Properties

Label 8013.2.a.d.1.3
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69445 q^{2} +1.00000 q^{3} +5.26005 q^{4} -1.49008 q^{5} -2.69445 q^{6} +1.50692 q^{7} -8.78405 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.69445 q^{2} +1.00000 q^{3} +5.26005 q^{4} -1.49008 q^{5} -2.69445 q^{6} +1.50692 q^{7} -8.78405 q^{8} +1.00000 q^{9} +4.01496 q^{10} -3.43638 q^{11} +5.26005 q^{12} +4.91212 q^{13} -4.06033 q^{14} -1.49008 q^{15} +13.1481 q^{16} +3.52996 q^{17} -2.69445 q^{18} +2.70051 q^{19} -7.83793 q^{20} +1.50692 q^{21} +9.25915 q^{22} +2.27825 q^{23} -8.78405 q^{24} -2.77965 q^{25} -13.2355 q^{26} +1.00000 q^{27} +7.92650 q^{28} +1.34718 q^{29} +4.01496 q^{30} +4.87386 q^{31} -17.8587 q^{32} -3.43638 q^{33} -9.51129 q^{34} -2.24544 q^{35} +5.26005 q^{36} +2.96022 q^{37} -7.27639 q^{38} +4.91212 q^{39} +13.0890 q^{40} +6.75006 q^{41} -4.06033 q^{42} +4.68543 q^{43} -18.0755 q^{44} -1.49008 q^{45} -6.13864 q^{46} -4.45336 q^{47} +13.1481 q^{48} -4.72918 q^{49} +7.48962 q^{50} +3.52996 q^{51} +25.8380 q^{52} +2.19540 q^{53} -2.69445 q^{54} +5.12050 q^{55} -13.2369 q^{56} +2.70051 q^{57} -3.62990 q^{58} +7.53224 q^{59} -7.83793 q^{60} +0.353338 q^{61} -13.1324 q^{62} +1.50692 q^{63} +21.8231 q^{64} -7.31948 q^{65} +9.25915 q^{66} -0.363045 q^{67} +18.5678 q^{68} +2.27825 q^{69} +6.05023 q^{70} +5.88873 q^{71} -8.78405 q^{72} -1.33635 q^{73} -7.97616 q^{74} -2.77965 q^{75} +14.2048 q^{76} -5.17836 q^{77} -13.2355 q^{78} +4.59245 q^{79} -19.5917 q^{80} +1.00000 q^{81} -18.1877 q^{82} -9.77403 q^{83} +7.92650 q^{84} -5.25994 q^{85} -12.6246 q^{86} +1.34718 q^{87} +30.1853 q^{88} +13.7570 q^{89} +4.01496 q^{90} +7.40219 q^{91} +11.9837 q^{92} +4.87386 q^{93} +11.9993 q^{94} -4.02399 q^{95} -17.8587 q^{96} +7.45956 q^{97} +12.7425 q^{98} -3.43638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69445 −1.90526 −0.952631 0.304127i \(-0.901635\pi\)
−0.952631 + 0.304127i \(0.901635\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.26005 2.63003
\(5\) −1.49008 −0.666386 −0.333193 0.942859i \(-0.608126\pi\)
−0.333193 + 0.942859i \(0.608126\pi\)
\(6\) −2.69445 −1.10000
\(7\) 1.50692 0.569564 0.284782 0.958592i \(-0.408079\pi\)
0.284782 + 0.958592i \(0.408079\pi\)
\(8\) −8.78405 −3.10563
\(9\) 1.00000 0.333333
\(10\) 4.01496 1.26964
\(11\) −3.43638 −1.03611 −0.518054 0.855348i \(-0.673343\pi\)
−0.518054 + 0.855348i \(0.673343\pi\)
\(12\) 5.26005 1.51845
\(13\) 4.91212 1.36238 0.681189 0.732108i \(-0.261463\pi\)
0.681189 + 0.732108i \(0.261463\pi\)
\(14\) −4.06033 −1.08517
\(15\) −1.49008 −0.384738
\(16\) 13.1481 3.28701
\(17\) 3.52996 0.856141 0.428070 0.903745i \(-0.359193\pi\)
0.428070 + 0.903745i \(0.359193\pi\)
\(18\) −2.69445 −0.635088
\(19\) 2.70051 0.619540 0.309770 0.950812i \(-0.399748\pi\)
0.309770 + 0.950812i \(0.399748\pi\)
\(20\) −7.83793 −1.75261
\(21\) 1.50692 0.328838
\(22\) 9.25915 1.97406
\(23\) 2.27825 0.475049 0.237524 0.971382i \(-0.423664\pi\)
0.237524 + 0.971382i \(0.423664\pi\)
\(24\) −8.78405 −1.79304
\(25\) −2.77965 −0.555929
\(26\) −13.2355 −2.59569
\(27\) 1.00000 0.192450
\(28\) 7.92650 1.49797
\(29\) 1.34718 0.250165 0.125082 0.992146i \(-0.460081\pi\)
0.125082 + 0.992146i \(0.460081\pi\)
\(30\) 4.01496 0.733028
\(31\) 4.87386 0.875372 0.437686 0.899128i \(-0.355798\pi\)
0.437686 + 0.899128i \(0.355798\pi\)
\(32\) −17.8587 −3.15700
\(33\) −3.43638 −0.598197
\(34\) −9.51129 −1.63117
\(35\) −2.24544 −0.379549
\(36\) 5.26005 0.876676
\(37\) 2.96022 0.486657 0.243328 0.969944i \(-0.421761\pi\)
0.243328 + 0.969944i \(0.421761\pi\)
\(38\) −7.27639 −1.18039
\(39\) 4.91212 0.786569
\(40\) 13.0890 2.06955
\(41\) 6.75006 1.05418 0.527091 0.849809i \(-0.323283\pi\)
0.527091 + 0.849809i \(0.323283\pi\)
\(42\) −4.06033 −0.626522
\(43\) 4.68543 0.714521 0.357260 0.934005i \(-0.383711\pi\)
0.357260 + 0.934005i \(0.383711\pi\)
\(44\) −18.0755 −2.72499
\(45\) −1.49008 −0.222129
\(46\) −6.13864 −0.905093
\(47\) −4.45336 −0.649589 −0.324795 0.945785i \(-0.605295\pi\)
−0.324795 + 0.945785i \(0.605295\pi\)
\(48\) 13.1481 1.89776
\(49\) −4.72918 −0.675597
\(50\) 7.48962 1.05919
\(51\) 3.52996 0.494293
\(52\) 25.8380 3.58309
\(53\) 2.19540 0.301561 0.150781 0.988567i \(-0.451821\pi\)
0.150781 + 0.988567i \(0.451821\pi\)
\(54\) −2.69445 −0.366668
\(55\) 5.12050 0.690448
\(56\) −13.2369 −1.76885
\(57\) 2.70051 0.357691
\(58\) −3.62990 −0.476629
\(59\) 7.53224 0.980614 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(60\) −7.83793 −1.01187
\(61\) 0.353338 0.0452403 0.0226202 0.999744i \(-0.492799\pi\)
0.0226202 + 0.999744i \(0.492799\pi\)
\(62\) −13.1324 −1.66781
\(63\) 1.50692 0.189855
\(64\) 21.8231 2.72789
\(65\) −7.31948 −0.907870
\(66\) 9.25915 1.13972
\(67\) −0.363045 −0.0443530 −0.0221765 0.999754i \(-0.507060\pi\)
−0.0221765 + 0.999754i \(0.507060\pi\)
\(68\) 18.5678 2.25167
\(69\) 2.27825 0.274270
\(70\) 6.05023 0.723141
\(71\) 5.88873 0.698864 0.349432 0.936962i \(-0.386375\pi\)
0.349432 + 0.936962i \(0.386375\pi\)
\(72\) −8.78405 −1.03521
