Properties

Label 4010.2.a.k.1.3
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 1.3
Root \(2.09866\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.86623 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.86623 q^{6} +0.981408 q^{7} -1.00000 q^{8} +5.21525 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.86623 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.86623 q^{6} +0.981408 q^{7} -1.00000 q^{8} +5.21525 q^{9} +1.00000 q^{10} +3.23699 q^{11} -2.86623 q^{12} -5.40206 q^{13} -0.981408 q^{14} +2.86623 q^{15} +1.00000 q^{16} -3.01470 q^{17} -5.21525 q^{18} +4.93600 q^{19} -1.00000 q^{20} -2.81294 q^{21} -3.23699 q^{22} +1.30284 q^{23} +2.86623 q^{24} +1.00000 q^{25} +5.40206 q^{26} -6.34940 q^{27} +0.981408 q^{28} -4.83903 q^{29} -2.86623 q^{30} -1.22857 q^{31} -1.00000 q^{32} -9.27794 q^{33} +3.01470 q^{34} -0.981408 q^{35} +5.21525 q^{36} -1.55379 q^{37} -4.93600 q^{38} +15.4835 q^{39} +1.00000 q^{40} +3.26728 q^{41} +2.81294 q^{42} -8.01745 q^{43} +3.23699 q^{44} -5.21525 q^{45} -1.30284 q^{46} +11.0348 q^{47} -2.86623 q^{48} -6.03684 q^{49} -1.00000 q^{50} +8.64082 q^{51} -5.40206 q^{52} -3.38794 q^{53} +6.34940 q^{54} -3.23699 q^{55} -0.981408 q^{56} -14.1477 q^{57} +4.83903 q^{58} -12.6162 q^{59} +2.86623 q^{60} +15.0176 q^{61} +1.22857 q^{62} +5.11829 q^{63} +1.00000 q^{64} +5.40206 q^{65} +9.27794 q^{66} -4.93266 q^{67} -3.01470 q^{68} -3.73423 q^{69} +0.981408 q^{70} -0.116467 q^{71} -5.21525 q^{72} +4.74753 q^{73} +1.55379 q^{74} -2.86623 q^{75} +4.93600 q^{76} +3.17681 q^{77} -15.4835 q^{78} -0.914963 q^{79} -1.00000 q^{80} +2.55308 q^{81} -3.26728 q^{82} +7.48174 q^{83} -2.81294 q^{84} +3.01470 q^{85} +8.01745 q^{86} +13.8698 q^{87} -3.23699 q^{88} +16.9966 q^{89} +5.21525 q^{90} -5.30162 q^{91} +1.30284 q^{92} +3.52136 q^{93} -11.0348 q^{94} -4.93600 q^{95} +2.86623 q^{96} +10.3353 q^{97} +6.03684 q^{98} +16.8817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −2.86623 −1.65482 −0.827408 0.561601i \(-0.810186\pi\)
−0.827408 + 0.561601i \(0.810186\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.86623 1.17013
\(7\) 0.981408 0.370937 0.185469 0.982650i \(-0.440620\pi\)
0.185469 + 0.982650i \(0.440620\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.21525 1.73842
\(10\) 1.00000 0.316228
\(11\) 3.23699 0.975989 0.487995 0.872847i \(-0.337729\pi\)
0.487995 + 0.872847i \(0.337729\pi\)
\(12\) −2.86623 −0.827408
\(13\) −5.40206 −1.49826 −0.749130 0.662423i \(-0.769528\pi\)
−0.749130 + 0.662423i \(0.769528\pi\)
\(14\) −0.981408 −0.262292
\(15\) 2.86623 0.740056
\(16\) 1.00000 0.250000
\(17\) −3.01470 −0.731173 −0.365587 0.930777i \(-0.619132\pi\)
−0.365587 + 0.930777i \(0.619132\pi\)
\(18\) −5.21525 −1.22925
\(19\) 4.93600 1.13240 0.566198 0.824269i \(-0.308414\pi\)
0.566198 + 0.824269i \(0.308414\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.81294 −0.613833
\(22\) −3.23699 −0.690128
\(23\) 1.30284 0.271660 0.135830 0.990732i \(-0.456630\pi\)
0.135830 + 0.990732i \(0.456630\pi\)
\(24\) 2.86623 0.585066
\(25\) 1.00000 0.200000
\(26\) 5.40206 1.05943
\(27\) −6.34940 −1.22194
\(28\) 0.981408 0.185469
\(29\) −4.83903 −0.898586 −0.449293 0.893385i \(-0.648324\pi\)
−0.449293 + 0.893385i \(0.648324\pi\)
\(30\) −2.86623 −0.523299
\(31\) −1.22857 −0.220658 −0.110329 0.993895i \(-0.535190\pi\)
−0.110329 + 0.993895i \(0.535190\pi\)
\(32\) −1.00000 −0.176777
\(33\) −9.27794 −1.61508
\(34\) 3.01470 0.517017
\(35\) −0.981408 −0.165888
\(36\) 5.21525 0.869208
\(37\) −1.55379 −0.255442 −0.127721 0.991810i \(-0.540766\pi\)
−0.127721 + 0.991810i \(0.540766\pi\)
\(38\) −4.93600 −0.800724
\(39\) 15.4835 2.47935
\(40\) 1.00000 0.158114
\(41\) 3.26728 0.510263 0.255131 0.966906i \(-0.417881\pi\)
0.255131 + 0.966906i \(0.417881\pi\)
\(42\) 2.81294 0.434046
\(43\) −8.01745 −1.22265 −0.611325 0.791380i \(-0.709363\pi\)
−0.611325 + 0.791380i \(0.709363\pi\)
\(44\) 3.23699 0.487995
\(45\) −5.21525 −0.777443
\(46\) −1.30284 −0.192093
\(47\) 11.0348 1.60959 0.804795 0.593553i \(-0.202275\pi\)
0.804795 + 0.593553i \(0.202275\pi\)
\(48\) −2.86623 −0.413704
\(49\) −6.03684 −0.862405
\(50\) −1.00000 −0.141421
\(51\) 8.64082 1.20996
\(52\) −5.40206 −0.749130
\(53\) −3.38794 −0.465370 −0.232685 0.972552i \(-0.574751\pi\)
−0.232685 + 0.972552i \(0.574751\pi\)
\(54\) 6.34940 0.864044
\(55\) −3.23699 −0.436476
\(56\) −0.981408 −0.131146
\(57\) −14.1477 −1.87391
\(58\) 4.83903 0.635396
\(59\) −12.6162 −1.64248 −0.821242 0.570580i \(-0.806718\pi\)
−0.821242 + 0.570580i \(0.806718\pi\)
\(60\) 2.86623 0.370028
\(61\) 15.0176 1.92281 0.961406 0.275133i \(-0.0887218\pi\)
0.961406 + 0.275133i \(0.0887218\pi\)
\(62\) 1.22857 0.156029
\(63\) 5.11829 0.644844
\(64\) 1.00000 0.125000
\(65\) 5.40206 0.670043
\(66\) 9.27794 1.14204
\(67\) −4.93266 −0.602620 −0.301310 0.953526i \(-0.597424\pi\)
−0.301310 + 0.953526i \(0.597424\pi\)
\(68\) −3.01470 −0.365587
\(69\) −3.73423 −0.449548
\(70\) 0.981408 0.117301
\(71\) −0.116467 −0.0138221 −0.00691103 0.999976i \(-0.502200\pi\)
−0.00691103 + 0.999976i \(0.502200\pi\)
