Properties

Label 8015.2.a.l.1.38
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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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 1.38
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.856487 q^{2} -2.63249 q^{3} -1.26643 q^{4} -1.00000 q^{5} -2.25469 q^{6} -1.00000 q^{7} -2.79765 q^{8} +3.92999 q^{9} +O(q^{10})\) \(q+0.856487 q^{2} -2.63249 q^{3} -1.26643 q^{4} -1.00000 q^{5} -2.25469 q^{6} -1.00000 q^{7} -2.79765 q^{8} +3.92999 q^{9} -0.856487 q^{10} +3.55049 q^{11} +3.33386 q^{12} +3.64418 q^{13} -0.856487 q^{14} +2.63249 q^{15} +0.136708 q^{16} +1.73278 q^{17} +3.36598 q^{18} -5.55244 q^{19} +1.26643 q^{20} +2.63249 q^{21} +3.04095 q^{22} -4.03981 q^{23} +7.36479 q^{24} +1.00000 q^{25} +3.12119 q^{26} -2.44818 q^{27} +1.26643 q^{28} +0.860600 q^{29} +2.25469 q^{30} +10.7794 q^{31} +5.71240 q^{32} -9.34663 q^{33} +1.48410 q^{34} +1.00000 q^{35} -4.97706 q^{36} +5.89164 q^{37} -4.75559 q^{38} -9.59326 q^{39} +2.79765 q^{40} -6.58941 q^{41} +2.25469 q^{42} -0.110729 q^{43} -4.49646 q^{44} -3.92999 q^{45} -3.46005 q^{46} -3.16720 q^{47} -0.359882 q^{48} +1.00000 q^{49} +0.856487 q^{50} -4.56152 q^{51} -4.61510 q^{52} -7.84850 q^{53} -2.09683 q^{54} -3.55049 q^{55} +2.79765 q^{56} +14.6167 q^{57} +0.737093 q^{58} -13.2508 q^{59} -3.33386 q^{60} +9.20667 q^{61} +9.23245 q^{62} -3.92999 q^{63} +4.61918 q^{64} -3.64418 q^{65} -8.00526 q^{66} -7.27971 q^{67} -2.19445 q^{68} +10.6348 q^{69} +0.856487 q^{70} -15.2682 q^{71} -10.9947 q^{72} +7.88613 q^{73} +5.04611 q^{74} -2.63249 q^{75} +7.03178 q^{76} -3.55049 q^{77} -8.21649 q^{78} -4.82787 q^{79} -0.136708 q^{80} -5.34516 q^{81} -5.64374 q^{82} +3.46176 q^{83} -3.33386 q^{84} -1.73278 q^{85} -0.0948379 q^{86} -2.26552 q^{87} -9.93306 q^{88} -14.6181 q^{89} -3.36598 q^{90} -3.64418 q^{91} +5.11615 q^{92} -28.3768 q^{93} -2.71266 q^{94} +5.55244 q^{95} -15.0378 q^{96} +12.2918 q^{97} +0.856487 q^{98} +13.9534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.856487 0.605627 0.302814 0.953050i \(-0.402074\pi\)
0.302814 + 0.953050i \(0.402074\pi\)
\(3\) −2.63249 −1.51987 −0.759934 0.650001i \(-0.774769\pi\)
−0.759934 + 0.650001i \(0.774769\pi\)
\(4\) −1.26643 −0.633215
\(5\) −1.00000 −0.447214
\(6\) −2.25469 −0.920473
\(7\) −1.00000 −0.377964
\(8\) −2.79765 −0.989120
\(9\) 3.92999 1.31000
\(10\) −0.856487 −0.270845
\(11\) 3.55049 1.07051 0.535257 0.844689i \(-0.320215\pi\)
0.535257 + 0.844689i \(0.320215\pi\)
\(12\) 3.33386 0.962403
\(13\) 3.64418 1.01071 0.505357 0.862910i \(-0.331361\pi\)
0.505357 + 0.862910i \(0.331361\pi\)
\(14\) −0.856487 −0.228906
\(15\) 2.63249 0.679705
\(16\) 0.136708 0.0341770
\(17\) 1.73278 0.420261 0.210130 0.977673i \(-0.432611\pi\)
0.210130 + 0.977673i \(0.432611\pi\)
\(18\) 3.36598 0.793369
\(19\) −5.55244 −1.27382 −0.636909 0.770939i \(-0.719787\pi\)
−0.636909 + 0.770939i \(0.719787\pi\)
\(20\) 1.26643 0.283183
\(21\) 2.63249 0.574456
\(22\) 3.04095 0.648333
\(23\) −4.03981 −0.842360 −0.421180 0.906977i \(-0.638384\pi\)
−0.421180 + 0.906977i \(0.638384\pi\)
\(24\) 7.36479 1.50333
\(25\) 1.00000 0.200000
\(26\) 3.12119 0.612116
\(27\) −2.44818 −0.471152
\(28\) 1.26643 0.239333
\(29\) 0.860600 0.159809 0.0799047 0.996803i \(-0.474538\pi\)
0.0799047 + 0.996803i \(0.474538\pi\)
\(30\) 2.25469 0.411648
\(31\) 10.7794 1.93605 0.968023 0.250861i \(-0.0807137\pi\)
0.968023 + 0.250861i \(0.0807137\pi\)
\(32\) 5.71240 1.00982
\(33\) −9.34663 −1.62704
\(34\) 1.48410 0.254522
\(35\) 1.00000 0.169031
\(36\) −4.97706 −0.829509
\(37\) 5.89164 0.968580 0.484290 0.874907i \(-0.339078\pi\)
0.484290 + 0.874907i \(0.339078\pi\)
\(38\) −4.75559 −0.771459
\(39\) −9.59326 −1.53615
\(40\) 2.79765 0.442348
\(41\) −6.58941 −1.02909 −0.514546 0.857463i \(-0.672040\pi\)
−0.514546 + 0.857463i \(0.672040\pi\)
\(42\) 2.25469 0.347906
\(43\) −0.110729 −0.0168860 −0.00844301 0.999964i \(-0.502688\pi\)
−0.00844301 + 0.999964i \(0.502688\pi\)
\(44\) −4.49646 −0.677866
\(45\) −3.92999 −0.585848
\(46\) −3.46005 −0.510156
\(47\) −3.16720 −0.461984 −0.230992 0.972956i \(-0.574197\pi\)
−0.230992 + 0.972956i \(0.574197\pi\)
\(48\) −0.359882 −0.0519445
\(49\) 1.00000 0.142857
\(50\) 0.856487 0.121125
\(51\) −4.56152 −0.638741
\(52\) −4.61510 −0.639999
\(53\) −7.84850 −1.07807 −0.539037 0.842282i \(-0.681212\pi\)
−0.539037 + 0.842282i \(0.681212\pi\)
\(54\) −2.09683 −0.285343
\(55\) −3.55049 −0.478749
\(56\) 2.79765 0.373852
\(57\) 14.6167 1.93603
\(58\) 0.737093 0.0967850
\(59\) −13.2508 −1.72510 −0.862550 0.505971i \(-0.831134\pi\)
−0.862550 + 0.505971i \(0.831134\pi\)
\(60\) −3.33386 −0.430400
\(61\) 9.20667 1.17879 0.589397 0.807844i \(-0.299365\pi\)
0.589397 + 0.807844i \(0.299365\pi\)
\(62\) 9.23245 1.17252
\(63\) −3.92999 −0.495132
\(64\) 4.61918 0.577397
\(65\) −3.64418 −0.452005
\(66\) −8.00526 −0.985380
\(67\) −7.27971 −0.889358 −0.444679 0.895690i \(-0.646682\pi\)
−0.444679 + 0.895690i \(0.646682\pi\)
\(68\) −2.19445 −0.266116
\(69\) 10.6348 1.28027
\(70\) 0.856487 0.102370
