Properties

Label 8015.2.a.l.1.57
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.57
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.42755 q^{2} +1.02702 q^{3} +3.89301 q^{4} -1.00000 q^{5} +2.49316 q^{6} -1.00000 q^{7} +4.59539 q^{8} -1.94522 q^{9} +O(q^{10})\) \(q+2.42755 q^{2} +1.02702 q^{3} +3.89301 q^{4} -1.00000 q^{5} +2.49316 q^{6} -1.00000 q^{7} +4.59539 q^{8} -1.94522 q^{9} -2.42755 q^{10} +0.740098 q^{11} +3.99822 q^{12} -0.862758 q^{13} -2.42755 q^{14} -1.02702 q^{15} +3.36953 q^{16} +2.25071 q^{17} -4.72213 q^{18} +4.76201 q^{19} -3.89301 q^{20} -1.02702 q^{21} +1.79663 q^{22} -0.0894125 q^{23} +4.71958 q^{24} +1.00000 q^{25} -2.09439 q^{26} -5.07886 q^{27} -3.89301 q^{28} +10.3886 q^{29} -2.49316 q^{30} +7.27024 q^{31} -1.01107 q^{32} +0.760098 q^{33} +5.46373 q^{34} +1.00000 q^{35} -7.57277 q^{36} +1.86231 q^{37} +11.5600 q^{38} -0.886074 q^{39} -4.59539 q^{40} +1.00466 q^{41} -2.49316 q^{42} +5.65130 q^{43} +2.88121 q^{44} +1.94522 q^{45} -0.217054 q^{46} +0.888047 q^{47} +3.46059 q^{48} +1.00000 q^{49} +2.42755 q^{50} +2.31154 q^{51} -3.35873 q^{52} +13.1121 q^{53} -12.3292 q^{54} -0.740098 q^{55} -4.59539 q^{56} +4.89070 q^{57} +25.2190 q^{58} +9.57154 q^{59} -3.99822 q^{60} +6.37429 q^{61} +17.6489 q^{62} +1.94522 q^{63} -9.19348 q^{64} +0.862758 q^{65} +1.84518 q^{66} -14.4564 q^{67} +8.76206 q^{68} -0.0918288 q^{69} +2.42755 q^{70} -9.82493 q^{71} -8.93906 q^{72} -14.0816 q^{73} +4.52085 q^{74} +1.02702 q^{75} +18.5386 q^{76} -0.740098 q^{77} -2.15099 q^{78} +8.20700 q^{79} -3.36953 q^{80} +0.619547 q^{81} +2.43887 q^{82} +5.30835 q^{83} -3.99822 q^{84} -2.25071 q^{85} +13.7188 q^{86} +10.6694 q^{87} +3.40104 q^{88} -11.9860 q^{89} +4.72213 q^{90} +0.862758 q^{91} -0.348084 q^{92} +7.46672 q^{93} +2.15578 q^{94} -4.76201 q^{95} -1.03839 q^{96} +16.9852 q^{97} +2.42755 q^{98} -1.43965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.42755 1.71654 0.858270 0.513199i \(-0.171540\pi\)
0.858270 + 0.513199i \(0.171540\pi\)
\(3\) 1.02702 0.592953 0.296476 0.955040i \(-0.404188\pi\)
0.296476 + 0.955040i \(0.404188\pi\)
\(4\) 3.89301 1.94651
\(5\) −1.00000 −0.447214
\(6\) 2.49316 1.01783
\(7\) −1.00000 −0.377964
\(8\) 4.59539 1.62472
\(9\) −1.94522 −0.648407
\(10\) −2.42755 −0.767660
\(11\) 0.740098 0.223148 0.111574 0.993756i \(-0.464411\pi\)
0.111574 + 0.993756i \(0.464411\pi\)
\(12\) 3.99822 1.15419
\(13\) −0.862758 −0.239286 −0.119643 0.992817i \(-0.538175\pi\)
−0.119643 + 0.992817i \(0.538175\pi\)
\(14\) −2.42755 −0.648791
\(15\) −1.02702 −0.265177
\(16\) 3.36953 0.842383
\(17\) 2.25071 0.545878 0.272939 0.962031i \(-0.412004\pi\)
0.272939 + 0.962031i \(0.412004\pi\)
\(18\) −4.72213 −1.11302
\(19\) 4.76201 1.09248 0.546240 0.837629i \(-0.316059\pi\)
0.546240 + 0.837629i \(0.316059\pi\)
\(20\) −3.89301 −0.870505
\(21\) −1.02702 −0.224115
\(22\) 1.79663 0.383042
\(23\) −0.0894125 −0.0186438 −0.00932190 0.999957i \(-0.502967\pi\)
−0.00932190 + 0.999957i \(0.502967\pi\)
\(24\) 4.71958 0.963380
\(25\) 1.00000 0.200000
\(26\) −2.09439 −0.410744
\(27\) −5.07886 −0.977428
\(28\) −3.89301 −0.735711
\(29\) 10.3886 1.92912 0.964562 0.263857i \(-0.0849948\pi\)
0.964562 + 0.263857i \(0.0849948\pi\)
\(30\) −2.49316 −0.455186
\(31\) 7.27024 1.30577 0.652887 0.757455i \(-0.273558\pi\)
0.652887 + 0.757455i \(0.273558\pi\)
\(32\) −1.01107 −0.178733
\(33\) 0.760098 0.132316
\(34\) 5.46373 0.937022
\(35\) 1.00000 0.169031
\(36\) −7.57277 −1.26213
\(37\) 1.86231 0.306161 0.153081 0.988214i \(-0.451081\pi\)
0.153081 + 0.988214i \(0.451081\pi\)
\(38\) 11.5600 1.87529
\(39\) −0.886074 −0.141885
\(40\) −4.59539 −0.726596
\(41\) 1.00466 0.156902 0.0784510 0.996918i \(-0.475003\pi\)
0.0784510 + 0.996918i \(0.475003\pi\)
\(42\) −2.49316 −0.384702
\(43\) 5.65130 0.861815 0.430908 0.902396i \(-0.358193\pi\)
0.430908 + 0.902396i \(0.358193\pi\)
\(44\) 2.88121 0.434359
\(45\) 1.94522 0.289976
\(46\) −0.217054 −0.0320028
\(47\) 0.888047 0.129535 0.0647675 0.997900i \(-0.479369\pi\)
0.0647675 + 0.997900i \(0.479369\pi\)
\(48\) 3.46059 0.499494
\(49\) 1.00000 0.142857
\(50\) 2.42755 0.343308
\(51\) 2.31154 0.323680
\(52\) −3.35873 −0.465772
\(53\) 13.1121 1.80109 0.900545 0.434764i \(-0.143168\pi\)
0.900545 + 0.434764i \(0.143168\pi\)
\(54\) −12.3292 −1.67779
\(55\) −0.740098 −0.0997948
\(56\) −4.59539 −0.614085
\(57\) 4.89070 0.647789
\(58\) 25.2190 3.31142
\(59\) 9.57154 1.24611 0.623054 0.782178i \(-0.285892\pi\)
0.623054 + 0.782178i \(0.285892\pi\)
\(60\) −3.99822 −0.516168
\(61\) 6.37429 0.816145 0.408072 0.912950i \(-0.366201\pi\)
0.408072 + 0.912950i \(0.366201\pi\)
\(62\) 17.6489 2.24141
\(63\) 1.94522 0.245075
\(64\) −9.19348 −1.14919
\(65\) 0.862758 0.107012
\(66\) 1.84518 0.227126
\(67\) −14.4564 −1.76613 −0.883066 0.469248i \(-0.844525\pi\)
−0.883066 + 0.469248i \(0.844525\pi\)
\(68\) 8.76206 1.06256
\(69\) −0.0918288 −0.0110549
\(70\) 2.42755 0.290148
\(71\) −9.82493 −1.16601 −0.583003 0.812470i \(-0.698122\pi\)
−0.583003 + 0.812470i \(0.698122\pi\)
\(72\) −8.93906 −1.05348
\(73\) −14.0816 −1.64813 −0.824066 0.566494i \(-0.808300\pi\)
