Properties

Label 4010.2.a.k.1.14
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(2.25248\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.71977 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.71977 q^{6} -0.594829 q^{7} -1.00000 q^{8} +4.39715 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.71977 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.71977 q^{6} -0.594829 q^{7} -1.00000 q^{8} +4.39715 q^{9} +1.00000 q^{10} -5.15188 q^{11} +2.71977 q^{12} +0.430765 q^{13} +0.594829 q^{14} -2.71977 q^{15} +1.00000 q^{16} +3.55242 q^{17} -4.39715 q^{18} -5.11480 q^{19} -1.00000 q^{20} -1.61780 q^{21} +5.15188 q^{22} +6.74147 q^{23} -2.71977 q^{24} +1.00000 q^{25} -0.430765 q^{26} +3.79991 q^{27} -0.594829 q^{28} -7.79165 q^{29} +2.71977 q^{30} -8.50979 q^{31} -1.00000 q^{32} -14.0119 q^{33} -3.55242 q^{34} +0.594829 q^{35} +4.39715 q^{36} -0.601851 q^{37} +5.11480 q^{38} +1.17158 q^{39} +1.00000 q^{40} +4.94186 q^{41} +1.61780 q^{42} +2.44358 q^{43} -5.15188 q^{44} -4.39715 q^{45} -6.74147 q^{46} -2.58807 q^{47} +2.71977 q^{48} -6.64618 q^{49} -1.00000 q^{50} +9.66177 q^{51} +0.430765 q^{52} +3.18711 q^{53} -3.79991 q^{54} +5.15188 q^{55} +0.594829 q^{56} -13.9111 q^{57} +7.79165 q^{58} -14.3834 q^{59} -2.71977 q^{60} -2.26604 q^{61} +8.50979 q^{62} -2.61555 q^{63} +1.00000 q^{64} -0.430765 q^{65} +14.0119 q^{66} +2.61956 q^{67} +3.55242 q^{68} +18.3352 q^{69} -0.594829 q^{70} +6.99728 q^{71} -4.39715 q^{72} +5.20733 q^{73} +0.601851 q^{74} +2.71977 q^{75} -5.11480 q^{76} +3.06449 q^{77} -1.17158 q^{78} -17.2296 q^{79} -1.00000 q^{80} -2.85655 q^{81} -4.94186 q^{82} -6.99067 q^{83} -1.61780 q^{84} -3.55242 q^{85} -2.44358 q^{86} -21.1915 q^{87} +5.15188 q^{88} -12.7136 q^{89} +4.39715 q^{90} -0.256231 q^{91} +6.74147 q^{92} -23.1447 q^{93} +2.58807 q^{94} +5.11480 q^{95} -2.71977 q^{96} -1.67993 q^{97} +6.64618 q^{98} -22.6536 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) 2.71977 1.57026 0.785130 0.619331i \(-0.212596\pi\)
0.785130 + 0.619331i \(0.212596\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.71977 −1.11034
\(7\) −0.594829 −0.224824 −0.112412 0.993662i \(-0.535858\pi\)
−0.112412 + 0.993662i \(0.535858\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.39715 1.46572
\(10\) 1.00000 0.316228
\(11\) −5.15188 −1.55335 −0.776675 0.629902i \(-0.783095\pi\)
−0.776675 + 0.629902i \(0.783095\pi\)
\(12\) 2.71977 0.785130
\(13\) 0.430765 0.119473 0.0597363 0.998214i \(-0.480974\pi\)
0.0597363 + 0.998214i \(0.480974\pi\)
\(14\) 0.594829 0.158975
\(15\) −2.71977 −0.702241
\(16\) 1.00000 0.250000
\(17\) 3.55242 0.861589 0.430795 0.902450i \(-0.358233\pi\)
0.430795 + 0.902450i \(0.358233\pi\)
\(18\) −4.39715 −1.03642
\(19\) −5.11480 −1.17342 −0.586708 0.809798i \(-0.699576\pi\)
−0.586708 + 0.809798i \(0.699576\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.61780 −0.353033
\(22\) 5.15188 1.09838
\(23\) 6.74147 1.40569 0.702847 0.711341i \(-0.251912\pi\)
0.702847 + 0.711341i \(0.251912\pi\)
\(24\) −2.71977 −0.555171
\(25\) 1.00000 0.200000
\(26\) −0.430765 −0.0844799
\(27\) 3.79991 0.731294
\(28\) −0.594829 −0.112412
\(29\) −7.79165 −1.44687 −0.723436 0.690391i \(-0.757439\pi\)
−0.723436 + 0.690391i \(0.757439\pi\)
\(30\) 2.71977 0.496560
\(31\) −8.50979 −1.52840 −0.764202 0.644977i \(-0.776867\pi\)
−0.764202 + 0.644977i \(0.776867\pi\)
\(32\) −1.00000 −0.176777
\(33\) −14.0119 −2.43916
\(34\) −3.55242 −0.609236
\(35\) 0.594829 0.100544
\(36\) 4.39715 0.732858
\(37\) −0.601851 −0.0989437 −0.0494719 0.998776i \(-0.515754\pi\)
−0.0494719 + 0.998776i \(0.515754\pi\)
\(38\) 5.11480 0.829731
\(39\) 1.17158 0.187603
\(40\) 1.00000 0.158114
\(41\) 4.94186 0.771789 0.385895 0.922543i \(-0.373893\pi\)
0.385895 + 0.922543i \(0.373893\pi\)
\(42\) 1.61780 0.249632
\(43\) 2.44358 0.372642 0.186321 0.982489i \(-0.440344\pi\)
0.186321 + 0.982489i \(0.440344\pi\)
\(44\) −5.15188 −0.776675
\(45\) −4.39715 −0.655488
\(46\) −6.74147 −0.993976
\(47\) −2.58807 −0.377509 −0.188755 0.982024i \(-0.560445\pi\)
−0.188755 + 0.982024i \(0.560445\pi\)
\(48\) 2.71977 0.392565
\(49\) −6.64618 −0.949454
\(50\) −1.00000 −0.141421
\(51\) 9.66177 1.35292
\(52\) 0.430765 0.0597363
\(53\) 3.18711 0.437783 0.218891 0.975749i \(-0.429756\pi\)
0.218891 + 0.975749i \(0.429756\pi\)
\(54\) −3.79991 −0.517103
\(55\) 5.15188 0.694679
\(56\) 0.594829 0.0794874
\(57\) −13.9111 −1.84257
\(58\) 7.79165 1.02309
\(59\) −14.3834 −1.87255 −0.936277 0.351261i \(-0.885753\pi\)
−0.936277 + 0.351261i \(0.885753\pi\)
\(60\) −2.71977 −0.351121
\(61\) −2.26604 −0.290137 −0.145068 0.989422i \(-0.546340\pi\)
−0.145068 + 0.989422i \(0.546340\pi\)
\(62\) 8.50979 1.08074
\(63\) −2.61555 −0.329528
\(64\) 1.00000 0.125000
\(65\) −0.430765 −0.0534298
\(66\) 14.0119 1.72475
\(67\) 2.61956 0.320031 0.160015 0.987115i \(-0.448846\pi\)
0.160015 + 0.987115i \(0.448846\pi\)
\(68\) 3.55242 0.430795
\(69\) 18.3352 2.20730
\(70\) −0.594829 −0.0710957
\(71\) 6.99728 0.830424 0.415212 0.909725i \(-0.363707\pi\)
0.415212 + 0.909725i \(0.363707\pi\)
