Properties

Label 8018.2.a.d.1.3
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.74076 q^{3} +1.00000 q^{4} +0.116951 q^{5} -2.74076 q^{6} -0.997196 q^{7} +1.00000 q^{8} +4.51179 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.74076 q^{3} +1.00000 q^{4} +0.116951 q^{5} -2.74076 q^{6} -0.997196 q^{7} +1.00000 q^{8} +4.51179 q^{9} +0.116951 q^{10} +3.52284 q^{11} -2.74076 q^{12} +1.83864 q^{13} -0.997196 q^{14} -0.320535 q^{15} +1.00000 q^{16} -2.74753 q^{17} +4.51179 q^{18} +1.00000 q^{19} +0.116951 q^{20} +2.73308 q^{21} +3.52284 q^{22} +3.51262 q^{23} -2.74076 q^{24} -4.98632 q^{25} +1.83864 q^{26} -4.14345 q^{27} -0.997196 q^{28} -2.84490 q^{29} -0.320535 q^{30} -7.76519 q^{31} +1.00000 q^{32} -9.65527 q^{33} -2.74753 q^{34} -0.116623 q^{35} +4.51179 q^{36} +1.28081 q^{37} +1.00000 q^{38} -5.03929 q^{39} +0.116951 q^{40} -5.75259 q^{41} +2.73308 q^{42} -9.54966 q^{43} +3.52284 q^{44} +0.527657 q^{45} +3.51262 q^{46} -12.0470 q^{47} -2.74076 q^{48} -6.00560 q^{49} -4.98632 q^{50} +7.53034 q^{51} +1.83864 q^{52} -1.96674 q^{53} -4.14345 q^{54} +0.411999 q^{55} -0.997196 q^{56} -2.74076 q^{57} -2.84490 q^{58} +13.5938 q^{59} -0.320535 q^{60} +13.4735 q^{61} -7.76519 q^{62} -4.49913 q^{63} +1.00000 q^{64} +0.215031 q^{65} -9.65527 q^{66} +8.40618 q^{67} -2.74753 q^{68} -9.62726 q^{69} -0.116623 q^{70} +5.48242 q^{71} +4.51179 q^{72} +10.8422 q^{73} +1.28081 q^{74} +13.6663 q^{75} +1.00000 q^{76} -3.51296 q^{77} -5.03929 q^{78} +2.10807 q^{79} +0.116951 q^{80} -2.17914 q^{81} -5.75259 q^{82} +0.895937 q^{83} +2.73308 q^{84} -0.321326 q^{85} -9.54966 q^{86} +7.79720 q^{87} +3.52284 q^{88} +4.04750 q^{89} +0.527657 q^{90} -1.83349 q^{91} +3.51262 q^{92} +21.2825 q^{93} -12.0470 q^{94} +0.116951 q^{95} -2.74076 q^{96} +2.54927 q^{97} -6.00560 q^{98} +15.8943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.74076 −1.58238 −0.791190 0.611570i \(-0.790538\pi\)
−0.791190 + 0.611570i \(0.790538\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.116951 0.0523020 0.0261510 0.999658i \(-0.491675\pi\)
0.0261510 + 0.999658i \(0.491675\pi\)
\(6\) −2.74076 −1.11891
\(7\) −0.997196 −0.376905 −0.188452 0.982082i \(-0.560347\pi\)
−0.188452 + 0.982082i \(0.560347\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.51179 1.50393
\(10\) 0.116951 0.0369831
\(11\) 3.52284 1.06218 0.531088 0.847317i \(-0.321783\pi\)
0.531088 + 0.847317i \(0.321783\pi\)
\(12\) −2.74076 −0.791190
\(13\) 1.83864 0.509948 0.254974 0.966948i \(-0.417933\pi\)
0.254974 + 0.966948i \(0.417933\pi\)
\(14\) −0.997196 −0.266512
\(15\) −0.320535 −0.0827617
\(16\) 1.00000 0.250000
\(17\) −2.74753 −0.666375 −0.333187 0.942861i \(-0.608124\pi\)
−0.333187 + 0.942861i \(0.608124\pi\)
\(18\) 4.51179 1.06344
\(19\) 1.00000 0.229416
\(20\) 0.116951 0.0261510
\(21\) 2.73308 0.596407
\(22\) 3.52284 0.751072
\(23\) 3.51262 0.732432 0.366216 0.930530i \(-0.380653\pi\)
0.366216 + 0.930530i \(0.380653\pi\)
\(24\) −2.74076 −0.559456
\(25\) −4.98632 −0.997265
\(26\) 1.83864 0.360588
\(27\) −4.14345 −0.797408
\(28\) −0.997196 −0.188452
\(29\) −2.84490 −0.528285 −0.264142 0.964484i \(-0.585089\pi\)
−0.264142 + 0.964484i \(0.585089\pi\)
\(30\) −0.320535 −0.0585213
\(31\) −7.76519 −1.39467 −0.697335 0.716746i \(-0.745631\pi\)
−0.697335 + 0.716746i \(0.745631\pi\)
\(32\) 1.00000 0.176777
\(33\) −9.65527 −1.68077
\(34\) −2.74753 −0.471198
\(35\) −0.116623 −0.0197129
\(36\) 4.51179 0.751964
\(37\) 1.28081 0.210563 0.105282 0.994442i \(-0.466426\pi\)
0.105282 + 0.994442i \(0.466426\pi\)
\(38\) 1.00000 0.162221
\(39\) −5.03929 −0.806932
\(40\) 0.116951 0.0184915
\(41\) −5.75259 −0.898403 −0.449201 0.893430i \(-0.648291\pi\)
−0.449201 + 0.893430i \(0.648291\pi\)
\(42\) 2.73308 0.421723
\(43\) −9.54966 −1.45631 −0.728155 0.685412i \(-0.759622\pi\)
−0.728155 + 0.685412i \(0.759622\pi\)
\(44\) 3.52284 0.531088
\(45\) 0.527657 0.0786585
\(46\) 3.51262 0.517907
\(47\) −12.0470 −1.75723 −0.878614 0.477532i \(-0.841532\pi\)
−0.878614 + 0.477532i \(0.841532\pi\)
\(48\) −2.74076 −0.395595
\(49\) −6.00560 −0.857943
\(50\) −4.98632 −0.705172
\(51\) 7.53034 1.05446
\(52\) 1.83864 0.254974
\(53\) −1.96674 −0.270153 −0.135076 0.990835i \(-0.543128\pi\)
−0.135076 + 0.990835i \(0.543128\pi\)
\(54\) −4.14345 −0.563852
\(55\) 0.411999 0.0555539
\(56\) −0.997196 −0.133256
\(57\) −2.74076 −0.363023
\(58\) −2.84490 −0.373554
\(59\) 13.5938 1.76976 0.884878 0.465823i \(-0.154242\pi\)
0.884878 + 0.465823i \(0.154242\pi\)
\(60\) −0.320535 −0.0413808
\(61\) 13.4735 1.72510 0.862550 0.505972i \(-0.168866\pi\)
0.862550 + 0.505972i \(0.168866\pi\)
\(62\) −7.76519 −0.986180
\(63\) −4.49913 −0.566838
\(64\) 1.00000 0.125000
\(65\) 0.215031 0.0266713
\(66\) −9.65527 −1.18848
\(67\) 8.40618 1.02698 0.513489 0.858096i \(-0.328353\pi\)
0.513489 + 0.858096i \(0.328353\pi\)
\(68\) −2.74753 −0.333187
\(69\) −9.62726 −1.15899
\(70\) −0.116623 −0.0139391
\(71\) 5.48242 0.650643 0.325322 0.945603i \(-0.394527\pi\)
0.325322 + 0.945603i \(0.394527\pi\)
\(72\) 4.51179 0.531719
\(73\) 10.8422 1.26898 0.634491 0.772930i \(-0.281210\pi\)