\(71\) −15.2682 −1.81200 −0.905998 0.423281i \(-0.860878\pi\)
−0.905998 + 0.423281i \(0.860878\pi\)
\(72\) −10.9947 −1.29574
\(73\) 7.88613 0.923002 0.461501 0.887140i \(-0.347311\pi\)
0.461501 + 0.887140i \(0.347311\pi\)
\(74\) 5.04611 0.586599
\(75\) −2.63249 −0.303973
\(76\) 7.03178 0.806601
\(77\) −3.55049 −0.404616
\(78\) −8.21649 −0.930335
\(79\) −4.82787 −0.543178 −0.271589 0.962413i \(-0.587549\pi\)
−0.271589 + 0.962413i \(0.587549\pi\)
\(80\) −0.136708 −0.0152844
\(81\) −5.34516 −0.593907
\(82\) −5.64374 −0.623247
\(83\) 3.46176 0.379978 0.189989 0.981786i \(-0.439155\pi\)
0.189989 + 0.981786i \(0.439155\pi\)
\(84\) −3.33386 −0.363754
\(85\) −1.73278 −0.187946
\(86\) −0.0948379 −0.0102266
\(87\) −2.26552 −0.242889
\(88\) −9.93306 −1.05887
\(89\) −14.6181 −1.54952 −0.774760 0.632255i \(-0.782129\pi\)
−0.774760 + 0.632255i \(0.782129\pi\)
\(90\) −3.36598 −0.354806
\(91\) −3.64418 −0.382014
\(92\) 5.11615 0.533395
\(93\) −28.3768 −2.94253
\(94\) −2.71266 −0.279790
\(95\) 5.55244 0.569668
\(96\) −15.0378 −1.53479
\(97\) 12.2918 1.24805 0.624023 0.781406i \(-0.285497\pi\)
0.624023 + 0.781406i \(0.285497\pi\)
\(98\) 0.856487 0.0865182
\(99\) 13.9534 1.40237
\(100\) −1.26643 −0.126643
\(101\) 13.3332 1.32671 0.663354 0.748306i \(-0.269132\pi\)
0.663354 + 0.748306i \(0.269132\pi\)
\(102\) −3.90688 −0.386839
\(103\) 18.2028 1.79357 0.896787 0.442462i \(-0.145895\pi\)
0.896787 + 0.442462i \(0.145895\pi\)
\(104\) −10.1952 −0.999717
\(105\) −2.63249 −0.256904
\(106\) −6.72214 −0.652912
\(107\) 9.09035 0.878797 0.439399 0.898292i \(-0.355192\pi\)
0.439399 + 0.898292i \(0.355192\pi\)
\(108\) 3.10045 0.298341
\(109\) 5.06523 0.485161 0.242581 0.970131i \(-0.422006\pi\)
0.242581 + 0.970131i \(0.422006\pi\)
\(110\) −3.04095 −0.289943
\(111\) −15.5097 −1.47211
\(112\) −0.136708 −0.0129177
\(113\) −9.84021 −0.925690 −0.462845 0.886439i \(-0.653171\pi\)
−0.462845 + 0.886439i \(0.653171\pi\)
\(114\) 12.5190 1.17251
\(115\) 4.03981 0.376715
\(116\) −1.08989 −0.101194
\(117\) 14.3216 1.32403
\(118\) −11.3491 −1.04477
\(119\) −1.73278 −0.158844
\(120\) −7.36479 −0.672310
\(121\) 1.60601 0.146001
\(122\) 7.88539 0.713910
\(123\) 17.3465 1.56408
\(124\) −13.6514 −1.22593
\(125\) −1.00000 −0.0894427
\(126\) −3.36598 −0.299865
\(127\) −15.4698 −1.37272 −0.686361 0.727261i \(-0.740793\pi\)
−0.686361 + 0.727261i \(0.740793\pi\)
\(128\) −7.46853 −0.660131
\(129\) 0.291493 0.0256645
\(130\) −3.12119 −0.273747
\(131\) −11.7321 −1.02504 −0.512521 0.858675i \(-0.671288\pi\)
−0.512521 + 0.858675i \(0.671288\pi\)
\(132\) 11.8369 1.03027
\(133\) 5.55244 0.481458
\(134\) −6.23498 −0.538620
\(135\) 2.44818 0.210706
\(136\) −4.84772 −0.415689
\(137\) −20.3100 −1.73520 −0.867601 0.497261i \(-0.834339\pi\)
−0.867601 + 0.497261i \(0.834339\pi\)
\(138\) 9.10853 0.775369
\(139\) −12.8852 −1.09290 −0.546452 0.837490i \(-0.684022\pi\)
−0.546452 + 0.837490i \(0.684022\pi\)
\(140\) −1.26643 −0.107033
\(141\) 8.33761 0.702154
\(142\) −13.0770 −1.09740
\(143\) 12.9386 1.08198
\(144\) 0.537261 0.0447718
\(145\) −0.860600 −0.0714690
\(146\) 6.75436 0.558995
\(147\) −2.63249 −0.217124
\(148\) −7.46136 −0.613320
\(149\) 5.99189 0.490875 0.245437 0.969412i \(-0.421068\pi\)
0.245437 + 0.969412i \(0.421068\pi\)
\(150\) −2.25469 −0.184095
\(151\) 15.9970 1.30181 0.650907 0.759157i \(-0.274389\pi\)
0.650907 + 0.759157i \(0.274389\pi\)
\(152\) 15.5338 1.25996
\(153\) 6.80980 0.550540
\(154\) −3.04095 −0.245047
\(155\) −10.7794 −0.865826
\(156\) 12.1492 0.972714
\(157\) 6.60969 0.527511 0.263755 0.964590i \(-0.415039\pi\)
0.263755 + 0.964590i \(0.415039\pi\)
\(158\) −4.13501 −0.328964
\(159\) 20.6611 1.63853
\(160\) −5.71240 −0.451605
\(161\) 4.03981 0.318382
\(162\) −4.57806 −0.359686
\(163\) 12.5705 0.984596 0.492298 0.870427i \(-0.336157\pi\)
0.492298 + 0.870427i \(0.336157\pi\)
\(164\) 8.34503 0.651637
\(165\) 9.34663 0.727634
\(166\) 2.96495 0.230125
\(167\) −7.77580 −0.601710 −0.300855 0.953670i \(-0.597272\pi\)
−0.300855 + 0.953670i \(0.597272\pi\)
\(168\) −7.36479 −0.568206
\(169\) 0.280046 0.0215420
\(170\) −1.48410 −0.113826
\(171\) −21.8210 −1.66870
\(172\) 0.140231 0.0106925
\(173\) 13.1364 0.998743 0.499372 0.866388i \(-0.333564\pi\)
0.499372 + 0.866388i \(0.333564\pi\)
\(174\) −1.94039 −0.147100
\(175\) −1.00000 −0.0755929
\(176\) 0.485381 0.0365870
\(177\) 34.8824 2.62192
\(178\) −12.5202 −0.938432
\(179\) −24.4689 −1.82889 −0.914446 0.404709i \(-0.867373\pi\)
−0.914446 + 0.404709i \(0.867373\pi\)
\(180\) 4.97706 0.370968
\(181\) −4.33981 −0.322576 −0.161288 0.986907i \(-0.551565\pi\)
−0.161288 + 0.986907i \(0.551565\pi\)
\(182\) −3.12119 −0.231358
\(183\) −24.2364 −1.79161
\(184\) 11.3020 0.833195
\(185\) −5.89164 −0.433162
\(186\) −24.3043 −1.78208
\(187\) 6.15223 0.449895
\(188\) 4.01104 0.292535
\(189\) 2.44818 0.178079
\(190\) 4.75559 0.345007
\(191\) 20.2980 1.46871 0.734354 0.678767i \(-0.237485\pi\)
0.734354 + 0.678767i \(0.237485\pi\)
\(192\) −12.1599 −0.877567
\(193\) −0.292300 −0.0210402 −0.0105201 0.999945i \(-0.503349\pi\)
−0.0105201 + 0.999945i \(0.503349\pi\)