\(73\) −1.33635 −0.156408 −0.0782039 0.996937i \(-0.524919\pi\)
−0.0782039 + 0.996937i \(0.524919\pi\)
\(74\) −7.97616 −0.927209
\(75\) −2.77965 −0.320966
\(76\) 14.2048 1.62941
\(77\) −5.17836 −0.590129
\(78\) −13.2355 −1.49862
\(79\) 4.59245 0.516691 0.258346 0.966053i \(-0.416823\pi\)
0.258346 + 0.966053i \(0.416823\pi\)
\(80\) −19.5917 −2.19042
\(81\) 1.00000 0.111111
\(82\) −18.1877 −2.00850
\(83\) −9.77403 −1.07284 −0.536420 0.843951i \(-0.680224\pi\)
−0.536420 + 0.843951i \(0.680224\pi\)
\(84\) 7.92650 0.864852
\(85\) −5.25994 −0.570521
\(86\) −12.6246 −1.36135
\(87\) 1.34718 0.144433
\(88\) 30.1853 3.21777
\(89\) 13.7570 1.45823 0.729117 0.684389i \(-0.239931\pi\)
0.729117 + 0.684389i \(0.239931\pi\)
\(90\) 4.01496 0.423214
\(91\) 7.40219 0.775961
\(92\) 11.9837 1.24939
\(93\) 4.87386 0.505396
\(94\) 11.9993 1.23764
\(95\) −4.02399 −0.412853
\(96\) −17.8587 −1.82269
\(97\) 7.45956 0.757403 0.378702 0.925519i \(-0.376371\pi\)
0.378702 + 0.925519i \(0.376371\pi\)
\(98\) 12.7425 1.28719
\(99\) −3.43638 −0.345369
\(100\) −14.6211 −1.46211
\(101\) −5.76271 −0.573411 −0.286705 0.958019i \(-0.592560\pi\)
−0.286705 + 0.958019i \(0.592560\pi\)
\(102\) −9.51129 −0.941759
\(103\) 5.05842 0.498421 0.249210 0.968449i \(-0.419829\pi\)
0.249210 + 0.968449i \(0.419829\pi\)
\(104\) −43.1483 −4.23104
\(105\) −2.24544 −0.219133
\(106\) −5.91539 −0.574553
\(107\) −10.9356 −1.05719 −0.528594 0.848875i \(-0.677281\pi\)
−0.528594 + 0.848875i \(0.677281\pi\)
\(108\) 5.26005 0.506149
\(109\) −18.1550 −1.73893 −0.869465 0.493994i \(-0.835536\pi\)
−0.869465 + 0.493994i \(0.835536\pi\)
\(110\) −13.7969 −1.31548
\(111\) 2.96022 0.280971
\(112\) 19.8131 1.87216
\(113\) −5.40530 −0.508488 −0.254244 0.967140i \(-0.581827\pi\)
−0.254244 + 0.967140i \(0.581827\pi\)
\(114\) −7.27639 −0.681496
\(115\) −3.39479 −0.316566
\(116\) 7.08623 0.657940
\(117\) 4.91212 0.454126
\(118\) −20.2952 −1.86833
\(119\) 5.31938 0.487627
\(120\) 13.0890 1.19485
\(121\) 0.808705 0.0735186
\(122\) −0.952052 −0.0861947
\(123\) 6.75006 0.608633
\(124\) 25.6368 2.30225
\(125\) 11.5923 1.03685
\(126\) −4.06033 −0.361723
\(127\) −19.9078 −1.76653 −0.883264 0.468875i \(-0.844659\pi\)
−0.883264 + 0.468875i \(0.844659\pi\)
\(128\) −23.0840 −2.04036
\(129\) 4.68543 0.412529
\(130\) 19.7220 1.72973
\(131\) −10.3354 −0.903010 −0.451505 0.892269i \(-0.649113\pi\)
−0.451505 + 0.892269i \(0.649113\pi\)
\(132\) −18.0755 −1.57327
\(133\) 4.06946 0.352867
\(134\) 0.978205 0.0845041
\(135\) −1.49008 −0.128246
\(136\) −31.0073 −2.65886
\(137\) 2.84782 0.243306 0.121653 0.992573i \(-0.461180\pi\)
0.121653 + 0.992573i \(0.461180\pi\)
\(138\) −6.13864 −0.522556
\(139\) −0.00779046 −0.000660778 0 −0.000330389 1.00000i \(-0.500105\pi\)
−0.000330389 1.00000i \(0.500105\pi\)
\(140\) −11.8112 −0.998225
\(141\) −4.45336 −0.375040
\(142\) −15.8669 −1.33152
\(143\) −16.8799 −1.41157
\(144\) 13.1481 1.09567
\(145\) −2.00741 −0.166706
\(146\) 3.60073 0.297998
\(147\) −4.72918 −0.390056
\(148\) 15.5709 1.27992
\(149\) 2.14426 0.175664 0.0878322 0.996135i \(-0.472006\pi\)
0.0878322 + 0.996135i \(0.472006\pi\)
\(150\) 7.48962 0.611525
\(151\) 21.4670 1.74696 0.873479 0.486862i \(-0.161859\pi\)
0.873479 + 0.486862i \(0.161859\pi\)
\(152\) −23.7214 −1.92406
\(153\) 3.52996 0.285380
\(154\) 13.9528 1.12435
\(155\) −7.26247 −0.583336
\(156\) 25.8380 2.06870
\(157\) −11.2946 −0.901406 −0.450703 0.892674i \(-0.648827\pi\)
−0.450703 + 0.892674i \(0.648827\pi\)
\(158\) −12.3741 −0.984433
\(159\) 2.19540 0.174106
\(160\) 26.6109 2.10378
\(161\) 3.43316 0.270571
\(162\) −2.69445 −0.211696
\(163\) −11.4107 −0.893754 −0.446877 0.894595i \(-0.647464\pi\)
−0.446877 + 0.894595i \(0.647464\pi\)
\(164\) 35.5057 2.77253
\(165\) 5.12050 0.398630
\(166\) 26.3356 2.04404
\(167\) 7.20853 0.557813 0.278906 0.960318i \(-0.410028\pi\)
0.278906 + 0.960318i \(0.410028\pi\)
\(168\) −13.2369 −1.02125
\(169\) 11.1289 0.856072
\(170\) 14.1726 1.08699
\(171\) 2.70051 0.206513
\(172\) 24.6456 1.87921
\(173\) 15.6954 1.19330 0.596649 0.802502i \(-0.296499\pi\)
0.596649 + 0.802502i \(0.296499\pi\)
\(174\) −3.62990 −0.275182
\(175\) −4.18872 −0.316637
\(176\) −45.1817 −3.40570
\(177\) 7.53224 0.566158
\(178\) −37.0674 −2.77832
\(179\) 15.8648 1.18579 0.592894 0.805280i \(-0.297985\pi\)
0.592894 + 0.805280i \(0.297985\pi\)
\(180\) −7.83793 −0.584205
\(181\) −7.80624 −0.580233 −0.290117 0.956991i \(-0.593694\pi\)
−0.290117 + 0.956991i \(0.593694\pi\)
\(182\) −19.9448 −1.47841
\(183\) 0.353338 0.0261195
\(184\) −20.0123 −1.47533
\(185\) −4.41098 −0.324301
\(186\) −13.1324 −0.962912
\(187\) −12.1303 −0.887054
\(188\) −23.4249 −1.70844
\(189\) 1.50692 0.109613
\(190\) 10.8424 0.786593
\(191\) −8.75646 −0.633595 −0.316798 0.948493i \(-0.602608\pi\)
−0.316798 + 0.948493i \(0.602608\pi\)
\(192\) 21.8231 1.57495
\(193\) 20.1714 1.45197 0.725986 0.687709i \(-0.241384\pi\)
0.725986 + 0.687709i \(0.241384\pi\)
\(194\) −20.0994 −1.44305
\(195\) −7.31948 −0.524159
\(196\) −24.8757 −1.77684
\(197\) 6.71182 0.478197 0.239099 0.970995i \(-0.423148\pi\)