0.634491 + 0.772930i \(0.281210\pi\)
\(74\) 1.28081 0.148891
\(75\) 13.6663 1.57805
\(76\) 1.00000 0.114708
\(77\) −3.51296 −0.400339
\(78\) −5.03929 −0.570587
\(79\) 2.10807 0.237176 0.118588 0.992944i \(-0.462163\pi\)
0.118588 + 0.992944i \(0.462163\pi\)
\(80\) 0.116951 0.0130755
\(81\) −2.17914 −0.242127
\(82\) −5.75259 −0.635267
\(83\) 0.895937 0.0983419 0.0491709 0.998790i \(-0.484342\pi\)
0.0491709 + 0.998790i \(0.484342\pi\)
\(84\) 2.73308 0.298203
\(85\) −0.321326 −0.0348527
\(86\) −9.54966 −1.02977
\(87\) 7.79720 0.835948
\(88\) 3.52284 0.375536
\(89\) 4.04750 0.429035 0.214517 0.976720i \(-0.431182\pi\)
0.214517 + 0.976720i \(0.431182\pi\)
\(90\) 0.527657 0.0556199
\(91\) −1.83349 −0.192202
\(92\) 3.51262 0.366216
\(93\) 21.2825 2.20690
\(94\) −12.0470 −1.24255
\(95\) 0.116951 0.0119989
\(96\) −2.74076 −0.279728
\(97\) 2.54927 0.258839 0.129420 0.991590i \(-0.458689\pi\)
0.129420 + 0.991590i \(0.458689\pi\)
\(98\) −6.00560 −0.606657
\(99\) 15.8943 1.59744
\(100\) −4.98632 −0.498632
\(101\) 15.7207 1.56427 0.782136 0.623107i \(-0.214130\pi\)
0.782136 + 0.623107i \(0.214130\pi\)
\(102\) 7.53034 0.745615
\(103\) 6.84497 0.674455 0.337228 0.941423i \(-0.390511\pi\)
0.337228 + 0.941423i \(0.390511\pi\)
\(104\) 1.83864 0.180294
\(105\) 0.319636 0.0311932
\(106\) −1.96674 −0.191027
\(107\) −2.33219 −0.225461 −0.112730 0.993626i \(-0.535960\pi\)
−0.112730 + 0.993626i \(0.535960\pi\)
\(108\) −4.14345 −0.398704
\(109\) −10.7889 −1.03339 −0.516694 0.856170i \(-0.672838\pi\)
−0.516694 + 0.856170i \(0.672838\pi\)
\(110\) 0.411999 0.0392826
\(111\) −3.51039 −0.333191
\(112\) −0.997196 −0.0942261
\(113\) −11.2605 −1.05930 −0.529650 0.848216i \(-0.677677\pi\)
−0.529650 + 0.848216i \(0.677677\pi\)
\(114\) −2.74076 −0.256696
\(115\) 0.410804 0.0383076
\(116\) −2.84490 −0.264142
\(117\) 8.29557 0.766925
\(118\) 13.5938 1.25141
\(119\) 2.73983 0.251160
\(120\) −0.320535 −0.0292607
\(121\) 1.41040 0.128218
\(122\) 13.4735 1.21983
\(123\) 15.7665 1.42162
\(124\) −7.76519 −0.697335
\(125\) −1.16791 −0.104461
\(126\) −4.49913 −0.400815
\(127\) −17.4328 −1.54692 −0.773458 0.633848i \(-0.781474\pi\)
−0.773458 + 0.633848i \(0.781474\pi\)
\(128\) 1.00000 0.0883883
\(129\) 26.1734 2.30444
\(130\) 0.215031 0.0188594
\(131\) −11.1103 −0.970708 −0.485354 0.874318i \(-0.661309\pi\)
−0.485354 + 0.874318i \(0.661309\pi\)
\(132\) −9.65527 −0.840384
\(133\) −0.997196 −0.0864678
\(134\) 8.40618 0.726183
\(135\) −0.484580 −0.0417060
\(136\) −2.74753 −0.235599
\(137\) −15.9828 −1.36550 −0.682750 0.730652i \(-0.739216\pi\)
−0.682750 + 0.730652i \(0.739216\pi\)
\(138\) −9.62726 −0.819527
\(139\) 3.16160 0.268163 0.134082 0.990970i \(-0.457192\pi\)
0.134082 + 0.990970i \(0.457192\pi\)
\(140\) −0.116623 −0.00985643
\(141\) 33.0179 2.78061
\(142\) 5.48242 0.460074
\(143\) 6.47725 0.541654
\(144\) 4.51179 0.375982
\(145\) −0.332713 −0.0276303
\(146\) 10.8422 0.897306
\(147\) 16.4599 1.35759
\(148\) 1.28081 0.105282
\(149\) −11.7345 −0.961331 −0.480665 0.876904i \(-0.659605\pi\)
−0.480665 + 0.876904i \(0.659605\pi\)
\(150\) 13.6663 1.11585
\(151\) −20.0544 −1.63201 −0.816004 0.578047i \(-0.803815\pi\)
−0.816004 + 0.578047i \(0.803815\pi\)
\(152\) 1.00000 0.0811107
\(153\) −12.3963 −1.00218
\(154\) −3.51296 −0.283082
\(155\) −0.908145 −0.0729440
\(156\) −5.03929 −0.403466
\(157\) 17.2770 1.37885 0.689427 0.724355i \(-0.257862\pi\)
0.689427 + 0.724355i \(0.257862\pi\)
\(158\) 2.10807 0.167709
\(159\) 5.39037 0.427484
\(160\) 0.116951 0.00924577
\(161\) −3.50277 −0.276057
\(162\) −2.17914 −0.171209
\(163\) −17.8246 −1.39613 −0.698065 0.716034i \(-0.745956\pi\)
−0.698065 + 0.716034i \(0.745956\pi\)
\(164\) −5.75259 −0.449201
\(165\) −1.12919 −0.0879075
\(166\) 0.895937 0.0695382
\(167\) −11.4034 −0.882424 −0.441212 0.897403i \(-0.645451\pi\)
−0.441212 + 0.897403i \(0.645451\pi\)
\(168\) 2.73308 0.210862
\(169\) −9.61939 −0.739953
\(170\) −0.321326 −0.0246446
\(171\) 4.51179 0.345025
\(172\) −9.54966 −0.728155
\(173\) −24.0155 −1.82587 −0.912933 0.408109i \(-0.866188\pi\)
−0.912933 + 0.408109i \(0.866188\pi\)
\(174\) 7.79720 0.591104
\(175\) 4.97234 0.375874
\(176\) 3.52284 0.265544
\(177\) −37.2573 −2.80043
\(178\) 4.04750 0.303373
\(179\) 8.40847 0.628479 0.314239 0.949344i \(-0.398251\pi\)
0.314239 + 0.949344i \(0.398251\pi\)
\(180\) 0.527657 0.0393292
\(181\) 4.80991 0.357518 0.178759 0.983893i \(-0.442792\pi\)
0.178759 + 0.983893i \(0.442792\pi\)
\(182\) −1.83349 −0.135907
\(183\) −36.9276 −2.72977
\(184\) 3.51262 0.258954
\(185\) 0.149791 0.0110129
\(186\) 21.2825 1.56051
\(187\) −9.67912 −0.707808
\(188\) −12.0470 −0.878614
\(189\) 4.13183 0.300547
\(190\) 0.116951 0.00848450
\(191\) 16.7800 1.21415 0.607077 0.794643i \(-0.292342\pi\)
0.607077 + 0.794643i \(0.292342\pi\)
\(192\) −2.74076 −0.197798
\(193\) 2.87542 0.206977 0.103488 0.994631i \(-0.467000\pi\)
0.103488 + 0.994631i \(0.467000\pi\)
\(194\) 2.54927 0.183027
\(195\) −0.589349 −0.0422041
\(196\) −6.00560 −0.428971
\(197\) −18.6932 −1.33184 −0.665919 0.746024i \(-0.731960\pi\)
−0.665919 + 0.746024i \(0.731960\pi\)