\(194\) 10.5278 0.755851
\(195\) 9.59326 0.686987
\(196\) −1.26643 −0.0904593
\(197\) 9.92841 0.707370 0.353685 0.935365i \(-0.384929\pi\)
0.353685 + 0.935365i \(0.384929\pi\)
\(198\) 11.9509 0.849313
\(199\) 22.1854 1.57268 0.786342 0.617792i \(-0.211973\pi\)
0.786342 + 0.617792i \(0.211973\pi\)
\(200\) −2.79765 −0.197824
\(201\) 19.1637 1.35171
\(202\) 11.4197 0.803491
\(203\) −0.860600 −0.0604023
\(204\) 5.77685 0.404460
\(205\) 6.58941 0.460224
\(206\) 15.5904 1.08624
\(207\) −15.8764 −1.10349
\(208\) 0.498189 0.0345432
\(209\) −19.7139 −1.36364
\(210\) −2.25469 −0.155588
\(211\) 23.0559 1.58723 0.793616 0.608420i \(-0.208196\pi\)
0.793616 + 0.608420i \(0.208196\pi\)
\(212\) 9.93959 0.682654
\(213\) 40.1932 2.75399
\(214\) 7.78576 0.532224
\(215\) 0.110729 0.00755166
\(216\) 6.84916 0.466026
\(217\) −10.7794 −0.731757
\(218\) 4.33830 0.293827
\(219\) −20.7601 −1.40284
\(220\) 4.49646 0.303151
\(221\) 6.31456 0.424763
\(222\) −13.2838 −0.891552
\(223\) 0.903309 0.0604901 0.0302450 0.999543i \(-0.490371\pi\)
0.0302450 + 0.999543i \(0.490371\pi\)
\(224\) −5.71240 −0.381676
\(225\) 3.92999 0.261999
\(226\) −8.42801 −0.560623
\(227\) 2.24378 0.148925 0.0744625 0.997224i \(-0.476276\pi\)
0.0744625 + 0.997224i \(0.476276\pi\)
\(228\) −18.5111 −1.22593
\(229\) 1.00000 0.0660819
\(230\) 3.46005 0.228149
\(231\) 9.34663 0.614963
\(232\) −2.40766 −0.158071
\(233\) −2.56766 −0.168213 −0.0841065 0.996457i \(-0.526804\pi\)
−0.0841065 + 0.996457i \(0.526804\pi\)
\(234\) 12.2662 0.801869
\(235\) 3.16720 0.206605
\(236\) 16.7812 1.09236
\(237\) 12.7093 0.825559
\(238\) −1.48410 −0.0962001
\(239\) −13.5580 −0.876997 −0.438498 0.898732i \(-0.644489\pi\)
−0.438498 + 0.898732i \(0.644489\pi\)
\(240\) 0.359882 0.0232303
\(241\) −11.4220 −0.735759 −0.367879 0.929874i \(-0.619916\pi\)
−0.367879 + 0.929874i \(0.619916\pi\)
\(242\) 1.37553 0.0884223
\(243\) 21.4156 1.37381
\(244\) −11.6596 −0.746430
\(245\) −1.00000 −0.0638877
\(246\) 14.8571 0.947252
\(247\) −20.2341 −1.28746
\(248\) −30.1572 −1.91498
\(249\) −9.11305 −0.577516
\(250\) −0.856487 −0.0541690
\(251\) −13.9311 −0.879325 −0.439662 0.898163i \(-0.644902\pi\)
−0.439662 + 0.898163i \(0.644902\pi\)
\(252\) 4.97706 0.313525
\(253\) −14.3433 −0.901758
\(254\) −13.2497 −0.831358
\(255\) 4.56152 0.285654
\(256\) −15.6350 −0.977191
\(257\) 21.8309 1.36178 0.680888 0.732387i \(-0.261594\pi\)
0.680888 + 0.732387i \(0.261594\pi\)
\(258\) 0.249660 0.0155431
\(259\) −5.89164 −0.366089
\(260\) 4.61510 0.286216
\(261\) 3.38215 0.209350
\(262\) −10.0484 −0.620794
\(263\) 25.8202 1.59214 0.796070 0.605205i \(-0.206909\pi\)
0.796070 + 0.605205i \(0.206909\pi\)
\(264\) 26.1486 1.60934
\(265\) 7.84850 0.482130
\(266\) 4.75559 0.291584
\(267\) 38.4821 2.35506
\(268\) 9.21925 0.563155
\(269\) 5.58452 0.340494 0.170247 0.985401i \(-0.445543\pi\)
0.170247 + 0.985401i \(0.445543\pi\)
\(270\) 2.09683 0.127609
\(271\) −16.9554 −1.02996 −0.514982 0.857201i \(-0.672202\pi\)
−0.514982 + 0.857201i \(0.672202\pi\)
\(272\) 0.236885 0.0143633
\(273\) 9.59326 0.580610
\(274\) −17.3953 −1.05089
\(275\) 3.55049 0.214103
\(276\) −13.4682 −0.810690
\(277\) 4.18846 0.251660 0.125830 0.992052i \(-0.459841\pi\)
0.125830 + 0.992052i \(0.459841\pi\)
\(278\) −11.0360 −0.661893
\(279\) 42.3631 2.53621
\(280\) −2.79765 −0.167192
\(281\) 16.4708 0.982563 0.491282 0.871001i \(-0.336529\pi\)
0.491282 + 0.871001i \(0.336529\pi\)
\(282\) 7.14105 0.425244
\(283\) −14.2253 −0.845603 −0.422802 0.906222i \(-0.638953\pi\)
−0.422802 + 0.906222i \(0.638953\pi\)
\(284\) 19.3361 1.14738
\(285\) −14.6167 −0.865820
\(286\) 11.0818 0.655279
\(287\) 6.58941 0.388960
\(288\) 22.4496 1.32286
\(289\) −13.9975 −0.823381
\(290\) −0.737093 −0.0432836
\(291\) −32.3581 −1.89686
\(292\) −9.98724 −0.584459
\(293\) −15.5453 −0.908168 −0.454084 0.890959i \(-0.650033\pi\)
−0.454084 + 0.890959i \(0.650033\pi\)
\(294\) −2.25469 −0.131496
\(295\) 13.2508 0.771489
\(296\) −16.4828 −0.958042
\(297\) −8.69225 −0.504375
\(298\) 5.13197 0.297287
\(299\) −14.7218 −0.851384
\(300\) 3.33386 0.192481
\(301\) 0.110729 0.00638231
\(302\) 13.7012 0.788415
\(303\) −35.0996 −2.01642
\(304\) −0.759064 −0.0435353
\(305\) −9.20667 −0.527173
\(306\) 5.83251 0.333422
\(307\) 8.51363 0.485899 0.242949 0.970039i \(-0.421885\pi\)
0.242949 + 0.970039i \(0.421885\pi\)
\(308\) 4.49646 0.256209
\(309\) −47.9186 −2.72599
\(310\) −9.23245 −0.524368
\(311\) 33.5618 1.90312 0.951559 0.307467i \(-0.0994815\pi\)
0.951559 + 0.307467i \(0.0994815\pi\)
\(312\) 26.8386 1.51944
\(313\) 21.6056 1.22122 0.610609 0.791932i \(-0.290925\pi\)
0.610609 + 0.791932i \(0.290925\pi\)
\(314\) 5.66111 0.319475
\(315\) 3.92999 0.221430
\(316\) 6.11417 0.343949
\(317\) 18.7062 1.05065 0.525323 0.850903i \(-0.323944\pi\)
0.525323 + 0.850903i \(0.323944\pi\)
\(318\) 17.6959 0.992339
\(319\) 3.05556 0.171078
\(320\) −4.61918 −0.258220
\(321\) −23.9302 −1.33565
\(322\) 3.46005 0.192821
\(323\) −9.62116 −0.535336
\(324\) 6.76928 0.376071
\(325\) 3.64418 0.202143
\(326\) 10.7664 0.596298
\(327\) −13.3342 −0.737380
