Properties

Label 8015.2.a.l.1.22
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.01597 q^{2} +3.29298 q^{3} -0.967811 q^{4} -1.00000 q^{5} -3.34556 q^{6} -1.00000 q^{7} +3.01520 q^{8} +7.84372 q^{9} +O(q^{10})\) \(q-1.01597 q^{2} +3.29298 q^{3} -0.967811 q^{4} -1.00000 q^{5} -3.34556 q^{6} -1.00000 q^{7} +3.01520 q^{8} +7.84372 q^{9} +1.01597 q^{10} -6.31839 q^{11} -3.18698 q^{12} -5.68874 q^{13} +1.01597 q^{14} -3.29298 q^{15} -1.12772 q^{16} +1.61361 q^{17} -7.96896 q^{18} +2.13466 q^{19} +0.967811 q^{20} -3.29298 q^{21} +6.41928 q^{22} -2.24317 q^{23} +9.92899 q^{24} +1.00000 q^{25} +5.77957 q^{26} +15.9503 q^{27} +0.967811 q^{28} -7.73433 q^{29} +3.34556 q^{30} +8.36953 q^{31} -4.88467 q^{32} -20.8063 q^{33} -1.63937 q^{34} +1.00000 q^{35} -7.59124 q^{36} +2.74919 q^{37} -2.16875 q^{38} -18.7329 q^{39} -3.01520 q^{40} +4.98382 q^{41} +3.34556 q^{42} -2.61371 q^{43} +6.11501 q^{44} -7.84372 q^{45} +2.27899 q^{46} +1.87840 q^{47} -3.71356 q^{48} +1.00000 q^{49} -1.01597 q^{50} +5.31358 q^{51} +5.50562 q^{52} +11.8377 q^{53} -16.2050 q^{54} +6.31839 q^{55} -3.01520 q^{56} +7.02941 q^{57} +7.85783 q^{58} +0.907289 q^{59} +3.18698 q^{60} +2.44556 q^{61} -8.50317 q^{62} -7.84372 q^{63} +7.21810 q^{64} +5.68874 q^{65} +21.1386 q^{66} -8.81817 q^{67} -1.56167 q^{68} -7.38672 q^{69} -1.01597 q^{70} -9.46632 q^{71} +23.6504 q^{72} +6.06503 q^{73} -2.79309 q^{74} +3.29298 q^{75} -2.06595 q^{76} +6.31839 q^{77} +19.0320 q^{78} -13.0557 q^{79} +1.12772 q^{80} +28.9928 q^{81} -5.06340 q^{82} -2.44346 q^{83} +3.18698 q^{84} -1.61361 q^{85} +2.65544 q^{86} -25.4690 q^{87} -19.0512 q^{88} +12.5853 q^{89} +7.96896 q^{90} +5.68874 q^{91} +2.17097 q^{92} +27.5607 q^{93} -1.90839 q^{94} -2.13466 q^{95} -16.0851 q^{96} +13.5945 q^{97} -1.01597 q^{98} -49.5597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.01597 −0.718397 −0.359199 0.933261i \(-0.616950\pi\)
−0.359199 + 0.933261i \(0.616950\pi\)
\(3\) 3.29298 1.90120 0.950602 0.310414i \(-0.100468\pi\)
0.950602 + 0.310414i \(0.100468\pi\)
\(4\) −0.967811 −0.483905
\(5\) −1.00000 −0.447214
\(6\) −3.34556 −1.36582
\(7\) −1.00000 −0.377964
\(8\) 3.01520 1.06603
\(9\) 7.84372 2.61457
\(10\) 1.01597 0.321277
\(11\) −6.31839 −1.90507 −0.952533 0.304435i \(-0.901532\pi\)
−0.952533 + 0.304435i \(0.901532\pi\)
\(12\) −3.18698 −0.920002
\(13\) −5.68874 −1.57777 −0.788886 0.614540i \(-0.789342\pi\)
−0.788886 + 0.614540i \(0.789342\pi\)
\(14\) 1.01597 0.271529
\(15\) −3.29298 −0.850244
\(16\) −1.12772 −0.281930
\(17\) 1.61361 0.391357 0.195679 0.980668i \(-0.437309\pi\)
0.195679 + 0.980668i \(0.437309\pi\)
\(18\) −7.96896 −1.87830
\(19\) 2.13466 0.489725 0.244863 0.969558i \(-0.421257\pi\)
0.244863 + 0.969558i \(0.421257\pi\)
\(20\) 0.967811 0.216409
\(21\) −3.29298 −0.718587
\(22\) 6.41928 1.36859