\(198\) 15.8943 1.12956
\(199\) 14.1949 1.00625 0.503125 0.864214i \(-0.332184\pi\)
0.503125 + 0.864214i \(0.332184\pi\)
\(200\) −4.98632 −0.352586
\(201\) −23.0394 −1.62507
\(202\) 15.7207 1.10611
\(203\) 2.83692 0.199113
\(204\) 7.53034 0.527229
\(205\) −0.672769 −0.0469883
\(206\) 6.84497 0.476912
\(207\) 15.8482 1.10153
\(208\) 1.83864 0.127487
\(209\) 3.52284 0.243680
\(210\) 0.319636 0.0220570
\(211\) −1.00000 −0.0688428
\(212\) −1.96674 −0.135076
\(213\) −15.0260 −1.02957
\(214\) −2.33219 −0.159425
\(215\) −1.11684 −0.0761679
\(216\) −4.14345 −0.281926
\(217\) 7.74341 0.525657
\(218\) −10.7889 −0.730716
\(219\) −29.7159 −2.00801
\(220\) 0.411999 0.0277770
\(221\) −5.05173 −0.339816
\(222\) −3.51039 −0.235602
\(223\) 14.2168 0.952026 0.476013 0.879438i \(-0.342081\pi\)
0.476013 + 0.879438i \(0.342081\pi\)
\(224\) −0.997196 −0.0666279
\(225\) −22.4972 −1.49981
\(226\) −11.2605 −0.749038
\(227\) −0.421693 −0.0279887 −0.0139944 0.999902i \(-0.504455\pi\)
−0.0139944 + 0.999902i \(0.504455\pi\)
\(228\) −2.74076 −0.181512
\(229\) −22.4671 −1.48467 −0.742335 0.670029i \(-0.766282\pi\)
−0.742335 + 0.670029i \(0.766282\pi\)
\(230\) 0.410804 0.0270876
\(231\) 9.62820 0.633489
\(232\) −2.84490 −0.186777
\(233\) 9.30220 0.609407 0.304704 0.952447i \(-0.401443\pi\)
0.304704 + 0.952447i \(0.401443\pi\)
\(234\) 8.29557 0.542298
\(235\) −1.40890 −0.0919066
\(236\) 13.5938 0.884878
\(237\) −5.77772 −0.375304
\(238\) 2.73983 0.177597
\(239\) −1.20314 −0.0778247 −0.0389123 0.999243i \(-0.512389\pi\)
−0.0389123 + 0.999243i \(0.512389\pi\)
\(240\) −0.320535 −0.0206904
\(241\) −7.81685 −0.503528 −0.251764 0.967789i \(-0.581011\pi\)
−0.251764 + 0.967789i \(0.581011\pi\)
\(242\) 1.41040 0.0906641
\(243\) 18.4029 1.18054
\(244\) 13.4735 0.862550
\(245\) −0.702360 −0.0448721
\(246\) 15.7665 1.00523
\(247\) 1.83864 0.116990
\(248\) −7.76519 −0.493090
\(249\) −2.45555 −0.155614
\(250\) −1.16791 −0.0738650
\(251\) 14.7296 0.929726 0.464863 0.885383i \(-0.346104\pi\)
0.464863 + 0.885383i \(0.346104\pi\)
\(252\) −4.49913 −0.283419
\(253\) 12.3744 0.777972
\(254\) −17.4328 −1.09383
\(255\) 0.880679 0.0551503
\(256\) 1.00000 0.0625000
\(257\) −22.9435 −1.43118 −0.715588 0.698522i \(-0.753841\pi\)
−0.715588 + 0.698522i \(0.753841\pi\)
\(258\) 26.1734 1.62948
\(259\) −1.27722 −0.0793623
\(260\) 0.215031 0.0133356
\(261\) −12.8356 −0.794503
\(262\) −11.1103 −0.686394
\(263\) −24.7062 −1.52345 −0.761724 0.647901i \(-0.775647\pi\)
−0.761724 + 0.647901i \(0.775647\pi\)
\(264\) −9.65527 −0.594241
\(265\) −0.230012 −0.0141295
\(266\) −0.997196 −0.0611420
\(267\) −11.0933 −0.678896
\(268\) 8.40618 0.513489
\(269\) −11.1971 −0.682702 −0.341351 0.939936i \(-0.610884\pi\)
−0.341351 + 0.939936i \(0.610884\pi\)
\(270\) −0.484580 −0.0294906
\(271\) −20.0777 −1.21963 −0.609816 0.792543i \(-0.708757\pi\)
−0.609816 + 0.792543i \(0.708757\pi\)
\(272\) −2.74753 −0.166594
\(273\) 5.02515 0.304136
\(274\) −15.9828 −0.965555
\(275\) −17.5660 −1.05927
\(276\) −9.62726 −0.579493
\(277\) −14.1896 −0.852571 −0.426286 0.904589i \(-0.640178\pi\)
−0.426286 + 0.904589i \(0.640178\pi\)
\(278\) 3.16160 0.189620
\(279\) −35.0349 −2.09748
\(280\) −0.116623 −0.00696955
\(281\) −17.2940 −1.03167 −0.515837 0.856687i \(-0.672519\pi\)
−0.515837 + 0.856687i \(0.672519\pi\)
\(282\) 33.0179 1.96618
\(283\) 6.98404 0.415158 0.207579 0.978218i \(-0.433442\pi\)
0.207579 + 0.978218i \(0.433442\pi\)
\(284\) 5.48242 0.325322
\(285\) −0.320535 −0.0189868
\(286\) 6.47725 0.383008
\(287\) 5.73645 0.338612
\(288\) 4.51179 0.265860
\(289\) −9.45106 −0.555945
\(290\) −0.332713 −0.0195376
\(291\) −6.98695 −0.409582
\(292\) 10.8422 0.634491
\(293\) 21.5432 1.25857 0.629283 0.777176i \(-0.283349\pi\)
0.629283 + 0.777176i \(0.283349\pi\)
\(294\) 16.4599 0.959963
\(295\) 1.58980 0.0925618
\(296\) 1.28081 0.0744454
\(297\) −14.5967 −0.846987
\(298\) −11.7345 −0.679763
\(299\) 6.45845 0.373502
\(300\) 13.6663 0.789026
\(301\) 9.52288 0.548890
\(302\) −20.0544 −1.15400
\(303\) −43.0868 −2.47527
\(304\) 1.00000 0.0573539
\(305\) 1.57573 0.0902262
\(306\) −12.3963 −0.708649
\(307\) 34.7514 1.98337 0.991684 0.128694i \(-0.0410784\pi\)
0.991684 + 0.128694i \(0.0410784\pi\)
\(308\) −3.51296 −0.200170
\(309\) −18.7605 −1.06724
\(310\) −0.908145 −0.0515792
\(311\) 19.8701 1.12673 0.563365 0.826208i \(-0.309507\pi\)
0.563365 + 0.826208i \(0.309507\pi\)
\(312\) −5.03929 −0.285293
\(313\) −8.40056 −0.474828 −0.237414 0.971409i \(-0.576300\pi\)
−0.237414 + 0.971409i \(0.576300\pi\)
\(314\) 17.2770 0.974997
\(315\) −0.526177 −0.0296467
\(316\) 2.10807 0.118588
\(317\) −11.8208 −0.663921 −0.331961 0.943293i \(-0.607710\pi\)
−0.331961 + 0.943293i \(0.607710\pi\)
\(318\) 5.39037 0.302277
\(319\) −10.0221 −0.561131
\(320\) 0.116951 0.00653775
\(321\) 6.39197 0.356765
\(322\) −3.50277 −0.195202
\(323\) −2.74753 −0.152877
\(324\) −2.17914 −0.121063
\(325\) −9.16807 −0.508553
\(326\) −17.8246 −0.987214
\(327\) 29.5698 1.63521
\(328\) −5.75259 −0.317633
\(329\) 12.0132 0.662308
\(330\) −1.12919 −0.0621600