\(72\) −5.21525 −0.614623
\(73\) 4.74753 0.555657 0.277828 0.960631i \(-0.410385\pi\)
0.277828 + 0.960631i \(0.410385\pi\)
\(74\) 1.55379 0.180625
\(75\) −2.86623 −0.330963
\(76\) 4.93600 0.566198
\(77\) 3.17681 0.362031
\(78\) −15.4835 −1.75316
\(79\) −0.914963 −0.102941 −0.0514707 0.998675i \(-0.516391\pi\)
−0.0514707 + 0.998675i \(0.516391\pi\)
\(80\) −1.00000 −0.111803
\(81\) 2.55308 0.283675
\(82\) −3.26728 −0.360810
\(83\) 7.48174 0.821227 0.410614 0.911809i \(-0.365315\pi\)
0.410614 + 0.911809i \(0.365315\pi\)
\(84\) −2.81294 −0.306917
\(85\) 3.01470 0.326991
\(86\) 8.01745 0.864544
\(87\) 13.8698 1.48699
\(88\) −3.23699 −0.345064
\(89\) 16.9966 1.80164 0.900820 0.434194i \(-0.142967\pi\)
0.900820 + 0.434194i \(0.142967\pi\)
\(90\) 5.21525 0.549736
\(91\) −5.30162 −0.555761
\(92\) 1.30284 0.135830
\(93\) 3.52136 0.365148
\(94\) −11.0348 −1.13815
\(95\) −4.93600 −0.506423
\(96\) 2.86623 0.292533
\(97\) 10.3353 1.04939 0.524696 0.851289i \(-0.324179\pi\)
0.524696 + 0.851289i \(0.324179\pi\)
\(98\) 6.03684 0.609813
\(99\) 16.8817 1.69668
\(100\) 1.00000 0.100000
\(101\) 11.1862 1.11307 0.556535 0.830824i \(-0.312131\pi\)
0.556535 + 0.830824i \(0.312131\pi\)
\(102\) −8.64082 −0.855569
\(103\) −1.10982 −0.109354 −0.0546769 0.998504i \(-0.517413\pi\)
−0.0546769 + 0.998504i \(0.517413\pi\)
\(104\) 5.40206 0.529715
\(105\) 2.81294 0.274515
\(106\) 3.38794 0.329066
\(107\) 16.0511 1.55171 0.775857 0.630909i \(-0.217318\pi\)
0.775857 + 0.630909i \(0.217318\pi\)
\(108\) −6.34940 −0.610972
\(109\) −15.0220 −1.43884 −0.719422 0.694573i \(-0.755593\pi\)
−0.719422 + 0.694573i \(0.755593\pi\)
\(110\) 3.23699 0.308635
\(111\) 4.45352 0.422710
\(112\) 0.981408 0.0927344
\(113\) −8.26597 −0.777597 −0.388798 0.921323i \(-0.627110\pi\)
−0.388798 + 0.921323i \(0.627110\pi\)
\(114\) 14.1477 1.32505
\(115\) −1.30284 −0.121490
\(116\) −4.83903 −0.449293
\(117\) −28.1731 −2.60460
\(118\) 12.6162 1.16141
\(119\) −2.95866 −0.271219
\(120\) −2.86623 −0.261649
\(121\) −0.521900 −0.0474455
\(122\) −15.0176 −1.35963
\(123\) −9.36475 −0.844391
\(124\) −1.22857 −0.110329
\(125\) −1.00000 −0.0894427
\(126\) −5.11829 −0.455973
\(127\) 11.8238 1.04919 0.524595 0.851352i \(-0.324217\pi\)
0.524595 + 0.851352i \(0.324217\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 22.9798 2.02326
\(130\) −5.40206 −0.473792
\(131\) −5.74416 −0.501870 −0.250935 0.968004i \(-0.580738\pi\)
−0.250935 + 0.968004i \(0.580738\pi\)
\(132\) −9.27794 −0.807541
\(133\) 4.84423 0.420048
\(134\) 4.93266 0.426117
\(135\) 6.34940 0.546470
\(136\) 3.01470 0.258509
\(137\) 13.5128 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(138\) 3.73423 0.317878
\(139\) 1.06732 0.0905289 0.0452644 0.998975i \(-0.485587\pi\)
0.0452644 + 0.998975i \(0.485587\pi\)
\(140\) −0.981408 −0.0829441
\(141\) −31.6282 −2.66358
\(142\) 0.116467 0.00977367
\(143\) −17.4864 −1.46229
\(144\) 5.21525 0.434604
\(145\) 4.83903 0.401860
\(146\) −4.74753 −0.392909
\(147\) 17.3029 1.42712
\(148\) −1.55379 −0.127721
\(149\) 13.3247 1.09160 0.545799 0.837916i \(-0.316226\pi\)
0.545799 + 0.837916i \(0.316226\pi\)
\(150\) 2.86623 0.234026
\(151\) −18.5077 −1.50614 −0.753069 0.657942i \(-0.771427\pi\)
−0.753069 + 0.657942i \(0.771427\pi\)
\(152\) −4.93600 −0.400362
\(153\) −15.7224 −1.27108
\(154\) −3.17681 −0.255995
\(155\) 1.22857 0.0986812
\(156\) 15.4835 1.23967
\(157\) −1.35261 −0.107950 −0.0539749 0.998542i \(-0.517189\pi\)
−0.0539749 + 0.998542i \(0.517189\pi\)
\(158\) 0.914963 0.0727905
\(159\) 9.71061 0.770102
\(160\) 1.00000 0.0790569
\(161\) 1.27862 0.100769
\(162\) −2.55308 −0.200589
\(163\) −3.44154 −0.269562 −0.134781 0.990875i \(-0.543033\pi\)
−0.134781 + 0.990875i \(0.543033\pi\)
\(164\) 3.26728 0.255131
\(165\) 9.27794 0.722287
\(166\) −7.48174 −0.580695
\(167\) 0.681978 0.0527730 0.0263865 0.999652i \(-0.491600\pi\)
0.0263865 + 0.999652i \(0.491600\pi\)
\(168\) 2.81294 0.217023
\(169\) 16.1822 1.24479
\(170\) −3.01470 −0.231217
\(171\) 25.7425 1.96857
\(172\) −8.01745 −0.611325
\(173\) 2.33733 0.177704 0.0888520 0.996045i \(-0.471680\pi\)
0.0888520 + 0.996045i \(0.471680\pi\)
\(174\) −13.8698 −1.05146
\(175\) 0.981408 0.0741875
\(176\) 3.23699 0.243997
\(177\) 36.1607 2.71801
\(178\) −16.9966 −1.27395
\(179\) −12.0967 −0.904151 −0.452075 0.891980i \(-0.649316\pi\)
−0.452075 + 0.891980i \(0.649316\pi\)
\(180\) −5.21525 −0.388722
\(181\) −5.64646 −0.419698 −0.209849 0.977734i \(-0.567297\pi\)
−0.209849 + 0.977734i \(0.567297\pi\)
\(182\) 5.30162 0.392982
\(183\) −43.0440 −3.18190
\(184\) −1.30284 −0.0960465
\(185\) 1.55379 0.114237
\(186\) −3.52136 −0.258199
\(187\) −9.75856 −0.713617
\(188\) 11.0348 0.804795
\(189\) −6.23136 −0.453265
\(190\) 4.93600 0.358095
\(191\) −2.53824 −0.183661 −0.0918303 0.995775i \(-0.529272\pi\)
−0.0918303 + 0.995775i \(0.529272\pi\)
\(192\) −2.86623 −0.206852
\(193\) −5.15005 −0.370709 −0.185354 0.982672i \(-0.559343\pi\)
−0.185354 + 0.982672i \(0.559343\pi\)
\(194\) −10.3353 −0.742033
\(195\) −15.4835 −1.10880
\(196\) −6.03684 −0.431203
\(197\) −8.93316 −0.636461 −0.318230 0.948013i \(-0.603089\pi\)