\(328\) 18.4349 1.01790
\(329\) 3.16720 0.174613
\(330\) 8.00526 0.440675
\(331\) −12.3498 −0.678806 −0.339403 0.940641i \(-0.610225\pi\)
−0.339403 + 0.940641i \(0.610225\pi\)
\(332\) −4.38408 −0.240608
\(333\) 23.1541 1.26884
\(334\) −6.65987 −0.364412
\(335\) 7.27971 0.397733
\(336\) 0.359882 0.0196332
\(337\) 24.4158 1.33001 0.665007 0.746837i \(-0.268428\pi\)
0.665007 + 0.746837i \(0.268428\pi\)
\(338\) 0.239855 0.0130464
\(339\) 25.9042 1.40693
\(340\) 2.19445 0.119011
\(341\) 38.2724 2.07257
\(342\) −18.6894 −1.01061
\(343\) −1.00000 −0.0539949
\(344\) 0.309782 0.0167023
\(345\) −10.6348 −0.572556
\(346\) 11.2512 0.604866
\(347\) −28.4587 −1.52774 −0.763870 0.645370i \(-0.776703\pi\)
−0.763870 + 0.645370i \(0.776703\pi\)
\(348\) 2.86912 0.153801
\(349\) −7.48265 −0.400537 −0.200269 0.979741i \(-0.564181\pi\)
−0.200269 + 0.979741i \(0.564181\pi\)
\(350\) −0.856487 −0.0457811
\(351\) −8.92161 −0.476200
\(352\) 20.2818 1.08103
\(353\) 34.5266 1.83767 0.918833 0.394645i \(-0.129133\pi\)
0.918833 + 0.394645i \(0.129133\pi\)
\(354\) 29.8763 1.58791
\(355\) 15.2682 0.810350
\(356\) 18.5129 0.981180
\(357\) 4.56152 0.241421
\(358\) −20.9573 −1.10763
\(359\) 27.0624 1.42830 0.714149 0.699994i \(-0.246814\pi\)
0.714149 + 0.699994i \(0.246814\pi\)
\(360\) 10.9947 0.579474
\(361\) 11.8296 0.622610
\(362\) −3.71699 −0.195361
\(363\) −4.22781 −0.221902
\(364\) 4.61510 0.241897
\(365\) −7.88613 −0.412779
\(366\) −20.7582 −1.08505
\(367\) −30.2584 −1.57948 −0.789738 0.613444i \(-0.789783\pi\)
−0.789738 + 0.613444i \(0.789783\pi\)
\(368\) −0.552275 −0.0287893
\(369\) −25.8963 −1.34811
\(370\) −5.04611 −0.262335
\(371\) 7.84850 0.407474
\(372\) 35.9372 1.86326
\(373\) 17.8223 0.922804 0.461402 0.887191i \(-0.347347\pi\)
0.461402 + 0.887191i \(0.347347\pi\)
\(374\) 5.26930 0.272469
\(375\) 2.63249 0.135941
\(376\) 8.86073 0.456957
\(377\) 3.13618 0.161522
\(378\) 2.09683 0.107849
\(379\) 19.4051 0.996772 0.498386 0.866955i \(-0.333926\pi\)
0.498386 + 0.866955i \(0.333926\pi\)
\(380\) −7.03178 −0.360723
\(381\) 40.7240 2.08635
\(382\) 17.3849 0.889490
\(383\) 2.54839 0.130217 0.0651084 0.997878i \(-0.479261\pi\)
0.0651084 + 0.997878i \(0.479261\pi\)
\(384\) 19.6608 1.00331
\(385\) 3.55049 0.180950
\(386\) −0.250351 −0.0127425
\(387\) −0.435164 −0.0221206
\(388\) −15.5667 −0.790282
\(389\) 25.9129 1.31384 0.656918 0.753962i \(-0.271860\pi\)
0.656918 + 0.753962i \(0.271860\pi\)
\(390\) 8.21649 0.416058
\(391\) −7.00011 −0.354011
\(392\) −2.79765 −0.141303
\(393\) 30.8847 1.55793
\(394\) 8.50355 0.428402
\(395\) 4.82787 0.242917
\(396\) −17.6710 −0.888002
\(397\) 21.3591 1.07198 0.535992 0.844223i \(-0.319938\pi\)
0.535992 + 0.844223i \(0.319938\pi\)
\(398\) 19.0015 0.952460
\(399\) −14.6167 −0.731752
\(400\) 0.136708 0.00683541
\(401\) −0.353510 −0.0176535 −0.00882673 0.999961i \(-0.502810\pi\)
−0.00882673 + 0.999961i \(0.502810\pi\)
\(402\) 16.4135 0.818631
\(403\) 39.2823 1.95679
\(404\) −16.8856 −0.840092
\(405\) 5.34516 0.265603
\(406\) −0.737093 −0.0365813
\(407\) 20.9182 1.03688
\(408\) 12.7616 0.631791
\(409\) 16.1106 0.796619 0.398310 0.917251i \(-0.369597\pi\)
0.398310 + 0.917251i \(0.369597\pi\)
\(410\) 5.64374 0.278724
\(411\) 53.4659 2.63728
\(412\) −23.0526 −1.13572
\(413\) 13.2508 0.652027
\(414\) −13.5979 −0.668302
\(415\) −3.46176 −0.169931
\(416\) 20.8170 1.02064
\(417\) 33.9200 1.66107
\(418\) −16.8847 −0.825858
\(419\) −8.54075 −0.417243 −0.208621 0.977996i \(-0.566898\pi\)
−0.208621 + 0.977996i \(0.566898\pi\)
\(420\) 3.33386 0.162676
\(421\) 2.00275 0.0976079 0.0488039 0.998808i \(-0.484459\pi\)
0.0488039 + 0.998808i \(0.484459\pi\)
\(422\) 19.7470 0.961271
\(423\) −12.4471 −0.605197
\(424\) 21.9574 1.06635
\(425\) 1.73278 0.0840522
\(426\) 34.4250 1.66789
\(427\) −9.20667 −0.445542
\(428\) −11.5123 −0.556468
\(429\) −34.0608 −1.64447
\(430\) 0.0948379 0.00457349
\(431\) 16.0059 0.770975 0.385488 0.922713i \(-0.374033\pi\)
0.385488 + 0.922713i \(0.374033\pi\)
\(432\) −0.334686 −0.0161026
\(433\) −32.3465 −1.55447 −0.777237 0.629207i \(-0.783380\pi\)
−0.777237 + 0.629207i \(0.783380\pi\)
\(434\) −9.23245 −0.443172
\(435\) 2.26552 0.108623
\(436\) −6.41476 −0.307211
\(437\) 22.4308 1.07301
\(438\) −17.7808 −0.849598
\(439\) 4.83225 0.230631 0.115315 0.993329i \(-0.463212\pi\)
0.115315 + 0.993329i \(0.463212\pi\)
\(440\) 9.93306 0.473540
\(441\) 3.92999 0.187142
\(442\) 5.40834 0.257248
\(443\) −19.0604 −0.905586 −0.452793 0.891616i \(-0.649572\pi\)
−0.452793 + 0.891616i \(0.649572\pi\)
\(444\) 19.6419 0.932165
\(445\) 14.6181 0.692967
\(446\) 0.773672 0.0366345
\(447\) −15.7736 −0.746064
\(448\) −4.61918 −0.218236
\(449\) −30.4444 −1.43676 −0.718380 0.695651i \(-0.755116\pi\)
−0.718380 + 0.695651i \(0.755116\pi\)
\(450\) 3.36598 0.158674
\(451\) −23.3957 −1.10166
\(452\) 12.4620 0.586161
\(453\) −42.1118 −1.97859
\(454\) 1.92177 0.0901930
\(455\) 3.64418 0.170842
\(456\) −40.8925 −1.91497
\(457\) −17.3648 −0.812292 −0.406146 0.913808i \(-0.633128\pi\)
−0.406146 + 0.913808i \(0.633128\pi\)
\(458\) 0.856487 0.0400210