\(72\) −4.39715 −0.518209
\(73\) 5.20733 0.609472 0.304736 0.952437i \(-0.401432\pi\)
0.304736 + 0.952437i \(0.401432\pi\)
\(74\) 0.601851 0.0699638
\(75\) 2.71977 0.314052
\(76\) −5.11480 −0.586708
\(77\) 3.06449 0.349231
\(78\) −1.17158 −0.132655
\(79\) −17.2296 −1.93848 −0.969242 0.246112i \(-0.920847\pi\)
−0.969242 + 0.246112i \(0.920847\pi\)
\(80\) −1.00000 −0.111803
\(81\) −2.85655 −0.317394
\(82\) −4.94186 −0.545738
\(83\) −6.99067 −0.767325 −0.383663 0.923473i \(-0.625337\pi\)
−0.383663 + 0.923473i \(0.625337\pi\)
\(84\) −1.61780 −0.176516
\(85\) −3.55242 −0.385314
\(86\) −2.44358 −0.263498
\(87\) −21.1915 −2.27197
\(88\) 5.15188 0.549192
\(89\) −12.7136 −1.34764 −0.673822 0.738894i \(-0.735349\pi\)
−0.673822 + 0.738894i \(0.735349\pi\)
\(90\) 4.39715 0.463500
\(91\) −0.256231 −0.0268603
\(92\) 6.74147 0.702847
\(93\) −23.1447 −2.39999
\(94\) 2.58807 0.266939
\(95\) 5.11480 0.524768
\(96\) −2.71977 −0.277585
\(97\) −1.67993 −0.170571 −0.0852857 0.996357i \(-0.527180\pi\)
−0.0852857 + 0.996357i \(0.527180\pi\)
\(98\) 6.64618 0.671365
\(99\) −22.6536 −2.27677
\(100\) 1.00000 0.100000
\(101\) 12.8386 1.27749 0.638743 0.769420i \(-0.279455\pi\)
0.638743 + 0.769420i \(0.279455\pi\)
\(102\) −9.66177 −0.956658
\(103\) 3.27639 0.322833 0.161416 0.986886i \(-0.448394\pi\)
0.161416 + 0.986886i \(0.448394\pi\)
\(104\) −0.430765 −0.0422399
\(105\) 1.61780 0.157881
\(106\) −3.18711 −0.309559
\(107\) 1.95485 0.188983 0.0944915 0.995526i \(-0.469877\pi\)
0.0944915 + 0.995526i \(0.469877\pi\)
\(108\) 3.79991 0.365647
\(109\) 0.904117 0.0865987 0.0432993 0.999062i \(-0.486213\pi\)
0.0432993 + 0.999062i \(0.486213\pi\)
\(110\) −5.15188 −0.491212
\(111\) −1.63690 −0.155367
\(112\) −0.594829 −0.0562061
\(113\) −12.5979 −1.18511 −0.592555 0.805530i \(-0.701881\pi\)
−0.592555 + 0.805530i \(0.701881\pi\)
\(114\) 13.9111 1.30289
\(115\) −6.74147 −0.628646
\(116\) −7.79165 −0.723436
\(117\) 1.89413 0.175113
\(118\) 14.3834 1.32410
\(119\) −2.11309 −0.193706
\(120\) 2.71977 0.248280
\(121\) 15.5418 1.41289
\(122\) 2.26604 0.205158
\(123\) 13.4407 1.21191
\(124\) −8.50979 −0.764202
\(125\) −1.00000 −0.0894427
\(126\) 2.61555 0.233012
\(127\) −15.4067 −1.36712 −0.683560 0.729895i \(-0.739569\pi\)
−0.683560 + 0.729895i \(0.739569\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.64597 0.585145
\(130\) 0.430765 0.0377806
\(131\) 4.16970 0.364308 0.182154 0.983270i \(-0.441693\pi\)
0.182154 + 0.983270i \(0.441693\pi\)
\(132\) −14.0119 −1.21958
\(133\) 3.04243 0.263813
\(134\) −2.61956 −0.226296
\(135\) −3.79991 −0.327045
\(136\) −3.55242 −0.304618
\(137\) 15.4928 1.32364 0.661819 0.749664i \(-0.269785\pi\)
0.661819 + 0.749664i \(0.269785\pi\)
\(138\) −18.3352 −1.56080
\(139\) −6.32300 −0.536309 −0.268155 0.963376i \(-0.586414\pi\)
−0.268155 + 0.963376i \(0.586414\pi\)
\(140\) 0.594829 0.0502722
\(141\) −7.03896 −0.592787
\(142\) −6.99728 −0.587199
\(143\) −2.21925 −0.185583
\(144\) 4.39715 0.366429
\(145\) 7.79165 0.647061
\(146\) −5.20733 −0.430962
\(147\) −18.0761 −1.49089
\(148\) −0.601851 −0.0494719
\(149\) 21.4347 1.75600 0.877998 0.478665i \(-0.158879\pi\)
0.877998 + 0.478665i \(0.158879\pi\)
\(150\) −2.71977 −0.222068
\(151\) −1.44587 −0.117663 −0.0588316 0.998268i \(-0.518738\pi\)
−0.0588316 + 0.998268i \(0.518738\pi\)
\(152\) 5.11480 0.414865
\(153\) 15.6205 1.26284
\(154\) −3.06449 −0.246943
\(155\) 8.50979 0.683523
\(156\) 1.17158 0.0938015
\(157\) −17.1502 −1.36873 −0.684367 0.729138i \(-0.739921\pi\)
−0.684367 + 0.729138i \(0.739921\pi\)
\(158\) 17.2296 1.37071
\(159\) 8.66819 0.687432
\(160\) 1.00000 0.0790569
\(161\) −4.01002 −0.316034
\(162\) 2.85655 0.224432
\(163\) −12.1007 −0.947800 −0.473900 0.880579i \(-0.657154\pi\)
−0.473900 + 0.880579i \(0.657154\pi\)
\(164\) 4.94186 0.385895
\(165\) 14.0119 1.09083
\(166\) 6.99067 0.542581
\(167\) −20.9442 −1.62071 −0.810357 0.585936i \(-0.800727\pi\)
−0.810357 + 0.585936i \(0.800727\pi\)
\(168\) 1.61780 0.124816
\(169\) −12.8144 −0.985726
\(170\) 3.55242 0.272458
\(171\) −22.4905 −1.71989
\(172\) 2.44358 0.186321
\(173\) 4.62138 0.351357 0.175678 0.984448i \(-0.443788\pi\)
0.175678 + 0.984448i \(0.443788\pi\)
\(174\) 21.1915 1.60652
\(175\) −0.594829 −0.0449649
\(176\) −5.15188 −0.388337
\(177\) −39.1194 −2.94040
\(178\) 12.7136 0.952928
\(179\) −13.5752 −1.01465 −0.507327 0.861753i \(-0.669366\pi\)
−0.507327 + 0.861753i \(0.669366\pi\)
\(180\) −4.39715 −0.327744
\(181\) 1.90393 0.141518 0.0707589 0.997493i \(-0.477458\pi\)
0.0707589 + 0.997493i \(0.477458\pi\)
\(182\) 0.256231 0.0189931
\(183\) −6.16311 −0.455590
\(184\) −6.74147 −0.496988
\(185\) 0.601851 0.0442490
\(186\) 23.1447 1.69705
\(187\) −18.3016 −1.33835
\(188\) −2.58807 −0.188755
\(189\) −2.26030 −0.164413
\(190\) −5.11480 −0.371067
\(191\) −11.4968 −0.831877 −0.415939 0.909393i \(-0.636547\pi\)
−0.415939 + 0.909393i \(0.636547\pi\)
\(192\) 2.71977 0.196282
\(193\) −21.6763 −1.56029 −0.780147 0.625596i \(-0.784856\pi\)
−0.780147 + 0.625596i \(0.784856\pi\)
\(194\) 1.67993 0.120612
\(195\) −1.17158 −0.0838986