−0.318230 + 0.948013i \(0.603089\pi\)
\(198\) −16.8817 −1.19973
\(199\) −8.47376 −0.600689 −0.300344 0.953831i \(-0.597102\pi\)
−0.300344 + 0.953831i \(0.597102\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 14.1381 0.997225
\(202\) −11.1862 −0.787059
\(203\) −4.74907 −0.333319
\(204\) 8.64082 0.604978
\(205\) −3.26728 −0.228196
\(206\) 1.10982 0.0773248
\(207\) 6.79462 0.472259
\(208\) −5.40206 −0.374565
\(209\) 15.9778 1.10521
\(210\) −2.81294 −0.194111
\(211\) 0.757364 0.0521391 0.0260696 0.999660i \(-0.491701\pi\)
0.0260696 + 0.999660i \(0.491701\pi\)
\(212\) −3.38794 −0.232685
\(213\) 0.333820 0.0228730
\(214\) −16.0511 −1.09723
\(215\) 8.01745 0.546786
\(216\) 6.34940 0.432022
\(217\) −1.20573 −0.0818503
\(218\) 15.0220 1.01742
\(219\) −13.6075 −0.919510
\(220\) −3.23699 −0.218238
\(221\) 16.2856 1.09549
\(222\) −4.45352 −0.298901
\(223\) 17.5519 1.17537 0.587683 0.809092i \(-0.300040\pi\)
0.587683 + 0.809092i \(0.300040\pi\)
\(224\) −0.981408 −0.0655731
\(225\) 5.21525 0.347683
\(226\) 8.26597 0.549844
\(227\) −25.8206 −1.71377 −0.856887 0.515504i \(-0.827605\pi\)
−0.856887 + 0.515504i \(0.827605\pi\)
\(228\) −14.1477 −0.936953
\(229\) −18.8698 −1.24695 −0.623477 0.781842i \(-0.714281\pi\)
−0.623477 + 0.781842i \(0.714281\pi\)
\(230\) 1.30284 0.0859066
\(231\) −9.10545 −0.599095
\(232\) 4.83903 0.317698
\(233\) −20.3884 −1.33569 −0.667845 0.744300i \(-0.732783\pi\)
−0.667845 + 0.744300i \(0.732783\pi\)
\(234\) 28.1731 1.84173
\(235\) −11.0348 −0.719831
\(236\) −12.6162 −0.821242
\(237\) 2.62249 0.170349
\(238\) 2.95866 0.191781
\(239\) −15.4040 −0.996400 −0.498200 0.867062i \(-0.666005\pi\)
−0.498200 + 0.867062i \(0.666005\pi\)
\(240\) 2.86623 0.185014
\(241\) −6.89885 −0.444394 −0.222197 0.975002i \(-0.571323\pi\)
−0.222197 + 0.975002i \(0.571323\pi\)
\(242\) 0.521900 0.0335490
\(243\) 11.7305 0.752513
\(244\) 15.0176 0.961406
\(245\) 6.03684 0.385679
\(246\) 9.36475 0.597074
\(247\) −26.6645 −1.69662
\(248\) 1.22857 0.0780143
\(249\) −21.4443 −1.35898
\(250\) 1.00000 0.0632456
\(251\) −11.2393 −0.709419 −0.354710 0.934976i \(-0.615420\pi\)
−0.354710 + 0.934976i \(0.615420\pi\)
\(252\) 5.11829 0.322422
\(253\) 4.21727 0.265138
\(254\) −11.8238 −0.741890
\(255\) −8.64082 −0.541109
\(256\) 1.00000 0.0625000
\(257\) −5.32977 −0.332462 −0.166231 0.986087i \(-0.553160\pi\)
−0.166231 + 0.986087i \(0.553160\pi\)
\(258\) −22.9798 −1.43066
\(259\) −1.52491 −0.0947530
\(260\) 5.40206 0.335021
\(261\) −25.2368 −1.56212
\(262\) 5.74416 0.354876
\(263\) −23.1323 −1.42640 −0.713200 0.700961i \(-0.752755\pi\)
−0.713200 + 0.700961i \(0.752755\pi\)
\(264\) 9.27794 0.571018
\(265\) 3.38794 0.208120
\(266\) −4.84423 −0.297019
\(267\) −48.7162 −2.98138
\(268\) −4.93266 −0.301310
\(269\) 18.7660 1.14418 0.572090 0.820191i \(-0.306133\pi\)
0.572090 + 0.820191i \(0.306133\pi\)
\(270\) −6.34940 −0.386412
\(271\) −2.18592 −0.132785 −0.0663925 0.997794i \(-0.521149\pi\)
−0.0663925 + 0.997794i \(0.521149\pi\)
\(272\) −3.01470 −0.182793
\(273\) 15.1956 0.919682
\(274\) −13.5128 −0.816336
\(275\) 3.23699 0.195198
\(276\) −3.73423 −0.224774
\(277\) 1.10562 0.0664304 0.0332152 0.999448i \(-0.489425\pi\)
0.0332152 + 0.999448i \(0.489425\pi\)
\(278\) −1.06732 −0.0640136
\(279\) −6.40730 −0.383595
\(280\) 0.981408 0.0586504
\(281\) 23.5114 1.40257 0.701285 0.712881i \(-0.252610\pi\)
0.701285 + 0.712881i \(0.252610\pi\)
\(282\) 31.6282 1.88343
\(283\) −16.7860 −0.997821 −0.498911 0.866653i \(-0.666266\pi\)
−0.498911 + 0.866653i \(0.666266\pi\)
\(284\) −0.116467 −0.00691103
\(285\) 14.1477 0.838036
\(286\) 17.4864 1.03399
\(287\) 3.20653 0.189276
\(288\) −5.21525 −0.307312
\(289\) −7.91156 −0.465386
\(290\) −4.83903 −0.284158
\(291\) −29.6234 −1.73655
\(292\) 4.74753 0.277828
\(293\) −10.9849 −0.641742 −0.320871 0.947123i \(-0.603976\pi\)
−0.320871 + 0.947123i \(0.603976\pi\)
\(294\) −17.3029 −1.00913
\(295\) 12.6162 0.734541
\(296\) 1.55379 0.0903124
\(297\) −20.5530 −1.19260
\(298\) −13.3247 −0.771877
\(299\) −7.03800 −0.407018
\(300\) −2.86623 −0.165482
\(301\) −7.86840 −0.453527
\(302\) 18.5077 1.06500
\(303\) −32.0622 −1.84193
\(304\) 4.93600 0.283099
\(305\) −15.0176 −0.859908
\(306\) 15.7224 0.898792
\(307\) −16.5978 −0.947287 −0.473644 0.880717i \(-0.657061\pi\)
−0.473644 + 0.880717i \(0.657061\pi\)
\(308\) 3.17681 0.181015
\(309\) 3.18099 0.180960
\(310\) −1.22857 −0.0697781
\(311\) −22.9342 −1.30048 −0.650239 0.759730i \(-0.725331\pi\)
−0.650239 + 0.759730i \(0.725331\pi\)
\(312\) −15.4835 −0.876581
\(313\) −24.0683 −1.36042 −0.680209 0.733018i \(-0.738111\pi\)
−0.680209 + 0.733018i \(0.738111\pi\)
\(314\) 1.35261 0.0763320
\(315\) −5.11829 −0.288383
\(316\) −0.914963 −0.0514707
\(317\) −10.9487 −0.614941 −0.307471 0.951558i \(-0.599483\pi\)
−0.307471 + 0.951558i \(0.599483\pi\)
\(318\) −9.71061 −0.544544
\(319\) −15.6639 −0.877010
\(320\) −1.00000 −0.0559017
\(321\) −46.0060 −2.56780
\(322\) −1.27862 −0.0712545
\(323\) −14.8806 −0.827977
\(324\) 2.55308 0.141838
\(325\) −5.40206 −0.299652