\(459\) −4.24216 −0.198007
\(460\) −5.11615 −0.238542
\(461\) −31.9156 −1.48646 −0.743230 0.669036i \(-0.766707\pi\)
−0.743230 + 0.669036i \(0.766707\pi\)
\(462\) 8.00526 0.372439
\(463\) −29.7968 −1.38477 −0.692386 0.721527i \(-0.743441\pi\)
−0.692386 + 0.721527i \(0.743441\pi\)
\(464\) 0.117651 0.00546181
\(465\) 28.3768 1.31594
\(466\) −2.19917 −0.101874
\(467\) 18.5892 0.860207 0.430103 0.902780i \(-0.358477\pi\)
0.430103 + 0.902780i \(0.358477\pi\)
\(468\) −18.1373 −0.838396
\(469\) 7.27971 0.336146
\(470\) 2.71266 0.125126
\(471\) −17.3999 −0.801746
\(472\) 37.0710 1.70633
\(473\) −0.393143 −0.0180767
\(474\) 10.8854 0.499981
\(475\) −5.55244 −0.254763
\(476\) 2.19445 0.100582
\(477\) −30.8445 −1.41227
\(478\) −11.6123 −0.531133
\(479\) 35.0047 1.59941 0.799703 0.600396i \(-0.204990\pi\)
0.799703 + 0.600396i \(0.204990\pi\)
\(480\) 15.0378 0.686379
\(481\) 21.4702 0.978957
\(482\) −9.78283 −0.445596
\(483\) −10.6348 −0.483898
\(484\) −2.03390 −0.0924502
\(485\) −12.2918 −0.558143
\(486\) 18.3422 0.832018
\(487\) −3.71353 −0.168276 −0.0841380 0.996454i \(-0.526814\pi\)
−0.0841380 + 0.996454i \(0.526814\pi\)
\(488\) −25.7571 −1.16597
\(489\) −33.0916 −1.49646
\(490\) −0.856487 −0.0386921
\(491\) −12.8128 −0.578233 −0.289116 0.957294i \(-0.593361\pi\)
−0.289116 + 0.957294i \(0.593361\pi\)
\(492\) −21.9682 −0.990402
\(493\) 1.49123 0.0671617
\(494\) −17.3302 −0.779724
\(495\) −13.9534 −0.627159
\(496\) 1.47364 0.0661683
\(497\) 15.2682 0.684870
\(498\) −7.80520 −0.349759
\(499\) 9.59370 0.429473 0.214736 0.976672i \(-0.431111\pi\)
0.214736 + 0.976672i \(0.431111\pi\)
\(500\) 1.26643 0.0566365
\(501\) 20.4697 0.914519
\(502\) −11.9318 −0.532543
\(503\) 27.6814 1.23425 0.617127 0.786864i \(-0.288296\pi\)
0.617127 + 0.786864i \(0.288296\pi\)
\(504\) 10.9947 0.489745
\(505\) −13.3332 −0.593322
\(506\) −12.2849 −0.546130
\(507\) −0.737217 −0.0327409
\(508\) 19.5914 0.869228
\(509\) −22.5672 −1.00028 −0.500138 0.865946i \(-0.666717\pi\)
−0.500138 + 0.865946i \(0.666717\pi\)
\(510\) 3.90688 0.173000
\(511\) −7.88613 −0.348862
\(512\) 1.54585 0.0683178
\(513\) 13.5934 0.600162
\(514\) 18.6979 0.824729
\(515\) −18.2028 −0.802111
\(516\) −0.369155 −0.0162512
\(517\) −11.2451 −0.494560
\(518\) −5.04611 −0.221714
\(519\) −34.5814 −1.51796
\(520\) 10.1952 0.447087
\(521\) 37.2192 1.63060 0.815301 0.579038i \(-0.196572\pi\)
0.815301 + 0.579038i \(0.196572\pi\)
\(522\) 2.89676 0.126788
\(523\) 30.7280 1.34364 0.671821 0.740714i \(-0.265513\pi\)
0.671821 + 0.740714i \(0.265513\pi\)
\(524\) 14.8579 0.649073
\(525\) 2.63249 0.114891
\(526\) 22.1146 0.964244
\(527\) 18.6784 0.813645
\(528\) −1.27776 −0.0556074
\(529\) −6.67990 −0.290430
\(530\) 6.72214 0.291991
\(531\) −52.0753 −2.25987
\(532\) −7.03178 −0.304866
\(533\) −24.0130 −1.04012
\(534\) 32.9594 1.42629
\(535\) −9.09035 −0.393010
\(536\) 20.3661 0.879682
\(537\) 64.4140 2.77967
\(538\) 4.78307 0.206213
\(539\) 3.55049 0.152931
\(540\) −3.10045 −0.133422
\(541\) −32.4936 −1.39701 −0.698506 0.715605i \(-0.746151\pi\)
−0.698506 + 0.715605i \(0.746151\pi\)
\(542\) −14.5220 −0.623775
\(543\) 11.4245 0.490272
\(544\) 9.89833 0.424387
\(545\) −5.06523 −0.216971
\(546\) 8.21649 0.351634
\(547\) 31.4853 1.34621 0.673107 0.739545i \(-0.264959\pi\)
0.673107 + 0.739545i \(0.264959\pi\)
\(548\) 25.7212 1.09876
\(549\) 36.1821 1.54421
\(550\) 3.04095 0.129667
\(551\) −4.77843 −0.203568
\(552\) −29.7524 −1.26635
\(553\) 4.82787 0.205302
\(554\) 3.58736 0.152412
\(555\) 15.5097 0.658349
\(556\) 16.3182 0.692044
\(557\) 21.6638 0.917923 0.458961 0.888456i \(-0.348222\pi\)
0.458961 + 0.888456i \(0.348222\pi\)
\(558\) 36.2834 1.53600
\(559\) −0.403516 −0.0170669
\(560\) 0.136708 0.00577697
\(561\) −16.1957 −0.683781
\(562\) 14.1070 0.595067
\(563\) −18.1117 −0.763318 −0.381659 0.924303i \(-0.624647\pi\)
−0.381659 + 0.924303i \(0.624647\pi\)
\(564\) −10.5590 −0.444614
\(565\) 9.84021 0.413981
\(566\) −12.1837 −0.512121
\(567\) 5.34516 0.224476
\(568\) 42.7150 1.79228
\(569\) 4.56776 0.191491 0.0957453 0.995406i \(-0.469477\pi\)
0.0957453 + 0.995406i \(0.469477\pi\)
\(570\) −12.5190 −0.524364
\(571\) −3.16213 −0.132331 −0.0661656 0.997809i \(-0.521077\pi\)
−0.0661656 + 0.997809i \(0.521077\pi\)
\(572\) −16.3859 −0.685129
\(573\) −53.4341 −2.23224
\(574\) 5.64374 0.235565
\(575\) −4.03981 −0.168472
\(576\) 18.1533 0.756388
\(577\) 37.6863 1.56890 0.784450 0.620192i \(-0.212945\pi\)
0.784450 + 0.620192i \(0.212945\pi\)
\(578\) −11.9886 −0.498662
\(579\) 0.769475 0.0319783
\(580\) 1.08989 0.0452552
\(581\) −3.46176 −0.143618
\(582\) −27.7142 −1.14879
\(583\) −27.8661 −1.15409
\(584\) −22.0627 −0.912959
\(585\) −14.3216 −0.592124
\(586\) −13.3144 −0.550012
\(587\) 14.6206 0.603455 0.301727 0.953394i \(-0.402437\pi\)
0.301727 + 0.953394i \(0.402437\pi\)
\(588\) 3.33386 0.137486
\(589\) −59.8522 −2.46617
\(590\) 11.3491 0.467235
\(591\) −26.1364 −1.07511
\(592\) 0.805435 0.0331032
\(593\) −22.8867 −0.939843 −0.469922 0.882708i \(-0.655718\pi\)
−0.469922 + 0.882708i \(0.655718\pi\)
\(594\) −7.44479 −0.305464