\(331\) 10.1127 0.555845 0.277923 0.960603i \(-0.410354\pi\)
0.277923 + 0.960603i \(0.410354\pi\)
\(332\) 0.895937 0.0491709
\(333\) 5.77873 0.316672
\(334\) −11.4034 −0.623968
\(335\) 0.983109 0.0537130
\(336\) 2.73308 0.149102
\(337\) 8.19049 0.446165 0.223082 0.974800i \(-0.428388\pi\)
0.223082 + 0.974800i \(0.428388\pi\)
\(338\) −9.61939 −0.523226
\(339\) 30.8624 1.67622
\(340\) −0.321326 −0.0174264
\(341\) −27.3555 −1.48138
\(342\) 4.51179 0.243969
\(343\) 12.9691 0.700267
\(344\) −9.54966 −0.514883
\(345\) −1.12592 −0.0606173
\(346\) −24.0155 −1.29108
\(347\) −10.5382 −0.565722 −0.282861 0.959161i \(-0.591284\pi\)
−0.282861 + 0.959161i \(0.591284\pi\)
\(348\) 7.79720 0.417974
\(349\) 15.8770 0.849876 0.424938 0.905222i \(-0.360296\pi\)
0.424938 + 0.905222i \(0.360296\pi\)
\(350\) 4.97234 0.265783
\(351\) −7.61833 −0.406636
\(352\) 3.52284 0.187768
\(353\) −18.0927 −0.962977 −0.481489 0.876452i \(-0.659904\pi\)
−0.481489 + 0.876452i \(0.659904\pi\)
\(354\) −37.2573 −1.98020
\(355\) 0.641173 0.0340299
\(356\) 4.04750 0.214517
\(357\) −7.50922 −0.397430
\(358\) 8.40847 0.444402
\(359\) 24.9033 1.31435 0.657173 0.753740i \(-0.271752\pi\)
0.657173 + 0.753740i \(0.271752\pi\)
\(360\) 0.527657 0.0278100
\(361\) 1.00000 0.0526316
\(362\) 4.80991 0.252803
\(363\) −3.86558 −0.202890
\(364\) −1.83349 −0.0961008
\(365\) 1.26800 0.0663703
\(366\) −36.9276 −1.93024
\(367\) 22.6852 1.18416 0.592078 0.805881i \(-0.298308\pi\)
0.592078 + 0.805881i \(0.298308\pi\)
\(368\) 3.51262 0.183108
\(369\) −25.9544 −1.35113
\(370\) 0.149791 0.00778728
\(371\) 1.96123 0.101822
\(372\) 21.2825 1.10345
\(373\) 0.627435 0.0324874 0.0162437 0.999868i \(-0.494829\pi\)
0.0162437 + 0.999868i \(0.494829\pi\)
\(374\) −9.67912 −0.500495
\(375\) 3.20096 0.165297
\(376\) −12.0470 −0.621274
\(377\) −5.23076 −0.269398
\(378\) 4.13183 0.212518
\(379\) −25.4763 −1.30863 −0.654314 0.756223i \(-0.727043\pi\)
−0.654314 + 0.756223i \(0.727043\pi\)
\(380\) 0.116951 0.00599945
\(381\) 47.7793 2.44781
\(382\) 16.7800 0.858537
\(383\) 10.8886 0.556381 0.278191 0.960526i \(-0.410265\pi\)
0.278191 + 0.960526i \(0.410265\pi\)
\(384\) −2.74076 −0.139864
\(385\) −0.410844 −0.0209385
\(386\) 2.87542 0.146355
\(387\) −43.0860 −2.19019
\(388\) 2.54927 0.129420
\(389\) −33.1823 −1.68241 −0.841203 0.540719i \(-0.818152\pi\)
−0.841203 + 0.540719i \(0.818152\pi\)
\(390\) −0.589349 −0.0298428
\(391\) −9.65104 −0.488074
\(392\) −6.00560 −0.303329
\(393\) 30.4506 1.53603
\(394\) −18.6932 −0.941751
\(395\) 0.246541 0.0124048
\(396\) 15.8943 0.798719
\(397\) −35.0174 −1.75747 −0.878737 0.477305i \(-0.841614\pi\)
−0.878737 + 0.477305i \(0.841614\pi\)
\(398\) 14.1949 0.711526
\(399\) 2.73308 0.136825
\(400\) −4.98632 −0.249316
\(401\) −2.43149 −0.121423 −0.0607114 0.998155i \(-0.519337\pi\)
−0.0607114 + 0.998155i \(0.519337\pi\)
\(402\) −23.0394 −1.14910
\(403\) −14.2774 −0.711208
\(404\) 15.7207 0.782136
\(405\) −0.254852 −0.0126637
\(406\) 2.83692 0.140794
\(407\) 4.51208 0.223655
\(408\) 7.53034 0.372807
\(409\) 17.4603 0.863358 0.431679 0.902027i \(-0.357921\pi\)
0.431679 + 0.902027i \(0.357921\pi\)
\(410\) −0.672769 −0.0332257
\(411\) 43.8050 2.16074
\(412\) 6.84497 0.337228
\(413\) −13.5556 −0.667029
\(414\) 15.8482 0.778896
\(415\) 0.104781 0.00514348
\(416\) 1.83864 0.0901469
\(417\) −8.66520 −0.424336
\(418\) 3.52284 0.172308
\(419\) 3.78517 0.184918 0.0924588 0.995717i \(-0.470527\pi\)
0.0924588 + 0.995717i \(0.470527\pi\)
\(420\) 0.319636 0.0155966
\(421\) −15.4466 −0.752824 −0.376412 0.926452i \(-0.622842\pi\)
−0.376412 + 0.926452i \(0.622842\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −54.3533 −2.64275
\(424\) −1.96674 −0.0955134
\(425\) 13.7001 0.664552
\(426\) −15.0260 −0.728012
\(427\) −13.4357 −0.650198
\(428\) −2.33219 −0.112730
\(429\) −17.7526 −0.857104
\(430\) −1.11684 −0.0538588
\(431\) 7.72797 0.372243 0.186122 0.982527i \(-0.440408\pi\)
0.186122 + 0.982527i \(0.440408\pi\)
\(432\) −4.14345 −0.199352
\(433\) −8.93362 −0.429322 −0.214661 0.976689i \(-0.568865\pi\)
−0.214661 + 0.976689i \(0.568865\pi\)
\(434\) 7.74341 0.371696
\(435\) 0.911889 0.0437217
\(436\) −10.7889 −0.516694
\(437\) 3.51262 0.168031
\(438\) −29.7159 −1.41988
\(439\) −3.21929 −0.153648 −0.0768241 0.997045i \(-0.524478\pi\)
−0.0768241 + 0.997045i \(0.524478\pi\)
\(440\) 0.411999 0.0196413
\(441\) −27.0960 −1.29029
\(442\) −5.05173 −0.240286
\(443\) −10.2920 −0.488986 −0.244493 0.969651i \(-0.578622\pi\)
−0.244493 + 0.969651i \(0.578622\pi\)
\(444\) −3.51039 −0.166596
\(445\) 0.473359 0.0224394
\(446\) 14.2168 0.673184
\(447\) 32.1616 1.52119
\(448\) −0.997196 −0.0471131
\(449\) −18.7701 −0.885818 −0.442909 0.896567i \(-0.646054\pi\)
−0.442909 + 0.896567i \(0.646054\pi\)
\(450\) −22.4972 −1.06053
\(451\) −20.2654 −0.954262
\(452\) −11.2605 −0.529650
\(453\) 54.9645 2.58246
\(454\) −0.421693 −0.0197910
\(455\) −0.214428 −0.0100525
\(456\) −2.74076 −0.128348
\(457\) 0.823220 0.0385086 0.0192543 0.999815i \(-0.493871\pi\)
0.0192543 + 0.999815i \(0.493871\pi\)
\(458\) −22.4671 −1.04982
\(459\) 11.3843 0.531372