0.239099 + 0.970995i \(0.423148\pi\)
\(198\) 9.25915 0.658019
\(199\) −5.63035 −0.399125 −0.199563 0.979885i \(-0.563952\pi\)
−0.199563 + 0.979885i \(0.563952\pi\)
\(200\) 24.4165 1.72651
\(201\) −0.363045 −0.0256072
\(202\) 15.5273 1.09250
\(203\) 2.03009 0.142485
\(204\) 18.5678 1.30000
\(205\) −10.0582 −0.702493
\(206\) −13.6297 −0.949623
\(207\) 2.27825 0.158350
\(208\) 64.5848 4.47815
\(209\) −9.27998 −0.641910
\(210\) 6.05023 0.417506
\(211\) 2.34181 0.161217 0.0806085 0.996746i \(-0.474314\pi\)
0.0806085 + 0.996746i \(0.474314\pi\)
\(212\) 11.5479 0.793114
\(213\) 5.88873 0.403489
\(214\) 29.4655 2.01422
\(215\) −6.98168 −0.476147
\(216\) −8.78405 −0.597679
\(217\) 7.34454 0.498580
\(218\) 48.9176 3.31312
\(219\) −1.33635 −0.0903021
\(220\) 26.9341 1.81590
\(221\) 17.3396 1.16639
\(222\) −7.97616 −0.535325
\(223\) −7.55314 −0.505796 −0.252898 0.967493i \(-0.581384\pi\)
−0.252898 + 0.967493i \(0.581384\pi\)
\(224\) −26.9116 −1.79811
\(225\) −2.77965 −0.185310
\(226\) 14.5643 0.968802
\(227\) 6.49732 0.431242 0.215621 0.976477i \(-0.430822\pi\)
0.215621 + 0.976477i \(0.430822\pi\)
\(228\) 14.2048 0.940738
\(229\) 14.4402 0.954234 0.477117 0.878840i \(-0.341682\pi\)
0.477117 + 0.878840i \(0.341682\pi\)
\(230\) 9.14710 0.603142
\(231\) −5.17836 −0.340711
\(232\) −11.8337 −0.776919
\(233\) −14.2475 −0.933385 −0.466692 0.884420i \(-0.654555\pi\)
−0.466692 + 0.884420i \(0.654555\pi\)
\(234\) −13.2355 −0.865229
\(235\) 6.63588 0.432877
\(236\) 39.6200 2.57904
\(237\) 4.59245 0.298312
\(238\) −14.3328 −0.929057
\(239\) 2.65802 0.171933 0.0859664 0.996298i \(-0.472602\pi\)
0.0859664 + 0.996298i \(0.472602\pi\)
\(240\) −19.5917 −1.26464
\(241\) −15.9169 −1.02530 −0.512649 0.858599i \(-0.671336\pi\)
−0.512649 + 0.858599i \(0.671336\pi\)
\(242\) −2.17901 −0.140072
\(243\) 1.00000 0.0641500
\(244\) 1.85858 0.118983
\(245\) 7.04688 0.450209
\(246\) −18.1877 −1.15961
\(247\) 13.2652 0.844047
\(248\) −42.8122 −2.71858
\(249\) −9.77403 −0.619404
\(250\) −31.2349 −1.97547
\(251\) 9.70611 0.612644 0.306322 0.951928i \(-0.400902\pi\)
0.306322 + 0.951928i \(0.400902\pi\)
\(252\) 7.92650 0.499322
\(253\) −7.82895 −0.492202
\(254\) 53.6405 3.36570
\(255\) −5.25994 −0.329390
\(256\) 18.5524 1.15953
\(257\) 2.17777 0.135845 0.0679227 0.997691i \(-0.478363\pi\)
0.0679227 + 0.997691i \(0.478363\pi\)
\(258\) −12.6246 −0.785976
\(259\) 4.46082 0.277182
\(260\) −38.5008 −2.38772
\(261\) 1.34718 0.0833882
\(262\) 27.8483 1.72047
\(263\) −16.2164 −0.999946 −0.499973 0.866041i \(-0.666657\pi\)
−0.499973 + 0.866041i \(0.666657\pi\)
\(264\) 30.1853 1.85778
\(265\) −3.27133 −0.200956
\(266\) −10.9650 −0.672305
\(267\) 13.7570 0.841912
\(268\) −1.90963 −0.116649
\(269\) −4.57106 −0.278702 −0.139351 0.990243i \(-0.544502\pi\)
−0.139351 + 0.990243i \(0.544502\pi\)
\(270\) 4.01496 0.244343
\(271\) 3.55016 0.215657 0.107828 0.994170i \(-0.465610\pi\)
0.107828 + 0.994170i \(0.465610\pi\)
\(272\) 46.4121 2.81415
\(273\) 7.40219 0.448001
\(274\) −7.67331 −0.463562
\(275\) 9.55192 0.576003
\(276\) 11.9837 0.721336
\(277\) 10.8796 0.653691 0.326845 0.945078i \(-0.394014\pi\)
0.326845 + 0.945078i \(0.394014\pi\)
\(278\) 0.0209910 0.00125896
\(279\) 4.87386 0.291791
\(280\) 19.7241 1.17874
\(281\) 8.91511 0.531831 0.265916 0.963996i \(-0.414326\pi\)
0.265916 + 0.963996i \(0.414326\pi\)
\(282\) 11.9993 0.714551
\(283\) 18.5547 1.10296 0.551481 0.834188i \(-0.314063\pi\)
0.551481 + 0.834188i \(0.314063\pi\)
\(284\) 30.9751 1.83803
\(285\) −4.02399 −0.238361
\(286\) 45.4821 2.68941
\(287\) 10.1718 0.600424
\(288\) −17.8587 −1.05233
\(289\) −4.53938 −0.267023
\(290\) 5.40886 0.317619
\(291\) 7.45956 0.437287
\(292\) −7.02927 −0.411357
\(293\) 19.2111 1.12232 0.561162 0.827706i \(-0.310354\pi\)
0.561162 + 0.827706i \(0.310354\pi\)
\(294\) 12.7425 0.743160
\(295\) −11.2237 −0.653468
\(296\) −26.0027 −1.51138
\(297\) −3.43638 −0.199399
\(298\) −5.77759 −0.334687
\(299\) 11.1911 0.647196
\(300\) −14.6211 −0.844149
\(301\) 7.06058 0.406965
\(302\) −57.8417 −3.32841
\(303\) −5.76271 −0.331059
\(304\) 35.5065 2.03643
\(305\) −0.526504 −0.0301475
\(306\) −9.51129 −0.543725
\(307\) 14.4492 0.824661 0.412330 0.911034i \(-0.364715\pi\)
0.412330 + 0.911034i \(0.364715\pi\)
\(308\) −27.2385 −1.55206
\(309\) 5.05842 0.287763
\(310\) 19.5684 1.11141
\(311\) 3.45502 0.195916 0.0979582 0.995191i \(-0.468769\pi\)
0.0979582 + 0.995191i \(0.468769\pi\)
\(312\) −43.1483 −2.44279
\(313\) −2.89756 −0.163780 −0.0818899 0.996641i \(-0.526096\pi\)
−0.0818899 + 0.996641i \(0.526096\pi\)
\(314\) 30.4327 1.71742
\(315\) −2.24544 −0.126516
\(316\) 24.1565 1.35891
\(317\) 23.6477 1.32819 0.664095 0.747649i \(-0.268817\pi\)
0.664095 + 0.747649i \(0.268817\pi\)
\(318\) −5.91539 −0.331718
\(319\) −4.62941 −0.259197
\(320\) −32.5183 −1.81783
\(321\) −10.9356 −0.610368
\(322\) −9.25046 −0.515508
\(323\) 9.53269 0.530413
\(324\) 5.26005 0.292225
\(325\) −13.6540 −0.757386
\(326\) 30.7455 1.70284
\(327\) −18.1550 −1.00397
\(328\) −59.2929 −3.27390