−0.824066 + 0.566494i \(0.808300\pi\)
\(74\) 4.52085 0.525538
\(75\) 1.02702 0.118591
\(76\) 18.5386 2.12652
\(77\) −0.740098 −0.0843420
\(78\) −2.15099 −0.243552
\(79\) 8.20700 0.923360 0.461680 0.887047i \(-0.347247\pi\)
0.461680 + 0.887047i \(0.347247\pi\)
\(80\) −3.36953 −0.376725
\(81\) 0.619547 0.0688386
\(82\) 2.43887 0.269328
\(83\) 5.30835 0.582667 0.291334 0.956621i \(-0.405901\pi\)
0.291334 + 0.956621i \(0.405901\pi\)
\(84\) −3.99822 −0.436242
\(85\) −2.25071 −0.244124
\(86\) 13.7188 1.47934
\(87\) 10.6694 1.14388
\(88\) 3.40104 0.362552
\(89\) −11.9860 −1.27052 −0.635258 0.772300i \(-0.719106\pi\)
−0.635258 + 0.772300i \(0.719106\pi\)
\(90\) 4.72213 0.497756
\(91\) 0.862758 0.0904416
\(92\) −0.348084 −0.0362903
\(93\) 7.46672 0.774262
\(94\) 2.15578 0.222352
\(95\) −4.76201 −0.488572
\(96\) −1.03839 −0.105980
\(97\) 16.9852 1.72459 0.862295 0.506406i \(-0.169026\pi\)
0.862295 + 0.506406i \(0.169026\pi\)
\(98\) 2.42755 0.245220
\(99\) −1.43965 −0.144691
\(100\) 3.89301 0.389301
\(101\) 8.16261 0.812210 0.406105 0.913826i \(-0.366887\pi\)
0.406105 + 0.913826i \(0.366887\pi\)
\(102\) 5.61138 0.555610
\(103\) −8.40818 −0.828483 −0.414241 0.910167i \(-0.635953\pi\)
−0.414241 + 0.910167i \(0.635953\pi\)
\(104\) −3.96471 −0.388772
\(105\) 1.02702 0.100227
\(106\) 31.8304 3.09164
\(107\) 11.4992 1.11167 0.555834 0.831294i \(-0.312399\pi\)
0.555834 + 0.831294i \(0.312399\pi\)
\(108\) −19.7721 −1.90257
\(109\) −1.37478 −0.131680 −0.0658399 0.997830i \(-0.520973\pi\)
−0.0658399 + 0.997830i \(0.520973\pi\)
\(110\) −1.79663 −0.171302
\(111\) 1.91263 0.181539
\(112\) −3.36953 −0.318391
\(113\) 8.92213 0.839323 0.419662 0.907681i \(-0.362149\pi\)
0.419662 + 0.907681i \(0.362149\pi\)
\(114\) 11.8724 1.11196
\(115\) 0.0894125 0.00833776
\(116\) 40.4432 3.75505
\(117\) 1.67826 0.155155
\(118\) 23.2354 2.13899
\(119\) −2.25071 −0.206323
\(120\) −4.71958 −0.430837
\(121\) −10.4523 −0.950205
\(122\) 15.4739 1.40094
\(123\) 1.03181 0.0930354
\(124\) 28.3032 2.54170
\(125\) −1.00000 −0.0894427
\(126\) 4.72213 0.420681
\(127\) 0.785135 0.0696695 0.0348347 0.999393i \(-0.488910\pi\)
0.0348347 + 0.999393i \(0.488910\pi\)
\(128\) −20.2955 −1.79389
\(129\) 5.80402 0.511016
\(130\) 2.09439 0.183690
\(131\) −4.24712 −0.371072 −0.185536 0.982637i \(-0.559402\pi\)
−0.185536 + 0.982637i \(0.559402\pi\)
\(132\) 2.95907 0.257554
\(133\) −4.76201 −0.412919
\(134\) −35.0937 −3.03164
\(135\) 5.07886 0.437119
\(136\) 10.3429 0.886898
\(137\) 21.6224 1.84733 0.923664 0.383204i \(-0.125179\pi\)
0.923664 + 0.383204i \(0.125179\pi\)
\(138\) −0.222919 −0.0189762
\(139\) −5.79999 −0.491949 −0.245974 0.969276i \(-0.579108\pi\)
−0.245974 + 0.969276i \(0.579108\pi\)
\(140\) 3.89301 0.329020
\(141\) 0.912046 0.0768081
\(142\) −23.8506 −2.00149
\(143\) −0.638525 −0.0533962
\(144\) −6.55449 −0.546207
\(145\) −10.3886 −0.862730
\(146\) −34.1840 −2.82908
\(147\) 1.02702 0.0847075
\(148\) 7.24999 0.595945
\(149\) −6.37255 −0.522060 −0.261030 0.965331i \(-0.584062\pi\)
−0.261030 + 0.965331i \(0.584062\pi\)
\(150\) 2.49316 0.203565
\(151\) −22.6558 −1.84370 −0.921852 0.387541i \(-0.873325\pi\)
−0.921852 + 0.387541i \(0.873325\pi\)
\(152\) 21.8833 1.77497
\(153\) −4.37814 −0.353951
\(154\) −1.79663 −0.144776
\(155\) −7.27024 −0.583960
\(156\) −3.44950 −0.276181
\(157\) 0.332918 0.0265697 0.0132849 0.999912i \(-0.495771\pi\)
0.0132849 + 0.999912i \(0.495771\pi\)
\(158\) 19.9229 1.58498
\(159\) 13.4665 1.06796
\(160\) 1.01107 0.0799318
\(161\) 0.0894125 0.00704669
\(162\) 1.50398 0.118164
\(163\) 10.2993 0.806700 0.403350 0.915046i \(-0.367846\pi\)
0.403350 + 0.915046i \(0.367846\pi\)
\(164\) 3.91117 0.305411
\(165\) −0.760098 −0.0591736
\(166\) 12.8863 1.00017
\(167\) 11.7609 0.910085 0.455042 0.890470i \(-0.349624\pi\)
0.455042 + 0.890470i \(0.349624\pi\)
\(168\) −4.71958 −0.364124
\(169\) −12.2556 −0.942742
\(170\) −5.46373 −0.419049
\(171\) −9.26316 −0.708372
\(172\) 22.0006 1.67753
\(173\) 1.63055 0.123969 0.0619843 0.998077i \(-0.480257\pi\)
0.0619843 + 0.998077i \(0.480257\pi\)
\(174\) 25.9005 1.96351
\(175\) −1.00000 −0.0755929
\(176\) 2.49378 0.187976
\(177\) 9.83021 0.738884
\(178\) −29.0967 −2.18089
\(179\) −17.9204 −1.33943 −0.669717 0.742616i \(-0.733585\pi\)
−0.669717 + 0.742616i \(0.733585\pi\)
\(180\) 7.57277 0.564441
\(181\) 8.17518 0.607656 0.303828 0.952727i \(-0.401735\pi\)
0.303828 + 0.952727i \(0.401735\pi\)
\(182\) 2.09439 0.155247
\(183\) 6.54656 0.483935
\(184\) −0.410886 −0.0302909
\(185\) −1.86231 −0.136919
\(186\) 18.1259 1.32905
\(187\) 1.66575 0.121812
\(188\) 3.45718 0.252141
\(189\) 5.07886 0.369433
\(190\) −11.5600 −0.838653
\(191\) −8.00026 −0.578878 −0.289439 0.957196i \(-0.593469\pi\)
−0.289439 + 0.957196i \(0.593469\pi\)
\(192\) −9.44193 −0.681413
\(193\) −16.3017 −1.17343 −0.586713 0.809795i \(-0.699578\pi\)
−0.586713 + 0.809795i \(0.699578\pi\)
\(194\) 41.2326 2.96033
\(195\) 0.886074 0.0634531
\(196\) 3.89301 0.278072
\(197\) −6.85481 −0.488385 −0.244193 0.969727i \(-0.578523\pi\)