\(196\) −6.64618 −0.474727
\(197\) −9.16597 −0.653048 −0.326524 0.945189i \(-0.605877\pi\)
−0.326524 + 0.945189i \(0.605877\pi\)
\(198\) 22.6536 1.60992
\(199\) −20.8817 −1.48027 −0.740133 0.672461i \(-0.765237\pi\)
−0.740133 + 0.672461i \(0.765237\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 7.12461 0.502531
\(202\) −12.8386 −0.903319
\(203\) 4.63470 0.325292
\(204\) 9.66177 0.676459
\(205\) −4.94186 −0.345155
\(206\) −3.27639 −0.228277
\(207\) 29.6432 2.06035
\(208\) 0.430765 0.0298682
\(209\) 26.3508 1.82273
\(210\) −1.61780 −0.111639
\(211\) 19.4256 1.33731 0.668657 0.743571i \(-0.266869\pi\)
0.668657 + 0.743571i \(0.266869\pi\)
\(212\) 3.18711 0.218891
\(213\) 19.0310 1.30398
\(214\) −1.95485 −0.133631
\(215\) −2.44358 −0.166651
\(216\) −3.79991 −0.258551
\(217\) 5.06187 0.343622
\(218\) −0.904117 −0.0612345
\(219\) 14.1627 0.957029
\(220\) 5.15188 0.347339
\(221\) 1.53026 0.102936
\(222\) 1.63690 0.109861
\(223\) 24.0478 1.61036 0.805181 0.593030i \(-0.202068\pi\)
0.805181 + 0.593030i \(0.202068\pi\)
\(224\) 0.594829 0.0397437
\(225\) 4.39715 0.293143
\(226\) 12.5979 0.837999
\(227\) 4.82553 0.320281 0.160141 0.987094i \(-0.448805\pi\)
0.160141 + 0.987094i \(0.448805\pi\)
\(228\) −13.9111 −0.921284
\(229\) 11.8566 0.783508 0.391754 0.920070i \(-0.371868\pi\)
0.391754 + 0.920070i \(0.371868\pi\)
\(230\) 6.74147 0.444520
\(231\) 8.33470 0.548383
\(232\) 7.79165 0.511547
\(233\) 23.3533 1.52992 0.764961 0.644076i \(-0.222758\pi\)
0.764961 + 0.644076i \(0.222758\pi\)
\(234\) −1.89413 −0.123823
\(235\) 2.58807 0.168827
\(236\) −14.3834 −0.936277
\(237\) −46.8606 −3.04392
\(238\) 2.11309 0.136971
\(239\) 17.3614 1.12301 0.561506 0.827473i \(-0.310222\pi\)
0.561506 + 0.827473i \(0.310222\pi\)
\(240\) −2.71977 −0.175560
\(241\) 10.5726 0.681039 0.340519 0.940237i \(-0.389397\pi\)
0.340519 + 0.940237i \(0.389397\pi\)
\(242\) −15.5418 −0.999067
\(243\) −19.1689 −1.22968
\(244\) −2.26604 −0.145068
\(245\) 6.64618 0.424609
\(246\) −13.4407 −0.856950
\(247\) −2.20328 −0.140191
\(248\) 8.50979 0.540372
\(249\) −19.0130 −1.20490
\(250\) 1.00000 0.0632456
\(251\) −11.0779 −0.699232 −0.349616 0.936893i \(-0.613688\pi\)
−0.349616 + 0.936893i \(0.613688\pi\)
\(252\) −2.61555 −0.164764
\(253\) −34.7312 −2.18353
\(254\) 15.4067 0.966699
\(255\) −9.66177 −0.605044
\(256\) 1.00000 0.0625000
\(257\) 23.2093 1.44775 0.723877 0.689929i \(-0.242358\pi\)
0.723877 + 0.689929i \(0.242358\pi\)
\(258\) −6.64597 −0.413760
\(259\) 0.357999 0.0222450
\(260\) −0.430765 −0.0267149
\(261\) −34.2610 −2.12070
\(262\) −4.16970 −0.257605
\(263\) 21.4733 1.32410 0.662049 0.749461i \(-0.269687\pi\)
0.662049 + 0.749461i \(0.269687\pi\)
\(264\) 14.0119 0.862374
\(265\) −3.18711 −0.195782
\(266\) −3.04243 −0.186544
\(267\) −34.5782 −2.11615
\(268\) 2.61956 0.160015
\(269\) 13.3091 0.811469 0.405735 0.913991i \(-0.367016\pi\)
0.405735 + 0.913991i \(0.367016\pi\)
\(270\) 3.79991 0.231255
\(271\) −27.6321 −1.67853 −0.839266 0.543721i \(-0.817015\pi\)
−0.839266 + 0.543721i \(0.817015\pi\)
\(272\) 3.55242 0.215397
\(273\) −0.696890 −0.0421777
\(274\) −15.4928 −0.935954
\(275\) −5.15188 −0.310670
\(276\) 18.3352 1.10365
\(277\) 11.5551 0.694278 0.347139 0.937814i \(-0.387153\pi\)
0.347139 + 0.937814i \(0.387153\pi\)
\(278\) 6.32300 0.379228
\(279\) −37.4188 −2.24021
\(280\) −0.594829 −0.0355478
\(281\) −12.2034 −0.727991 −0.363996 0.931401i \(-0.618588\pi\)
−0.363996 + 0.931401i \(0.618588\pi\)
\(282\) 7.03896 0.419164
\(283\) −21.0410 −1.25076 −0.625378 0.780322i \(-0.715055\pi\)
−0.625378 + 0.780322i \(0.715055\pi\)
\(284\) 6.99728 0.415212
\(285\) 13.9111 0.824022
\(286\) 2.21925 0.131227
\(287\) −2.93956 −0.173517
\(288\) −4.39715 −0.259104
\(289\) −4.38028 −0.257664
\(290\) −7.79165 −0.457541
\(291\) −4.56903 −0.267842
\(292\) 5.20733 0.304736
\(293\) 6.73977 0.393742 0.196871 0.980429i \(-0.436922\pi\)
0.196871 + 0.980429i \(0.436922\pi\)
\(294\) 18.0761 1.05422
\(295\) 14.3834 0.837432
\(296\) 0.601851 0.0349819
\(297\) −19.5767 −1.13595
\(298\) −21.4347 −1.24168
\(299\) 2.90399 0.167942
\(300\) 2.71977 0.157026
\(301\) −1.45351 −0.0837790
\(302\) 1.44587 0.0832005
\(303\) 34.9180 2.00599
\(304\) −5.11480 −0.293354
\(305\) 2.26604 0.129753
\(306\) −15.6205 −0.892966
\(307\) 21.8952 1.24962 0.624811 0.780776i \(-0.285176\pi\)
0.624811 + 0.780776i \(0.285176\pi\)
\(308\) 3.06449 0.174615
\(309\) 8.91103 0.506931
\(310\) −8.50979 −0.483324
\(311\) 19.9821 1.13308 0.566541 0.824033i \(-0.308281\pi\)
0.566541 + 0.824033i \(0.308281\pi\)
\(312\) −1.17158 −0.0663277
\(313\) 6.20088 0.350494 0.175247 0.984524i \(-0.443928\pi\)
0.175247 + 0.984524i \(0.443928\pi\)
\(314\) 17.1502 0.967841
\(315\) 2.61555 0.147370
\(316\) −17.2296 −0.969242
\(317\) −10.6814 −0.599929 −0.299965 0.953950i \(-0.596975\pi\)
−0.299965 + 0.953950i \(0.596975\pi\)
\(318\) −8.66819 −0.486088
\(319\) 40.1416 2.24750
\(320\) −1.00000 −0.0559017
\(321\) 5.31675 0.296752
\(322\) 4.01002 0.223470
\(323\) −18.1700 −1.01100
\(324\) −2.85655 −0.158697
\(325\) 0.430765 0.0238945
\(326\) 12.1007 0.670196