\(329\) −6.71087 −0.369982
\(330\) −13.7969 −0.759495
\(331\) 33.0088 1.81433 0.907163 0.420779i \(-0.138243\pi\)
0.907163 + 0.420779i \(0.138243\pi\)
\(332\) −51.4119 −2.82160
\(333\) 2.96022 0.162219
\(334\) −19.4230 −1.06278
\(335\) 0.540967 0.0295562
\(336\) 19.8131 1.08089
\(337\) −32.3579 −1.76265 −0.881324 0.472513i \(-0.843347\pi\)
−0.881324 + 0.472513i \(0.843347\pi\)
\(338\) −29.9864 −1.63104
\(339\) −5.40530 −0.293575
\(340\) −27.6676 −1.50048
\(341\) −16.7484 −0.906979
\(342\) −7.27639 −0.393462
\(343\) −17.6750 −0.954359
\(344\) −41.1570 −2.21904
\(345\) −3.39479 −0.182770
\(346\) −42.2904 −2.27355
\(347\) 7.60837 0.408439 0.204219 0.978925i \(-0.434534\pi\)
0.204219 + 0.978925i \(0.434534\pi\)
\(348\) 7.08623 0.379862
\(349\) −18.8286 −1.00787 −0.503935 0.863741i \(-0.668115\pi\)
−0.503935 + 0.863741i \(0.668115\pi\)
\(350\) 11.2863 0.603277
\(351\) 4.91212 0.262190
\(352\) 61.3692 3.27099
\(353\) −18.9760 −1.00999 −0.504995 0.863123i \(-0.668505\pi\)
−0.504995 + 0.863123i \(0.668505\pi\)
\(354\) −20.2952 −1.07868
\(355\) −8.77471 −0.465713
\(356\) 72.3623 3.83520
\(357\) 5.31938 0.281531
\(358\) −42.7468 −2.25924
\(359\) −11.0853 −0.585057 −0.292529 0.956257i \(-0.594497\pi\)
−0.292529 + 0.956257i \(0.594497\pi\)
\(360\) 13.0890 0.689850
\(361\) −11.7072 −0.616171
\(362\) 21.0335 1.10550
\(363\) 0.808705 0.0424460
\(364\) 38.9359 2.04080
\(365\) 1.99127 0.104228
\(366\) −0.952052 −0.0497645
\(367\) 19.6682 1.02667 0.513335 0.858188i \(-0.328410\pi\)
0.513335 + 0.858188i \(0.328410\pi\)
\(368\) 29.9546 1.56149
\(369\) 6.75006 0.351394
\(370\) 11.8851 0.617879
\(371\) 3.30830 0.171758
\(372\) 25.6368 1.32921
\(373\) 10.2362 0.530008 0.265004 0.964247i \(-0.414627\pi\)
0.265004 + 0.964247i \(0.414627\pi\)
\(374\) 32.6844 1.69007
\(375\) 11.5923 0.598626
\(376\) 39.1185 2.01738
\(377\) 6.61750 0.340819
\(378\) −4.06033 −0.208841
\(379\) 14.0293 0.720636 0.360318 0.932830i \(-0.382668\pi\)
0.360318 + 0.932830i \(0.382668\pi\)
\(380\) −21.1664 −1.08581
\(381\) −19.9078 −1.01991
\(382\) 23.5938 1.20717
\(383\) 19.2195 0.982069 0.491034 0.871140i \(-0.336619\pi\)
0.491034 + 0.871140i \(0.336619\pi\)
\(384\) −23.0840 −1.17800
\(385\) 7.71620 0.393254
\(386\) −54.3509 −2.76639
\(387\) 4.68543 0.238174
\(388\) 39.2377 1.99199
\(389\) −3.06767 −0.155537 −0.0777684 0.996971i \(-0.524779\pi\)
−0.0777684 + 0.996971i \(0.524779\pi\)
\(390\) 19.7220 0.998660
\(391\) 8.04215 0.406709
\(392\) 41.5414 2.09816
\(393\) −10.3354 −0.521353
\(394\) −18.0846 −0.911091
\(395\) −6.84314 −0.344316
\(396\) −18.0755 −0.908330
\(397\) 5.95531 0.298888 0.149444 0.988770i \(-0.452252\pi\)
0.149444 + 0.988770i \(0.452252\pi\)
\(398\) 15.1707 0.760438
\(399\) 4.06946 0.203728
\(400\) −36.5469 −1.82735
\(401\) −11.5855 −0.578551 −0.289276 0.957246i \(-0.593414\pi\)
−0.289276 + 0.957246i \(0.593414\pi\)
\(402\) 0.978205 0.0487884
\(403\) 23.9410 1.19259
\(404\) −30.3121 −1.50809
\(405\) −1.49008 −0.0740429
\(406\) −5.46998 −0.271471
\(407\) −10.1724 −0.504229
\(408\) −31.0073 −1.53509
\(409\) −13.4808 −0.666583 −0.333291 0.942824i \(-0.608159\pi\)
−0.333291 + 0.942824i \(0.608159\pi\)
\(410\) 27.1012 1.33843
\(411\) 2.84782 0.140473
\(412\) 26.6076 1.31086
\(413\) 11.3505 0.558522
\(414\) −6.13864 −0.301698
\(415\) 14.5641 0.714926
\(416\) −87.7239 −4.30102
\(417\) −0.00779046 −0.000381500 0
\(418\) 25.0044 1.22301
\(419\) 18.1085 0.884657 0.442328 0.896853i \(-0.354153\pi\)
0.442328 + 0.896853i \(0.354153\pi\)
\(420\) −11.8112 −0.576325
\(421\) 12.1754 0.593394 0.296697 0.954972i \(-0.404115\pi\)
0.296697 + 0.954972i \(0.404115\pi\)
\(422\) −6.30989 −0.307161
\(423\) −4.45336 −0.216530
\(424\) −19.2845 −0.936537
\(425\) −9.81204 −0.475954
\(426\) −15.8669 −0.768753
\(427\) 0.532454 0.0257672
\(428\) −57.5221 −2.78043
\(429\) −16.8799 −0.814970
\(430\) 18.8118 0.907185
\(431\) 4.03955 0.194578 0.0972892 0.995256i \(-0.468983\pi\)
0.0972892 + 0.995256i \(0.468983\pi\)
\(432\) 13.1481 0.632586
\(433\) −14.4964 −0.696655 −0.348327 0.937373i \(-0.613250\pi\)
−0.348327 + 0.937373i \(0.613250\pi\)
\(434\) −19.7895 −0.949925
\(435\) −2.00741 −0.0962479
\(436\) −95.4961 −4.57343
\(437\) 6.15245 0.294312
\(438\) 3.60073 0.172049
\(439\) −2.53159 −0.120826 −0.0604131 0.998173i \(-0.519242\pi\)
−0.0604131 + 0.998173i \(0.519242\pi\)
\(440\) −44.9787 −2.14427
\(441\) −4.72918 −0.225199
\(442\) −46.7206 −2.22227
\(443\) −7.85596 −0.373248 −0.186624 0.982431i \(-0.559755\pi\)
−0.186624 + 0.982431i \(0.559755\pi\)
\(444\) 15.5709 0.738962
\(445\) −20.4990 −0.971747
\(446\) 20.3516 0.963674
\(447\) 2.14426 0.101420
\(448\) 32.8858 1.55371
\(449\) −15.1317 −0.714110 −0.357055 0.934083i \(-0.616219\pi\)
−0.357055 + 0.934083i \(0.616219\pi\)
\(450\) 7.48962 0.353064
\(451\) −23.1958 −1.09225
\(452\) −28.4322 −1.33734
\(453\) 21.4670 1.00861
\(454\) −17.5067 −0.821630
\(455\) −11.0299 −0.517089
\(456\) −23.7214 −1.11086
\(457\) 7.32482 0.342641 0.171320 0.985215i \(-0.445197\pi\)
0.171320 + 0.985215i \(0.445197\pi\)
\(458\) −38.9083 −1.81807