\(460\) 0.410804 0.0191538
\(461\) 39.0053 1.81666 0.908328 0.418258i \(-0.137359\pi\)
0.908328 + 0.418258i \(0.137359\pi\)
\(462\) 9.62820 0.447944
\(463\) −25.6145 −1.19041 −0.595203 0.803575i \(-0.702928\pi\)
−0.595203 + 0.803575i \(0.702928\pi\)
\(464\) −2.84490 −0.132071
\(465\) 2.48901 0.115425
\(466\) 9.30220 0.430916
\(467\) −11.2528 −0.520720 −0.260360 0.965512i \(-0.583841\pi\)
−0.260360 + 0.965512i \(0.583841\pi\)
\(468\) 8.29557 0.383463
\(469\) −8.38261 −0.387073
\(470\) −1.40890 −0.0649878
\(471\) −47.3521 −2.18187
\(472\) 13.5938 0.625703
\(473\) −33.6419 −1.54686
\(474\) −5.77772 −0.265380
\(475\) −4.98632 −0.228788
\(476\) 2.73983 0.125580
\(477\) −8.87351 −0.406290
\(478\) −1.20314 −0.0550303
\(479\) −25.9292 −1.18473 −0.592367 0.805668i \(-0.701807\pi\)
−0.592367 + 0.805668i \(0.701807\pi\)
\(480\) −0.320535 −0.0146303
\(481\) 2.35495 0.107376
\(482\) −7.81685 −0.356048
\(483\) 9.60026 0.436827
\(484\) 1.41040 0.0641092
\(485\) 0.298139 0.0135378
\(486\) 18.4029 0.834771
\(487\) 34.5869 1.56728 0.783642 0.621213i \(-0.213360\pi\)
0.783642 + 0.621213i \(0.213360\pi\)
\(488\) 13.4735 0.609915
\(489\) 48.8530 2.20921
\(490\) −0.702360 −0.0317294
\(491\) 28.2296 1.27399 0.636993 0.770870i \(-0.280178\pi\)
0.636993 + 0.770870i \(0.280178\pi\)
\(492\) 15.7665 0.710808
\(493\) 7.81646 0.352036
\(494\) 1.83864 0.0827245
\(495\) 1.85885 0.0835492
\(496\) −7.76519 −0.348667
\(497\) −5.46704 −0.245230
\(498\) −2.45555 −0.110036
\(499\) 2.64444 0.118381 0.0591907 0.998247i \(-0.481148\pi\)
0.0591907 + 0.998247i \(0.481148\pi\)
\(500\) −1.16791 −0.0522305
\(501\) 31.2541 1.39633
\(502\) 14.7296 0.657415
\(503\) −22.0493 −0.983131 −0.491565 0.870841i \(-0.663575\pi\)
−0.491565 + 0.870841i \(0.663575\pi\)
\(504\) −4.49913 −0.200407
\(505\) 1.83855 0.0818146
\(506\) 12.3744 0.550109
\(507\) 26.3645 1.17089
\(508\) −17.4328 −0.773458
\(509\) 4.65666 0.206403 0.103201 0.994660i \(-0.467091\pi\)
0.103201 + 0.994660i \(0.467091\pi\)
\(510\) 0.880679 0.0389971
\(511\) −10.8118 −0.478285
\(512\) 1.00000 0.0441942
\(513\) −4.14345 −0.182938
\(514\) −22.9435 −1.01199
\(515\) 0.800525 0.0352753
\(516\) 26.1734 1.15222
\(517\) −42.4395 −1.86649
\(518\) −1.27722 −0.0561176
\(519\) 65.8209 2.88922
\(520\) 0.215031 0.00942972
\(521\) −30.8508 −1.35160 −0.675798 0.737086i \(-0.736201\pi\)
−0.675798 + 0.737086i \(0.736201\pi\)
\(522\) −12.8356 −0.561798
\(523\) −36.3519 −1.58956 −0.794778 0.606900i \(-0.792413\pi\)
−0.794778 + 0.606900i \(0.792413\pi\)
\(524\) −11.1103 −0.485354
\(525\) −13.6280 −0.594775
\(526\) −24.7062 −1.07724
\(527\) 21.3351 0.929372
\(528\) −9.65527 −0.420192
\(529\) −10.6615 −0.463544
\(530\) −0.230012 −0.00999108
\(531\) 61.3321 2.66159
\(532\) −0.997196 −0.0432339
\(533\) −10.5770 −0.458139
\(534\) −11.0933 −0.480052
\(535\) −0.272751 −0.0117921
\(536\) 8.40618 0.363092
\(537\) −23.0456 −0.994493
\(538\) −11.1971 −0.482743
\(539\) −21.1568 −0.911287
\(540\) −0.484580 −0.0208530
\(541\) 14.3989 0.619058 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(542\) −20.0777 −0.862410
\(543\) −13.1828 −0.565730
\(544\) −2.74753 −0.117800
\(545\) −1.26177 −0.0540483
\(546\) 5.02515 0.215057
\(547\) −2.98632 −0.127686 −0.0638428 0.997960i \(-0.520336\pi\)
−0.0638428 + 0.997960i \(0.520336\pi\)
\(548\) −15.9828 −0.682750
\(549\) 60.7894 2.59443
\(550\) −17.5660 −0.749017
\(551\) −2.84490 −0.121197
\(552\) −9.62726 −0.409763
\(553\) −2.10216 −0.0893929
\(554\) −14.1896 −0.602859
\(555\) −0.410543 −0.0174266
\(556\) 3.16160 0.134082
\(557\) −45.7883 −1.94011 −0.970057 0.242877i \(-0.921909\pi\)
−0.970057 + 0.242877i \(0.921909\pi\)
\(558\) −35.0349 −1.48314
\(559\) −17.5584 −0.742642
\(560\) −0.116623 −0.00492821
\(561\) 26.5282 1.12002
\(562\) −17.2940 −0.729504
\(563\) −10.7441 −0.452809 −0.226404 0.974033i \(-0.572697\pi\)
−0.226404 + 0.974033i \(0.572697\pi\)
\(564\) 33.0179 1.39030
\(565\) −1.31693 −0.0554035
\(566\) 6.98404 0.293561
\(567\) 2.17303 0.0912586
\(568\) 5.48242 0.230037
\(569\) 24.7561 1.03783 0.518916 0.854825i \(-0.326336\pi\)
0.518916 + 0.854825i \(0.326336\pi\)
\(570\) −0.320535 −0.0134257
\(571\) −39.3234 −1.64563 −0.822817 0.568306i \(-0.807599\pi\)
−0.822817 + 0.568306i \(0.807599\pi\)
\(572\) 6.47725 0.270827
\(573\) −45.9899 −1.92126
\(574\) 5.73645 0.239435
\(575\) −17.5151 −0.730428
\(576\) 4.51179 0.187991
\(577\) −44.3664 −1.84700 −0.923498 0.383604i \(-0.874683\pi\)
−0.923498 + 0.383604i \(0.874683\pi\)
\(578\) −9.45106 −0.393112
\(579\) −7.88083 −0.327516
\(580\) −0.332713 −0.0138152
\(581\) −0.893425 −0.0370655
\(582\) −6.98695 −0.289618
\(583\) −6.92851 −0.286950
\(584\) 10.8422 0.448653
\(585\) 0.970173 0.0401117
\(586\) 21.5432 0.889941
\(587\) −27.7204 −1.14414 −0.572072 0.820204i \(-0.693860\pi\)
−0.572072 + 0.820204i \(0.693860\pi\)
\(588\) 16.4599 0.678796
\(589\) −7.76519 −0.319959
\(590\) 1.58980 0.0654510
\(591\) 51.2337 2.10747
\(592\) 1.28081 0.0526408
\(593\) 23.1732 0.951611 0.475805 0.879551i \(-0.342157\pi\)
0.475805 + 0.879551i \(0.342157\pi\)
\(594\) −14.5967 −0.598910
\(595\) 0.320425 0.0131362