\(23\) −2.24317 −0.467734 −0.233867 0.972269i \(-0.575138\pi\)
−0.233867 + 0.972269i \(0.575138\pi\)
\(24\) 9.92899 2.02675
\(25\) 1.00000 0.200000
\(26\) 5.77957 1.13347
\(27\) 15.9503 3.06963
\(28\) 0.967811 0.182899
\(29\) −7.73433 −1.43623 −0.718115 0.695925i \(-0.754995\pi\)
−0.718115 + 0.695925i \(0.754995\pi\)
\(30\) 3.34556 0.610813
\(31\) 8.36953 1.50321 0.751606 0.659613i \(-0.229280\pi\)
0.751606 + 0.659613i \(0.229280\pi\)
\(32\) −4.88467 −0.863496
\(33\) −20.8063 −3.62192
\(34\) −1.63937 −0.281150
\(35\) 1.00000 0.169031
\(36\) −7.59124 −1.26521
\(37\) 2.74919 0.451965 0.225982 0.974131i \(-0.427441\pi\)
0.225982 + 0.974131i \(0.427441\pi\)
\(38\) −2.16875 −0.351817
\(39\) −18.7329 −2.99966
\(40\) −3.01520 −0.476745
\(41\) 4.98382 0.778342 0.389171 0.921165i \(-0.372761\pi\)
0.389171 + 0.921165i \(0.372761\pi\)
\(42\) 3.34556 0.516231
\(43\) −2.61371 −0.398587 −0.199294 0.979940i \(-0.563865\pi\)
−0.199294 + 0.979940i \(0.563865\pi\)
\(44\) 6.11501 0.921872
\(45\) −7.84372 −1.16927
\(46\) 2.27899 0.336019
\(47\) 1.87840 0.273993 0.136996 0.990572i \(-0.456255\pi\)
0.136996 + 0.990572i \(0.456255\pi\)
\(48\) −3.71356 −0.536007
\(49\) 1.00000 0.142857
\(50\) −1.01597 −0.143679
\(51\) 5.31358 0.744049
\(52\) 5.50562 0.763492
\(53\) 11.8377 1.62603 0.813017 0.582240i \(-0.197824\pi\)
0.813017 + 0.582240i \(0.197824\pi\)
\(54\) −16.2050 −2.20522
\(55\) 6.31839 0.851972
\(56\) −3.01520 −0.402923
\(57\) 7.02941 0.931068
\(58\) 7.85783 1.03178
\(59\) 0.907289 0.118119 0.0590595 0.998254i \(-0.481190\pi\)
0.0590595 + 0.998254i \(0.481190\pi\)
\(60\) 3.18698 0.411438
\(61\) 2.44556 0.313122 0.156561 0.987668i \(-0.449959\pi\)
0.156561 + 0.987668i \(0.449959\pi\)
\(62\) −8.50317 −1.07990
\(63\) −7.84372 −0.988216
\(64\) 7.21810 0.902263
\(65\) 5.68874 0.705601
\(66\) 21.1386 2.60198
\(67\) −8.81817 −1.07731 −0.538655 0.842526i \(-0.681068\pi\)
−0.538655 + 0.842526i \(0.681068\pi\)
\(68\) −1.56167 −0.189380
\(69\) −7.38672 −0.889257
\(70\) −1.01597 −0.121431
\(71\) −9.46632 −1.12345 −0.561723 0.827325i \(-0.689861\pi\)
−0.561723 + 0.827325i \(0.689861\pi\)
\(72\) 23.6504 2.78722
\(73\) 6.06503 0.709858 0.354929 0.934893i \(-0.384505\pi\)
0.354929 + 0.934893i \(0.384505\pi\)
\(74\) −2.79309 −0.324690
\(75\) 3.29298 0.380241
\(76\) −2.06595 −0.236981
\(77\) 6.31839 0.720047
\(78\) 19.0320 2.15495
\(79\) −13.0557 −1.46888 −0.734440 0.678674i \(-0.762555\pi\)
−0.734440 + 0.678674i \(0.762555\pi\)
\(80\) 1.12772 0.126083
\(81\) 28.9928 3.22142
\(82\) −5.06340 −0.559159
\(83\) −2.44346 −0.268204 −0.134102 0.990968i \(-0.542815\pi\)
−0.134102 + 0.990968i \(0.542815\pi\)
\(84\) 3.18698 0.347728
\(85\) −1.61361 −0.175020
\(86\) 2.65544 0.286344
\(87\) −25.4690 −2.73056
\(88\) −19.0512 −2.03086
\(89\) 12.5853 1.33404 0.667020 0.745040i \(-0.267570\pi\)