\(459\) 3.52996 0.164764
\(460\) −17.8568 −0.832577
\(461\) 2.41454 0.112456 0.0562281 0.998418i \(-0.482093\pi\)
0.0562281 + 0.998418i \(0.482093\pi\)
\(462\) 13.9528 0.649144
\(463\) 39.2195 1.82268 0.911342 0.411651i \(-0.135048\pi\)
0.911342 + 0.411651i \(0.135048\pi\)
\(464\) 17.7128 0.822295
\(465\) −7.26247 −0.336789
\(466\) 38.3892 1.77834
\(467\) 35.1839 1.62811 0.814057 0.580784i \(-0.197254\pi\)
0.814057 + 0.580784i \(0.197254\pi\)
\(468\) 25.8380 1.19436
\(469\) −0.547081 −0.0252618
\(470\) −17.8800 −0.824745
\(471\) −11.2946 −0.520427
\(472\) −66.1636 −3.04542
\(473\) −16.1009 −0.740320
\(474\) −12.3741 −0.568363
\(475\) −7.50646 −0.344420
\(476\) 27.9802 1.28247
\(477\) 2.19540 0.100520
\(478\) −7.16189 −0.327577
\(479\) −12.7392 −0.582068 −0.291034 0.956713i \(-0.593999\pi\)
−0.291034 + 0.956713i \(0.593999\pi\)
\(480\) 26.6109 1.21462
\(481\) 14.5410 0.663010
\(482\) 42.8872 1.95346
\(483\) 3.43316 0.156214
\(484\) 4.25383 0.193356
\(485\) −11.1154 −0.504723
\(486\) −2.69445 −0.122223
\(487\) −16.8985 −0.765745 −0.382873 0.923801i \(-0.625065\pi\)
−0.382873 + 0.923801i \(0.625065\pi\)
\(488\) −3.10374 −0.140500
\(489\) −11.4107 −0.516009
\(490\) −18.9875 −0.857766
\(491\) −34.1655 −1.54187 −0.770934 0.636915i \(-0.780210\pi\)
−0.770934 + 0.636915i \(0.780210\pi\)
\(492\) 35.5057 1.60072
\(493\) 4.75548 0.214176
\(494\) −35.7425 −1.60813
\(495\) 5.12050 0.230149
\(496\) 64.0818 2.87736
\(497\) 8.87387 0.398048
\(498\) 26.3356 1.18013
\(499\) −42.1032 −1.88480 −0.942399 0.334491i \(-0.891436\pi\)
−0.942399 + 0.334491i \(0.891436\pi\)
\(500\) 60.9763 2.72694
\(501\) 7.20853 0.322053
\(502\) −26.1526 −1.16725
\(503\) 5.81822 0.259422 0.129711 0.991552i \(-0.458595\pi\)
0.129711 + 0.991552i \(0.458595\pi\)
\(504\) −13.2369 −0.589618
\(505\) 8.58692 0.382113
\(506\) 21.0947 0.937774
\(507\) 11.1289 0.494254
\(508\) −104.716 −4.64602
\(509\) 15.7494 0.698081 0.349041 0.937108i \(-0.386508\pi\)
0.349041 + 0.937108i \(0.386508\pi\)
\(510\) 14.1726 0.627575
\(511\) −2.01378 −0.0890842
\(512\) −3.82046 −0.168842
\(513\) 2.70051 0.119230
\(514\) −5.86788 −0.258821
\(515\) −7.53747 −0.332141
\(516\) 24.6456 1.08496
\(517\) 15.3034 0.673044
\(518\) −12.0195 −0.528105
\(519\) 15.6954 0.688951
\(520\) 64.2946 2.81951
\(521\) −16.9094 −0.740816 −0.370408 0.928869i \(-0.620782\pi\)
−0.370408 + 0.928869i \(0.620782\pi\)
\(522\) −3.62990 −0.158876
\(523\) 37.4422 1.63723 0.818616 0.574342i \(-0.194742\pi\)
0.818616 + 0.574342i \(0.194742\pi\)
\(524\) −54.3649 −2.37494
\(525\) −4.18872 −0.182811
\(526\) 43.6942 1.90516
\(527\) 17.2045 0.749441
\(528\) −45.1817 −1.96628
\(529\) −17.8096 −0.774329
\(530\) 8.81443 0.382874
\(531\) 7.53224 0.326871
\(532\) 21.4056 0.928050
\(533\) 33.1571 1.43619
\(534\) −37.0674 −1.60406
\(535\) 16.2950 0.704496
\(536\) 3.18900 0.137744
\(537\) 15.8648 0.684615
\(538\) 12.3165 0.531001
\(539\) 16.2513 0.699991
\(540\) −7.83793 −0.337291
\(541\) −7.67011 −0.329764 −0.164882 0.986313i \(-0.552724\pi\)
−0.164882 + 0.986313i \(0.552724\pi\)
\(542\) −9.56573 −0.410883
\(543\) −7.80624 −0.334998
\(544\) −63.0404 −2.70283
\(545\) 27.0524 1.15880
\(546\) −19.9448 −0.853560
\(547\) −3.54863 −0.151729 −0.0758643 0.997118i \(-0.524172\pi\)
−0.0758643 + 0.997118i \(0.524172\pi\)
\(548\) 14.9797 0.639901
\(549\) 0.353338 0.0150801
\(550\) −25.7372 −1.09744
\(551\) 3.63807 0.154987
\(552\) −20.0123 −0.851780
\(553\) 6.92047 0.294289
\(554\) −29.3145 −1.24545
\(555\) −4.41098 −0.187236
\(556\) −0.0409782 −0.00173786
\(557\) 20.0678 0.850302 0.425151 0.905123i \(-0.360221\pi\)
0.425151 + 0.905123i \(0.360221\pi\)
\(558\) −13.1324 −0.555938
\(559\) 23.0154 0.973447
\(560\) −29.5232 −1.24758
\(561\) −12.1303 −0.512141
\(562\) −24.0213 −1.01328
\(563\) −23.7846 −1.00240 −0.501201 0.865331i \(-0.667108\pi\)
−0.501201 + 0.865331i \(0.667108\pi\)
\(564\) −23.4249 −0.986366
\(565\) 8.05435 0.338849
\(566\) −49.9946 −2.10143
\(567\) 1.50692 0.0632848
\(568\) −51.7269 −2.17041
\(569\) 3.95952 0.165992 0.0829959 0.996550i \(-0.473551\pi\)
0.0829959 + 0.996550i \(0.473551\pi\)
\(570\) 10.8424 0.454140
\(571\) −14.0648 −0.588592 −0.294296 0.955714i \(-0.595085\pi\)
−0.294296 + 0.955714i \(0.595085\pi\)
\(572\) −88.7893 −3.71247
\(573\) −8.75646 −0.365806
\(574\) −27.4075 −1.14397
\(575\) −6.33274 −0.264094
\(576\) 21.8231 0.909298
\(577\) 14.6107 0.608252 0.304126 0.952632i \(-0.401636\pi\)
0.304126 + 0.952632i \(0.401636\pi\)
\(578\) 12.2311 0.508748
\(579\) 20.1714 0.838296
\(580\) −10.5591 −0.438442
\(581\) −14.7287 −0.611050
\(582\) −20.0994 −0.833147
\(583\) −7.54422 −0.312450
\(584\) 11.7386 0.485745
\(585\) −7.31948 −0.302623
\(586\) −51.7633 −2.13832
\(587\) −14.7550 −0.609003 −0.304502 0.952512i \(-0.598490\pi\)
−0.304502 + 0.952512i \(0.598490\pi\)
\(588\) −24.8757 −1.02586
\(589\) 13.1619 0.542327
\(590\) 30.2416 1.24503
\(591\) 6.71182 0.276087
\(592\) 38.9211 1.59965
\(593\) −19.4336 −0.798040 −0.399020 0.916942i \(-0.630650\pi\)
−0.399020 + 0.916942i \(0.630650\pi\)