\(327\) 2.45899 0.135982
\(328\) −4.94186 −0.272869
\(329\) 1.53946 0.0848732
\(330\) −14.0119 −0.771331
\(331\) −13.2248 −0.726898 −0.363449 0.931614i \(-0.618401\pi\)
−0.363449 + 0.931614i \(0.618401\pi\)
\(332\) −6.99067 −0.383663
\(333\) −2.64643 −0.145023
\(334\) 20.9442 1.14602
\(335\) −2.61956 −0.143122
\(336\) −1.61780 −0.0882581
\(337\) 10.7103 0.583427 0.291713 0.956506i \(-0.405775\pi\)
0.291713 + 0.956506i \(0.405775\pi\)
\(338\) 12.8144 0.697014
\(339\) −34.2633 −1.86093
\(340\) −3.55242 −0.192657
\(341\) 43.8414 2.37415
\(342\) 22.4905 1.21615
\(343\) 8.11715 0.438285
\(344\) −2.44358 −0.131749
\(345\) −18.3352 −0.987137
\(346\) −4.62138 −0.248447
\(347\) 26.7432 1.43565 0.717825 0.696223i \(-0.245138\pi\)
0.717825 + 0.696223i \(0.245138\pi\)
\(348\) −21.1915 −1.13598
\(349\) 19.1024 1.02253 0.511264 0.859424i \(-0.329177\pi\)
0.511264 + 0.859424i \(0.329177\pi\)
\(350\) 0.594829 0.0317950
\(351\) 1.63687 0.0873696
\(352\) 5.15188 0.274596
\(353\) −2.45986 −0.130925 −0.0654625 0.997855i \(-0.520852\pi\)
−0.0654625 + 0.997855i \(0.520852\pi\)
\(354\) 39.1194 2.07917
\(355\) −6.99728 −0.371377
\(356\) −12.7136 −0.673822
\(357\) −5.74711 −0.304169
\(358\) 13.5752 0.717469
\(359\) 3.91065 0.206396 0.103198 0.994661i \(-0.467092\pi\)
0.103198 + 0.994661i \(0.467092\pi\)
\(360\) 4.39715 0.231750
\(361\) 7.16122 0.376906
\(362\) −1.90393 −0.100068
\(363\) 42.2702 2.21861
\(364\) −0.256231 −0.0134302
\(365\) −5.20733 −0.272564
\(366\) 6.16311 0.322151
\(367\) 29.4789 1.53879 0.769393 0.638776i \(-0.220559\pi\)
0.769393 + 0.638776i \(0.220559\pi\)
\(368\) 6.74147 0.351424
\(369\) 21.7301 1.13122
\(370\) −0.601851 −0.0312888
\(371\) −1.89578 −0.0984242
\(372\) −23.1447 −1.20000
\(373\) 25.0946 1.29935 0.649676 0.760211i \(-0.274905\pi\)
0.649676 + 0.760211i \(0.274905\pi\)
\(374\) 18.3016 0.946356
\(375\) −2.71977 −0.140448
\(376\) 2.58807 0.133470
\(377\) −3.35637 −0.172862
\(378\) 2.26030 0.116257
\(379\) −7.83169 −0.402287 −0.201143 0.979562i \(-0.564466\pi\)
−0.201143 + 0.979562i \(0.564466\pi\)
\(380\) 5.11480 0.262384
\(381\) −41.9025 −2.14673
\(382\) 11.4968 0.588226
\(383\) 10.0381 0.512925 0.256463 0.966554i \(-0.417443\pi\)
0.256463 + 0.966554i \(0.417443\pi\)
\(384\) −2.71977 −0.138793
\(385\) −3.06449 −0.156181
\(386\) 21.6763 1.10329
\(387\) 10.7448 0.546188
\(388\) −1.67993 −0.0852857
\(389\) −8.12206 −0.411805 −0.205902 0.978573i \(-0.566013\pi\)
−0.205902 + 0.978573i \(0.566013\pi\)
\(390\) 1.17158 0.0593253
\(391\) 23.9486 1.21113
\(392\) 6.64618 0.335683
\(393\) 11.3406 0.572058
\(394\) 9.16597 0.461775
\(395\) 17.2296 0.866916
\(396\) −22.6536 −1.13838
\(397\) −26.4713 −1.32856 −0.664279 0.747485i \(-0.731261\pi\)
−0.664279 + 0.747485i \(0.731261\pi\)
\(398\) 20.8817 1.04671
\(399\) 8.27472 0.414254
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −7.12461 −0.355343
\(403\) −3.66572 −0.182602
\(404\) 12.8386 0.638743
\(405\) 2.85655 0.141943
\(406\) −4.63470 −0.230016
\(407\) 3.10066 0.153694
\(408\) −9.66177 −0.478329
\(409\) −3.19920 −0.158190 −0.0790952 0.996867i \(-0.525203\pi\)
−0.0790952 + 0.996867i \(0.525203\pi\)
\(410\) 4.94186 0.244061
\(411\) 42.1368 2.07846
\(412\) 3.27639 0.161416
\(413\) 8.55565 0.420996
\(414\) −29.6432 −1.45689
\(415\) 6.99067 0.343158
\(416\) −0.430765 −0.0211200
\(417\) −17.1971 −0.842145
\(418\) −26.3508 −1.28886
\(419\) 9.80519 0.479015 0.239507 0.970895i \(-0.423014\pi\)
0.239507 + 0.970895i \(0.423014\pi\)
\(420\) 1.61780 0.0789405
\(421\) −34.3451 −1.67388 −0.836939 0.547296i \(-0.815657\pi\)
−0.836939 + 0.547296i \(0.815657\pi\)
\(422\) −19.4256 −0.945624
\(423\) −11.3801 −0.553321
\(424\) −3.18711 −0.154780
\(425\) 3.55242 0.172318
\(426\) −19.0310 −0.922054
\(427\) 1.34791 0.0652298
\(428\) 1.95485 0.0944915
\(429\) −6.03584 −0.291413
\(430\) 2.44358 0.117840
\(431\) 22.5844 1.08785 0.543927 0.839133i \(-0.316937\pi\)
0.543927 + 0.839133i \(0.316937\pi\)
\(432\) 3.79991 0.182823
\(433\) −26.8669 −1.29114 −0.645570 0.763701i \(-0.723380\pi\)
−0.645570 + 0.763701i \(0.723380\pi\)
\(434\) −5.06187 −0.242978
\(435\) 21.1915 1.01605
\(436\) 0.904117 0.0432993
\(437\) −34.4813 −1.64946
\(438\) −14.1627 −0.676722
\(439\) 2.51933 0.120241 0.0601205 0.998191i \(-0.480852\pi\)
0.0601205 + 0.998191i \(0.480852\pi\)
\(440\) −5.15188 −0.245606
\(441\) −29.2242 −1.39163
\(442\) −1.53026 −0.0727870
\(443\) −15.6162 −0.741950 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(444\) −1.63690 −0.0776837
\(445\) 12.7136 0.602685
\(446\) −24.0478 −1.13870
\(447\) 58.2973 2.75737
\(448\) −0.594829 −0.0281030
\(449\) −3.09920 −0.146260 −0.0731301 0.997322i \(-0.523299\pi\)
−0.0731301 + 0.997322i \(0.523299\pi\)
\(450\) −4.39715 −0.207283
\(451\) −25.4599 −1.19886
\(452\) −12.5979 −0.592555
\(453\) −3.93243 −0.184762
\(454\) −4.82553 −0.226473
\(455\) 0.256231 0.0120123
\(456\) 13.9111 0.651446
\(457\) −2.80648 −0.131282 −0.0656409 0.997843i \(-0.520909\pi\)
−0.0656409 + 0.997843i \(0.520909\pi\)
\(458\) −11.8566 −0.554024
\(459\) 13.4989 0.630075