−0.244193 + 0.969727i \(0.578523\pi\)
\(198\) −3.49484 −0.248367
\(199\) 1.90350 0.134935 0.0674677 0.997721i \(-0.478508\pi\)
0.0674677 + 0.997721i \(0.478508\pi\)
\(200\) 4.59539 0.324943
\(201\) −14.8471 −1.04723
\(202\) 19.8152 1.39419
\(203\) −10.3886 −0.729140
\(204\) 8.99885 0.630046
\(205\) −1.00466 −0.0701687
\(206\) −20.4113 −1.42212
\(207\) 0.173927 0.0120888
\(208\) −2.90709 −0.201571
\(209\) 3.52435 0.243785
\(210\) 2.49316 0.172044
\(211\) −10.3078 −0.709619 −0.354810 0.934939i \(-0.615454\pi\)
−0.354810 + 0.934939i \(0.615454\pi\)
\(212\) 51.0457 3.50583
\(213\) −10.0904 −0.691386
\(214\) 27.9149 1.90822
\(215\) −5.65130 −0.385416
\(216\) −23.3394 −1.58804
\(217\) −7.27024 −0.493536
\(218\) −3.33734 −0.226033
\(219\) −14.4622 −0.977265
\(220\) −2.88121 −0.194251
\(221\) −1.94182 −0.130621
\(222\) 4.64302 0.311619
\(223\) 15.4523 1.03476 0.517381 0.855755i \(-0.326907\pi\)
0.517381 + 0.855755i \(0.326907\pi\)
\(224\) 1.01107 0.0675547
\(225\) −1.94522 −0.129681
\(226\) 21.6589 1.44073
\(227\) −6.62030 −0.439405 −0.219702 0.975567i \(-0.570509\pi\)
−0.219702 + 0.975567i \(0.570509\pi\)
\(228\) 19.0396 1.26093
\(229\) 1.00000 0.0660819
\(230\) 0.217054 0.0143121
\(231\) −0.760098 −0.0500108
\(232\) 47.7399 3.13428
\(233\) −5.37938 −0.352415 −0.176208 0.984353i \(-0.556383\pi\)
−0.176208 + 0.984353i \(0.556383\pi\)
\(234\) 4.07405 0.266329
\(235\) −0.888047 −0.0579298
\(236\) 37.2622 2.42556
\(237\) 8.42879 0.547509
\(238\) −5.46373 −0.354161
\(239\) −19.9990 −1.29363 −0.646815 0.762647i \(-0.723899\pi\)
−0.646815 + 0.762647i \(0.723899\pi\)
\(240\) −3.46059 −0.223380
\(241\) −7.25801 −0.467530 −0.233765 0.972293i \(-0.575105\pi\)
−0.233765 + 0.972293i \(0.575105\pi\)
\(242\) −25.3734 −1.63106
\(243\) 15.8729 1.01825
\(244\) 24.8152 1.58863
\(245\) −1.00000 −0.0638877
\(246\) 2.50478 0.159699
\(247\) −4.10846 −0.261415
\(248\) 33.4096 2.12151
\(249\) 5.45181 0.345494
\(250\) −2.42755 −0.153532
\(251\) 12.3043 0.776644 0.388322 0.921524i \(-0.373055\pi\)
0.388322 + 0.921524i \(0.373055\pi\)
\(252\) 7.57277 0.477040
\(253\) −0.0661740 −0.00416032
\(254\) 1.90596 0.119590
\(255\) −2.31154 −0.144754
\(256\) −30.8815 −1.93010
\(257\) −6.09684 −0.380310 −0.190155 0.981754i \(-0.560899\pi\)
−0.190155 + 0.981754i \(0.560899\pi\)
\(258\) 14.0896 0.877179
\(259\) −1.86231 −0.115718
\(260\) 3.35873 0.208300
\(261\) −20.2082 −1.25086
\(262\) −10.3101 −0.636960
\(263\) −9.85239 −0.607525 −0.303762 0.952748i \(-0.598243\pi\)
−0.303762 + 0.952748i \(0.598243\pi\)
\(264\) 3.49295 0.214976
\(265\) −13.1121 −0.805472
\(266\) −11.5600 −0.708791
\(267\) −12.3099 −0.753356
\(268\) −56.2790 −3.43779
\(269\) −2.05818 −0.125489 −0.0627446 0.998030i \(-0.519985\pi\)
−0.0627446 + 0.998030i \(0.519985\pi\)
\(270\) 12.3292 0.750332
\(271\) −3.42212 −0.207879 −0.103939 0.994584i \(-0.533145\pi\)
−0.103939 + 0.994584i \(0.533145\pi\)
\(272\) 7.58386 0.459839
\(273\) 0.886074 0.0536276
\(274\) 52.4896 3.17101
\(275\) 0.740098 0.0446296
\(276\) −0.357491 −0.0215184
\(277\) 32.3702 1.94494 0.972469 0.233034i \(-0.0748653\pi\)
0.972469 + 0.233034i \(0.0748653\pi\)
\(278\) −14.0798 −0.844449
\(279\) −14.1422 −0.846673
\(280\) 4.59539 0.274627
\(281\) 1.93110 0.115200 0.0576000 0.998340i \(-0.481655\pi\)
0.0576000 + 0.998340i \(0.481655\pi\)
\(282\) 2.21404 0.131844
\(283\) 19.5305 1.16097 0.580483 0.814273i \(-0.302864\pi\)
0.580483 + 0.814273i \(0.302864\pi\)
\(284\) −38.2486 −2.26964
\(285\) −4.89070 −0.289700
\(286\) −1.55005 −0.0916566
\(287\) −1.00466 −0.0593034
\(288\) 1.96675 0.115892
\(289\) −11.9343 −0.702017
\(290\) −25.2190 −1.48091
\(291\) 17.4443 1.02260
\(292\) −54.8201 −3.20810
\(293\) −25.2603 −1.47572 −0.737862 0.674952i \(-0.764164\pi\)
−0.737862 + 0.674952i \(0.764164\pi\)
\(294\) 2.49316 0.145404
\(295\) −9.57154 −0.557277
\(296\) 8.55803 0.497425
\(297\) −3.75885 −0.218111
\(298\) −15.4697 −0.896136
\(299\) 0.0771414 0.00446120
\(300\) 3.99822 0.230837
\(301\) −5.65130 −0.325736
\(302\) −54.9982 −3.16479
\(303\) 8.38320 0.481602
\(304\) 16.0458 0.920287
\(305\) −6.37429 −0.364991
\(306\) −10.6282 −0.607572
\(307\) 11.1238 0.634867 0.317434 0.948280i \(-0.397179\pi\)
0.317434 + 0.948280i \(0.397179\pi\)
\(308\) −2.88121 −0.164172
\(309\) −8.63541 −0.491251
\(310\) −17.6489 −1.00239
\(311\) 27.6045 1.56531 0.782654 0.622457i \(-0.213866\pi\)
0.782654 + 0.622457i \(0.213866\pi\)
\(312\) −4.07186 −0.230524
\(313\) −18.7243 −1.05836 −0.529181 0.848509i \(-0.677501\pi\)
−0.529181 + 0.848509i \(0.677501\pi\)
\(314\) 0.808175 0.0456080
\(315\) −1.94522 −0.109601
\(316\) 31.9500 1.79733
\(317\) −1.46196 −0.0821117 −0.0410558 0.999157i \(-0.513072\pi\)
−0.0410558 + 0.999157i \(0.513072\pi\)
\(318\) 32.6906 1.83320
\(319\) 7.68861 0.430480
\(320\) 9.19348 0.513931
\(321\) 11.8099 0.659166
\(322\) 0.217054 0.0120959
\(323\) 10.7179 0.596361
\(324\) 2.41191 0.133995
\(325\) −0.862758 −0.0478572
\(326\) 25.0020 1.38473
\(327\) −1.41193 −0.0780799
\(328\) 4.61682 0.254921
\(329\) −0.888047 −0.0489596
\(330\) −1.84518 −0.101574