\(326\) 3.44154 0.190609
\(327\) 43.0564 2.38102
\(328\) −3.26728 −0.180405
\(329\) 10.8296 0.597057
\(330\) −9.27794 −0.510734
\(331\) 12.5841 0.691683 0.345841 0.938293i \(-0.387594\pi\)
0.345841 + 0.938293i \(0.387594\pi\)
\(332\) 7.48174 0.410614
\(333\) −8.10342 −0.444065
\(334\) −0.681978 −0.0373162
\(335\) 4.93266 0.269500
\(336\) −2.81294 −0.153458
\(337\) 13.0258 0.709560 0.354780 0.934950i \(-0.384556\pi\)
0.354780 + 0.934950i \(0.384556\pi\)
\(338\) −16.1822 −0.880196
\(339\) 23.6921 1.28678
\(340\) 3.01470 0.163495
\(341\) −3.97687 −0.215360
\(342\) −25.7425 −1.39199
\(343\) −12.7945 −0.690836
\(344\) 8.01745 0.432272
\(345\) 3.73423 0.201044
\(346\) −2.33733 −0.125656
\(347\) −11.7323 −0.629821 −0.314911 0.949121i \(-0.601975\pi\)
−0.314911 + 0.949121i \(0.601975\pi\)
\(348\) 13.8698 0.743497
\(349\) −25.2634 −1.35232 −0.676159 0.736756i \(-0.736357\pi\)
−0.676159 + 0.736756i \(0.736357\pi\)
\(350\) −0.981408 −0.0524585
\(351\) 34.2998 1.83079
\(352\) −3.23699 −0.172532
\(353\) 29.8560 1.58907 0.794537 0.607215i \(-0.207713\pi\)
0.794537 + 0.607215i \(0.207713\pi\)
\(354\) −36.1607 −1.92192
\(355\) 0.116467 0.00618141
\(356\) 16.9966 0.900820
\(357\) 8.48017 0.448818
\(358\) 12.0967 0.639331
\(359\) 32.6092 1.72105 0.860525 0.509409i \(-0.170136\pi\)
0.860525 + 0.509409i \(0.170136\pi\)
\(360\) 5.21525 0.274868
\(361\) 5.36407 0.282319
\(362\) 5.64646 0.296772
\(363\) 1.49588 0.0785135
\(364\) −5.30162 −0.277881
\(365\) −4.74753 −0.248497
\(366\) 43.0440 2.24994
\(367\) 15.6372 0.816257 0.408129 0.912924i \(-0.366182\pi\)
0.408129 + 0.912924i \(0.366182\pi\)
\(368\) 1.30284 0.0679151
\(369\) 17.0397 0.887049
\(370\) −1.55379 −0.0807779
\(371\) −3.32496 −0.172623
\(372\) 3.52136 0.182574
\(373\) 18.8479 0.975909 0.487955 0.872869i \(-0.337743\pi\)
0.487955 + 0.872869i \(0.337743\pi\)
\(374\) 9.75856 0.504603
\(375\) 2.86623 0.148011
\(376\) −11.0348 −0.569076
\(377\) 26.1407 1.34632
\(378\) 6.23136 0.320506
\(379\) −32.5777 −1.67341 −0.836703 0.547658i \(-0.815520\pi\)
−0.836703 + 0.547658i \(0.815520\pi\)
\(380\) −4.93600 −0.253211
\(381\) −33.8896 −1.73622
\(382\) 2.53824 0.129868
\(383\) 0.283228 0.0144723 0.00723613 0.999974i \(-0.497697\pi\)
0.00723613 + 0.999974i \(0.497697\pi\)
\(384\) 2.86623 0.146266
\(385\) −3.17681 −0.161905
\(386\) 5.15005 0.262131
\(387\) −41.8130 −2.12548
\(388\) 10.3353 0.524696
\(389\) 28.7129 1.45580 0.727900 0.685683i \(-0.240496\pi\)
0.727900 + 0.685683i \(0.240496\pi\)
\(390\) 15.4835 0.784038
\(391\) −3.92767 −0.198631
\(392\) 6.03684 0.304906
\(393\) 16.4641 0.830503
\(394\) 8.93316 0.450046
\(395\) 0.914963 0.0460368
\(396\) 16.8817 0.848338
\(397\) 12.1688 0.610733 0.305367 0.952235i \(-0.401221\pi\)
0.305367 + 0.952235i \(0.401221\pi\)
\(398\) 8.47376 0.424751
\(399\) −13.8847 −0.695102
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −14.1381 −0.705145
\(403\) 6.63681 0.330603
\(404\) 11.1862 0.556535
\(405\) −2.55308 −0.126863
\(406\) 4.74907 0.235692
\(407\) −5.02961 −0.249309
\(408\) −8.64082 −0.427784
\(409\) −8.12653 −0.401831 −0.200916 0.979609i \(-0.564392\pi\)
−0.200916 + 0.979609i \(0.564392\pi\)
\(410\) 3.26728 0.161359
\(411\) −38.7306 −1.91044
\(412\) −1.10982 −0.0546769
\(413\) −12.3816 −0.609259
\(414\) −6.79462 −0.333937
\(415\) −7.48174 −0.367264
\(416\) 5.40206 0.264858
\(417\) −3.05918 −0.149809
\(418\) −15.9778 −0.781498
\(419\) 31.2448 1.52641 0.763205 0.646156i \(-0.223625\pi\)
0.763205 + 0.646156i \(0.223625\pi\)
\(420\) 2.81294 0.137257
\(421\) −1.26922 −0.0618578 −0.0309289 0.999522i \(-0.509847\pi\)
−0.0309289 + 0.999522i \(0.509847\pi\)
\(422\) −0.757364 −0.0368679
\(423\) 57.5492 2.79814
\(424\) 3.38794 0.164533
\(425\) −3.01470 −0.146235
\(426\) −0.333820 −0.0161736
\(427\) 14.7384 0.713243
\(428\) 16.0511 0.775857
\(429\) 50.1200 2.41981
\(430\) −8.01745 −0.386636
\(431\) −11.9607 −0.576129 −0.288064 0.957611i \(-0.593012\pi\)
−0.288064 + 0.957611i \(0.593012\pi\)
\(432\) −6.34940 −0.305486
\(433\) −40.3389 −1.93856 −0.969281 0.245956i \(-0.920898\pi\)
−0.969281 + 0.245956i \(0.920898\pi\)
\(434\) 1.20573 0.0578769
\(435\) −13.8698 −0.665004
\(436\) −15.0220 −0.719422
\(437\) 6.43080 0.307627
\(438\) 13.6075 0.650191
\(439\) −35.8412 −1.71061 −0.855303 0.518129i \(-0.826629\pi\)
−0.855303 + 0.518129i \(0.826629\pi\)
\(440\) 3.23699 0.154317
\(441\) −31.4836 −1.49922
\(442\) −16.2856 −0.774627
\(443\) −25.8381 −1.22761 −0.613803 0.789460i \(-0.710361\pi\)
−0.613803 + 0.789460i \(0.710361\pi\)
\(444\) 4.45352 0.211355
\(445\) −16.9966 −0.805717
\(446\) −17.5519 −0.831109
\(447\) −38.1915 −1.80640
\(448\) 0.981408 0.0463672
\(449\) −10.2434 −0.483417 −0.241709 0.970349i \(-0.577708\pi\)
−0.241709 + 0.970349i \(0.577708\pi\)
\(450\) −5.21525 −0.245849
\(451\) 10.5761 0.498011
\(452\) −8.26597 −0.388798
\(453\) 53.0473 2.49238
\(454\) 25.8206 1.21182
\(455\) 5.30162 0.248544
\(456\) 14.1477 0.662526
\(457\) −23.6779 −1.10760 −0.553802 0.832648i \(-0.686824\pi\)
−0.553802 + 0.832648i \(0.686824\pi\)
\(458\) 18.8698 0.881730
\(459\) 19.1416 0.893452