\(595\) 1.73278 0.0710371
\(596\) −7.58831 −0.310829
\(597\) −58.4028 −2.39027
\(598\) −12.6090 −0.515622
\(599\) −33.3985 −1.36463 −0.682313 0.731061i \(-0.739026\pi\)
−0.682313 + 0.731061i \(0.739026\pi\)
\(600\) 7.36479 0.300666
\(601\) 22.8200 0.930847 0.465424 0.885088i \(-0.345902\pi\)
0.465424 + 0.885088i \(0.345902\pi\)
\(602\) 0.0948379 0.00386531
\(603\) −28.6092 −1.16506
\(604\) −20.2591 −0.824329
\(605\) −1.60601 −0.0652937
\(606\) −30.0623 −1.22120
\(607\) 9.56943 0.388411 0.194206 0.980961i \(-0.437787\pi\)
0.194206 + 0.980961i \(0.437787\pi\)
\(608\) −31.7177 −1.28632
\(609\) 2.26552 0.0918035
\(610\) −7.88539 −0.319270
\(611\) −11.5418 −0.466933
\(612\) −8.62415 −0.348610
\(613\) 20.6257 0.833066 0.416533 0.909121i \(-0.363245\pi\)
0.416533 + 0.909121i \(0.363245\pi\)
\(614\) 7.29181 0.294274
\(615\) −17.3465 −0.699480
\(616\) 9.93306 0.400214
\(617\) −17.5933 −0.708281 −0.354141 0.935192i \(-0.615227\pi\)
−0.354141 + 0.935192i \(0.615227\pi\)
\(618\) −41.0416 −1.65094
\(619\) −6.00625 −0.241412 −0.120706 0.992688i \(-0.538516\pi\)
−0.120706 + 0.992688i \(0.538516\pi\)
\(620\) 13.6514 0.548254
\(621\) 9.89019 0.396880
\(622\) 28.7453 1.15258
\(623\) 14.6181 0.585664
\(624\) −1.31148 −0.0525011
\(625\) 1.00000 0.0400000
\(626\) 18.5049 0.739603
\(627\) 51.8966 2.07255
\(628\) −8.37072 −0.334028
\(629\) 10.2089 0.407056
\(630\) 3.36598 0.134104
\(631\) 6.01438 0.239429 0.119714 0.992808i \(-0.461802\pi\)
0.119714 + 0.992808i \(0.461802\pi\)
\(632\) 13.5067 0.537269
\(633\) −60.6943 −2.41238
\(634\) 16.0216 0.636301
\(635\) 15.4698 0.613899
\(636\) −26.1658 −1.03754
\(637\) 3.64418 0.144388
\(638\) 2.61704 0.103610
\(639\) −60.0037 −2.37371
\(640\) 7.46853 0.295220
\(641\) −46.0811 −1.82009 −0.910046 0.414506i \(-0.863954\pi\)
−0.910046 + 0.414506i \(0.863954\pi\)
\(642\) −20.4959 −0.808909
\(643\) 17.8923 0.705602 0.352801 0.935698i \(-0.385229\pi\)
0.352801 + 0.935698i \(0.385229\pi\)
\(644\) −5.11615 −0.201604
\(645\) −0.291493 −0.0114775
\(646\) −8.24039 −0.324214
\(647\) 34.0425 1.33835 0.669174 0.743106i \(-0.266648\pi\)
0.669174 + 0.743106i \(0.266648\pi\)
\(648\) 14.9539 0.587445
\(649\) −47.0467 −1.84675
\(650\) 3.12119 0.122423
\(651\) 28.3768 1.11217
\(652\) −15.9196 −0.623461
\(653\) −26.9418 −1.05431 −0.527157 0.849768i \(-0.676742\pi\)
−0.527157 + 0.849768i \(0.676742\pi\)
\(654\) −11.4205 −0.446578
\(655\) 11.7321 0.458413
\(656\) −0.900825 −0.0351713
\(657\) 30.9924 1.20913
\(658\) 2.71266 0.105751
\(659\) 8.55450 0.333236 0.166618 0.986022i \(-0.446715\pi\)
0.166618 + 0.986022i \(0.446715\pi\)
\(660\) −11.8369 −0.460749
\(661\) 11.8917 0.462533 0.231267 0.972890i \(-0.425713\pi\)
0.231267 + 0.972890i \(0.425713\pi\)
\(662\) −10.5774 −0.411103
\(663\) −16.6230 −0.645584
\(664\) −9.68481 −0.375844
\(665\) −5.55244 −0.215314
\(666\) 19.8312 0.768442
\(667\) −3.47667 −0.134617
\(668\) 9.84751 0.381012
\(669\) −2.37795 −0.0919369
\(670\) 6.23498 0.240878
\(671\) 32.6882 1.26192
\(672\) 15.0378 0.580096
\(673\) 41.9195 1.61588 0.807939 0.589266i \(-0.200583\pi\)
0.807939 + 0.589266i \(0.200583\pi\)
\(674\) 20.9118 0.805493
\(675\) −2.44818 −0.0942305
\(676\) −0.354659 −0.0136407
\(677\) 28.3631 1.09008 0.545041 0.838409i \(-0.316514\pi\)
0.545041 + 0.838409i \(0.316514\pi\)
\(678\) 22.1866 0.852072
\(679\) −12.2918 −0.471717
\(680\) 4.84772 0.185902
\(681\) −5.90672 −0.226346
\(682\) 32.7798 1.25520
\(683\) −24.8857 −0.952225 −0.476112 0.879384i \(-0.657954\pi\)
−0.476112 + 0.879384i \(0.657954\pi\)
\(684\) 27.6348 1.05664
\(685\) 20.3100 0.776006
\(686\) −0.856487 −0.0327008
\(687\) −2.63249 −0.100436
\(688\) −0.0151376 −0.000577114 0
\(689\) −28.6014 −1.08962
\(690\) −9.10853 −0.346756
\(691\) −42.4390 −1.61445 −0.807227 0.590240i \(-0.799033\pi\)
−0.807227 + 0.590240i \(0.799033\pi\)
\(692\) −16.6364 −0.632419
\(693\) −13.9534 −0.530046
\(694\) −24.3745 −0.925242
\(695\) 12.8852 0.488762
\(696\) 6.33814 0.240247
\(697\) −11.4180 −0.432487
\(698\) −6.40879 −0.242576
\(699\) 6.75933 0.255662
\(700\) 1.26643 0.0478666
\(701\) −46.0102 −1.73778 −0.868891 0.495003i \(-0.835167\pi\)
−0.868891 + 0.495003i \(0.835167\pi\)
\(702\) −7.64124 −0.288400
\(703\) −32.7130 −1.23379
\(704\) 16.4004 0.618112
\(705\) −8.33761 −0.314013
\(706\) 29.5716 1.11294
\(707\) −13.3332 −0.501448
\(708\) −44.1762 −1.66024
\(709\) −16.9925 −0.638167 −0.319083 0.947727i \(-0.603375\pi\)
−0.319083 + 0.947727i \(0.603375\pi\)
\(710\) 13.0770 0.490770
\(711\) −18.9735 −0.711561
\(712\) 40.8965 1.53266
\(713\) −43.5470 −1.63085
\(714\) 3.90688 0.146211
\(715\) −12.9386 −0.483878
\(716\) 30.9882 1.15808
\(717\) 35.6914 1.33292
\(718\) 23.1786 0.865017
\(719\) −10.0471 −0.374695 −0.187348 0.982294i \(-0.559989\pi\)
−0.187348 + 0.982294i \(0.559989\pi\)
\(720\) −0.537261 −0.0200225
\(721\) −18.2028 −0.677907
\(722\) 10.1319 0.377070
\(723\) 30.0684 1.11826
\(724\) 5.49607 0.204260
\(725\) 0.860600 0.0319619
\(726\) −3.62106 −0.134390
\(727\) −12.4464 −0.461613 −0.230806 0.973000i \(-0.574136\pi\)
−0.230806 + 0.973000i \(0.574136\pi\)