\(331\) 10.0826 0.554190 0.277095 0.960843i \(-0.410628\pi\)
0.277095 + 0.960843i \(0.410628\pi\)
\(332\) 20.6655 1.13417
\(333\) −3.62260 −0.198517
\(334\) 28.5502 1.56220
\(335\) 14.4564 0.789838
\(336\) −3.46059 −0.188791
\(337\) −16.4132 −0.894086 −0.447043 0.894512i \(-0.647523\pi\)
−0.447043 + 0.894512i \(0.647523\pi\)
\(338\) −29.7512 −1.61825
\(339\) 9.16324 0.497679
\(340\) −8.76206 −0.475190
\(341\) 5.38069 0.291381
\(342\) −22.4868 −1.21595
\(343\) −1.00000 −0.0539949
\(344\) 25.9700 1.40021
\(345\) 0.0918288 0.00494390
\(346\) 3.95825 0.212797
\(347\) −31.8614 −1.71041 −0.855204 0.518291i \(-0.826568\pi\)
−0.855204 + 0.518291i \(0.826568\pi\)
\(348\) 41.5361 2.22657
\(349\) 14.7371 0.788858 0.394429 0.918926i \(-0.370942\pi\)
0.394429 + 0.918926i \(0.370942\pi\)
\(350\) −2.42755 −0.129758
\(351\) 4.38183 0.233885
\(352\) −0.748287 −0.0398839
\(353\) 32.6134 1.73584 0.867919 0.496706i \(-0.165457\pi\)
0.867919 + 0.496706i \(0.165457\pi\)
\(354\) 23.8634 1.26832
\(355\) 9.82493 0.521453
\(356\) −46.6618 −2.47307
\(357\) −2.31154 −0.122340
\(358\) −43.5027 −2.29919
\(359\) −33.7478 −1.78114 −0.890569 0.454848i \(-0.849694\pi\)
−0.890569 + 0.454848i \(0.849694\pi\)
\(360\) 8.93906 0.471130
\(361\) 3.67674 0.193513
\(362\) 19.8457 1.04307
\(363\) −10.7347 −0.563427
\(364\) 3.35873 0.176045
\(365\) 14.0816 0.737067
\(366\) 15.8921 0.830694
\(367\) 27.9198 1.45740 0.728701 0.684831i \(-0.240124\pi\)
0.728701 + 0.684831i \(0.240124\pi\)
\(368\) −0.301278 −0.0157052
\(369\) −1.95429 −0.101736
\(370\) −4.52085 −0.235028
\(371\) −13.1121 −0.680748
\(372\) 29.0680 1.50711
\(373\) −0.956503 −0.0495258 −0.0247629 0.999693i \(-0.507883\pi\)
−0.0247629 + 0.999693i \(0.507883\pi\)
\(374\) 4.04369 0.209094
\(375\) −1.02702 −0.0530353
\(376\) 4.08093 0.210458
\(377\) −8.96289 −0.461612
\(378\) 12.3292 0.634146
\(379\) 25.1473 1.29173 0.645864 0.763452i \(-0.276497\pi\)
0.645864 + 0.763452i \(0.276497\pi\)
\(380\) −18.5386 −0.951009
\(381\) 0.806353 0.0413107
\(382\) −19.4211 −0.993667
\(383\) −27.6762 −1.41419 −0.707095 0.707118i \(-0.749995\pi\)
−0.707095 + 0.707118i \(0.749995\pi\)
\(384\) −20.8440 −1.06369
\(385\) 0.740098 0.0377189
\(386\) −39.5734 −2.01423
\(387\) −10.9930 −0.558807
\(388\) 66.1238 3.35693
\(389\) 7.36030 0.373182 0.186591 0.982438i \(-0.440256\pi\)
0.186591 + 0.982438i \(0.440256\pi\)
\(390\) 2.15099 0.108920
\(391\) −0.201242 −0.0101772
\(392\) 4.59539 0.232102
\(393\) −4.36189 −0.220028
\(394\) −16.6404 −0.838333
\(395\) −8.20700 −0.412939
\(396\) −5.60459 −0.281641
\(397\) −27.2854 −1.36941 −0.684707 0.728819i \(-0.740070\pi\)
−0.684707 + 0.728819i \(0.740070\pi\)
\(398\) 4.62084 0.231622
\(399\) −4.89070 −0.244841
\(400\) 3.36953 0.168477
\(401\) 17.8903 0.893401 0.446700 0.894684i \(-0.352599\pi\)
0.446700 + 0.894684i \(0.352599\pi\)
\(402\) −36.0421 −1.79762
\(403\) −6.27246 −0.312454
\(404\) 31.7772 1.58097
\(405\) −0.619547 −0.0307855
\(406\) −25.2190 −1.25160
\(407\) 1.37829 0.0683192
\(408\) 10.6224 0.525889
\(409\) 9.77211 0.483200 0.241600 0.970376i \(-0.422328\pi\)
0.241600 + 0.970376i \(0.422328\pi\)
\(410\) −2.43887 −0.120447
\(411\) 22.2067 1.09538
\(412\) −32.7332 −1.61265
\(413\) −9.57154 −0.470985
\(414\) 0.422217 0.0207508
\(415\) −5.30835 −0.260577
\(416\) 0.872305 0.0427683
\(417\) −5.95673 −0.291702
\(418\) 8.55555 0.418466
\(419\) −5.52138 −0.269737 −0.134868 0.990864i \(-0.543061\pi\)
−0.134868 + 0.990864i \(0.543061\pi\)
\(420\) 3.99822 0.195093
\(421\) 2.37531 0.115766 0.0578828 0.998323i \(-0.481565\pi\)
0.0578828 + 0.998323i \(0.481565\pi\)
\(422\) −25.0228 −1.21809
\(423\) −1.72745 −0.0839914
\(424\) 60.2554 2.92626
\(425\) 2.25071 0.109176
\(426\) −24.4951 −1.18679
\(427\) −6.37429 −0.308474
\(428\) 44.7664 2.16387
\(429\) −0.655781 −0.0316614
\(430\) −13.7188 −0.661581
\(431\) −15.0116 −0.723085 −0.361542 0.932356i \(-0.617750\pi\)
−0.361542 + 0.932356i \(0.617750\pi\)
\(432\) −17.1134 −0.823369
\(433\) −5.97353 −0.287069 −0.143535 0.989645i \(-0.545847\pi\)
−0.143535 + 0.989645i \(0.545847\pi\)
\(434\) −17.6489 −0.847174
\(435\) −10.6694 −0.511558
\(436\) −5.35203 −0.256316
\(437\) −0.425783 −0.0203680
\(438\) −35.1078 −1.67751
\(439\) −35.1370 −1.67700 −0.838498 0.544905i \(-0.816566\pi\)
−0.838498 + 0.544905i \(0.816566\pi\)
\(440\) −3.40104 −0.162138
\(441\) −1.94522 −0.0926296
\(442\) −4.71388 −0.224216
\(443\) −14.8550 −0.705783 −0.352892 0.935664i \(-0.614802\pi\)
−0.352892 + 0.935664i \(0.614802\pi\)
\(444\) 7.44591 0.353367
\(445\) 11.9860 0.568192
\(446\) 37.5112 1.77621
\(447\) −6.54477 −0.309557
\(448\) 9.19348 0.434351
\(449\) 13.3464 0.629855 0.314927 0.949116i \(-0.398020\pi\)
0.314927 + 0.949116i \(0.398020\pi\)
\(450\) −4.72213 −0.222603
\(451\) 0.743548 0.0350123
\(452\) 34.7340 1.63375
\(453\) −23.2681 −1.09323
\(454\) −16.0711 −0.754256
\(455\) −0.862758 −0.0404467
\(456\) 22.4747 1.05247
\(457\) 15.9288 0.745118 0.372559 0.928009i \(-0.378480\pi\)
0.372559 + 0.928009i \(0.378480\pi\)
\(458\) 2.42755 0.113432
\(459\) −11.4311 −0.533557
\(460\) 0.348084 0.0162295