\(460\) −1.30284 −0.0607451
\(461\) 0.150219 0.00699642 0.00349821 0.999994i \(-0.498886\pi\)
0.00349821 + 0.999994i \(0.498886\pi\)
\(462\) 9.10545 0.423624
\(463\) 28.3404 1.31709 0.658544 0.752542i \(-0.271173\pi\)
0.658544 + 0.752542i \(0.271173\pi\)
\(464\) −4.83903 −0.224646
\(465\) −3.52136 −0.163299
\(466\) 20.3884 0.944476
\(467\) −6.79712 −0.314533 −0.157267 0.987556i \(-0.550268\pi\)
−0.157267 + 0.987556i \(0.550268\pi\)
\(468\) −28.1731 −1.30230
\(469\) −4.84095 −0.223534
\(470\) 11.0348 0.508997
\(471\) 3.87688 0.178637
\(472\) 12.6162 0.580706
\(473\) −25.9524 −1.19329
\(474\) −2.62249 −0.120455
\(475\) 4.93600 0.226479
\(476\) −2.95866 −0.135610
\(477\) −17.6690 −0.809007
\(478\) 15.4040 0.704561
\(479\) 37.2822 1.70347 0.851735 0.523974i \(-0.175551\pi\)
0.851735 + 0.523974i \(0.175551\pi\)
\(480\) −2.86623 −0.130825
\(481\) 8.39368 0.382719
\(482\) 6.89885 0.314234
\(483\) −3.66480 −0.166754
\(484\) −0.521900 −0.0237227
\(485\) −10.3353 −0.469303
\(486\) −11.7305 −0.532107
\(487\) −1.95947 −0.0887922 −0.0443961 0.999014i \(-0.514136\pi\)
−0.0443961 + 0.999014i \(0.514136\pi\)
\(488\) −15.0176 −0.679817
\(489\) 9.86422 0.446076
\(490\) −6.03684 −0.272717
\(491\) −26.0586 −1.17601 −0.588004 0.808858i \(-0.700086\pi\)
−0.588004 + 0.808858i \(0.700086\pi\)
\(492\) −9.36475 −0.422195
\(493\) 14.5882 0.657022
\(494\) 26.6645 1.19969
\(495\) −16.8817 −0.758776
\(496\) −1.22857 −0.0551645
\(497\) −0.114301 −0.00512712
\(498\) 21.4443 0.960944
\(499\) −2.70819 −0.121235 −0.0606176 0.998161i \(-0.519307\pi\)
−0.0606176 + 0.998161i \(0.519307\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −1.95470 −0.0873297
\(502\) 11.2393 0.501635
\(503\) 29.7184 1.32508 0.662540 0.749027i \(-0.269479\pi\)
0.662540 + 0.749027i \(0.269479\pi\)
\(504\) −5.11829 −0.227987
\(505\) −11.1862 −0.497780
\(506\) −4.21727 −0.187481
\(507\) −46.3819 −2.05989
\(508\) 11.8238 0.524595
\(509\) −6.03921 −0.267683 −0.133842 0.991003i \(-0.542731\pi\)
−0.133842 + 0.991003i \(0.542731\pi\)
\(510\) 8.64082 0.382622
\(511\) 4.65927 0.206114
\(512\) −1.00000 −0.0441942
\(513\) −31.3406 −1.38372
\(514\) 5.32977 0.235086
\(515\) 1.10982 0.0489045
\(516\) 22.9798 1.01163
\(517\) 35.7195 1.57094
\(518\) 1.52491 0.0670005
\(519\) −6.69932 −0.294067
\(520\) −5.40206 −0.236896
\(521\) −24.3339 −1.06609 −0.533044 0.846088i \(-0.678952\pi\)
−0.533044 + 0.846088i \(0.678952\pi\)
\(522\) 25.2368 1.10458
\(523\) −33.3422 −1.45795 −0.728977 0.684538i \(-0.760004\pi\)
−0.728977 + 0.684538i \(0.760004\pi\)
\(524\) −5.74416 −0.250935
\(525\) −2.81294 −0.122767
\(526\) 23.1323 1.00862
\(527\) 3.70378 0.161339
\(528\) −9.27794 −0.403771
\(529\) −21.3026 −0.926201
\(530\) −3.38794 −0.147163
\(531\) −65.7964 −2.85532
\(532\) 4.84423 0.210024
\(533\) −17.6500 −0.764506
\(534\) 48.7162 2.10815
\(535\) −16.0511 −0.693948
\(536\) 4.93266 0.213058
\(537\) 34.6719 1.49620
\(538\) −18.7660 −0.809058
\(539\) −19.5412 −0.841698
\(540\) 6.34940 0.273235
\(541\) 6.10904 0.262648 0.131324 0.991339i \(-0.458077\pi\)
0.131324 + 0.991339i \(0.458077\pi\)
\(542\) 2.18592 0.0938932
\(543\) 16.1840 0.694524
\(544\) 3.01470 0.129254
\(545\) 15.0220 0.643471
\(546\) −15.1956 −0.650314
\(547\) −43.0814 −1.84203 −0.921014 0.389529i \(-0.872638\pi\)
−0.921014 + 0.389529i \(0.872638\pi\)
\(548\) 13.5128 0.577236
\(549\) 78.3208 3.34265
\(550\) −3.23699 −0.138026
\(551\) −23.8854 −1.01755
\(552\) 3.73423 0.158939
\(553\) −0.897952 −0.0381848
\(554\) −1.10562 −0.0469734
\(555\) −4.45352 −0.189042
\(556\) 1.06732 0.0452644
\(557\) −4.45115 −0.188601 −0.0943007 0.995544i \(-0.530062\pi\)
−0.0943007 + 0.995544i \(0.530062\pi\)
\(558\) 6.40730 0.271243
\(559\) 43.3107 1.83185
\(560\) −0.981408 −0.0414721
\(561\) 27.9702 1.18090
\(562\) −23.5114 −0.991767
\(563\) −10.2067 −0.430162 −0.215081 0.976596i \(-0.569002\pi\)
−0.215081 + 0.976596i \(0.569002\pi\)
\(564\) −31.6282 −1.33179
\(565\) 8.26597 0.347752
\(566\) 16.7860 0.705566
\(567\) 2.50561 0.105226
\(568\) 0.116467 0.00488684
\(569\) 11.7620 0.493089 0.246544 0.969132i \(-0.420705\pi\)
0.246544 + 0.969132i \(0.420705\pi\)
\(570\) −14.1477 −0.592581
\(571\) −37.3525 −1.56315 −0.781577 0.623809i \(-0.785585\pi\)
−0.781577 + 0.623809i \(0.785585\pi\)
\(572\) −17.4864 −0.731143
\(573\) 7.27517 0.303924
\(574\) −3.20653 −0.133838
\(575\) 1.30284 0.0543321
\(576\) 5.21525 0.217302
\(577\) 26.4195 1.09986 0.549930 0.835211i \(-0.314654\pi\)
0.549930 + 0.835211i \(0.314654\pi\)
\(578\) 7.91156 0.329078
\(579\) 14.7612 0.613455
\(580\) 4.83903 0.200930
\(581\) 7.34264 0.304624
\(582\) 29.6234 1.22793
\(583\) −10.9667 −0.454196
\(584\) −4.74753 −0.196454
\(585\) 28.1731 1.16481
\(586\) 10.9849 0.453780
\(587\) 45.8820 1.89375 0.946877 0.321595i \(-0.104219\pi\)
0.946877 + 0.321595i \(0.104219\pi\)
\(588\) 17.3029 0.713561
\(589\) −6.06422 −0.249872
\(590\) −12.6162 −0.519399
\(591\) 25.6044 1.05323
\(592\) −1.55379 −0.0638605
\(593\) 28.1648 1.15659 0.578296 0.815827i \(-0.303718\pi\)
0.578296 + 0.815827i \(0.303718\pi\)
\(594\) 20.5530 0.843298