\(596\) −11.7345 −0.480665
\(597\) −38.9049 −1.59227
\(598\) 6.45845 0.264106
\(599\) 16.6771 0.681406 0.340703 0.940171i \(-0.389335\pi\)
0.340703 + 0.940171i \(0.389335\pi\)
\(600\) 13.6663 0.557926
\(601\) −34.6691 −1.41418 −0.707092 0.707122i \(-0.749993\pi\)
−0.707092 + 0.707122i \(0.749993\pi\)
\(602\) 9.52288 0.388124
\(603\) 37.9269 1.54450
\(604\) −20.0544 −0.816004
\(605\) 0.164948 0.00670607
\(606\) −43.0868 −1.75028
\(607\) −38.2887 −1.55409 −0.777045 0.629445i \(-0.783282\pi\)
−0.777045 + 0.629445i \(0.783282\pi\)
\(608\) 1.00000 0.0405554
\(609\) −7.77533 −0.315072
\(610\) 1.57573 0.0637995
\(611\) −22.1500 −0.896095
\(612\) −12.3963 −0.501090
\(613\) −30.2695 −1.22257 −0.611286 0.791409i \(-0.709348\pi\)
−0.611286 + 0.791409i \(0.709348\pi\)
\(614\) 34.7514 1.40245
\(615\) 1.84390 0.0743533
\(616\) −3.51296 −0.141541
\(617\) 21.0103 0.845842 0.422921 0.906167i \(-0.361005\pi\)
0.422921 + 0.906167i \(0.361005\pi\)
\(618\) −18.7605 −0.754656
\(619\) 14.1126 0.567232 0.283616 0.958938i \(-0.408466\pi\)
0.283616 + 0.958938i \(0.408466\pi\)
\(620\) −0.908145 −0.0364720
\(621\) −14.5544 −0.584047
\(622\) 19.8701 0.796718
\(623\) −4.03615 −0.161705
\(624\) −5.03929 −0.201733
\(625\) 24.7950 0.991801
\(626\) −8.40056 −0.335754
\(627\) −9.65527 −0.385594
\(628\) 17.2770 0.689427
\(629\) −3.51906 −0.140314
\(630\) −0.526177 −0.0209634
\(631\) −1.93725 −0.0771209 −0.0385604 0.999256i \(-0.512277\pi\)
−0.0385604 + 0.999256i \(0.512277\pi\)
\(632\) 2.10807 0.0838546
\(633\) 2.74076 0.108936
\(634\) −11.8208 −0.469463
\(635\) −2.03879 −0.0809067
\(636\) 5.39037 0.213742
\(637\) −11.0422 −0.437506
\(638\) −10.0221 −0.396780
\(639\) 24.7355 0.978521
\(640\) 0.116951 0.00462289
\(641\) −18.4449 −0.728528 −0.364264 0.931296i \(-0.618679\pi\)
−0.364264 + 0.931296i \(0.618679\pi\)
\(642\) 6.39197 0.252271
\(643\) 20.1818 0.795891 0.397946 0.917409i \(-0.369723\pi\)
0.397946 + 0.917409i \(0.369723\pi\)
\(644\) −3.50277 −0.138028
\(645\) 3.06100 0.120527
\(646\) −2.74753 −0.108100
\(647\) −10.2365 −0.402440 −0.201220 0.979546i \(-0.564491\pi\)
−0.201220 + 0.979546i \(0.564491\pi\)
\(648\) −2.17914 −0.0856047
\(649\) 47.8886 1.87979
\(650\) −9.16807 −0.359601
\(651\) −21.2229 −0.831790
\(652\) −17.8246 −0.698065
\(653\) −34.5819 −1.35330 −0.676648 0.736307i \(-0.736568\pi\)
−0.676648 + 0.736307i \(0.736568\pi\)
\(654\) 29.5698 1.15627
\(655\) −1.29935 −0.0507699
\(656\) −5.75259 −0.224601
\(657\) 48.9176 1.90846
\(658\) 12.0132 0.468322
\(659\) 47.6677 1.85687 0.928435 0.371495i \(-0.121155\pi\)
0.928435 + 0.371495i \(0.121155\pi\)
\(660\) −1.12919 −0.0439537
\(661\) −9.67695 −0.376390 −0.188195 0.982132i \(-0.560264\pi\)
−0.188195 + 0.982132i \(0.560264\pi\)
\(662\) 10.1127 0.393042
\(663\) 13.8456 0.537719
\(664\) 0.895937 0.0347691
\(665\) −0.116623 −0.00452244
\(666\) 5.77873 0.223921
\(667\) −9.99305 −0.386932
\(668\) −11.4034 −0.441212
\(669\) −38.9649 −1.50647
\(670\) 0.983109 0.0379808
\(671\) 47.4649 1.83236
\(672\) 2.73308 0.105431
\(673\) 25.4400 0.980639 0.490319 0.871543i \(-0.336880\pi\)
0.490319 + 0.871543i \(0.336880\pi\)
\(674\) 8.19049 0.315486
\(675\) 20.6606 0.795226
\(676\) −9.61939 −0.369977
\(677\) 10.1150 0.388752 0.194376 0.980927i \(-0.437732\pi\)
0.194376 + 0.980927i \(0.437732\pi\)
\(678\) 30.8624 1.18526
\(679\) −2.54212 −0.0975577
\(680\) −0.321326 −0.0123223
\(681\) 1.15576 0.0442888
\(682\) −27.3555 −1.04750
\(683\) 48.3321 1.84938 0.924688 0.380725i \(-0.124326\pi\)
0.924688 + 0.380725i \(0.124326\pi\)
\(684\) 4.51179 0.172512
\(685\) −1.86920 −0.0714184
\(686\) 12.9691 0.495164
\(687\) 61.5771 2.34931
\(688\) −9.54966 −0.364078
\(689\) −3.61613 −0.137764
\(690\) −1.12592 −0.0428629
\(691\) −31.0727 −1.18206 −0.591030 0.806649i \(-0.701279\pi\)
−0.591030 + 0.806649i \(0.701279\pi\)
\(692\) −24.0155 −0.912933
\(693\) −15.8497 −0.602081
\(694\) −10.5382 −0.400026
\(695\) 0.369752 0.0140255
\(696\) 7.79720 0.295552
\(697\) 15.8054 0.598673
\(698\) 15.8770 0.600953
\(699\) −25.4951 −0.964314
\(700\) 4.97234 0.187937
\(701\) −30.7180 −1.16020 −0.580101 0.814545i \(-0.696987\pi\)
−0.580101 + 0.814545i \(0.696987\pi\)
\(702\) −7.61833 −0.287535
\(703\) 1.28081 0.0483065
\(704\) 3.52284 0.132772
\(705\) 3.86146 0.145431
\(706\) −18.0927 −0.680928
\(707\) −15.6767 −0.589581
\(708\) −37.2573 −1.40021
\(709\) 4.71652 0.177133 0.0885663 0.996070i \(-0.471771\pi\)
0.0885663 + 0.996070i \(0.471771\pi\)
\(710\) 0.641173 0.0240628
\(711\) 9.51117 0.356697
\(712\) 4.04750 0.151687
\(713\) −27.2762 −1.02150
\(714\) −7.50922 −0.281026
\(715\) 0.757519 0.0283296
\(716\) 8.40847 0.314239
\(717\) 3.29752 0.123148
\(718\) 24.9033 0.929383
\(719\) −4.46961 −0.166688 −0.0833442 0.996521i \(-0.526560\pi\)
−0.0833442 + 0.996521i \(0.526560\pi\)
\(720\) 0.527657 0.0196646
\(721\) −6.82578 −0.254205
\(722\) 1.00000 0.0372161
\(723\) 21.4241 0.796773
\(724\) 4.80991 0.178759
\(725\) 14.1856 0.526840
\(726\) −3.86558 −0.143465
\(727\) 5.63650 0.209046 0.104523 0.994522i \(-0.466668\pi\)
0.104523 + 0.994522i \(0.466668\pi\)