\(461\) 28.4199 1.32365 0.661824 0.749659i \(-0.269783\pi\)
0.661824 + 0.749659i \(0.269783\pi\)
\(462\) −1.84518 −0.0858455
\(463\) 9.35157 0.434605 0.217302 0.976104i \(-0.430274\pi\)
0.217302 + 0.976104i \(0.430274\pi\)
\(464\) 35.0049 1.62506
\(465\) −7.46672 −0.346261
\(466\) −13.0587 −0.604934
\(467\) −3.27005 −0.151320 −0.0756598 0.997134i \(-0.524106\pi\)
−0.0756598 + 0.997134i \(0.524106\pi\)
\(468\) 6.53347 0.302010
\(469\) 14.4564 0.667535
\(470\) −2.15578 −0.0994388
\(471\) 0.341915 0.0157546
\(472\) 43.9850 2.02457
\(473\) 4.18252 0.192312
\(474\) 20.4613 0.939820
\(475\) 4.76201 0.218496
\(476\) −8.76206 −0.401609
\(477\) −25.5060 −1.16784
\(478\) −48.5487 −2.22057
\(479\) 18.5245 0.846408 0.423204 0.906034i \(-0.360905\pi\)
0.423204 + 0.906034i \(0.360905\pi\)
\(480\) 1.03839 0.0473958
\(481\) −1.60672 −0.0732601
\(482\) −17.6192 −0.802533
\(483\) 0.0918288 0.00417836
\(484\) −40.6908 −1.84958
\(485\) −16.9852 −0.771260
\(486\) 38.5323 1.74786
\(487\) −9.59755 −0.434907 −0.217453 0.976071i \(-0.569775\pi\)
−0.217453 + 0.976071i \(0.569775\pi\)
\(488\) 29.2924 1.32600
\(489\) 10.5776 0.478335
\(490\) −2.42755 −0.109666
\(491\) −20.5181 −0.925968 −0.462984 0.886367i \(-0.653221\pi\)
−0.462984 + 0.886367i \(0.653221\pi\)
\(492\) 4.01686 0.181094
\(493\) 23.3819 1.05307
\(494\) −9.97352 −0.448730
\(495\) 1.43965 0.0647076
\(496\) 24.4973 1.09996
\(497\) 9.82493 0.440709
\(498\) 13.2346 0.593055
\(499\) 10.6166 0.475264 0.237632 0.971355i \(-0.423629\pi\)
0.237632 + 0.971355i \(0.423629\pi\)
\(500\) −3.89301 −0.174101
\(501\) 12.0787 0.539637
\(502\) 29.8695 1.33314
\(503\) −19.1511 −0.853906 −0.426953 0.904274i \(-0.640413\pi\)
−0.426953 + 0.904274i \(0.640413\pi\)
\(504\) 8.93906 0.398177
\(505\) −8.16261 −0.363231
\(506\) −0.160641 −0.00714136
\(507\) −12.5868 −0.559002
\(508\) 3.05654 0.135612
\(509\) −7.65209 −0.339173 −0.169586 0.985515i \(-0.554243\pi\)
−0.169586 + 0.985515i \(0.554243\pi\)
\(510\) −5.61138 −0.248476
\(511\) 14.0816 0.622935
\(512\) −34.3755 −1.51920
\(513\) −24.1856 −1.06782
\(514\) −14.8004 −0.652818
\(515\) 8.40818 0.370509
\(516\) 22.5952 0.994696
\(517\) 0.657242 0.0289055
\(518\) −4.52085 −0.198635
\(519\) 1.67462 0.0735076
\(520\) 3.96471 0.173864
\(521\) −26.2816 −1.15142 −0.575708 0.817655i \(-0.695274\pi\)
−0.575708 + 0.817655i \(0.695274\pi\)
\(522\) −49.0565 −2.14715
\(523\) 12.2118 0.533986 0.266993 0.963698i \(-0.413970\pi\)
0.266993 + 0.963698i \(0.413970\pi\)
\(524\) −16.5341 −0.722295
\(525\) −1.02702 −0.0448230
\(526\) −23.9172 −1.04284
\(527\) 16.3632 0.712794
\(528\) 2.56118 0.111461
\(529\) −22.9920 −0.999652
\(530\) −31.8304 −1.38262
\(531\) −18.6188 −0.807986
\(532\) −18.5386 −0.803749
\(533\) −0.866781 −0.0375445
\(534\) −29.8830 −1.29317
\(535\) −11.4992 −0.497153
\(536\) −66.4329 −2.86947
\(537\) −18.4047 −0.794221
\(538\) −4.99633 −0.215407
\(539\) 0.740098 0.0318783
\(540\) 19.7721 0.850855
\(541\) 23.8332 1.02467 0.512334 0.858786i \(-0.328781\pi\)
0.512334 + 0.858786i \(0.328781\pi\)
\(542\) −8.30737 −0.356832
\(543\) 8.39611 0.360312
\(544\) −2.27562 −0.0975664
\(545\) 1.37478 0.0588890
\(546\) 2.15099 0.0920539
\(547\) 31.5100 1.34727 0.673636 0.739063i \(-0.264732\pi\)
0.673636 + 0.739063i \(0.264732\pi\)
\(548\) 84.1764 3.59584
\(549\) −12.3994 −0.529194
\(550\) 1.79663 0.0766084
\(551\) 49.4708 2.10753
\(552\) −0.421990 −0.0179611
\(553\) −8.20700 −0.348997
\(554\) 78.5804 3.33856
\(555\) −1.91263 −0.0811868
\(556\) −22.5794 −0.957582
\(557\) 15.8148 0.670096 0.335048 0.942201i \(-0.391248\pi\)
0.335048 + 0.942201i \(0.391248\pi\)
\(558\) −34.3310 −1.45335
\(559\) −4.87571 −0.206220
\(560\) 3.36953 0.142389
\(561\) 1.71076 0.0722285
\(562\) 4.68785 0.197745
\(563\) 31.3699 1.32208 0.661041 0.750350i \(-0.270115\pi\)
0.661041 + 0.750350i \(0.270115\pi\)
\(564\) 3.55061 0.149508
\(565\) −8.92213 −0.375357
\(566\) 47.4112 1.99284
\(567\) −0.619547 −0.0260185
\(568\) −45.1494 −1.89443
\(569\) −43.9884 −1.84409 −0.922044 0.387085i \(-0.873482\pi\)
−0.922044 + 0.387085i \(0.873482\pi\)
\(570\) −11.8724 −0.497282
\(571\) −31.3586 −1.31231 −0.656157 0.754624i \(-0.727819\pi\)
−0.656157 + 0.754624i \(0.727819\pi\)
\(572\) −2.48579 −0.103936
\(573\) −8.21646 −0.343248
\(574\) −2.43887 −0.101797
\(575\) −0.0894125 −0.00372876
\(576\) 17.8834 0.745140
\(577\) −8.86781 −0.369172 −0.184586 0.982816i \(-0.559094\pi\)
−0.184586 + 0.982816i \(0.559094\pi\)
\(578\) −28.9711 −1.20504
\(579\) −16.7423 −0.695786
\(580\) −40.4432 −1.67931
\(581\) −5.30835 −0.220228
\(582\) 42.3469 1.75533
\(583\) 9.70426 0.401909
\(584\) −64.7107 −2.67775
\(585\) −1.67826 −0.0693873
\(586\) −61.3208 −2.53314
\(587\) 36.7954 1.51871 0.759354 0.650678i \(-0.225515\pi\)
0.759354 + 0.650678i \(0.225515\pi\)
\(588\) 3.99822 0.164884
\(589\) 34.6210 1.42653
\(590\) −23.2354 −0.956588
\(591\) −7.04006 −0.289589
\(592\) 6.27510 0.257905
\(593\) −10.1339 −0.416151 −0.208075 0.978113i \(-0.566720\pi\)
−0.208075 + 0.978113i \(0.566720\pi\)
\(594\) −9.12482 −0.374396
\(595\) 2.25071 0.0922703
\(596\) −24.8084 −1.01619