\(595\) 2.95866 0.121293
\(596\) 13.3247 0.545799
\(597\) 24.2877 0.994029
\(598\) 7.03800 0.287805
\(599\) −15.8266 −0.646657 −0.323329 0.946287i \(-0.604802\pi\)
−0.323329 + 0.946287i \(0.604802\pi\)
\(600\) 2.86623 0.117013
\(601\) 41.2359 1.68205 0.841024 0.540998i \(-0.181953\pi\)
0.841024 + 0.540998i \(0.181953\pi\)
\(602\) 7.86840 0.320692
\(603\) −25.7250 −1.04760
\(604\) −18.5077 −0.753069
\(605\) 0.521900 0.0212183
\(606\) 32.0622 1.30244
\(607\) −11.9281 −0.484146 −0.242073 0.970258i \(-0.577827\pi\)
−0.242073 + 0.970258i \(0.577827\pi\)
\(608\) −4.93600 −0.200181
\(609\) 13.6119 0.551582
\(610\) 15.0176 0.608047
\(611\) −59.6106 −2.41159
\(612\) −15.7224 −0.635542
\(613\) 0.285543 0.0115330 0.00576648 0.999983i \(-0.498164\pi\)
0.00576648 + 0.999983i \(0.498164\pi\)
\(614\) 16.5978 0.669833
\(615\) 9.36475 0.377623
\(616\) −3.17681 −0.127997
\(617\) −44.6205 −1.79635 −0.898177 0.439635i \(-0.855108\pi\)
−0.898177 + 0.439635i \(0.855108\pi\)
\(618\) −3.18099 −0.127958
\(619\) −4.94927 −0.198928 −0.0994639 0.995041i \(-0.531713\pi\)
−0.0994639 + 0.995041i \(0.531713\pi\)
\(620\) 1.22857 0.0493406
\(621\) −8.27224 −0.331954
\(622\) 22.9342 0.919577
\(623\) 16.6806 0.668295
\(624\) 15.4835 0.619837
\(625\) 1.00000 0.0400000
\(626\) 24.0683 0.961961
\(627\) −45.7959 −1.82891
\(628\) −1.35261 −0.0539749
\(629\) 4.68423 0.186772
\(630\) 5.11829 0.203918
\(631\) −21.2275 −0.845054 −0.422527 0.906350i \(-0.638857\pi\)
−0.422527 + 0.906350i \(0.638857\pi\)
\(632\) 0.914963 0.0363953
\(633\) −2.17078 −0.0862806
\(634\) 10.9487 0.434829
\(635\) −11.8238 −0.469212
\(636\) 9.71061 0.385051
\(637\) 32.6113 1.29211
\(638\) 15.6639 0.620139
\(639\) −0.607403 −0.0240285
\(640\) 1.00000 0.0395285
\(641\) 6.25157 0.246922 0.123461 0.992349i \(-0.460601\pi\)
0.123461 + 0.992349i \(0.460601\pi\)
\(642\) 46.0060 1.81571
\(643\) −7.27224 −0.286789 −0.143395 0.989666i \(-0.545802\pi\)
−0.143395 + 0.989666i \(0.545802\pi\)
\(644\) 1.27862 0.0503845
\(645\) −22.9798 −0.904830
\(646\) 14.8806 0.585468
\(647\) −24.6580 −0.969406 −0.484703 0.874679i \(-0.661072\pi\)
−0.484703 + 0.874679i \(0.661072\pi\)
\(648\) −2.55308 −0.100294
\(649\) −40.8384 −1.60305
\(650\) 5.40206 0.211886
\(651\) 3.45589 0.135447
\(652\) −3.44154 −0.134781
\(653\) −14.9540 −0.585196 −0.292598 0.956236i \(-0.594520\pi\)
−0.292598 + 0.956236i \(0.594520\pi\)
\(654\) −43.0564 −1.68364
\(655\) 5.74416 0.224443
\(656\) 3.26728 0.127566
\(657\) 24.7596 0.965963
\(658\) −10.8296 −0.422183
\(659\) −40.4956 −1.57749 −0.788743 0.614723i \(-0.789268\pi\)
−0.788743 + 0.614723i \(0.789268\pi\)
\(660\) 9.27794 0.361143
\(661\) −2.19717 −0.0854600 −0.0427300 0.999087i \(-0.513606\pi\)
−0.0427300 + 0.999087i \(0.513606\pi\)
\(662\) −12.5841 −0.489094
\(663\) −46.6782 −1.81283
\(664\) −7.48174 −0.290348
\(665\) −4.84423 −0.187851
\(666\) 8.10342 0.314001
\(667\) −6.30447 −0.244110
\(668\) 0.681978 0.0263865
\(669\) −50.3078 −1.94501
\(670\) −4.93266 −0.190565
\(671\) 48.6120 1.87664
\(672\) 2.81294 0.108511
\(673\) −10.2059 −0.393410 −0.196705 0.980463i \(-0.563024\pi\)
−0.196705 + 0.980463i \(0.563024\pi\)
\(674\) −13.0258 −0.501735
\(675\) −6.34940 −0.244389
\(676\) 16.1822 0.622393
\(677\) 41.6339 1.60012 0.800061 0.599919i \(-0.204800\pi\)
0.800061 + 0.599919i \(0.204800\pi\)
\(678\) −23.6921 −0.909891
\(679\) 10.1432 0.389259
\(680\) −3.01470 −0.115609
\(681\) 74.0077 2.83598
\(682\) 3.97687 0.152282
\(683\) 15.5843 0.596317 0.298158 0.954516i \(-0.403628\pi\)
0.298158 + 0.954516i \(0.403628\pi\)
\(684\) 25.7425 0.984287
\(685\) −13.5128 −0.516296
\(686\) 12.7945 0.488495
\(687\) 54.0852 2.06348
\(688\) −8.01745 −0.305663
\(689\) 18.3019 0.697246
\(690\) −3.73423 −0.142160
\(691\) 8.82809 0.335836 0.167918 0.985801i \(-0.446296\pi\)
0.167918 + 0.985801i \(0.446296\pi\)
\(692\) 2.33733 0.0888520
\(693\) 16.5678 0.629360
\(694\) 11.7323 0.445351
\(695\) −1.06732 −0.0404857
\(696\) −13.8698 −0.525732
\(697\) −9.84987 −0.373090
\(698\) 25.2634 0.956233
\(699\) 58.4378 2.21032
\(700\) 0.981408 0.0370937
\(701\) −1.55139 −0.0585950 −0.0292975 0.999571i \(-0.509327\pi\)
−0.0292975 + 0.999571i \(0.509327\pi\)
\(702\) −34.2998 −1.29456
\(703\) −7.66952 −0.289261
\(704\) 3.23699 0.121999
\(705\) 31.6282 1.19119
\(706\) −29.8560 −1.12365
\(707\) 10.9782 0.412879
\(708\) 36.1607 1.35900
\(709\) −51.6685 −1.94045 −0.970226 0.242202i \(-0.922130\pi\)
−0.970226 + 0.242202i \(0.922130\pi\)
\(710\) −0.116467 −0.00437092
\(711\) −4.77176 −0.178955
\(712\) −16.9966 −0.636976
\(713\) −1.60063 −0.0599440
\(714\) −8.48017 −0.317363
\(715\) 17.4864 0.653954
\(716\) −12.0967 −0.452075
\(717\) 44.1512 1.64886
\(718\) −32.6092 −1.21697
\(719\) 32.1417 1.19868 0.599341 0.800494i \(-0.295429\pi\)
0.599341 + 0.800494i \(0.295429\pi\)
\(720\) −5.21525 −0.194361
\(721\) −1.08919 −0.0405634
\(722\) −5.36407 −0.199630
\(723\) 19.7736 0.735390
\(724\) −5.64646 −0.209849
\(725\) −4.83903 −0.179717
\(726\) −1.49588 −0.0555174
\(727\) −15.1473 −0.561784 −0.280892 0.959739i \(-0.590630\pi\)
−0.280892 + 0.959739i \(0.590630\pi\)