0.667020 + 0.745040i \(0.267570\pi\)
\(90\) 7.96896 0.840002
\(91\) 5.68874 0.596342
\(92\) 2.17097 0.226339
\(93\) 27.5607 2.85791
\(94\) −1.90839 −0.196836
\(95\) −2.13466 −0.219012
\(96\) −16.0851 −1.64168
\(97\) 13.5945 1.38031 0.690156 0.723661i \(-0.257542\pi\)
0.690156 + 0.723661i \(0.257542\pi\)
\(98\) −1.01597 −0.102628
\(99\) −49.5597 −4.98094
\(100\) −0.967811 −0.0967811
\(101\) 5.21352 0.518764 0.259382 0.965775i \(-0.416481\pi\)
0.259382 + 0.965775i \(0.416481\pi\)
\(102\) −5.39842 −0.534523
\(103\) −9.87704 −0.973213 −0.486607 0.873621i \(-0.661766\pi\)
−0.486607 + 0.873621i \(0.661766\pi\)
\(104\) −17.1527 −1.68196
\(105\) 3.29298 0.321362
\(106\) −12.0267 −1.16814
\(107\) −2.78424 −0.269162 −0.134581 0.990903i \(-0.542969\pi\)
−0.134581 + 0.990903i \(0.542969\pi\)
\(108\) −15.4369 −1.48541
\(109\) 7.30708 0.699891 0.349946 0.936770i \(-0.386200\pi\)
0.349946 + 0.936770i \(0.386200\pi\)
\(110\) −6.41928 −0.612054
\(111\) 9.05305 0.859277
\(112\) 1.12772 0.106560
\(113\) 9.62182 0.905145 0.452572 0.891728i \(-0.350506\pi\)
0.452572 + 0.891728i \(0.350506\pi\)
\(114\) −7.14165 −0.668876
\(115\) 2.24317 0.209177
\(116\) 7.48537 0.694999
\(117\) −44.6209 −4.12520
\(118\) −0.921776 −0.0848564
\(119\) −1.61361 −0.147919
\(120\) −9.92899 −0.906389
\(121\) 28.9221 2.62928
\(122\) −2.48461 −0.224946
\(123\) 16.4116 1.47979
\(124\) −8.10012 −0.727412
\(125\) −1.00000 −0.0894427
\(126\) 7.96896 0.709932
\(127\) 20.1099 1.78447 0.892233 0.451575i \(-0.149138\pi\)
0.892233 + 0.451575i \(0.149138\pi\)
\(128\) 2.43598 0.215312
\(129\) −8.60690 −0.757795
\(130\) −5.77957 −0.506902
\(131\) −16.7769 −1.46580 −0.732901 0.680335i \(-0.761834\pi\)
−0.732901 + 0.680335i \(0.761834\pi\)
\(132\) 20.1366 1.75267
\(133\) −2.13466 −0.185099
\(134\) 8.95897 0.773937
\(135\) −15.9503 −1.37278
\(136\) 4.86534 0.417200
\(137\) 9.23069 0.788631 0.394315 0.918975i \(-0.370982\pi\)
0.394315 + 0.918975i \(0.370982\pi\)
\(138\) 7.50467 0.638840
\(139\) 15.4136 1.30736 0.653682 0.756770i \(-0.273224\pi\)
0.653682 + 0.756770i \(0.273224\pi\)
\(140\) −0.967811 −0.0817949
\(141\) 6.18554 0.520916
\(142\) 9.61748 0.807081
\(143\) 35.9437 3.00576
\(144\) −8.84553 −0.737127
\(145\) 7.73433 0.642301
\(146\) −6.16187 −0.509960
\(147\) 3.29298 0.271600
\(148\) −2.66070 −0.218708
\(149\) −16.5159 −1.35303 −0.676517 0.736427i \(-0.736511\pi\)
−0.676517 + 0.736427i \(0.736511\pi\)
\(150\) −3.34556 −0.273164
\(151\) 14.8509 1.20855 0.604275 0.796776i \(-0.293463\pi\)
0.604275 + 0.796776i \(0.293463\pi\)
\(152\) 6.43643 0.522064
\(153\) 12.6567 1.02323
\(154\) −6.41928 −0.517280
\(155\) −8.36953 −0.672257
\(156\) 18.1299 1.45155
\(157\) 2.69423 0.215023 0.107512 0.994204i \(-0.465712\pi\)
0.107512 + 0.994204i \(0.465712\pi\)