\(597\) 1.95494 0.0800103
\(598\) 0.187265 0.00765783
\(599\) −40.0591 −1.63677 −0.818385 0.574670i \(-0.805130\pi\)
−0.818385 + 0.574670i \(0.805130\pi\)
\(600\) 4.71958 0.192676
\(601\) −20.7435 −0.846145 −0.423073 0.906096i \(-0.639048\pi\)
−0.423073 + 0.906096i \(0.639048\pi\)
\(602\) −13.7188 −0.559138
\(603\) 28.1209 1.14517
\(604\) −88.1995 −3.58878
\(605\) 10.4523 0.424945
\(606\) 20.3507 0.826689
\(607\) −26.5072 −1.07589 −0.537947 0.842978i \(-0.680800\pi\)
−0.537947 + 0.842978i \(0.680800\pi\)
\(608\) −4.81471 −0.195262
\(609\) −10.6694 −0.432346
\(610\) −15.4739 −0.626522
\(611\) −0.766170 −0.0309959
\(612\) −17.0442 −0.688969
\(613\) 9.87842 0.398986 0.199493 0.979899i \(-0.436071\pi\)
0.199493 + 0.979899i \(0.436071\pi\)
\(614\) 27.0036 1.08977
\(615\) −1.03181 −0.0416067
\(616\) −3.40104 −0.137032
\(617\) 12.0395 0.484692 0.242346 0.970190i \(-0.422083\pi\)
0.242346 + 0.970190i \(0.422083\pi\)
\(618\) −20.9629 −0.843252
\(619\) −13.2428 −0.532275 −0.266137 0.963935i \(-0.585747\pi\)
−0.266137 + 0.963935i \(0.585747\pi\)
\(620\) −28.3032 −1.13668
\(621\) 0.454114 0.0182230
\(622\) 67.0114 2.68691
\(623\) 11.9860 0.480210
\(624\) −2.98566 −0.119522
\(625\) 1.00000 0.0400000
\(626\) −45.4543 −1.81672
\(627\) 3.61960 0.144553
\(628\) 1.29605 0.0517182
\(629\) 4.19152 0.167127
\(630\) −4.72213 −0.188134
\(631\) −1.71942 −0.0684492 −0.0342246 0.999414i \(-0.510896\pi\)
−0.0342246 + 0.999414i \(0.510896\pi\)
\(632\) 37.7144 1.50020
\(633\) −10.5864 −0.420771
\(634\) −3.54898 −0.140948
\(635\) −0.785135 −0.0311571
\(636\) 52.4252 2.07879
\(637\) −0.862758 −0.0341837
\(638\) 18.6645 0.738935
\(639\) 19.1117 0.756046
\(640\) 20.2955 0.802252
\(641\) −12.9327 −0.510811 −0.255405 0.966834i \(-0.582209\pi\)
−0.255405 + 0.966834i \(0.582209\pi\)
\(642\) 28.6692 1.13148
\(643\) 22.2330 0.876782 0.438391 0.898784i \(-0.355549\pi\)
0.438391 + 0.898784i \(0.355549\pi\)
\(644\) 0.348084 0.0137164
\(645\) −5.80402 −0.228533
\(646\) 26.0183 1.02368
\(647\) 4.19045 0.164744 0.0823718 0.996602i \(-0.473751\pi\)
0.0823718 + 0.996602i \(0.473751\pi\)
\(648\) 2.84706 0.111843
\(649\) 7.08388 0.278067
\(650\) −2.09439 −0.0821488
\(651\) −7.46672 −0.292644
\(652\) 40.0952 1.57025
\(653\) −22.2995 −0.872646 −0.436323 0.899790i \(-0.643720\pi\)
−0.436323 + 0.899790i \(0.643720\pi\)
\(654\) −3.42753 −0.134027
\(655\) 4.24712 0.165949
\(656\) 3.38524 0.132172
\(657\) 27.3919 1.06866
\(658\) −2.15578 −0.0840411
\(659\) 23.4989 0.915389 0.457694 0.889110i \(-0.348675\pi\)
0.457694 + 0.889110i \(0.348675\pi\)
\(660\) −2.95907 −0.115182
\(661\) 28.0632 1.09153 0.545767 0.837937i \(-0.316239\pi\)
0.545767 + 0.837937i \(0.316239\pi\)
\(662\) 24.4760 0.951288
\(663\) −1.99430 −0.0774522
\(664\) 24.3940 0.946670
\(665\) 4.76201 0.184663
\(666\) −8.79405 −0.340762
\(667\) −0.928875 −0.0359662
\(668\) 45.7853 1.77149
\(669\) 15.8699 0.613565
\(670\) 35.0937 1.35579
\(671\) 4.71760 0.182121
\(672\) 1.03839 0.0400567
\(673\) −32.3781 −1.24809 −0.624043 0.781390i \(-0.714511\pi\)
−0.624043 + 0.781390i \(0.714511\pi\)
\(674\) −39.8440 −1.53473
\(675\) −5.07886 −0.195486
\(676\) −47.7114 −1.83505
\(677\) 41.4384 1.59261 0.796303 0.604898i \(-0.206786\pi\)
0.796303 + 0.604898i \(0.206786\pi\)
\(678\) 22.2443 0.854286
\(679\) −16.9852 −0.651834
\(680\) −10.3429 −0.396633
\(681\) −6.79921 −0.260546
\(682\) 13.0619 0.500166
\(683\) −9.20148 −0.352085 −0.176042 0.984383i \(-0.556330\pi\)
−0.176042 + 0.984383i \(0.556330\pi\)
\(684\) −36.0616 −1.37885
\(685\) −21.6224 −0.826150
\(686\) −2.42755 −0.0926844
\(687\) 1.02702 0.0391834
\(688\) 19.0422 0.725979
\(689\) −11.3126 −0.430976
\(690\) 0.222919 0.00848639
\(691\) 45.6389 1.73619 0.868093 0.496402i \(-0.165346\pi\)
0.868093 + 0.496402i \(0.165346\pi\)
\(692\) 6.34777 0.241306
\(693\) 1.43965 0.0546879
\(694\) −77.3452 −2.93598
\(695\) 5.79999 0.220006
\(696\) 49.0301 1.85848
\(697\) 2.26121 0.0856494
\(698\) 35.7751 1.35411
\(699\) −5.52476 −0.208966
\(700\) −3.89301 −0.147142
\(701\) −38.9258 −1.47021 −0.735104 0.677954i \(-0.762867\pi\)
−0.735104 + 0.677954i \(0.762867\pi\)
\(702\) 10.6371 0.401473
\(703\) 8.86832 0.334475
\(704\) −6.80408 −0.256438
\(705\) −0.912046 −0.0343496
\(706\) 79.1709 2.97963
\(707\) −8.16261 −0.306987
\(708\) 38.2691 1.43824
\(709\) −41.2626 −1.54965 −0.774825 0.632176i \(-0.782162\pi\)
−0.774825 + 0.632176i \(0.782162\pi\)
\(710\) 23.8506 0.895095
\(711\) −15.9644 −0.598713
\(712\) −55.0805 −2.06423
\(713\) −0.650051 −0.0243446
\(714\) −5.61138 −0.210001
\(715\) 0.638525 0.0238795
\(716\) −69.7644 −2.60722
\(717\) −20.5395 −0.767061
\(718\) −81.9245 −3.05739
\(719\) 12.8627 0.479699 0.239849 0.970810i \(-0.422902\pi\)
0.239849 + 0.970810i \(0.422902\pi\)
\(720\) 6.55449 0.244271
\(721\) 8.40818 0.313137
\(722\) 8.92549 0.332172
\(723\) −7.45416 −0.277223
\(724\) 31.8261 1.18281
\(725\) 10.3886 0.385825
\(726\) −26.0591 −0.967144
\(727\) 7.79574 0.289128 0.144564 0.989495i \(-0.453822\pi\)
0.144564 + 0.989495i \(0.453822\pi\)
\(728\) 3.96471 0.146942
\(729\) 14.4432 0.534933