\(728\) −1.83349 −0.0679535
\(729\) −43.9005 −1.62594
\(730\) 1.26800 0.0469309
\(731\) 26.2380 0.970448
\(732\) −36.9276 −1.36488
\(733\) −35.1414 −1.29798 −0.648988 0.760799i \(-0.724808\pi\)
−0.648988 + 0.760799i \(0.724808\pi\)
\(734\) 22.6852 0.837325
\(735\) 1.92500 0.0710048
\(736\) 3.51262 0.129477
\(737\) 29.6136 1.09083
\(738\) −25.9544 −0.955396
\(739\) 41.0747 1.51096 0.755478 0.655174i \(-0.227405\pi\)
0.755478 + 0.655174i \(0.227405\pi\)
\(740\) 0.149791 0.00550644
\(741\) −5.03929 −0.185123
\(742\) 1.96123 0.0719988
\(743\) 50.3060 1.84555 0.922775 0.385340i \(-0.125916\pi\)
0.922775 + 0.385340i \(0.125916\pi\)
\(744\) 21.2825 0.780256
\(745\) −1.37236 −0.0502795
\(746\) 0.627435 0.0229720
\(747\) 4.04228 0.147899
\(748\) −9.67912 −0.353904
\(749\) 2.32565 0.0849773
\(750\) 3.20096 0.116883
\(751\) 9.37159 0.341974 0.170987 0.985273i \(-0.445304\pi\)
0.170987 + 0.985273i \(0.445304\pi\)
\(752\) −12.0470 −0.439307
\(753\) −40.3704 −1.47118
\(754\) −5.23076 −0.190493
\(755\) −2.34538 −0.0853572
\(756\) 4.13183 0.150273
\(757\) −26.6216 −0.967580 −0.483790 0.875184i \(-0.660740\pi\)
−0.483790 + 0.875184i \(0.660740\pi\)
\(758\) −25.4763 −0.925340
\(759\) −33.9153 −1.23105
\(760\) 0.116951 0.00424225
\(761\) −32.0753 −1.16273 −0.581363 0.813644i \(-0.697481\pi\)
−0.581363 + 0.813644i \(0.697481\pi\)
\(762\) 47.7793 1.73086
\(763\) 10.7586 0.389489
\(764\) 16.7800 0.607077
\(765\) −1.44976 −0.0524160
\(766\) 10.8886 0.393421
\(767\) 24.9941 0.902483
\(768\) −2.74076 −0.0988988
\(769\) −23.1112 −0.833412 −0.416706 0.909041i \(-0.636816\pi\)
−0.416706 + 0.909041i \(0.636816\pi\)
\(770\) −0.410844 −0.0148058
\(771\) 62.8827 2.26467
\(772\) 2.87542 0.103488
\(773\) 13.1814 0.474100 0.237050 0.971497i \(-0.423819\pi\)
0.237050 + 0.971497i \(0.423819\pi\)
\(774\) −43.0860 −1.54870
\(775\) 38.7197 1.39085
\(776\) 2.54927 0.0915135
\(777\) 3.50055 0.125581
\(778\) −33.1823 −1.18964
\(779\) −5.75259 −0.206108
\(780\) −0.589349 −0.0211021
\(781\) 19.3137 0.691098
\(782\) −9.65104 −0.345121
\(783\) 11.7877 0.421258
\(784\) −6.00560 −0.214486
\(785\) 2.02056 0.0721168
\(786\) 30.4506 1.08614
\(787\) 45.1276 1.60863 0.804313 0.594207i \(-0.202534\pi\)
0.804313 + 0.594207i \(0.202534\pi\)
\(788\) −18.6932 −0.665919
\(789\) 67.7138 2.41068
\(790\) 0.246541 0.00877152
\(791\) 11.2289 0.399255
\(792\) 15.8943 0.564779
\(793\) 24.7729 0.879711
\(794\) −35.0174 −1.24272
\(795\) 0.630408 0.0223583
\(796\) 14.1949 0.503125
\(797\) 7.39822 0.262058 0.131029 0.991379i \(-0.458172\pi\)
0.131029 + 0.991379i \(0.458172\pi\)
\(798\) 2.73308 0.0967499
\(799\) 33.0994 1.17097
\(800\) −4.98632 −0.176293
\(801\) 18.2615 0.645237
\(802\) −2.43149 −0.0858589
\(803\) 38.1953 1.34788
\(804\) −23.0394 −0.812535
\(805\) −0.409652 −0.0144383
\(806\) −14.2774 −0.502900
\(807\) 30.6887 1.08029
\(808\) 15.7207 0.553054
\(809\) −23.0333 −0.809807 −0.404904 0.914359i \(-0.632695\pi\)
−0.404904 + 0.914359i \(0.632695\pi\)
\(810\) −0.254852 −0.00895459
\(811\) 23.1348 0.812373 0.406187 0.913790i \(-0.366858\pi\)
0.406187 + 0.913790i \(0.366858\pi\)
\(812\) 2.83692 0.0995565
\(813\) 55.0282 1.92992
\(814\) 4.51208 0.158148
\(815\) −2.08460 −0.0730204
\(816\) 7.53034 0.263615
\(817\) −9.54966 −0.334100
\(818\) 17.4603 0.610486
\(819\) −8.27230 −0.289058
\(820\) −0.672769 −0.0234941
\(821\) −33.0686 −1.15410 −0.577051 0.816708i \(-0.695797\pi\)
−0.577051 + 0.816708i \(0.695797\pi\)
\(822\) 43.8050 1.52788
\(823\) −19.0969 −0.665677 −0.332839 0.942984i \(-0.608006\pi\)
−0.332839 + 0.942984i \(0.608006\pi\)
\(824\) 6.84497 0.238456
\(825\) 48.1443 1.67617
\(826\) −13.5556 −0.471661
\(827\) −11.8054 −0.410513 −0.205257 0.978708i \(-0.565803\pi\)
−0.205257 + 0.978708i \(0.565803\pi\)
\(828\) 15.8482 0.550763
\(829\) 35.9121 1.24728 0.623639 0.781712i \(-0.285653\pi\)
0.623639 + 0.781712i \(0.285653\pi\)
\(830\) 0.104781 0.00363699
\(831\) 38.8904 1.34909
\(832\) 1.83864 0.0637435
\(833\) 16.5006 0.571712
\(834\) −8.66520 −0.300051
\(835\) −1.33364 −0.0461525
\(836\) 3.52284 0.121840
\(837\) 32.1747 1.11212
\(838\) 3.78517 0.130756
\(839\) −33.1393 −1.14410 −0.572048 0.820220i \(-0.693851\pi\)
−0.572048 + 0.820220i \(0.693851\pi\)
\(840\) 0.319636 0.0110285
\(841\) −20.9065 −0.720915
\(842\) −15.4466 −0.532327
\(843\) 47.3988 1.63250
\(844\) −1.00000 −0.0344214
\(845\) −1.12500 −0.0387010
\(846\) −54.3533 −1.86870
\(847\) −1.40645 −0.0483261
\(848\) −1.96674 −0.0675381
\(849\) −19.1416 −0.656939
\(850\) 13.7001 0.469909
\(851\) 4.49899 0.154223
\(852\) −15.0260 −0.514783
\(853\) −16.6918 −0.571517 −0.285759 0.958302i \(-0.592246\pi\)
−0.285759 + 0.958302i \(0.592246\pi\)
\(854\) −13.4357 −0.459759
\(855\) 0.527657 0.0180455
\(856\) −2.33219 −0.0797125
\(857\) 52.3734 1.78904 0.894520 0.447028i \(-0.147518\pi\)
0.894520 + 0.447028i \(0.147518\pi\)
\(858\) −17.7526 −0.606064
\(859\) 14.8912 0.508081 0.254040 0.967194i \(-0.418240\pi\)
0.254040 + 0.967194i \(0.418240\pi\)
\(860\) −1.11684 −0.0380840
\(861\) −15.7223 −0.535813
\(862\) 7.72797 0.263216
