −0.777729 −0.388864 0.921295i \(-0.627133\pi\)
−0.388864 + 0.921295i \(0.627133\pi\)
\(972\) −0.272577 −0.00874291
\(973\) 0 0
\(974\) −17.7728 −0.569478
\(975\) −15.2671 −0.488938
\(976\) 28.1411 0.900775
\(977\) −33.0385 −1.05700 −0.528498 0.848934i \(-0.677245\pi\)
−0.528498 + 0.848934i \(0.677245\pi\)
\(978\) −34.0781 −1.08970
\(979\) 3.22547 0.103087
\(980\) 0 0
\(981\) −1.98301 −0.0633126
\(982\) −63.0371 −2.01159
\(983\) −21.3362 −0.680518 −0.340259 0.940332i \(-0.610515\pi\)
−0.340259 + 0.940332i \(0.610515\pi\)
\(984\) 2.60410 0.0830157
\(985\) −16.2514 −0.517813
\(986\) −2.19439 −0.0698836
\(987\) 0 0
\(988\) 3.06200 0.0974151
\(989\) 41.3449 1.31469
\(990\) −6.25441 −0.198778
\(991\) 6.34983 0.201709 0.100854 0.994901i \(-0.467842\pi\)
0.100854 + 0.994901i \(0.467842\pi\)
\(992\) 4.69695 0.149128
\(993\) −0.784765 −0.0249038
\(994\) 0 0
\(995\) −17.7030 −0.561224
\(996\) −2.88646 −0.0914609
\(997\) 39.8519 1.26212 0.631061 0.775733i \(-0.282620\pi\)
0.631061 + 0.775733i \(0.282620\pi\)
\(998\) −28.3296 −0.896757
\(999\) 8.99346 0.284540
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 \(a_p\))