\(730\) 34.1840 1.26520
\(731\) 12.7195 0.470446
\(732\) 25.4858 0.941984
\(733\) −9.51550 −0.351463 −0.175732 0.984438i \(-0.556229\pi\)
−0.175732 + 0.984438i \(0.556229\pi\)
\(734\) 67.7769 2.50169
\(735\) −1.02702 −0.0378824
\(736\) 0.0904019 0.00333226
\(737\) −10.6992 −0.394109
\(738\) −4.74414 −0.174634
\(739\) 18.8977 0.695165 0.347582 0.937649i \(-0.387003\pi\)
0.347582 + 0.937649i \(0.387003\pi\)
\(740\) −7.24999 −0.266515
\(741\) −4.21949 −0.155007
\(742\) −31.8304 −1.16853
\(743\) 45.6012 1.67294 0.836472 0.548010i \(-0.184614\pi\)
0.836472 + 0.548010i \(0.184614\pi\)
\(744\) 34.3125 1.25796
\(745\) 6.37255 0.233472
\(746\) −2.32196 −0.0850130
\(747\) −10.3259 −0.377806
\(748\) 6.48478 0.237107
\(749\) −11.4992 −0.420171
\(750\) −2.49316 −0.0910372
\(751\) 13.4090 0.489302 0.244651 0.969611i \(-0.421327\pi\)
0.244651 + 0.969611i \(0.421327\pi\)
\(752\) 2.99230 0.109118
\(753\) 12.6369 0.460513
\(754\) −21.7579 −0.792376
\(755\) 22.6558 0.824530
\(756\) 19.7721 0.719104
\(757\) −36.5920 −1.32996 −0.664979 0.746862i \(-0.731560\pi\)
−0.664979 + 0.746862i \(0.731560\pi\)
\(758\) 61.0463 2.21730
\(759\) −0.0679623 −0.00246687
\(760\) −21.8833 −0.793791
\(761\) 51.2608 1.85820 0.929101 0.369827i \(-0.120583\pi\)
0.929101 + 0.369827i \(0.120583\pi\)
\(762\) 1.95746 0.0709115
\(763\) 1.37478 0.0497703
\(764\) −31.1451 −1.12679
\(765\) 4.37814 0.158292
\(766\) −67.1856 −2.42751
\(767\) −8.25793 −0.298177
\(768\) −31.7161 −1.14446
\(769\) −29.3683 −1.05905 −0.529524 0.848295i \(-0.677629\pi\)
−0.529524 + 0.848295i \(0.677629\pi\)
\(770\) 1.79663 0.0647459
\(771\) −6.26160 −0.225506
\(772\) −63.4629 −2.28408
\(773\) −13.6105 −0.489537 −0.244769 0.969582i \(-0.578712\pi\)
−0.244769 + 0.969582i \(0.578712\pi\)
\(774\) −26.6862 −0.959214
\(775\) 7.27024 0.261155
\(776\) 78.0539 2.80197
\(777\) −1.91263 −0.0686154
\(778\) 17.8675 0.640581
\(779\) 4.78421 0.171412
\(780\) 3.44950 0.123512
\(781\) −7.27141 −0.260192
\(782\) −0.488526 −0.0174696
\(783\) −52.7625 −1.88558
\(784\) 3.36953 0.120340
\(785\) −0.332918 −0.0118823
\(786\) −10.5887 −0.377687
\(787\) 6.09675 0.217326 0.108663 0.994079i \(-0.465343\pi\)
0.108663 + 0.994079i \(0.465343\pi\)
\(788\) −26.6859 −0.950646
\(789\) −10.1186 −0.360233
\(790\) −19.9229 −0.708826
\(791\) −8.92213 −0.317234
\(792\) −6.61577 −0.235081
\(793\) −5.49948 −0.195292
\(794\) −66.2367 −2.35065
\(795\) −13.4665 −0.477607
\(796\) 7.41035 0.262653
\(797\) 1.10018 0.0389702 0.0194851 0.999810i \(-0.493797\pi\)
0.0194851 + 0.999810i \(0.493797\pi\)
\(798\) −11.8724 −0.420280
\(799\) 1.99874 0.0707104
\(800\) −1.01107 −0.0357466
\(801\) 23.3155 0.823812
\(802\) 43.4297 1.53356
\(803\) −10.4218 −0.367777
\(804\) −57.7999 −2.03845
\(805\) −0.0894125 −0.00315138
\(806\) −15.2267 −0.536339
\(807\) −2.11380 −0.0744092
\(808\) 37.5104 1.31961
\(809\) −6.31862 −0.222151 −0.111076 0.993812i \(-0.535430\pi\)
−0.111076 + 0.993812i \(0.535430\pi\)
\(810\) −1.50398 −0.0528446
\(811\) −19.3061 −0.677929 −0.338964 0.940799i \(-0.610077\pi\)
−0.338964 + 0.940799i \(0.610077\pi\)
\(812\) −40.4432 −1.41928
\(813\) −3.51460 −0.123262
\(814\) 3.34587 0.117273
\(815\) −10.2993 −0.360767
\(816\) 7.78881 0.272663
\(817\) 26.9116 0.941516
\(818\) 23.7223 0.829431
\(819\) −1.67826 −0.0586430
\(820\) −3.91117 −0.136584
\(821\) −42.5637 −1.48548 −0.742741 0.669579i \(-0.766475\pi\)
−0.742741 + 0.669579i \(0.766475\pi\)
\(822\) 53.9081 1.88026
\(823\) −47.9332 −1.67084 −0.835422 0.549608i \(-0.814777\pi\)
−0.835422 + 0.549608i \(0.814777\pi\)
\(824\) −38.6389 −1.34605
\(825\) 0.760098 0.0264632
\(826\) −23.2354 −0.808464
\(827\) 2.82311 0.0981690 0.0490845 0.998795i \(-0.484370\pi\)
0.0490845 + 0.998795i \(0.484370\pi\)
\(828\) 0.677101 0.0235309
\(829\) 54.3745 1.88851 0.944253 0.329221i \(-0.106786\pi\)
0.944253 + 0.329221i \(0.106786\pi\)
\(830\) −12.8863 −0.447290
\(831\) 33.2450 1.15326
\(832\) 7.93175 0.274984
\(833\) 2.25071 0.0779826
\(834\) −14.4603 −0.500719
\(835\) −11.7609 −0.407002
\(836\) 13.7204 0.474528
\(837\) −36.9246 −1.27630
\(838\) −13.4034 −0.463014
\(839\) −10.8966 −0.376193 −0.188097 0.982151i \(-0.560232\pi\)
−0.188097 + 0.982151i \(0.560232\pi\)
\(840\) 4.71958 0.162841
\(841\) 78.9240 2.72152
\(842\) 5.76619 0.198716
\(843\) 1.98329 0.0683081
\(844\) −40.1285 −1.38128
\(845\) 12.2556 0.421607
\(846\) −4.19347 −0.144175
\(847\) 10.4523 0.359144
\(848\) 44.1818 1.51721
\(849\) 20.0583 0.688397
\(850\) 5.46373 0.187404
\(851\) −0.166513 −0.00570801
\(852\) −39.2823 −1.34579
\(853\) 8.16287 0.279491 0.139746 0.990187i \(-0.455372\pi\)
0.139746 + 0.990187i \(0.455372\pi\)
\(854\) −15.4739 −0.529507
\(855\) 9.26316 0.316793
\(856\) 52.8432 1.80614
\(857\) 1.47516 0.0503906 0.0251953 0.999683i \(-0.491979\pi\)
0.0251953 + 0.999683i \(0.491979\pi\)
\(858\) −1.59194 −0.0543481
\(859\) 11.2257 0.383016 0.191508 0.981491i \(-0.438662\pi\)
0.191508 + 0.981491i \(0.438662\pi\)
\(860\) −22.0006 −0.750214
\(861\) −1.03181 −0.0351641
\(862\) −36.4415 −1.24120
\(863\) 5.66106 0.192705 0.0963524 0.995347i \(-0.469282\pi\)