\(863\) 16.7562 0.570388 0.285194 0.958470i \(-0.407942\pi\)
0.285194 + 0.958470i \(0.407942\pi\)
\(864\) −4.14345 −0.140963
\(865\) −2.80863 −0.0954964
\(866\) −8.93362 −0.303577
\(867\) 25.9031 0.879716
\(868\) 7.74341 0.262829
\(869\) 7.42640 0.251923
\(870\) 0.911889 0.0309159
\(871\) 15.4560 0.523705
\(872\) −10.7889 −0.365358
\(873\) 11.5018 0.389276
\(874\) 3.51262 0.118816
\(875\) 1.16463 0.0393718
\(876\) −29.7159 −1.00401
\(877\) 51.5232 1.73981 0.869907 0.493216i \(-0.164179\pi\)
0.869907 + 0.493216i \(0.164179\pi\)
\(878\) −3.21929 −0.108646
\(879\) −59.0448 −1.99153
\(880\) 0.411999 0.0138885
\(881\) 54.1095 1.82299 0.911497 0.411306i \(-0.134927\pi\)
0.911497 + 0.411306i \(0.134927\pi\)
\(882\) −27.0960 −0.912369
\(883\) 13.3154 0.448100 0.224050 0.974578i \(-0.428072\pi\)
0.224050 + 0.974578i \(0.428072\pi\)
\(884\) −5.05173 −0.169908
\(885\) −4.35727 −0.146468
\(886\) −10.2920 −0.345766
\(887\) −31.3735 −1.05342 −0.526709 0.850046i \(-0.676574\pi\)
−0.526709 + 0.850046i \(0.676574\pi\)
\(888\) −3.51039 −0.117801
\(889\) 17.3840 0.583039
\(890\) 0.473359 0.0158670
\(891\) −7.67676 −0.257181
\(892\) 14.2168 0.476013
\(893\) −12.0470 −0.403136
\(894\) 32.1616 1.07564
\(895\) 0.983378 0.0328707
\(896\) −0.997196 −0.0333140
\(897\) −17.7011 −0.591022
\(898\) −18.7701 −0.626368
\(899\) 22.0912 0.736782
\(900\) −22.4972 −0.749907
\(901\) 5.40369 0.180023
\(902\) −20.2654 −0.674765
\(903\) −26.1000 −0.868553
\(904\) −11.2605 −0.374519
\(905\) 0.562523 0.0186989
\(906\) 54.9645 1.82607
\(907\) −7.36776 −0.244642 −0.122321 0.992491i \(-0.539034\pi\)
−0.122321 + 0.992491i \(0.539034\pi\)
\(908\) −0.421693 −0.0139944
\(909\) 70.9286 2.35255
\(910\) −0.214428 −0.00710821
\(911\) −37.4948 −1.24226 −0.621129 0.783709i \(-0.713326\pi\)
−0.621129 + 0.783709i \(0.713326\pi\)
\(912\) −2.74076 −0.0907558
\(913\) 3.15624 0.104456
\(914\) 0.823220 0.0272297
\(915\) −4.31871 −0.142772
\(916\) −22.4671 −0.742335
\(917\) 11.0791 0.365864
\(918\) 11.3843 0.375737
\(919\) −38.0095 −1.25382 −0.626908 0.779093i \(-0.715680\pi\)
−0.626908 + 0.779093i \(0.715680\pi\)
\(920\) 0.410804 0.0135438
\(921\) −95.2455 −3.13844
\(922\) 39.0053 1.28457
\(923\) 10.0802 0.331794
\(924\) 9.62820 0.316744
\(925\) −6.38652 −0.209987
\(926\) −25.6145 −0.841744
\(927\) 30.8831 1.01433
\(928\) −2.84490 −0.0933884
\(929\) 43.9473 1.44186 0.720932 0.693006i \(-0.243714\pi\)
0.720932 + 0.693006i \(0.243714\pi\)
\(930\) 2.48901 0.0816179
\(931\) −6.00560 −0.196826
\(932\) 9.30220 0.304704
\(933\) −54.4592 −1.78291
\(934\) −11.2528 −0.368204
\(935\) −1.13198 −0.0370197
\(936\) 8.29557 0.271149
\(937\) 25.8418 0.844214 0.422107 0.906546i \(-0.361291\pi\)
0.422107 + 0.906546i \(0.361291\pi\)
\(938\) −8.38261 −0.273702
\(939\) 23.0240 0.751359
\(940\) −1.40890 −0.0459533
\(941\) −23.6252 −0.770160 −0.385080 0.922883i \(-0.625826\pi\)
−0.385080 + 0.922883i \(0.625826\pi\)
\(942\) −47.3521 −1.54282
\(943\) −20.2066 −0.658019
\(944\) 13.5938 0.442439
\(945\) 0.483221 0.0157192
\(946\) −33.6419 −1.09379
\(947\) 0.951940 0.0309339 0.0154669 0.999880i \(-0.495077\pi\)
0.0154669 + 0.999880i \(0.495077\pi\)
\(948\) −5.77772 −0.187652
\(949\) 19.9349 0.647115
\(950\) −4.98632 −0.161778
\(951\) 32.3980 1.05058
\(952\) 2.73983 0.0887984
\(953\) −3.80277 −0.123184 −0.0615918 0.998101i \(-0.519618\pi\)
−0.0615918 + 0.998101i \(0.519618\pi\)
\(954\) −8.87351 −0.287291
\(955\) 1.96243 0.0635027
\(956\) −1.20314 −0.0389123
\(957\) 27.4683 0.887924
\(958\) −25.9292 −0.837734
\(959\) 15.9380 0.514663
\(960\) −0.320535 −0.0103452
\(961\) 29.2982 0.945102
\(962\) 2.35495 0.0759265
\(963\) −10.5223 −0.339077
\(964\) −7.81685 −0.251764
\(965\) 0.336282 0.0108253
\(966\) 9.60026 0.308883
\(967\) 59.5148 1.91387 0.956933 0.290308i \(-0.0937579\pi\)
0.956933 + 0.290308i \(0.0937579\pi\)
\(968\) 1.41040 0.0453320
\(969\) 7.53034 0.241909
\(970\) 0.298139 0.00957267
\(971\) 12.6012 0.404392 0.202196 0.979345i \(-0.435192\pi\)
0.202196 + 0.979345i \(0.435192\pi\)
\(972\) 18.4029 0.590272
\(973\) −3.15273 −0.101072
\(974\) 34.5869 1.10824
\(975\) 25.1275 0.804724
\(976\) 13.4735 0.431275
\(977\) 25.1943 0.806036 0.403018 0.915192i \(-0.367961\pi\)
0.403018 + 0.915192i \(0.367961\pi\)
\(978\) 48.8530 1.56215
\(979\) 14.2587 0.455710
\(980\) −0.702360 −0.0224361
\(981\) −48.6772 −1.55414
\(982\) 28.2296 0.900844
\(983\) −30.4475 −0.971123 −0.485562 0.874202i \(-0.661385\pi\)
−0.485562 + 0.874202i \(0.661385\pi\)
\(984\) 15.7665 0.502617
\(985\) −2.18619 −0.0696577
\(986\) 7.81646 0.248927
\(987\) −32.9253 −1.04802
\(988\) 1.83864 0.0584950
\(989\) −33.5443 −1.06665
\(990\) 1.85885 0.0590782
\(991\) 50.2206 1.59531 0.797655 0.603114i \(-0.206074\pi\)
0.797655 + 0.603114i \(0.206074\pi\)
\(992\) −7.76519 −0.246545
\(993\) −27.7166 −0.879559
\(994\) −5.46704 −0.173404
\(995\) 1.66011 0.0526289
\(996\) −2.45555 −0.0778072
\(997\) 13.4416 0.425700 0.212850 0.977085i \(-0.431725\pi\)
0.212850 + 0.977085i \(0.431725\pi\)
\(998\) 2.64444 0.0837083
\(999\) −5.30696 −0.167905
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 \(a_p\))