\(460\) −6.74147 −0.314323
\(461\) 10.1931 0.474742 0.237371 0.971419i \(-0.423714\pi\)
0.237371 + 0.971419i \(0.423714\pi\)
\(462\) −8.33470 −0.387765
\(463\) −1.35804 −0.0631136 −0.0315568 0.999502i \(-0.510047\pi\)
−0.0315568 + 0.999502i \(0.510047\pi\)
\(464\) −7.79165 −0.361718
\(465\) 23.1447 1.07331
\(466\) −23.3533 −1.08182
\(467\) −3.75856 −0.173925 −0.0869627 0.996212i \(-0.527716\pi\)
−0.0869627 + 0.996212i \(0.527716\pi\)
\(468\) 1.89413 0.0875564
\(469\) −1.55819 −0.0719507
\(470\) −2.58807 −0.119379
\(471\) −46.6445 −2.14927
\(472\) 14.3834 0.662048
\(473\) −12.5890 −0.578844
\(474\) 46.8606 2.15238
\(475\) −5.11480 −0.234683
\(476\) −2.11309 −0.0968531
\(477\) 14.0142 0.641665
\(478\) −17.3614 −0.794090
\(479\) −11.0719 −0.505887 −0.252943 0.967481i \(-0.581399\pi\)
−0.252943 + 0.967481i \(0.581399\pi\)
\(480\) 2.71977 0.124140
\(481\) −0.259256 −0.0118211
\(482\) −10.5726 −0.481567
\(483\) −10.9063 −0.496256
\(484\) 15.5418 0.706447
\(485\) 1.67993 0.0762819
\(486\) 19.1689 0.869519
\(487\) −16.7406 −0.758587 −0.379294 0.925276i \(-0.623833\pi\)
−0.379294 + 0.925276i \(0.623833\pi\)
\(488\) 2.26604 0.102579
\(489\) −32.9111 −1.48829
\(490\) −6.64618 −0.300244
\(491\) −21.5509 −0.972576 −0.486288 0.873798i \(-0.661649\pi\)
−0.486288 + 0.873798i \(0.661649\pi\)
\(492\) 13.4407 0.605955
\(493\) −27.6792 −1.24661
\(494\) 2.20328 0.0991301
\(495\) 22.6536 1.01820
\(496\) −8.50979 −0.382101
\(497\) −4.16219 −0.186700
\(498\) 19.0130 0.851993
\(499\) −16.3321 −0.731125 −0.365563 0.930787i \(-0.619123\pi\)
−0.365563 + 0.930787i \(0.619123\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −56.9635 −2.54494
\(502\) 11.0779 0.494431
\(503\) 36.2525 1.61642 0.808208 0.588896i \(-0.200437\pi\)
0.808208 + 0.588896i \(0.200437\pi\)
\(504\) 2.61555 0.116506
\(505\) −12.8386 −0.571309
\(506\) 34.7312 1.54399
\(507\) −34.8523 −1.54785
\(508\) −15.4067 −0.683560
\(509\) 38.3403 1.69940 0.849702 0.527263i \(-0.176782\pi\)
0.849702 + 0.527263i \(0.176782\pi\)
\(510\) 9.66177 0.427831
\(511\) −3.09747 −0.137024
\(512\) −1.00000 −0.0441942
\(513\) −19.4358 −0.858112
\(514\) −23.2093 −1.02372
\(515\) −3.27639 −0.144375
\(516\) 6.64597 0.292573
\(517\) 13.3334 0.586403
\(518\) −0.357999 −0.0157296
\(519\) 12.5691 0.551722
\(520\) 0.430765 0.0188903
\(521\) −30.3563 −1.32993 −0.664966 0.746873i \(-0.731554\pi\)
−0.664966 + 0.746873i \(0.731554\pi\)
\(522\) 34.2610 1.49956
\(523\) 34.4281 1.50544 0.752718 0.658343i \(-0.228743\pi\)
0.752718 + 0.658343i \(0.228743\pi\)
\(524\) 4.16970 0.182154
\(525\) −1.61780 −0.0706065
\(526\) −21.4733 −0.936278
\(527\) −30.2304 −1.31686
\(528\) −14.0119 −0.609790
\(529\) 22.4474 0.975976
\(530\) 3.18711 0.138439
\(531\) −63.2458 −2.74463
\(532\) 3.04243 0.131906
\(533\) 2.12878 0.0922077
\(534\) 34.5782 1.49634
\(535\) −1.95485 −0.0845157
\(536\) −2.61956 −0.113148
\(537\) −36.9213 −1.59327
\(538\) −13.3091 −0.573795
\(539\) 34.2403 1.47483
\(540\) −3.79991 −0.163522
\(541\) −38.4208 −1.65184 −0.825920 0.563788i \(-0.809344\pi\)
−0.825920 + 0.563788i \(0.809344\pi\)
\(542\) 27.6321 1.18690
\(543\) 5.17824 0.222220
\(544\) −3.55242 −0.152309
\(545\) −0.904117 −0.0387281
\(546\) 0.696890 0.0298242
\(547\) 5.93390 0.253715 0.126858 0.991921i \(-0.459511\pi\)
0.126858 + 0.991921i \(0.459511\pi\)
\(548\) 15.4928 0.661819
\(549\) −9.96412 −0.425258
\(550\) 5.15188 0.219677
\(551\) 39.8528 1.69778
\(552\) −18.3352 −0.780400
\(553\) 10.2487 0.435818
\(554\) −11.5551 −0.490928
\(555\) 1.63690 0.0694824
\(556\) −6.32300 −0.268155
\(557\) −12.8056 −0.542592 −0.271296 0.962496i \(-0.587452\pi\)
−0.271296 + 0.962496i \(0.587452\pi\)
\(558\) 37.4188 1.58406
\(559\) 1.05261 0.0445206
\(560\) 0.594829 0.0251361
\(561\) −49.7763 −2.10156
\(562\) 12.2034 0.514768
\(563\) −26.7424 −1.12706 −0.563529 0.826096i \(-0.690557\pi\)
−0.563529 + 0.826096i \(0.690557\pi\)
\(564\) −7.03896 −0.296394
\(565\) 12.5979 0.529997
\(566\) 21.0410 0.884418
\(567\) 1.69916 0.0713579
\(568\) −6.99728 −0.293599
\(569\) −16.0171 −0.671473 −0.335737 0.941956i \(-0.608985\pi\)
−0.335737 + 0.941956i \(0.608985\pi\)
\(570\) −13.9111 −0.582671
\(571\) −2.12746 −0.0890314 −0.0445157 0.999009i \(-0.514174\pi\)
−0.0445157 + 0.999009i \(0.514174\pi\)
\(572\) −2.21925 −0.0927913
\(573\) −31.2686 −1.30626
\(574\) 2.93956 0.122695
\(575\) 6.74147 0.281139
\(576\) 4.39715 0.183214
\(577\) 13.4658 0.560589 0.280294 0.959914i \(-0.409568\pi\)
0.280294 + 0.959914i \(0.409568\pi\)
\(578\) 4.38028 0.182196
\(579\) −58.9545 −2.45007
\(580\) 7.79165 0.323531
\(581\) 4.15825 0.172513
\(582\) 4.56903 0.189393
\(583\) −16.4196 −0.680029
\(584\) −5.20733 −0.215481
\(585\) −1.89413 −0.0783128
\(586\) −6.73977 −0.278417
\(587\) −42.7090 −1.76279 −0.881394 0.472382i \(-0.843394\pi\)
−0.881394 + 0.472382i \(0.843394\pi\)
\(588\) −18.0761 −0.745445
\(589\) 43.5259 1.79345
\(590\) −14.3834 −0.592154
\(591\) −24.9293 −1.02546
\(592\) −0.601851 −0.0247359
\(593\) 3.95945 0.162595 0.0812976 0.996690i \(-0.474094\pi\)
0.0812976 + 0.996690i \(0.474094\pi\)