\(594\) 9.25915 0.379907
\(595\) −7.92633 −0.324948
\(596\) 11.2789 0.462002
\(597\) −5.63035 −0.230435
\(598\) −30.1537 −1.23308
\(599\) 24.8726 1.01627 0.508134 0.861278i \(-0.330336\pi\)
0.508134 + 0.861278i \(0.330336\pi\)
\(600\) 24.4165 0.996801
\(601\) −18.7850 −0.766255 −0.383128 0.923695i \(-0.625153\pi\)
−0.383128 + 0.923695i \(0.625153\pi\)
\(602\) −19.0244 −0.775375
\(603\) −0.363045 −0.0147843
\(604\) 112.917 4.59454
\(605\) −1.20504 −0.0489918
\(606\) 15.5273 0.630754
\(607\) 27.5344 1.11759 0.558793 0.829307i \(-0.311264\pi\)
0.558793 + 0.829307i \(0.311264\pi\)
\(608\) −48.2275 −1.95588
\(609\) 2.03009 0.0822636
\(610\) 1.41864 0.0574390
\(611\) −21.8754 −0.884986
\(612\) 18.5678 0.750558
\(613\) 12.5034 0.505008 0.252504 0.967596i \(-0.418746\pi\)
0.252504 + 0.967596i \(0.418746\pi\)
\(614\) −38.9327 −1.57120
\(615\) −10.0582 −0.405584
\(616\) 45.4870 1.83272
\(617\) 17.6714 0.711425 0.355713 0.934595i \(-0.384238\pi\)
0.355713 + 0.934595i \(0.384238\pi\)
\(618\) −13.6297 −0.548265
\(619\) −1.23977 −0.0498304 −0.0249152 0.999690i \(-0.507932\pi\)
−0.0249152 + 0.999690i \(0.507932\pi\)
\(620\) −38.2010 −1.53419
\(621\) 2.27825 0.0914232
\(622\) −9.30938 −0.373272
\(623\) 20.7307 0.830557
\(624\) 64.5848 2.58546
\(625\) −3.37533 −0.135013
\(626\) 7.80733 0.312044
\(627\) −9.27998 −0.370607
\(628\) −59.4101 −2.37072
\(629\) 10.4495 0.416647
\(630\) 6.05023 0.241047
\(631\) −22.0578 −0.878106 −0.439053 0.898461i \(-0.644686\pi\)
−0.439053 + 0.898461i \(0.644686\pi\)
\(632\) −40.3403 −1.60465
\(633\) 2.34181 0.0930787
\(634\) −63.7176 −2.53055
\(635\) 29.6643 1.17719
\(636\) 11.5479 0.457904
\(637\) −23.2303 −0.920419
\(638\) 12.4737 0.493839
\(639\) 5.88873 0.232955
\(640\) 34.3971 1.35967
\(641\) −14.8551 −0.586741 −0.293371 0.955999i \(-0.594777\pi\)
−0.293371 + 0.955999i \(0.594777\pi\)
\(642\) 29.4655 1.16291
\(643\) 2.61576 0.103156 0.0515778 0.998669i \(-0.483575\pi\)
0.0515778 + 0.998669i \(0.483575\pi\)
\(644\) 18.0586 0.711608
\(645\) −6.98168 −0.274904
\(646\) −25.6853 −1.01058
\(647\) 4.59772 0.180755 0.0903775 0.995908i \(-0.471193\pi\)
0.0903775 + 0.995908i \(0.471193\pi\)
\(648\) −8.78405 −0.345070
\(649\) −25.8836 −1.01602
\(650\) 36.7899 1.44302
\(651\) 7.34454 0.287855
\(652\) −60.0208 −2.35060
\(653\) −37.5115 −1.46794 −0.733970 0.679182i \(-0.762335\pi\)
−0.733970 + 0.679182i \(0.762335\pi\)
\(654\) 48.9176 1.91283
\(655\) 15.4007 0.601753
\(656\) 88.7502 3.46511
\(657\) −1.33635 −0.0521360
\(658\) 18.0821 0.704914
\(659\) −8.76825 −0.341563 −0.170781 0.985309i \(-0.554629\pi\)
−0.170781 + 0.985309i \(0.554629\pi\)
\(660\) 26.9341 1.04841
\(661\) 27.7453 1.07917 0.539584 0.841932i \(-0.318582\pi\)
0.539584 + 0.841932i \(0.318582\pi\)
\(662\) −88.9405 −3.45677
\(663\) 17.3396 0.673414
\(664\) 85.8556 3.33184
\(665\) −6.06384 −0.235146
\(666\) −7.97616 −0.309070
\(667\) 3.06921 0.118840
\(668\) 37.9173 1.46706
\(669\) −7.55314 −0.292021
\(670\) −1.45761 −0.0563123
\(671\) −1.21420 −0.0468738
\(672\) −26.9116 −1.03814
\(673\) 27.7714 1.07051 0.535255 0.844690i \(-0.320215\pi\)
0.535255 + 0.844690i \(0.320215\pi\)
\(674\) 87.1867 3.35831
\(675\) −2.77965 −0.106989
\(676\) 58.5388 2.25149
\(677\) −14.4120 −0.553899 −0.276949 0.960885i \(-0.589323\pi\)
−0.276949 + 0.960885i \(0.589323\pi\)
\(678\) 14.5643 0.559338
\(679\) 11.2410 0.431389
\(680\) 46.2036 1.77183
\(681\) 6.49732 0.248978
\(682\) 45.1278 1.72803
\(683\) −45.4710 −1.73990 −0.869949 0.493141i \(-0.835849\pi\)
−0.869949 + 0.493141i \(0.835849\pi\)
\(684\) 14.2048 0.543135
\(685\) −4.24350 −0.162136
\(686\) 47.6243 1.81831
\(687\) 14.4402 0.550928
\(688\) 61.6042 2.34864
\(689\) 10.7841 0.410840
\(690\) 9.14710 0.348224
\(691\) −3.14223 −0.119536 −0.0597681 0.998212i \(-0.519036\pi\)
−0.0597681 + 0.998212i \(0.519036\pi\)
\(692\) 82.5585 3.13841
\(693\) −5.17836 −0.196710
\(694\) −20.5004 −0.778183
\(695\) 0.0116084 0.000440333 0
\(696\) −11.8337 −0.448554
\(697\) 23.8275 0.902529
\(698\) 50.7326 1.92026
\(699\) −14.2475 −0.538890
\(700\) −22.0329 −0.832764
\(701\) 30.3793 1.14741 0.573706 0.819062i \(-0.305505\pi\)
0.573706 + 0.819062i \(0.305505\pi\)
\(702\) −13.2355 −0.499540
\(703\) 7.99410 0.301503
\(704\) −74.9926 −2.82639
\(705\) 6.63588 0.249922
\(706\) 51.1298 1.92429
\(707\) −8.68396 −0.326594
\(708\) 39.6200 1.48901
\(709\) −13.8027 −0.518372 −0.259186 0.965827i \(-0.583454\pi\)
−0.259186 + 0.965827i \(0.583454\pi\)
\(710\) 23.6430 0.887307
\(711\) 4.59245 0.172230
\(712\) −120.842 −4.52874
\(713\) 11.1039 0.415844
\(714\) −14.3328 −0.536391
\(715\) 25.1525 0.940650
\(716\) 83.4495 3.11865
\(717\) 2.65802 0.0992655
\(718\) 29.8687 1.11469
\(719\) −21.9795 −0.819696 −0.409848 0.912154i \(-0.634418\pi\)
−0.409848 + 0.912154i \(0.634418\pi\)
\(720\) −19.5917 −0.730140
\(721\) 7.62265 0.283882
\(722\) 31.5446 1.17397
\(723\) −15.9169 −0.591956
\(724\) −41.0612 −1.52603
\(725\) −3.74468 −0.139074
\(726\) −2.17901 −0.0808708
\(727\) 23.8810 0.885698 0.442849 0.896596i \(-0.353968\pi\)