0.0963524 + 0.995347i \(0.469282\pi\)
\(864\) 5.13506 0.174698
\(865\) −1.63055 −0.0554405
\(866\) −14.5011 −0.492766
\(867\) −12.2568 −0.416263
\(868\) −28.3032 −0.960672
\(869\) 6.07398 0.206046
\(870\) −25.9005 −0.878110
\(871\) 12.4724 0.422611
\(872\) −6.31764 −0.213942
\(873\) −33.0400 −1.11824
\(874\) −1.03361 −0.0349624
\(875\) 1.00000 0.0338062
\(876\) −56.3015 −1.90225
\(877\) 2.87821 0.0971901 0.0485951 0.998819i \(-0.484526\pi\)
0.0485951 + 0.998819i \(0.484526\pi\)
\(878\) −85.2968 −2.87863
\(879\) −25.9430 −0.875034
\(880\) −2.49378 −0.0840654
\(881\) −26.6780 −0.898805 −0.449403 0.893329i \(-0.648363\pi\)
−0.449403 + 0.893329i \(0.648363\pi\)
\(882\) −4.72213 −0.159002
\(883\) −26.6351 −0.896341 −0.448171 0.893948i \(-0.647924\pi\)
−0.448171 + 0.893948i \(0.647924\pi\)
\(884\) −7.55954 −0.254255
\(885\) −9.83021 −0.330439
\(886\) −36.0613 −1.21150
\(887\) −2.75874 −0.0926293 −0.0463146 0.998927i \(-0.514748\pi\)
−0.0463146 + 0.998927i \(0.514748\pi\)
\(888\) 8.78931 0.294950
\(889\) −0.785135 −0.0263326
\(890\) 29.0967 0.975324
\(891\) 0.458525 0.0153612
\(892\) 60.1560 2.01417
\(893\) 4.22889 0.141514
\(894\) −15.8878 −0.531366
\(895\) 17.9204 0.599013
\(896\) 20.2955 0.678026
\(897\) 0.0792261 0.00264528
\(898\) 32.3990 1.08117
\(899\) 75.5280 2.51900
\(900\) −7.57277 −0.252426
\(901\) 29.5117 0.983176
\(902\) 1.80500 0.0601000
\(903\) −5.80402 −0.193146
\(904\) 41.0007 1.36366
\(905\) −8.17518 −0.271752
\(906\) −56.4845 −1.87657
\(907\) 32.6785 1.08507 0.542536 0.840032i \(-0.317464\pi\)
0.542536 + 0.840032i \(0.317464\pi\)
\(908\) −25.7729 −0.855305
\(909\) −15.8781 −0.526643
\(910\) −2.09439 −0.0694284
\(911\) 5.72577 0.189703 0.0948516 0.995491i \(-0.469762\pi\)
0.0948516 + 0.995491i \(0.469762\pi\)
\(912\) 16.4794 0.545687
\(913\) 3.92870 0.130021
\(914\) 38.6680 1.27902
\(915\) −6.54656 −0.216422
\(916\) 3.89301 0.128629
\(917\) 4.24712 0.140252
\(918\) −27.7495 −0.915871
\(919\) −50.5430 −1.66726 −0.833630 0.552323i \(-0.813742\pi\)
−0.833630 + 0.552323i \(0.813742\pi\)
\(920\) 0.410886 0.0135465
\(921\) 11.4244 0.376446
\(922\) 68.9909 2.27209
\(923\) 8.47654 0.279009
\(924\) −2.95907 −0.0973464
\(925\) 1.86231 0.0612323
\(926\) 22.7014 0.746016
\(927\) 16.3558 0.537194
\(928\) −10.5036 −0.344798
\(929\) −36.4764 −1.19675 −0.598377 0.801215i \(-0.704187\pi\)
−0.598377 + 0.801215i \(0.704187\pi\)
\(930\) −18.1259 −0.594370
\(931\) 4.76201 0.156069
\(932\) −20.9420 −0.685979
\(933\) 28.3505 0.928154
\(934\) −7.93821 −0.259746
\(935\) −1.66575 −0.0544758
\(936\) 7.71224 0.252083
\(937\) 26.1983 0.855860 0.427930 0.903812i \(-0.359243\pi\)
0.427930 + 0.903812i \(0.359243\pi\)
\(938\) 35.0937 1.14585
\(939\) −19.2303 −0.627559
\(940\) −3.45718 −0.112761
\(941\) 1.11635 0.0363918 0.0181959 0.999834i \(-0.494208\pi\)
0.0181959 + 0.999834i \(0.494208\pi\)
\(942\) 0.830016 0.0270434
\(943\) −0.0898294 −0.00292525
\(944\) 32.2516 1.04970
\(945\) −5.07886 −0.165215
\(946\) 10.1533 0.330112
\(947\) 46.3600 1.50650 0.753249 0.657735i \(-0.228485\pi\)
0.753249 + 0.657735i \(0.228485\pi\)
\(948\) 32.8134 1.06573
\(949\) 12.1491 0.394375
\(950\) 11.5600 0.375057
\(951\) −1.50147 −0.0486884
\(952\) −10.3429 −0.335216
\(953\) 48.8790 1.58335 0.791673 0.610945i \(-0.209210\pi\)
0.791673 + 0.610945i \(0.209210\pi\)
\(954\) −61.9171 −2.00464
\(955\) 8.00026 0.258882
\(956\) −77.8565 −2.51806
\(957\) 7.89639 0.255254
\(958\) 44.9693 1.45289
\(959\) −21.6224 −0.698224
\(960\) 9.44193 0.304737
\(961\) 21.8564 0.705046
\(962\) −3.90040 −0.125754
\(963\) −22.3684 −0.720813
\(964\) −28.2556 −0.910050
\(965\) 16.3017 0.524772
\(966\) 0.222919 0.00717231
\(967\) 5.25610 0.169025 0.0845124 0.996422i \(-0.473067\pi\)
0.0845124 + 0.996422i \(0.473067\pi\)
\(968\) −48.0322 −1.54381
\(969\) 11.0076 0.353614
\(970\) −41.2326 −1.32390
\(971\) −2.41366 −0.0774581 −0.0387290 0.999250i \(-0.512331\pi\)
−0.0387290 + 0.999250i \(0.512331\pi\)
\(972\) 61.7933 1.98202
\(973\) 5.79999 0.185939
\(974\) −23.2986 −0.746534
\(975\) −0.886074 −0.0283771
\(976\) 21.4784 0.687507
\(977\) −8.57934 −0.274477 −0.137239 0.990538i \(-0.543823\pi\)
−0.137239 + 0.990538i \(0.543823\pi\)
\(978\) 25.6777 0.821081
\(979\) −8.87083 −0.283513
\(980\) −3.89301 −0.124358
\(981\) 2.67425 0.0853821
\(982\) −49.8087 −1.58946
\(983\) −31.5729 −1.00702 −0.503510 0.863989i \(-0.667958\pi\)
−0.503510 + 0.863989i \(0.667958\pi\)
\(984\) 4.74159 0.151156
\(985\) 6.85481 0.218413
\(986\) 56.7608 1.80763
\(987\) −0.912046 −0.0290307
\(988\) −15.9943 −0.508847
\(989\) −0.505297 −0.0160675
\(990\) 3.49484 0.111073
\(991\) 10.7656 0.341980 0.170990 0.985273i \(-0.445303\pi\)
0.170990 + 0.985273i \(0.445303\pi\)
\(992\) −7.35069 −0.233385
\(993\) 10.3551 0.328608
\(994\) 23.8506 0.756494
\(995\) −1.90350 −0.0603450
\(996\) 21.2240 0.672507
\(997\) −14.5568 −0.461017 −0.230509 0.973070i \(-0.574039\pi\)
−0.230509 + 0.973070i \(0.574039\pi\)
\(998\) 25.7723 0.815809
\(999\) −9.45840 −0.299250
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 \(a_p\))