\(728\) 10.1952 0.377858
\(729\) −40.3408 −1.49410
\(730\) −6.75436 −0.249990
\(731\) −0.191869 −0.00709653
\(732\) 30.6938 1.13447
\(733\) 11.6226 0.429290 0.214645 0.976692i \(-0.431141\pi\)
0.214645 + 0.976692i \(0.431141\pi\)
\(734\) −25.9159 −0.956574
\(735\) 2.63249 0.0971007
\(736\) −23.0770 −0.850630
\(737\) −25.8466 −0.952071
\(738\) −22.1798 −0.816451
\(739\) −23.1131 −0.850228 −0.425114 0.905140i \(-0.639766\pi\)
−0.425114 + 0.905140i \(0.639766\pi\)
\(740\) 7.46136 0.274285
\(741\) 53.2660 1.95677
\(742\) 6.72214 0.246777
\(743\) −21.3039 −0.781563 −0.390781 0.920484i \(-0.627795\pi\)
−0.390781 + 0.920484i \(0.627795\pi\)
\(744\) 79.3884 2.91052
\(745\) −5.99189 −0.219526
\(746\) 15.2646 0.558875
\(747\) 13.6047 0.497769
\(748\) −7.79137 −0.284881
\(749\) −9.09035 −0.332154
\(750\) 2.25469 0.0823296
\(751\) −4.55756 −0.166308 −0.0831539 0.996537i \(-0.526499\pi\)
−0.0831539 + 0.996537i \(0.526499\pi\)
\(752\) −0.432982 −0.0157892
\(753\) 36.6735 1.33646
\(754\) 2.68610 0.0978219
\(755\) −15.9970 −0.582189
\(756\) −3.10045 −0.112762
\(757\) −20.7668 −0.754781 −0.377390 0.926054i \(-0.623178\pi\)
−0.377390 + 0.926054i \(0.623178\pi\)
\(758\) 16.6202 0.603672
\(759\) 37.7587 1.37055
\(760\) −15.5338 −0.563470
\(761\) 29.2905 1.06178 0.530889 0.847441i \(-0.321858\pi\)
0.530889 + 0.847441i \(0.321858\pi\)
\(762\) 34.8796 1.26355
\(763\) −5.06523 −0.183374
\(764\) −25.7059 −0.930009
\(765\) −6.80980 −0.246209
\(766\) 2.18267 0.0788629
\(767\) −48.2881 −1.74358
\(768\) 41.1591 1.48520
\(769\) 27.8095 1.00284 0.501419 0.865205i \(-0.332812\pi\)
0.501419 + 0.865205i \(0.332812\pi\)
\(770\) 3.04095 0.109588
\(771\) −57.4697 −2.06972
\(772\) 0.370177 0.0133230
\(773\) 19.0304 0.684475 0.342237 0.939614i \(-0.388815\pi\)
0.342237 + 0.939614i \(0.388815\pi\)
\(774\) −0.372712 −0.0133969
\(775\) 10.7794 0.387209
\(776\) −34.3883 −1.23447
\(777\) 15.5097 0.556406
\(778\) 22.1941 0.795696
\(779\) 36.5873 1.31088
\(780\) −12.1492 −0.435011
\(781\) −54.2095 −1.93977
\(782\) −5.99550 −0.214399
\(783\) −2.10690 −0.0752946
\(784\) 0.136708 0.00488243
\(785\) −6.60969 −0.235910
\(786\) 26.4523 0.943524
\(787\) 6.21902 0.221684 0.110842 0.993838i \(-0.464645\pi\)
0.110842 + 0.993838i \(0.464645\pi\)
\(788\) −12.5736 −0.447917
\(789\) −67.9712 −2.41984
\(790\) 4.13501 0.147117
\(791\) 9.84021 0.349878
\(792\) −39.0368 −1.38711
\(793\) 33.5508 1.19142
\(794\) 18.2938 0.649223
\(795\) −20.6611 −0.732773
\(796\) −28.0963 −0.995847
\(797\) 31.0263 1.09901 0.549504 0.835491i \(-0.314817\pi\)
0.549504 + 0.835491i \(0.314817\pi\)
\(798\) −12.5190 −0.443169
\(799\) −5.48806 −0.194154
\(800\) 5.71240 0.201964
\(801\) −57.4491 −2.02987
\(802\) −0.302777 −0.0106914
\(803\) 27.9997 0.988087
\(804\) −24.2696 −0.855921
\(805\) −4.03981 −0.142385
\(806\) 33.6447 1.18508
\(807\) −14.7012 −0.517506
\(808\) −37.3018 −1.31227
\(809\) 30.8294 1.08390 0.541952 0.840410i \(-0.317686\pi\)
0.541952 + 0.840410i \(0.317686\pi\)
\(810\) 4.57806 0.160857
\(811\) −5.90206 −0.207249 −0.103625 0.994616i \(-0.533044\pi\)
−0.103625 + 0.994616i \(0.533044\pi\)
\(812\) 1.08989 0.0382477
\(813\) 44.6348 1.56541
\(814\) 17.9162 0.627962
\(815\) −12.5705 −0.440325
\(816\) −0.623597 −0.0218303
\(817\) 0.614816 0.0215097
\(818\) 13.7985 0.482455
\(819\) −14.3216 −0.500437
\(820\) −8.34503 −0.291421
\(821\) 12.5323 0.437381 0.218690 0.975794i \(-0.429821\pi\)
0.218690 + 0.975794i \(0.429821\pi\)
\(822\) 45.7928 1.59721
\(823\) 24.7168 0.861573 0.430787 0.902454i \(-0.358236\pi\)
0.430787 + 0.902454i \(0.358236\pi\)
\(824\) −50.9251 −1.77406
\(825\) −9.34663 −0.325408
\(826\) 11.3491 0.394885
\(827\) −40.7361 −1.41653 −0.708267 0.705944i \(-0.750523\pi\)
−0.708267 + 0.705944i \(0.750523\pi\)
\(828\) 20.1064 0.698745
\(829\) 19.2353 0.668071 0.334036 0.942560i \(-0.391589\pi\)
0.334036 + 0.942560i \(0.391589\pi\)
\(830\) −2.96495 −0.102915
\(831\) −11.0261 −0.382490
\(832\) 16.8331 0.583583
\(833\) 1.73278 0.0600373
\(834\) 29.0520 1.00599
\(835\) 7.77580 0.269093
\(836\) 24.9663 0.863478
\(837\) −26.3900 −0.912173
\(838\) −7.31503 −0.252694
\(839\) 37.9958 1.31176 0.655881 0.754864i \(-0.272297\pi\)
0.655881 + 0.754864i \(0.272297\pi\)
\(840\) 7.36479 0.254109
\(841\) −28.2594 −0.974461
\(842\) 1.71532 0.0591140
\(843\) −43.3591 −1.49337
\(844\) −29.1987 −1.00506
\(845\) −0.280046 −0.00963387
\(846\) −10.6607 −0.366524
\(847\) −1.60601 −0.0551833
\(848\) −1.07295 −0.0368454
\(849\) 37.4478 1.28520
\(850\) 1.48410 0.0509043
\(851\) −23.8011 −0.815893
\(852\) −50.9019 −1.74387
\(853\) 28.9980 0.992874 0.496437 0.868073i \(-0.334641\pi\)
0.496437 + 0.868073i \(0.334641\pi\)
\(854\) −7.88539 −0.269833
\(855\) 21.8210 0.746263
\(856\) −25.4317 −0.869236
\(857\) 44.4439 1.51817 0.759087 0.650990i \(-0.225646\pi\)
0.759087 + 0.650990i \(0.225646\pi\)
\(858\) −29.1726 −0.995937
\(859\) −25.3916 −0.866352 −0.433176 0.901309i \(-0.642607\pi\)
−0.433176 + 0.901309i \(0.642607\pi\)
\(860\) −0.140231 −0.00478182
\(861\) −17.3465 −0.591168
\(862\) 13.7088 0.466924