\(158\) 13.2642 1.05524
\(159\) 38.9813 3.09142
\(160\) 4.88467 0.386167
\(161\) 2.24317 0.176787
\(162\) −29.4557 −2.31426
\(163\) 19.6605 1.53993 0.769963 0.638088i \(-0.220274\pi\)
0.769963 + 0.638088i \(0.220274\pi\)
\(164\) −4.82340 −0.376644
\(165\) 20.8063 1.61977
\(166\) 2.48247 0.192677
\(167\) −8.86477 −0.685976 −0.342988 0.939340i \(-0.611439\pi\)
−0.342988 + 0.939340i \(0.611439\pi\)
\(168\) −9.92899 −0.766038
\(169\) 19.3617 1.48936
\(170\) 1.63937 0.125734
\(171\) 16.7437 1.28042
\(172\) 2.52958 0.192878
\(173\) −5.04724 −0.383734 −0.191867 0.981421i \(-0.561454\pi\)
−0.191867 + 0.981421i \(0.561454\pi\)
\(174\) 25.8757 1.96163
\(175\) −1.00000 −0.0755929
\(176\) 7.12538 0.537096
\(177\) 2.98769 0.224568
\(178\) −12.7863 −0.958370
\(179\) 16.8738 1.26121 0.630605 0.776104i \(-0.282807\pi\)
0.630605 + 0.776104i \(0.282807\pi\)
\(180\) 7.59124 0.565817
\(181\) 6.92207 0.514513 0.257257 0.966343i \(-0.417181\pi\)
0.257257 + 0.966343i \(0.417181\pi\)
\(182\) −5.77957 −0.428410
\(183\) 8.05319 0.595309
\(184\) −6.76361 −0.498620
\(185\) −2.74919 −0.202125
\(186\) −28.0008 −2.05312
\(187\) −10.1954 −0.745561
\(188\) −1.81794 −0.132587
\(189\) −15.9503 −1.16021
\(190\) 2.16875 0.157338
\(191\) 16.9601 1.22719 0.613594 0.789622i \(-0.289723\pi\)
0.613594 + 0.789622i \(0.289723\pi\)
\(192\) 23.7691 1.71539
\(193\) 20.0077 1.44018 0.720092 0.693879i \(-0.244100\pi\)
0.720092 + 0.693879i \(0.244100\pi\)
\(194\) −13.8116 −0.991612
\(195\) 18.7329 1.34149
\(196\) −0.967811 −0.0691293
\(197\) 10.0601 0.716754 0.358377 0.933577i \(-0.383330\pi\)
0.358377 + 0.933577i \(0.383330\pi\)
\(198\) 50.3510 3.57829
\(199\) −6.78095 −0.480689 −0.240344 0.970688i \(-0.577260\pi\)
−0.240344 + 0.970688i \(0.577260\pi\)
\(200\) 3.01520 0.213207
\(201\) −29.0381 −2.04819
\(202\) −5.29676 −0.372679
\(203\) 7.73433 0.542844
\(204\) −5.14254 −0.360050
\(205\) −4.98382 −0.348085
\(206\) 10.0347 0.699154
\(207\) −17.5948 −1.22292
\(208\) 6.41531 0.444822
\(209\) −13.4876 −0.932959
\(210\) −3.34556 −0.230866
\(211\) −6.26952 −0.431612 −0.215806 0.976436i \(-0.569238\pi\)
−0.215806 + 0.976436i \(0.569238\pi\)
\(212\) −11.4567 −0.786847
\(213\) −31.1724 −2.13590
\(214\) 2.82869 0.193365
\(215\) 2.61371 0.178254
\(216\) 48.0932 3.27233
\(217\) −8.36953 −0.568161
\(218\) −7.42375 −0.502800
\(219\) 19.9720 1.34958
\(220\) −6.11501 −0.412274
\(221\) −9.17939 −0.617472
\(222\) −9.19760 −0.617302
\(223\) −27.2744 −1.82643 −0.913214 0.407481i \(-0.866407\pi\)
−0.913214 + 0.407481i \(0.866407\pi\)
\(224\) 4.88467 0.326371
\(225\) 7.84372 0.522915
\(226\) −9.77545 −0.650254
\(227\) −29.8729 −1.98273 −0.991367 0.131113i \(-0.958145\pi\)
−0.991367 + 0.131113i \(0.958145\pi\)
\(228\) −6.80313 −0.450549
\(229\) 1.00000 0.0660819
\(230\) −2.27899 −0.150272