\(594\) 19.5767 0.803241
\(595\) 2.11309 0.0866281
\(596\) 21.4347 0.877998
\(597\) −56.7934 −2.32440
\(598\) −2.90399 −0.118753
\(599\) 5.57202 0.227666 0.113833 0.993500i \(-0.463687\pi\)
0.113833 + 0.993500i \(0.463687\pi\)
\(600\) −2.71977 −0.111034
\(601\) −34.0271 −1.38799 −0.693997 0.719977i \(-0.744152\pi\)
−0.693997 + 0.719977i \(0.744152\pi\)
\(602\) 1.45351 0.0592407
\(603\) 11.5186 0.469074
\(604\) −1.44587 −0.0588316
\(605\) −15.5418 −0.631865
\(606\) −34.9180 −1.41845
\(607\) 22.1670 0.899733 0.449866 0.893096i \(-0.351472\pi\)
0.449866 + 0.893096i \(0.351472\pi\)
\(608\) 5.11480 0.207433
\(609\) 12.6053 0.510793
\(610\) −2.26604 −0.0917494
\(611\) −1.11485 −0.0451020
\(612\) 15.6205 0.631422
\(613\) −19.0501 −0.769424 −0.384712 0.923037i \(-0.625699\pi\)
−0.384712 + 0.923037i \(0.625699\pi\)
\(614\) −21.8952 −0.883617
\(615\) −13.4407 −0.541983
\(616\) −3.06449 −0.123472
\(617\) 26.3274 1.05990 0.529951 0.848028i \(-0.322210\pi\)
0.529951 + 0.848028i \(0.322210\pi\)
\(618\) −8.91103 −0.358454
\(619\) 35.2029 1.41492 0.707461 0.706752i \(-0.249840\pi\)
0.707461 + 0.706752i \(0.249840\pi\)
\(620\) 8.50979 0.341762
\(621\) 25.6170 1.02798
\(622\) −19.9821 −0.801211
\(623\) 7.56245 0.302983
\(624\) 1.17158 0.0469008
\(625\) 1.00000 0.0400000
\(626\) −6.20088 −0.247837
\(627\) 71.6682 2.86215
\(628\) −17.1502 −0.684367
\(629\) −2.13803 −0.0852489
\(630\) −2.61555 −0.104206
\(631\) 19.0064 0.756635 0.378317 0.925676i \(-0.376503\pi\)
0.378317 + 0.925676i \(0.376503\pi\)
\(632\) 17.2296 0.685357
\(633\) 52.8332 2.09993
\(634\) 10.6814 0.424214
\(635\) 15.4067 0.611394
\(636\) 8.66819 0.343716
\(637\) −2.86294 −0.113434
\(638\) −40.1416 −1.58922
\(639\) 30.7681 1.21717
\(640\) 1.00000 0.0395285
\(641\) −22.7832 −0.899883 −0.449942 0.893058i \(-0.648555\pi\)
−0.449942 + 0.893058i \(0.648555\pi\)
\(642\) −5.31675 −0.209836
\(643\) 3.83924 0.151405 0.0757024 0.997130i \(-0.475880\pi\)
0.0757024 + 0.997130i \(0.475880\pi\)
\(644\) −4.01002 −0.158017
\(645\) −6.64597 −0.261685
\(646\) 18.1700 0.714887
\(647\) 1.36012 0.0534719 0.0267359 0.999643i \(-0.491489\pi\)
0.0267359 + 0.999643i \(0.491489\pi\)
\(648\) 2.85655 0.112216
\(649\) 74.1013 2.90873
\(650\) −0.430765 −0.0168960
\(651\) 13.7671 0.539576
\(652\) −12.1007 −0.473900
\(653\) −3.84236 −0.150363 −0.0751815 0.997170i \(-0.523954\pi\)
−0.0751815 + 0.997170i \(0.523954\pi\)
\(654\) −2.45899 −0.0961541
\(655\) −4.16970 −0.162923
\(656\) 4.94186 0.192947
\(657\) 22.8974 0.893312
\(658\) −1.53946 −0.0600144
\(659\) −49.9855 −1.94716 −0.973580 0.228348i \(-0.926668\pi\)
−0.973580 + 0.228348i \(0.926668\pi\)
\(660\) 14.0119 0.545413
\(661\) 41.3643 1.60889 0.804443 0.594029i \(-0.202464\pi\)
0.804443 + 0.594029i \(0.202464\pi\)
\(662\) 13.2248 0.513995
\(663\) 4.16195 0.161637
\(664\) 6.99067 0.271290
\(665\) −3.04243 −0.117981
\(666\) 2.64643 0.102547
\(667\) −52.5272 −2.03386
\(668\) −20.9442 −0.810357
\(669\) 65.4045 2.52869
\(670\) 2.61956 0.101203
\(671\) 11.6744 0.450684
\(672\) 1.61780 0.0624079
\(673\) 19.3094 0.744323 0.372162 0.928168i \(-0.378617\pi\)
0.372162 + 0.928168i \(0.378617\pi\)
\(674\) −10.7103 −0.412545
\(675\) 3.79991 0.146259
\(676\) −12.8144 −0.492863
\(677\) −50.0450 −1.92338 −0.961692 0.274133i \(-0.911609\pi\)
−0.961692 + 0.274133i \(0.911609\pi\)
\(678\) 34.2633 1.31588
\(679\) 0.999274 0.0383486
\(680\) 3.55242 0.136229
\(681\) 13.1243 0.502925
\(682\) −43.8414 −1.67877
\(683\) −9.28981 −0.355465 −0.177732 0.984079i \(-0.556876\pi\)
−0.177732 + 0.984079i \(0.556876\pi\)
\(684\) −22.4905 −0.859947
\(685\) −15.4928 −0.591949
\(686\) −8.11715 −0.309914
\(687\) 32.2473 1.23031
\(688\) 2.44358 0.0931606
\(689\) 1.37289 0.0523030
\(690\) 18.3352 0.698011
\(691\) −23.1226 −0.879624 −0.439812 0.898090i \(-0.644955\pi\)
−0.439812 + 0.898090i \(0.644955\pi\)
\(692\) 4.62138 0.175678
\(693\) 13.4750 0.511873
\(694\) −26.7432 −1.01516
\(695\) 6.32300 0.239845
\(696\) 21.1915 0.803261
\(697\) 17.5556 0.664966
\(698\) −19.1024 −0.723036
\(699\) 63.5155 2.40238
\(700\) −0.594829 −0.0224824
\(701\) 40.1712 1.51725 0.758623 0.651530i \(-0.225872\pi\)
0.758623 + 0.651530i \(0.225872\pi\)
\(702\) −1.63687 −0.0617796
\(703\) 3.07835 0.116102
\(704\) −5.15188 −0.194169
\(705\) 7.03896 0.265102
\(706\) 2.45986 0.0925779
\(707\) −7.63676 −0.287210
\(708\) −39.1194 −1.47020
\(709\) −14.6968 −0.551949 −0.275974 0.961165i \(-0.589000\pi\)
−0.275974 + 0.961165i \(0.589000\pi\)
\(710\) 6.99728 0.262603
\(711\) −75.7611 −2.84126
\(712\) 12.7136 0.476464
\(713\) −57.3685 −2.14847
\(714\) 5.74711 0.215080
\(715\) 2.21925 0.0829951
\(716\) −13.5752 −0.507327
\(717\) 47.2189 1.76342
\(718\) −3.91065 −0.145944
\(719\) 43.7984 1.63341 0.816703 0.577059i \(-0.195800\pi\)
0.816703 + 0.577059i \(0.195800\pi\)
\(720\) −4.39715 −0.163872
\(721\) −1.94889 −0.0725806
\(722\) −7.16122 −0.266513
\(723\) 28.7549 1.06941
\(724\) 1.90393 0.0707589
\(725\) −7.79165 −0.289375
\(726\) −42.2702 −1.56879
\(727\) 39.0805 1.44942 0.724708 0.689056i \(-0.241975\pi\)
0.724708 + 0.689056i \(0.241975\pi\)