0.442849 + 0.896596i \(0.353968\pi\)
\(728\) −65.0212 −2.40985
\(729\) 1.00000 0.0370370
\(730\) −5.36539 −0.198582
\(731\) 16.5394 0.611731
\(732\) 1.85858 0.0686950
\(733\) −22.5416 −0.832594 −0.416297 0.909229i \(-0.636672\pi\)
−0.416297 + 0.909229i \(0.636672\pi\)
\(734\) −52.9949 −1.95608
\(735\) 7.04688 0.259928
\(736\) −40.6866 −1.49973
\(737\) 1.24756 0.0459544
\(738\) −18.1877 −0.669498
\(739\) −22.6645 −0.833726 −0.416863 0.908969i \(-0.636870\pi\)
−0.416863 + 0.908969i \(0.636870\pi\)
\(740\) −23.2020 −0.852921
\(741\) 13.2652 0.487311
\(742\) −8.91403 −0.327244
\(743\) 44.2832 1.62459 0.812296 0.583245i \(-0.198217\pi\)
0.812296 + 0.583245i \(0.198217\pi\)
\(744\) −42.8122 −1.56957
\(745\) −3.19513 −0.117060
\(746\) −27.5808 −1.00981
\(747\) −9.77403 −0.357613
\(748\) −63.8059 −2.33298
\(749\) −16.4792 −0.602136
\(750\) −31.2349 −1.14054
\(751\) 33.7227 1.23056 0.615279 0.788310i \(-0.289044\pi\)
0.615279 + 0.788310i \(0.289044\pi\)
\(752\) −58.5530 −2.13521
\(753\) 9.70611 0.353710
\(754\) −17.8305 −0.649349
\(755\) −31.9876 −1.16415
\(756\) 7.92650 0.288284
\(757\) −19.4413 −0.706606 −0.353303 0.935509i \(-0.614942\pi\)
−0.353303 + 0.935509i \(0.614942\pi\)
\(758\) −37.8012 −1.37300
\(759\) −7.82895 −0.284173
\(760\) 35.3469 1.28217
\(761\) 2.61052 0.0946312 0.0473156 0.998880i \(-0.484933\pi\)
0.0473156 + 0.998880i \(0.484933\pi\)
\(762\) 53.6405 1.94319
\(763\) −27.3581 −0.990431
\(764\) −46.0595 −1.66637
\(765\) −5.25994 −0.190174
\(766\) −51.7859 −1.87110
\(767\) 36.9993 1.33597
\(768\) 18.5524 0.669452
\(769\) 38.0088 1.37063 0.685317 0.728245i \(-0.259664\pi\)
0.685317 + 0.728245i \(0.259664\pi\)
\(770\) −20.7909 −0.749252
\(771\) 2.17777 0.0784304
\(772\) 106.103 3.81873
\(773\) 11.5236 0.414476 0.207238 0.978291i \(-0.433552\pi\)
0.207238 + 0.978291i \(0.433552\pi\)
\(774\) −12.6246 −0.453783
\(775\) −13.5476 −0.486645
\(776\) −65.5251 −2.35221
\(777\) 4.46082 0.160031
\(778\) 8.26567 0.296339
\(779\) 18.2286 0.653108
\(780\) −38.5008 −1.37855
\(781\) −20.2359 −0.724098
\(782\) −21.6692 −0.774887
\(783\) 1.34718 0.0481442
\(784\) −62.1795 −2.22070
\(785\) 16.8299 0.600685
\(786\) 27.8483 0.993314
\(787\) 15.2081 0.542110 0.271055 0.962564i \(-0.412628\pi\)
0.271055 + 0.962564i \(0.412628\pi\)
\(788\) 35.3045 1.25767
\(789\) −16.2164 −0.577319
\(790\) 18.4385 0.656012
\(791\) −8.14537 −0.289616
\(792\) 30.1853 1.07259
\(793\) 1.73564 0.0616344
\(794\) −16.0463 −0.569461
\(795\) −3.27133 −0.116022
\(796\) −29.6160 −1.04971
\(797\) −10.1453 −0.359364 −0.179682 0.983725i \(-0.557507\pi\)
−0.179682 + 0.983725i \(0.557507\pi\)
\(798\) −10.9650 −0.388155
\(799\) −15.7202 −0.556140
\(800\) 49.6408 1.75507
\(801\) 13.7570 0.486078
\(802\) 31.2165 1.10229
\(803\) 4.59220 0.162055
\(804\) −1.90963 −0.0673476
\(805\) −5.11569 −0.180304
\(806\) −64.5078 −2.27219
\(807\) −4.57106 −0.160909
\(808\) 50.6199 1.78080
\(809\) 23.6810 0.832579 0.416289 0.909232i \(-0.363330\pi\)
0.416289 + 0.909232i \(0.363330\pi\)
\(810\) 4.01496 0.141071
\(811\) 48.2674 1.69490 0.847450 0.530876i \(-0.178137\pi\)
0.847450 + 0.530876i \(0.178137\pi\)
\(812\) 10.6784 0.374738
\(813\) 3.55016 0.124510
\(814\) 27.4091 0.960688
\(815\) 17.0029 0.595585
\(816\) 46.4121 1.62475
\(817\) 12.6530 0.442674
\(818\) 36.3233 1.27002
\(819\) 7.40219 0.258654
\(820\) −52.9065 −1.84758
\(821\) −25.1480 −0.877673 −0.438836 0.898567i \(-0.644609\pi\)
−0.438836 + 0.898567i \(0.644609\pi\)
\(822\) −7.67331 −0.267638
\(823\) −53.1406 −1.85236 −0.926182 0.377078i \(-0.876929\pi\)
−0.926182 + 0.377078i \(0.876929\pi\)
\(824\) −44.4334 −1.54791
\(825\) 9.55192 0.332555
\(826\) −30.5834 −1.06413
\(827\) 43.9948 1.52985 0.764925 0.644119i \(-0.222776\pi\)
0.764925 + 0.644119i \(0.222776\pi\)
\(828\) 11.9837 0.416464
\(829\) 27.2343 0.945887 0.472943 0.881093i \(-0.343191\pi\)
0.472943 + 0.881093i \(0.343191\pi\)
\(830\) −39.2423 −1.36212
\(831\) 10.8796 0.377408
\(832\) 107.198 3.71642
\(833\) −16.6938 −0.578407
\(834\) 0.0209910 0.000726859 0
\(835\) −10.7413 −0.371719
\(836\) −48.8132 −1.68824
\(837\) 4.87386 0.168465
\(838\) −48.7923 −1.68550
\(839\) 11.2646 0.388897 0.194448 0.980913i \(-0.437708\pi\)
0.194448 + 0.980913i \(0.437708\pi\)
\(840\) 19.7241 0.680546
\(841\) −27.1851 −0.937418
\(842\) −32.8060 −1.13057
\(843\) 8.91511 0.307053
\(844\) 12.3181 0.424005
\(845\) −16.5831 −0.570475
\(846\) 11.9993 0.412546
\(847\) 1.21866 0.0418735
\(848\) 28.8652 0.991235
\(849\) 18.5547 0.636795
\(850\) 26.4380 0.906817
\(851\) 6.74413 0.231186
\(852\) 30.9751 1.06119
\(853\) 45.0905 1.54387 0.771935 0.635701i \(-0.219289\pi\)
0.771935 + 0.635701i \(0.219289\pi\)
\(854\) −1.43467 −0.0490934
\(855\) −4.02399 −0.137618
\(856\) 96.0592 3.28323
\(857\) 28.9214 0.987938 0.493969 0.869480i \(-0.335546\pi\)
0.493969 + 0.869480i \(0.335546\pi\)
\(858\) 45.4821 1.55273
\(859\) 54.0903 1.84554 0.922769 0.385354i \(-0.125921\pi\)
0.922769 + 0.385354i \(0.125921\pi\)
\(860\) −36.7240 −1.25228
\(861\) 10.1718 0.346655
\(862\) −10.8844 −0.370723