\(728\) 5.30162 0.196491
\(729\) −41.2815 −1.52895
\(730\) 4.74753 0.175714
\(731\) 24.1703 0.893969
\(732\) −43.0440 −1.59095
\(733\) −12.2881 −0.453870 −0.226935 0.973910i \(-0.572870\pi\)
−0.226935 + 0.973910i \(0.572870\pi\)
\(734\) −15.6372 −0.577181
\(735\) −17.3029 −0.638229
\(736\) −1.30284 −0.0480232
\(737\) −15.9670 −0.588150
\(738\) −17.0397 −0.627238
\(739\) 37.5098 1.37982 0.689911 0.723894i \(-0.257650\pi\)
0.689911 + 0.723894i \(0.257650\pi\)
\(740\) 1.55379 0.0571186
\(741\) 76.4266 2.80760
\(742\) 3.32496 0.122063
\(743\) −42.9813 −1.57683 −0.788416 0.615142i \(-0.789099\pi\)
−0.788416 + 0.615142i \(0.789099\pi\)
\(744\) −3.52136 −0.129099
\(745\) −13.3247 −0.488178
\(746\) −18.8479 −0.690072
\(747\) 39.0191 1.42764
\(748\) −9.75856 −0.356808
\(749\) 15.7526 0.575589
\(750\) −2.86623 −0.104660
\(751\) −13.1162 −0.478617 −0.239309 0.970944i \(-0.576921\pi\)
−0.239309 + 0.970944i \(0.576921\pi\)
\(752\) 11.0348 0.402398
\(753\) 32.2144 1.17396
\(754\) −26.1407 −0.951989
\(755\) 18.5077 0.673565
\(756\) −6.23136 −0.226632
\(757\) −21.2470 −0.772234 −0.386117 0.922450i \(-0.626184\pi\)
−0.386117 + 0.922450i \(0.626184\pi\)
\(758\) 32.5777 1.18328
\(759\) −12.0877 −0.438754
\(760\) 4.93600 0.179047
\(761\) −4.30816 −0.156171 −0.0780854 0.996947i \(-0.524881\pi\)
−0.0780854 + 0.996947i \(0.524881\pi\)
\(762\) 33.8896 1.22769
\(763\) −14.7427 −0.533721
\(764\) −2.53824 −0.0918303
\(765\) 15.7224 0.568446
\(766\) −0.283228 −0.0102334
\(767\) 68.1532 2.46087
\(768\) −2.86623 −0.103426
\(769\) 40.7149 1.46822 0.734109 0.679032i \(-0.237600\pi\)
0.734109 + 0.679032i \(0.237600\pi\)
\(770\) 3.17681 0.114484
\(771\) 15.2763 0.550164
\(772\) −5.15005 −0.185354
\(773\) 19.5182 0.702020 0.351010 0.936372i \(-0.385838\pi\)
0.351010 + 0.936372i \(0.385838\pi\)
\(774\) 41.8130 1.50294
\(775\) −1.22857 −0.0441316
\(776\) −10.3353 −0.371016
\(777\) 4.37072 0.156799
\(778\) −28.7129 −1.02941
\(779\) 16.1273 0.577819
\(780\) −15.4835 −0.554399
\(781\) −0.377002 −0.0134902
\(782\) 3.92767 0.140453
\(783\) 30.7250 1.09802
\(784\) −6.03684 −0.215601
\(785\) 1.35261 0.0482766
\(786\) −16.4641 −0.587254
\(787\) −26.2803 −0.936793 −0.468396 0.883518i \(-0.655168\pi\)
−0.468396 + 0.883518i \(0.655168\pi\)
\(788\) −8.93316 −0.318230
\(789\) 66.3024 2.36043
\(790\) −0.914963 −0.0325529
\(791\) −8.11229 −0.288440
\(792\) −16.8817 −0.599865
\(793\) −81.1262 −2.88087
\(794\) −12.1688 −0.431854
\(795\) −9.71061 −0.344400
\(796\) −8.47376 −0.300344
\(797\) −32.6893 −1.15792 −0.578958 0.815358i \(-0.696540\pi\)
−0.578958 + 0.815358i \(0.696540\pi\)
\(798\) 13.8847 0.491511
\(799\) −33.2666 −1.17689
\(800\) −1.00000 −0.0353553
\(801\) 88.6417 3.13200
\(802\) 1.00000 0.0353112
\(803\) 15.3677 0.542315
\(804\) 14.1381 0.498612
\(805\) −1.27862 −0.0450653
\(806\) −6.63681 −0.233772
\(807\) −53.7875 −1.89341
\(808\) −11.1862 −0.393530
\(809\) 37.1799 1.30718 0.653588 0.756851i \(-0.273263\pi\)
0.653588 + 0.756851i \(0.273263\pi\)
\(810\) 2.55308 0.0897060
\(811\) −12.4269 −0.436368 −0.218184 0.975908i \(-0.570013\pi\)
−0.218184 + 0.975908i \(0.570013\pi\)
\(812\) −4.74907 −0.166660
\(813\) 6.26534 0.219735
\(814\) 5.02961 0.176288
\(815\) 3.44154 0.120552
\(816\) 8.64082 0.302489
\(817\) −39.5741 −1.38452
\(818\) 8.12653 0.284138
\(819\) −27.6493 −0.966144
\(820\) −3.26728 −0.114098
\(821\) 12.0558 0.420750 0.210375 0.977621i \(-0.432532\pi\)
0.210375 + 0.977621i \(0.432532\pi\)
\(822\) 38.7306 1.35089
\(823\) 40.1242 1.39864 0.699321 0.714808i \(-0.253486\pi\)
0.699321 + 0.714808i \(0.253486\pi\)
\(824\) 1.10982 0.0386624
\(825\) −9.27794 −0.323016
\(826\) 12.3816 0.430811
\(827\) 14.4220 0.501502 0.250751 0.968052i \(-0.419323\pi\)
0.250751 + 0.968052i \(0.419323\pi\)
\(828\) 6.79462 0.236129
\(829\) −3.22843 −0.112128 −0.0560641 0.998427i \(-0.517855\pi\)
−0.0560641 + 0.998427i \(0.517855\pi\)
\(830\) 7.48174 0.259695
\(831\) −3.16896 −0.109930
\(832\) −5.40206 −0.187283
\(833\) 18.1993 0.630568
\(834\) 3.05918 0.105931
\(835\) −0.681978 −0.0236008
\(836\) 15.9778 0.552603
\(837\) 7.80069 0.269631
\(838\) −31.2448 −1.07934
\(839\) −8.87424 −0.306373 −0.153186 0.988197i \(-0.548953\pi\)
−0.153186 + 0.988197i \(0.548953\pi\)
\(840\) −2.81294 −0.0970556
\(841\) −5.58378 −0.192544
\(842\) 1.26922 0.0437401
\(843\) −67.3888 −2.32100
\(844\) 0.757364 0.0260696
\(845\) −16.1822 −0.556685
\(846\) −57.5492 −1.97858
\(847\) −0.512197 −0.0175993
\(848\) −3.38794 −0.116342
\(849\) 48.1123 1.65121
\(850\) 3.01470 0.103403
\(851\) −2.02434 −0.0693935
\(852\) 0.333820 0.0114365
\(853\) −48.4722 −1.65966 −0.829828 0.558019i \(-0.811562\pi\)
−0.829828 + 0.558019i \(0.811562\pi\)
\(854\) −14.7384 −0.504339
\(855\) −25.7425 −0.880373
\(856\) −16.0511 −0.548614
\(857\) −15.2432 −0.520698 −0.260349 0.965515i \(-0.583838\pi\)
−0.260349 + 0.965515i \(0.583838\pi\)
\(858\) −50.1200 −1.71107
\(859\) 0.988211 0.0337173 0.0168587 0.999858i \(-0.494633\pi\)
0.0168587 + 0.999858i \(0.494633\pi\)
\(860\) 8.01745 0.273393
\(861\) −9.19064 −0.313216