\(728\) 0.256231 0.00949657
\(729\) −43.5653 −1.61353
\(730\) 5.20733 0.192732
\(731\) 8.68063 0.321065
\(732\) −6.16311 −0.227795
\(733\) −6.76627 −0.249918 −0.124959 0.992162i \(-0.539880\pi\)
−0.124959 + 0.992162i \(0.539880\pi\)
\(734\) −29.4789 −1.08809
\(735\) 18.0761 0.666746
\(736\) −6.74147 −0.248494
\(737\) −13.4957 −0.497119
\(738\) −21.7301 −0.799896
\(739\) −6.77570 −0.249248 −0.124624 0.992204i \(-0.539773\pi\)
−0.124624 + 0.992204i \(0.539773\pi\)
\(740\) 0.601851 0.0221245
\(741\) −5.99240 −0.220136
\(742\) 1.89578 0.0695964
\(743\) 8.62411 0.316388 0.158194 0.987408i \(-0.449433\pi\)
0.158194 + 0.987408i \(0.449433\pi\)
\(744\) 23.1447 0.848525
\(745\) −21.4347 −0.785305
\(746\) −25.0946 −0.918780
\(747\) −30.7390 −1.12468
\(748\) −18.3016 −0.669175
\(749\) −1.16280 −0.0424880
\(750\) 2.71977 0.0993119
\(751\) 36.6638 1.33788 0.668940 0.743316i \(-0.266748\pi\)
0.668940 + 0.743316i \(0.266748\pi\)
\(752\) −2.58807 −0.0943773
\(753\) −30.1294 −1.09797
\(754\) 3.35637 0.122232
\(755\) 1.44587 0.0526206
\(756\) −2.26030 −0.0822063
\(757\) −38.8656 −1.41259 −0.706296 0.707916i \(-0.749635\pi\)
−0.706296 + 0.707916i \(0.749635\pi\)
\(758\) 7.83169 0.284460
\(759\) −94.4609 −3.42871
\(760\) −5.11480 −0.185533
\(761\) 37.6874 1.36617 0.683083 0.730341i \(-0.260639\pi\)
0.683083 + 0.730341i \(0.260639\pi\)
\(762\) 41.9025 1.51797
\(763\) −0.537795 −0.0194695
\(764\) −11.4968 −0.415939
\(765\) −15.6205 −0.564761
\(766\) −10.0381 −0.362693
\(767\) −6.19585 −0.223719
\(768\) 2.71977 0.0981412
\(769\) 27.4527 0.989968 0.494984 0.868902i \(-0.335174\pi\)
0.494984 + 0.868902i \(0.335174\pi\)
\(770\) 3.06449 0.110436
\(771\) 63.1238 2.27335
\(772\) −21.6763 −0.780147
\(773\) −14.4256 −0.518854 −0.259427 0.965763i \(-0.583534\pi\)
−0.259427 + 0.965763i \(0.583534\pi\)
\(774\) −10.7448 −0.386213
\(775\) −8.50979 −0.305681
\(776\) 1.67993 0.0603061
\(777\) 0.973674 0.0349304
\(778\) 8.12206 0.291190
\(779\) −25.2767 −0.905631
\(780\) −1.17158 −0.0419493
\(781\) −36.0491 −1.28994
\(782\) −23.9486 −0.856399
\(783\) −29.6076 −1.05809
\(784\) −6.64618 −0.237364
\(785\) 17.1502 0.612116
\(786\) −11.3406 −0.404506
\(787\) −44.7132 −1.59385 −0.796927 0.604076i \(-0.793542\pi\)
−0.796927 + 0.604076i \(0.793542\pi\)
\(788\) −9.16597 −0.326524
\(789\) 58.4023 2.07918
\(790\) −17.2296 −0.613002
\(791\) 7.49359 0.266441
\(792\) 22.6536 0.804959
\(793\) −0.976131 −0.0346634
\(794\) 26.4713 0.939433
\(795\) −8.66819 −0.307429
\(796\) −20.8817 −0.740133
\(797\) 20.3035 0.719186 0.359593 0.933109i \(-0.382915\pi\)
0.359593 + 0.933109i \(0.382915\pi\)
\(798\) −8.27472 −0.292922
\(799\) −9.19393 −0.325258
\(800\) −1.00000 −0.0353553
\(801\) −55.9038 −1.97526
\(802\) 1.00000 0.0353112
\(803\) −26.8275 −0.946722
\(804\) 7.12461 0.251266
\(805\) 4.01002 0.141335
\(806\) 3.66572 0.129119
\(807\) 36.1976 1.27422
\(808\) −12.8386 −0.451660
\(809\) 32.4567 1.14112 0.570559 0.821257i \(-0.306727\pi\)
0.570559 + 0.821257i \(0.306727\pi\)
\(810\) −2.85655 −0.100369
\(811\) 31.4619 1.10478 0.552388 0.833587i \(-0.313717\pi\)
0.552388 + 0.833587i \(0.313717\pi\)
\(812\) 4.63470 0.162646
\(813\) −75.1530 −2.63573
\(814\) −3.10066 −0.108678
\(815\) 12.1007 0.423869
\(816\) 9.66177 0.338230
\(817\) −12.4984 −0.437265
\(818\) 3.19920 0.111858
\(819\) −1.12669 −0.0393696
\(820\) −4.94186 −0.172577
\(821\) 27.9797 0.976500 0.488250 0.872704i \(-0.337635\pi\)
0.488250 + 0.872704i \(0.337635\pi\)
\(822\) −42.1368 −1.46969
\(823\) 45.4505 1.58431 0.792153 0.610323i \(-0.208960\pi\)
0.792153 + 0.610323i \(0.208960\pi\)
\(824\) −3.27639 −0.114139
\(825\) −14.0119 −0.487832
\(826\) −8.55565 −0.297689
\(827\) −42.2763 −1.47009 −0.735045 0.678019i \(-0.762839\pi\)
−0.735045 + 0.678019i \(0.762839\pi\)
\(828\) 29.6432 1.03017
\(829\) −39.1815 −1.36083 −0.680415 0.732827i \(-0.738200\pi\)
−0.680415 + 0.732827i \(0.738200\pi\)
\(830\) −6.99067 −0.242650
\(831\) 31.4272 1.09020
\(832\) 0.430765 0.0149341
\(833\) −23.6100 −0.818040
\(834\) 17.1971 0.595486
\(835\) 20.9442 0.724805
\(836\) 26.3508 0.911363
\(837\) −32.3365 −1.11771
\(838\) −9.80519 −0.338715
\(839\) 7.17337 0.247652 0.123826 0.992304i \(-0.460483\pi\)
0.123826 + 0.992304i \(0.460483\pi\)
\(840\) −1.61780 −0.0558193
\(841\) 31.7098 1.09344
\(842\) 34.3451 1.18361
\(843\) −33.1903 −1.14314
\(844\) 19.4256 0.668657
\(845\) 12.8144 0.440830
\(846\) 11.3801 0.391257
\(847\) −9.24473 −0.317653
\(848\) 3.18711 0.109446
\(849\) −57.2266 −1.96401
\(850\) −3.55242 −0.121847
\(851\) −4.05736 −0.139085
\(852\) 19.0310 0.651991
\(853\) −21.4921 −0.735876 −0.367938 0.929850i \(-0.619936\pi\)
−0.367938 + 0.929850i \(0.619936\pi\)
\(854\) −1.34791 −0.0461245
\(855\) 22.4905 0.769160
\(856\) −1.95485 −0.0668156
\(857\) 27.8792 0.952335 0.476168 0.879355i \(-0.342026\pi\)
0.476168 + 0.879355i \(0.342026\pi\)
\(858\) 6.03584 0.206060
\(859\) −41.6685 −1.42171 −0.710856 0.703337i \(-0.751692\pi\)
−0.710856 + 0.703337i \(0.751692\pi\)
\(860\) −2.44358 −0.0833254
\(861\) −7.99494 −0.272467
\(862\) −22.5844 −0.769228