\(863\) −55.3151 −1.88295 −0.941474 0.337086i \(-0.890559\pi\)
−0.941474 + 0.337086i \(0.890559\pi\)
\(864\) −17.8587 −0.607564
\(865\) −23.3875 −0.795197
\(866\) 39.0599 1.32731
\(867\) −4.53938 −0.154166
\(868\) 38.6327 1.31128
\(869\) −15.7814 −0.535348
\(870\) 5.40886 0.183378
\(871\) −1.78332 −0.0604255
\(872\) 159.474 5.40047
\(873\) 7.45956 0.252468
\(874\) −16.5775 −0.560741
\(875\) 17.4688 0.590552
\(876\) −7.02927 −0.237497
\(877\) 53.0430 1.79114 0.895568 0.444926i \(-0.146770\pi\)
0.895568 + 0.444926i \(0.146770\pi\)
\(878\) 6.82124 0.230206
\(879\) 19.2111 0.647974
\(880\) 67.3246 2.26951
\(881\) 15.4740 0.521331 0.260665 0.965429i \(-0.416058\pi\)
0.260665 + 0.965429i \(0.416058\pi\)
\(882\) 12.7425 0.429064
\(883\) −4.54640 −0.152999 −0.0764993 0.997070i \(-0.524374\pi\)
−0.0764993 + 0.997070i \(0.524374\pi\)
\(884\) 91.2072 3.06763
\(885\) −11.2237 −0.377280
\(886\) 21.1675 0.711136
\(887\) 30.0987 1.01062 0.505308 0.862939i \(-0.331379\pi\)
0.505308 + 0.862939i \(0.331379\pi\)
\(888\) −26.0027 −0.872593
\(889\) −29.9995 −1.00615
\(890\) 55.2336 1.85143
\(891\) −3.43638 −0.115123
\(892\) −39.7299 −1.33026
\(893\) −12.0263 −0.402446
\(894\) −5.77759 −0.193232
\(895\) −23.6398 −0.790193
\(896\) −34.7858 −1.16211
\(897\) 11.1911 0.373659
\(898\) 40.7716 1.36057
\(899\) 6.56596 0.218987
\(900\) −14.6211 −0.487370
\(901\) 7.74967 0.258179
\(902\) 62.4998 2.08102
\(903\) 7.06058 0.234961
\(904\) 47.4804 1.57917
\(905\) 11.6320 0.386659
\(906\) −57.8417 −1.92166
\(907\) 30.2716 1.00515 0.502577 0.864533i \(-0.332386\pi\)
0.502577 + 0.864533i \(0.332386\pi\)
\(908\) 34.1763 1.13418
\(909\) −5.76271 −0.191137
\(910\) 29.7195 0.985191
\(911\) 12.3652 0.409678 0.204839 0.978796i \(-0.434333\pi\)
0.204839 + 0.978796i \(0.434333\pi\)
\(912\) 35.5065 1.17574
\(913\) 33.5873 1.11158
\(914\) −19.7364 −0.652821
\(915\) −0.526504 −0.0174057
\(916\) 75.9562 2.50966
\(917\) −15.5747 −0.514321
\(918\) −9.51129 −0.313920
\(919\) −13.0382 −0.430090 −0.215045 0.976604i \(-0.568990\pi\)
−0.215045 + 0.976604i \(0.568990\pi\)
\(920\) 29.8200 0.983137
\(921\) 14.4492 0.476118
\(922\) −6.50584 −0.214259
\(923\) 28.9262 0.952117
\(924\) −27.2385 −0.896079
\(925\) −8.22836 −0.270547
\(926\) −105.675 −3.47269
\(927\) 5.05842 0.166140
\(928\) −24.0588 −0.789769
\(929\) 47.8506 1.56993 0.784964 0.619541i \(-0.212681\pi\)
0.784964 + 0.619541i \(0.212681\pi\)
\(930\) 19.5684 0.641671
\(931\) −12.7712 −0.418559
\(932\) −74.9426 −2.45483
\(933\) 3.45502 0.113112
\(934\) −94.8011 −3.10199
\(935\) 18.0751 0.591121
\(936\) −43.1483 −1.41035
\(937\) 12.4249 0.405905 0.202953 0.979189i \(-0.434946\pi\)
0.202953 + 0.979189i \(0.434946\pi\)
\(938\) 1.47408 0.0481304
\(939\) −2.89756 −0.0945583
\(940\) 34.9051 1.13848
\(941\) 36.6279 1.19404 0.597018 0.802228i \(-0.296352\pi\)
0.597018 + 0.802228i \(0.296352\pi\)
\(942\) 30.4327 0.991550
\(943\) 15.3784 0.500788
\(944\) 99.0343 3.22329
\(945\) −2.24544 −0.0730443
\(946\) 43.3831 1.41050
\(947\) −13.0801 −0.425047 −0.212524 0.977156i \(-0.568168\pi\)
−0.212524 + 0.977156i \(0.568168\pi\)
\(948\) 24.1565 0.784568
\(949\) −6.56431 −0.213087
\(950\) 20.2258 0.656211
\(951\) 23.6477 0.766830
\(952\) −46.7257 −1.51439
\(953\) 49.8672 1.61536 0.807678 0.589623i \(-0.200724\pi\)
0.807678 + 0.589623i \(0.200724\pi\)
\(954\) −5.91539 −0.191518
\(955\) 13.0479 0.422219
\(956\) 13.9813 0.452188
\(957\) −4.62941 −0.149648
\(958\) 34.3250 1.10899
\(959\) 4.29145 0.138578
\(960\) −32.5183 −1.04952
\(961\) −7.24546 −0.233725
\(962\) −39.1798 −1.26321
\(963\) −10.9356 −0.352396
\(964\) −83.7237 −2.69656
\(965\) −30.0572 −0.967574
\(966\) −9.25046 −0.297629
\(967\) −9.42033 −0.302937 −0.151469 0.988462i \(-0.548400\pi\)
−0.151469 + 0.988462i \(0.548400\pi\)
\(968\) −7.10370 −0.228322
\(969\) 9.53269 0.306234
\(970\) 29.9498 0.961630
\(971\) −18.1184 −0.581448 −0.290724 0.956807i \(-0.593896\pi\)
−0.290724 + 0.956807i \(0.593896\pi\)
\(972\) 5.26005 0.168716
\(973\) −0.0117396 −0.000376355 0
\(974\) 45.5322 1.45895
\(975\) −13.6540 −0.437277
\(976\) 4.64571 0.148706
\(977\) 40.4912 1.29543 0.647714 0.761884i \(-0.275725\pi\)
0.647714 + 0.761884i \(0.275725\pi\)
\(978\) 30.7455 0.983133
\(979\) −47.2741 −1.51089
\(980\) 37.0670 1.18406
\(981\) −18.1550 −0.579643
\(982\) 92.0572 2.93766
\(983\) 6.46332 0.206148 0.103074 0.994674i \(-0.467132\pi\)
0.103074 + 0.994674i \(0.467132\pi\)
\(984\) −59.2929 −1.89019
\(985\) −10.0012 −0.318664
\(986\) −12.8134 −0.408062
\(987\) −6.71087 −0.213609
\(988\) 69.7758 2.21987
\(989\) 10.6746 0.339432
\(990\) −13.7969 −0.438495
\(991\) 22.6474 0.719417 0.359708 0.933065i \(-0.382876\pi\)
0.359708 + 0.933065i \(0.382876\pi\)
\(992\) −87.0407 −2.76354
\(993\) 33.0088 1.04750
\(994\) −23.9102 −0.758385
\(995\) 8.38971 0.265972
\(996\) −51.4119 −1.62905
\(997\) 33.3858 1.05734 0.528669 0.848828i \(-0.322691\pi\)
0.528669 + 0.848828i \(0.322691\pi\)
\(998\) 113.445 3.59104
\(999\) 2.96022 0.0936572
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 \(a_p\))