\(863\) 10.9023 0.371119 0.185559 0.982633i \(-0.440590\pi\)
0.185559 + 0.982633i \(0.440590\pi\)
\(864\) −13.9850 −0.475778
\(865\) −13.1364 −0.446651
\(866\) −27.7044 −0.941433
\(867\) 36.8482 1.25143
\(868\) 13.6514 0.463360
\(869\) −17.1413 −0.581480
\(870\) 1.94039 0.0657853
\(871\) −26.5286 −0.898887
\(872\) −14.1708 −0.479883
\(873\) 48.3067 1.63493
\(874\) 19.2117 0.649846
\(875\) 1.00000 0.0338062
\(876\) 26.2913 0.888300
\(877\) 5.88907 0.198860 0.0994299 0.995045i \(-0.468298\pi\)
0.0994299 + 0.995045i \(0.468298\pi\)
\(878\) 4.13876 0.139676
\(879\) 40.9229 1.38029
\(880\) −0.485381 −0.0163622
\(881\) −50.5002 −1.70139 −0.850697 0.525656i \(-0.823820\pi\)
−0.850697 + 0.525656i \(0.823820\pi\)
\(882\) 3.36598 0.113338
\(883\) −53.2629 −1.79244 −0.896220 0.443610i \(-0.853698\pi\)
−0.896220 + 0.443610i \(0.853698\pi\)
\(884\) −7.99696 −0.268967
\(885\) −34.8824 −1.17256
\(886\) −16.3250 −0.548448
\(887\) −6.12696 −0.205723 −0.102862 0.994696i \(-0.532800\pi\)
−0.102862 + 0.994696i \(0.532800\pi\)
\(888\) 43.3907 1.45610
\(889\) 15.4698 0.518840
\(890\) 12.5202 0.419680
\(891\) −18.9780 −0.635786
\(892\) −1.14398 −0.0383032
\(893\) 17.5857 0.588483
\(894\) −13.5098 −0.451837
\(895\) 24.4689 0.817905
\(896\) 7.46853 0.249506
\(897\) 38.7550 1.29399
\(898\) −26.0752 −0.870141
\(899\) 9.27680 0.309399
\(900\) −4.97706 −0.165902
\(901\) −13.5997 −0.453073
\(902\) −20.0381 −0.667195
\(903\) −0.291493 −0.00970027
\(904\) 27.5295 0.915618
\(905\) 4.33981 0.144260
\(906\) −36.0682 −1.19829
\(907\) −0.680992 −0.0226120 −0.0113060 0.999936i \(-0.503599\pi\)
−0.0113060 + 0.999936i \(0.503599\pi\)
\(908\) −2.84159 −0.0943016
\(909\) 52.3995 1.73798
\(910\) 3.12119 0.103466
\(911\) 27.1975 0.901095 0.450547 0.892752i \(-0.351229\pi\)
0.450547 + 0.892752i \(0.351229\pi\)
\(912\) 1.99823 0.0661678
\(913\) 12.2910 0.406772
\(914\) −14.8727 −0.491947
\(915\) 24.2364 0.801232
\(916\) −1.26643 −0.0418440
\(917\) 11.7321 0.387430
\(918\) −3.63335 −0.119918
\(919\) 52.4848 1.73132 0.865658 0.500636i \(-0.166901\pi\)
0.865658 + 0.500636i \(0.166901\pi\)
\(920\) −11.3020 −0.372616
\(921\) −22.4120 −0.738501
\(922\) −27.3353 −0.900241
\(923\) −55.6399 −1.83141
\(924\) −11.8369 −0.389404
\(925\) 5.89164 0.193716
\(926\) −25.5205 −0.838657
\(927\) 71.5367 2.34957
\(928\) 4.91609 0.161379
\(929\) 24.4566 0.802396 0.401198 0.915991i \(-0.368594\pi\)
0.401198 + 0.915991i \(0.368594\pi\)
\(930\) 24.3043 0.796970
\(931\) −5.55244 −0.181974
\(932\) 3.25176 0.106515
\(933\) −88.3511 −2.89249
\(934\) 15.9214 0.520965
\(935\) −6.15223 −0.201199
\(936\) −40.0668 −1.30963
\(937\) −22.7369 −0.742782 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(938\) 6.23498 0.203579
\(939\) −56.8763 −1.85609
\(940\) −4.01104 −0.130826
\(941\) 55.5343 1.81037 0.905183 0.425022i \(-0.139734\pi\)
0.905183 + 0.425022i \(0.139734\pi\)
\(942\) −14.9028 −0.485560
\(943\) 26.6200 0.866866
\(944\) −1.81149 −0.0589588
\(945\) −2.44818 −0.0796393
\(946\) −0.336722 −0.0109478
\(947\) −28.2234 −0.917138 −0.458569 0.888659i \(-0.651638\pi\)
−0.458569 + 0.888659i \(0.651638\pi\)
\(948\) −16.0955 −0.522757
\(949\) 28.7385 0.932890
\(950\) −4.75559 −0.154292
\(951\) −49.2439 −1.59684
\(952\) 4.84772 0.157116
\(953\) 0.665028 0.0215424 0.0107712 0.999942i \(-0.496571\pi\)
0.0107712 + 0.999942i \(0.496571\pi\)
\(954\) −26.4179 −0.855312
\(955\) −20.2980 −0.656826
\(956\) 17.1703 0.555328
\(957\) −8.04371 −0.260016
\(958\) 29.9811 0.968644
\(959\) 20.3100 0.655845
\(960\) 12.1599 0.392460
\(961\) 85.1965 2.74828
\(962\) 18.3889 0.592883
\(963\) 35.7250 1.15122
\(964\) 14.4652 0.465894
\(965\) 0.292300 0.00940946
\(966\) −9.10853 −0.293062
\(967\) −30.8715 −0.992760 −0.496380 0.868105i \(-0.665338\pi\)
−0.496380 + 0.868105i \(0.665338\pi\)
\(968\) −4.49307 −0.144413
\(969\) 25.3276 0.813639
\(970\) −10.5278 −0.338027
\(971\) −33.4091 −1.07215 −0.536075 0.844170i \(-0.680094\pi\)
−0.536075 + 0.844170i \(0.680094\pi\)
\(972\) −27.1214 −0.869919
\(973\) 12.8852 0.413079
\(974\) −3.18059 −0.101913
\(975\) −9.59326 −0.307230
\(976\) 1.25863 0.0402877
\(977\) −25.2855 −0.808954 −0.404477 0.914548i \(-0.632546\pi\)
−0.404477 + 0.914548i \(0.632546\pi\)
\(978\) −28.3425 −0.906294
\(979\) −51.9016 −1.65878
\(980\) 1.26643 0.0404546
\(981\) 19.9063 0.635559
\(982\) −10.9740 −0.350194
\(983\) 13.0141 0.415085 0.207543 0.978226i \(-0.433453\pi\)
0.207543 + 0.978226i \(0.433453\pi\)
\(984\) −48.5296 −1.54707
\(985\) −9.92841 −0.316345
\(986\) 1.27722 0.0406750
\(987\) −8.33761 −0.265389
\(988\) 25.6251 0.815242
\(989\) 0.447325 0.0142241
\(990\) −11.9509 −0.379825
\(991\) −3.00882 −0.0955783 −0.0477891 0.998857i \(-0.515218\pi\)
−0.0477891 + 0.998857i \(0.515218\pi\)
\(992\) 61.5765 1.95506
\(993\) 32.5106 1.03169
\(994\) 13.0770 0.414776
\(995\) −22.1854 −0.703325
\(996\) 11.5410 0.365692
\(997\) 13.0191 0.412319 0.206160 0.978518i \(-0.433903\pi\)
0.206160 + 0.978518i \(0.433903\pi\)
\(998\) 8.21687 0.260101
\(999\) −14.4238 −0.456349
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 \(a_p\))