\(862\) 11.9607 0.407384
\(863\) 21.0637 0.717016 0.358508 0.933527i \(-0.383286\pi\)
0.358508 + 0.933527i \(0.383286\pi\)
\(864\) 6.34940 0.216011
\(865\) −2.33733 −0.0794716
\(866\) 40.3389 1.37077
\(867\) 22.6763 0.770128
\(868\) −1.20573 −0.0409251
\(869\) −2.96172 −0.100470
\(870\) 13.8698 0.470229
\(871\) 26.6465 0.902882
\(872\) 15.0220 0.508708
\(873\) 53.9013 1.82428
\(874\) −6.43080 −0.217525
\(875\) −0.981408 −0.0331777
\(876\) −13.6075 −0.459755
\(877\) 0.602518 0.0203456 0.0101728 0.999948i \(-0.496762\pi\)
0.0101728 + 0.999948i \(0.496762\pi\)
\(878\) 35.8412 1.20958
\(879\) 31.4851 1.06197
\(880\) −3.23699 −0.109119
\(881\) −31.8197 −1.07203 −0.536017 0.844207i \(-0.680072\pi\)
−0.536017 + 0.844207i \(0.680072\pi\)
\(882\) 31.4836 1.06011
\(883\) 3.26342 0.109823 0.0549115 0.998491i \(-0.482512\pi\)
0.0549115 + 0.998491i \(0.482512\pi\)
\(884\) 16.2856 0.547744
\(885\) −36.1607 −1.21553
\(886\) 25.8381 0.868048
\(887\) −22.7994 −0.765528 −0.382764 0.923846i \(-0.625028\pi\)
−0.382764 + 0.923846i \(0.625028\pi\)
\(888\) −4.45352 −0.149450
\(889\) 11.6040 0.389184
\(890\) 16.9966 0.569728
\(891\) 8.26428 0.276864
\(892\) 17.5519 0.587683
\(893\) 54.4677 1.82269
\(894\) 38.1915 1.27731
\(895\) 12.0967 0.404349
\(896\) −0.981408 −0.0327866
\(897\) 20.1725 0.673540
\(898\) 10.2434 0.341828
\(899\) 5.94509 0.198280
\(900\) 5.21525 0.173842
\(901\) 10.2136 0.340266
\(902\) −10.5761 −0.352147
\(903\) 22.5526 0.750504
\(904\) 8.26597 0.274922
\(905\) 5.64646 0.187695
\(906\) −53.0473 −1.76238
\(907\) −25.4084 −0.843671 −0.421835 0.906672i \(-0.638614\pi\)
−0.421835 + 0.906672i \(0.638614\pi\)
\(908\) −25.8206 −0.856887
\(909\) 58.3389 1.93498
\(910\) −5.30162 −0.175747
\(911\) 3.34150 0.110709 0.0553544 0.998467i \(-0.482371\pi\)
0.0553544 + 0.998467i \(0.482371\pi\)
\(912\) −14.1477 −0.468477
\(913\) 24.2183 0.801509
\(914\) 23.6779 0.783194
\(915\) 43.0440 1.42299
\(916\) −18.8698 −0.623477
\(917\) −5.63737 −0.186162
\(918\) −19.1416 −0.631766
\(919\) 44.5860 1.47076 0.735379 0.677656i \(-0.237004\pi\)
0.735379 + 0.677656i \(0.237004\pi\)
\(920\) 1.30284 0.0429533
\(921\) 47.5731 1.56759
\(922\) −0.150219 −0.00494722
\(923\) 0.629160 0.0207091
\(924\) −9.10545 −0.299547
\(925\) −1.55379 −0.0510884
\(926\) −28.3404 −0.931322
\(927\) −5.78798 −0.190102
\(928\) 4.83903 0.158849
\(929\) 6.30033 0.206707 0.103354 0.994645i \(-0.467043\pi\)
0.103354 + 0.994645i \(0.467043\pi\)
\(930\) 3.52136 0.115470
\(931\) −29.7978 −0.976584
\(932\) −20.3884 −0.667845
\(933\) 65.7345 2.15205
\(934\) 6.79712 0.222408
\(935\) 9.75856 0.319139
\(936\) 28.1731 0.920866
\(937\) −9.79260 −0.319910 −0.159955 0.987124i \(-0.551135\pi\)
−0.159955 + 0.987124i \(0.551135\pi\)
\(938\) 4.84095 0.158063
\(939\) 68.9851 2.25124
\(940\) −11.0348 −0.359915
\(941\) 9.26615 0.302068 0.151034 0.988529i \(-0.451740\pi\)
0.151034 + 0.988529i \(0.451740\pi\)
\(942\) −3.87688 −0.126315
\(943\) 4.25673 0.138618
\(944\) −12.6162 −0.410621
\(945\) 6.23136 0.202706
\(946\) 25.9524 0.843786
\(947\) 42.2598 1.37326 0.686630 0.727007i \(-0.259089\pi\)
0.686630 + 0.727007i \(0.259089\pi\)
\(948\) 2.62249 0.0851745
\(949\) −25.6464 −0.832519
\(950\) −4.93600 −0.160145
\(951\) 31.3815 1.01761
\(952\) 2.95866 0.0958906
\(953\) −56.9411 −1.84450 −0.922251 0.386591i \(-0.873653\pi\)
−0.922251 + 0.386591i \(0.873653\pi\)
\(954\) 17.6690 0.572054
\(955\) 2.53824 0.0821355
\(956\) −15.4040 −0.498200
\(957\) 44.8962 1.45129
\(958\) −37.2822 −1.20453
\(959\) 13.2615 0.428237
\(960\) 2.86623 0.0925070
\(961\) −29.4906 −0.951310
\(962\) −8.39368 −0.270623
\(963\) 83.7103 2.69753
\(964\) −6.89885 −0.222197
\(965\) 5.15005 0.165786
\(966\) 3.66480 0.117913
\(967\) 15.1523 0.487265 0.243633 0.969868i \(-0.421661\pi\)
0.243633 + 0.969868i \(0.421661\pi\)
\(968\) 0.521900 0.0167745
\(969\) 42.6511 1.37015
\(970\) 10.3353 0.331847
\(971\) 18.5151 0.594178 0.297089 0.954850i \(-0.403984\pi\)
0.297089 + 0.954850i \(0.403984\pi\)
\(972\) 11.7305 0.376257
\(973\) 1.04748 0.0335805
\(974\) 1.95947 0.0627856
\(975\) 15.4835 0.495869
\(976\) 15.0176 0.480703
\(977\) −2.34607 −0.0750575 −0.0375288 0.999296i \(-0.511949\pi\)
−0.0375288 + 0.999296i \(0.511949\pi\)
\(978\) −9.86422 −0.315423
\(979\) 55.0179 1.75838
\(980\) 6.03684 0.192840
\(981\) −78.3434 −2.50131
\(982\) 26.0586 0.831563
\(983\) 51.5565 1.64440 0.822198 0.569202i \(-0.192748\pi\)
0.822198 + 0.569202i \(0.192748\pi\)
\(984\) 9.36475 0.298537
\(985\) 8.93316 0.284634
\(986\) −14.5882 −0.464584
\(987\) −31.0402 −0.988020
\(988\) −26.6645 −0.848312
\(989\) −10.4454 −0.332146
\(990\) 16.8817 0.536536
\(991\) −45.4156 −1.44268 −0.721338 0.692584i \(-0.756472\pi\)
−0.721338 + 0.692584i \(0.756472\pi\)
\(992\) 1.22857 0.0390072
\(993\) −36.0688 −1.14461
\(994\) 0.114301 0.00362542
\(995\) 8.47376 0.268636
\(996\) −21.4443 −0.679490
\(997\) 10.7484 0.340405 0.170203 0.985409i \(-0.445558\pi\)
0.170203 + 0.985409i \(0.445558\pi\)
\(998\) 2.70819 0.0857262
\(999\) 9.86566 0.312136
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 \(a_p\))