\(863\) 12.9026 0.439211 0.219605 0.975589i \(-0.429523\pi\)
0.219605 + 0.975589i \(0.429523\pi\)
\(864\) −3.79991 −0.129276
\(865\) −4.62138 −0.157132
\(866\) 26.8669 0.912975
\(867\) −11.9134 −0.404599
\(868\) 5.06187 0.171811
\(869\) 88.7648 3.01114
\(870\) −21.1915 −0.718459
\(871\) 1.12842 0.0382349
\(872\) −0.904117 −0.0306173
\(873\) −7.38692 −0.250009
\(874\) 34.4813 1.16635
\(875\) 0.594829 0.0201089
\(876\) 14.1627 0.478514
\(877\) −13.9215 −0.470095 −0.235047 0.971984i \(-0.575525\pi\)
−0.235047 + 0.971984i \(0.575525\pi\)
\(878\) −2.51933 −0.0850232
\(879\) 18.3306 0.618276
\(880\) 5.15188 0.173670
\(881\) 15.0713 0.507765 0.253882 0.967235i \(-0.418292\pi\)
0.253882 + 0.967235i \(0.418292\pi\)
\(882\) 29.2242 0.984030
\(883\) 28.6998 0.965825 0.482912 0.875669i \(-0.339579\pi\)
0.482912 + 0.875669i \(0.339579\pi\)
\(884\) 1.53026 0.0514682
\(885\) 39.1194 1.31499
\(886\) 15.6162 0.524638
\(887\) −49.9217 −1.67621 −0.838103 0.545512i \(-0.816335\pi\)
−0.838103 + 0.545512i \(0.816335\pi\)
\(888\) 1.63690 0.0549307
\(889\) 9.16433 0.307362
\(890\) −12.7136 −0.426163
\(891\) 14.7166 0.493024
\(892\) 24.0478 0.805181
\(893\) 13.2375 0.442975
\(894\) −58.2973 −1.94975
\(895\) 13.5752 0.453767
\(896\) 0.594829 0.0198718
\(897\) 7.89818 0.263712
\(898\) 3.09920 0.103422
\(899\) 66.3053 2.21141
\(900\) 4.39715 0.146572
\(901\) 11.3220 0.377189
\(902\) 25.4599 0.847721
\(903\) −3.95322 −0.131555
\(904\) 12.5979 0.418999
\(905\) −1.90393 −0.0632887
\(906\) 3.93243 0.130646
\(907\) −34.9319 −1.15989 −0.579947 0.814654i \(-0.696927\pi\)
−0.579947 + 0.814654i \(0.696927\pi\)
\(908\) 4.82553 0.160141
\(909\) 56.4531 1.87243
\(910\) −0.256231 −0.00849399
\(911\) 26.7853 0.887437 0.443718 0.896166i \(-0.353659\pi\)
0.443718 + 0.896166i \(0.353659\pi\)
\(912\) −13.9111 −0.460642
\(913\) 36.0150 1.19192
\(914\) 2.80648 0.0928303
\(915\) 6.16311 0.203746
\(916\) 11.8566 0.391754
\(917\) −2.48026 −0.0819053
\(918\) −13.4989 −0.445530
\(919\) −14.8975 −0.491424 −0.245712 0.969343i \(-0.579022\pi\)
−0.245712 + 0.969343i \(0.579022\pi\)
\(920\) 6.74147 0.222260
\(921\) 59.5498 1.96223
\(922\) −10.1931 −0.335693
\(923\) 3.01418 0.0992130
\(924\) 8.33470 0.274191
\(925\) −0.601851 −0.0197887
\(926\) 1.35804 0.0446280
\(927\) 14.4068 0.473181
\(928\) 7.79165 0.255773
\(929\) 9.69067 0.317940 0.158970 0.987283i \(-0.449183\pi\)
0.158970 + 0.987283i \(0.449183\pi\)
\(930\) −23.1447 −0.758944
\(931\) 33.9939 1.11411
\(932\) 23.3533 0.764961
\(933\) 54.3468 1.77923
\(934\) 3.75856 0.122984
\(935\) 18.3016 0.598528
\(936\) −1.89413 −0.0619117
\(937\) 36.7285 1.19987 0.599933 0.800050i \(-0.295194\pi\)
0.599933 + 0.800050i \(0.295194\pi\)
\(938\) 1.55819 0.0508768
\(939\) 16.8650 0.550367
\(940\) 2.58807 0.0844136
\(941\) −18.2824 −0.595990 −0.297995 0.954567i \(-0.596318\pi\)
−0.297995 + 0.954567i \(0.596318\pi\)
\(942\) 46.6445 1.51976
\(943\) 33.3154 1.08490
\(944\) −14.3834 −0.468139
\(945\) 2.26030 0.0735276
\(946\) 12.5890 0.409304
\(947\) 17.8109 0.578778 0.289389 0.957212i \(-0.406548\pi\)
0.289389 + 0.957212i \(0.406548\pi\)
\(948\) −46.8606 −1.52196
\(949\) 2.24313 0.0728152
\(950\) 5.11480 0.165946
\(951\) −29.0510 −0.942045
\(952\) 2.11309 0.0684855
\(953\) 15.7490 0.510162 0.255081 0.966920i \(-0.417898\pi\)
0.255081 + 0.966920i \(0.417898\pi\)
\(954\) −14.0142 −0.453725
\(955\) 11.4968 0.372027
\(956\) 17.3614 0.561506
\(957\) 109.176 3.52916
\(958\) 11.0719 0.357716
\(959\) −9.21556 −0.297586
\(960\) −2.71977 −0.0877802
\(961\) 41.4166 1.33602
\(962\) 0.259256 0.00835876
\(963\) 8.59578 0.276995
\(964\) 10.5726 0.340519
\(965\) 21.6763 0.697785
\(966\) 10.9063 0.350906
\(967\) −7.50734 −0.241420 −0.120710 0.992688i \(-0.538517\pi\)
−0.120710 + 0.992688i \(0.538517\pi\)
\(968\) −15.5418 −0.499533
\(969\) −49.4181 −1.58754
\(970\) −1.67993 −0.0539394
\(971\) 43.3159 1.39007 0.695037 0.718974i \(-0.255388\pi\)
0.695037 + 0.718974i \(0.255388\pi\)
\(972\) −19.1689 −0.614842
\(973\) 3.76110 0.120575
\(974\) 16.7406 0.536402
\(975\) 1.17158 0.0375206
\(976\) −2.26604 −0.0725342
\(977\) −49.8233 −1.59399 −0.796994 0.603987i \(-0.793578\pi\)
−0.796994 + 0.603987i \(0.793578\pi\)
\(978\) 32.9111 1.05238
\(979\) 65.4992 2.09336
\(980\) 6.64618 0.212304
\(981\) 3.97553 0.126929
\(982\) 21.5509 0.687715
\(983\) −3.02102 −0.0963555 −0.0481777 0.998839i \(-0.515341\pi\)
−0.0481777 + 0.998839i \(0.515341\pi\)
\(984\) −13.4407 −0.428475
\(985\) 9.16597 0.292052
\(986\) 27.6792 0.881487
\(987\) 4.18698 0.133273
\(988\) −2.20328 −0.0700956
\(989\) 16.4733 0.523821
\(990\) −22.6536 −0.719977
\(991\) −35.2163 −1.11868 −0.559342 0.828937i \(-0.688946\pi\)
−0.559342 + 0.828937i \(0.688946\pi\)
\(992\) 8.50979 0.270186
\(993\) −35.9683 −1.14142
\(994\) 4.16219 0.132017
\(995\) 20.8817 0.661995
\(996\) −19.0130 −0.602450
\(997\) 52.2631 1.65519 0.827594 0.561327i \(-0.189709\pi\)
0.827594 + 0.561327i \(0.189709\pi\)
\(998\) 16.3321 0.516984
\(999\) −2.28698 −0.0723569
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 \(a_p\))