\(231\) 20.8063 1.36896
\(232\) −23.3205 −1.53107
\(233\) 25.7669 1.68805 0.844024 0.536306i \(-0.180181\pi\)
0.844024 + 0.536306i \(0.180181\pi\)
\(234\) 45.3333 2.96353
\(235\) −1.87840 −0.122533
\(236\) −0.878084 −0.0571584
\(237\) −42.9921 −2.79264
\(238\) 1.63937 0.106265
\(239\) 10.1204 0.654633 0.327316 0.944915i \(-0.393856\pi\)
0.327316 + 0.944915i \(0.393856\pi\)
\(240\) 3.71356 0.239709
\(241\) −11.2252 −0.723079 −0.361539 0.932357i \(-0.617749\pi\)
−0.361539 + 0.932357i \(0.617749\pi\)
\(242\) −29.3839 −1.88887
\(243\) 47.6219 3.05494
\(244\) −2.36684 −0.151522
\(245\) −1.00000 −0.0638877
\(246\) −16.6737 −1.06308
\(247\) −12.1435 −0.772675
\(248\) 25.2358 1.60247
\(249\) −8.04626 −0.509911
\(250\) 1.01597 0.0642554
\(251\) −17.8922 −1.12935 −0.564674 0.825314i \(-0.690998\pi\)
−0.564674 + 0.825314i \(0.690998\pi\)
\(252\) 7.59124 0.478203
\(253\) 14.1732 0.891064
\(254\) −20.4310 −1.28196
\(255\) −5.31358 −0.332749
\(256\) −16.9111 −1.05694
\(257\) 9.99749 0.623626 0.311813 0.950143i \(-0.399064\pi\)
0.311813 + 0.950143i \(0.399064\pi\)
\(258\) 8.74432 0.544398
\(259\) −2.74919 −0.170827
\(260\) −5.50562 −0.341444
\(261\) −60.6659 −3.75513
\(262\) 17.0447 1.05303
\(263\) −16.2638 −1.00287 −0.501435 0.865195i \(-0.667194\pi\)
−0.501435 + 0.865195i \(0.667194\pi\)
\(264\) −62.7352 −3.86109
\(265\) −11.8377 −0.727184
\(266\) 2.16875 0.132974
\(267\) 41.4432 2.53628
\(268\) 8.53432 0.521317
\(269\) −3.28699 −0.200411 −0.100206 0.994967i \(-0.531950\pi\)
−0.100206 + 0.994967i \(0.531950\pi\)
\(270\) 16.2050 0.986202
\(271\) 25.6005 1.55512 0.777561 0.628808i \(-0.216457\pi\)
0.777561 + 0.628808i \(0.216457\pi\)
\(272\) −1.81970 −0.110335
\(273\) 18.7329 1.13377
\(274\) −9.37807 −0.566550
\(275\) −6.31839 −0.381013
\(276\) 7.14895 0.430316
\(277\) −5.08975 −0.305813 −0.152907 0.988241i \(-0.548863\pi\)
−0.152907 + 0.988241i \(0.548863\pi\)
\(278\) −15.6597 −0.939206
\(279\) 65.6482 3.93026
\(280\) 3.01520 0.180193
\(281\) 13.1386 0.783786 0.391893 0.920011i \(-0.371820\pi\)
0.391893 + 0.920011i \(0.371820\pi\)
\(282\) −6.28430 −0.374225
\(283\) −5.30575 −0.315394 −0.157697 0.987488i \(-0.550407\pi\)
−0.157697 + 0.987488i \(0.550407\pi\)
\(284\) 9.16161 0.543642
\(285\) −7.02941 −0.416386
\(286\) −36.5176 −2.15933
\(287\) −4.98382 −0.294186
\(288\) −38.3140 −2.25767
\(289\) −14.3963 −0.846840
\(290\) −7.85783 −0.461428
\(291\) 44.7664 2.62425
\(292\) −5.86980 −0.343504
\(293\) 16.5534 0.967061 0.483530 0.875328i \(-0.339354\pi\)
0.483530 + 0.875328i \(0.339354\pi\)
\(294\) −3.34556 −0.195117
\(295\) −0.907289 −0.0528244
\(296\) 8.28937 0.481810
\(297\) −100.780 −5.84785
\(298\) 16.7796 0.972016
\(299\) 12.7608 0.737977
\(300\) −3.18698 −0.184000
\(301\) 2.61371 0.150652
\(302\) −15.0880 −0.868220
\(303\) 17.1680 0.986276
\(304\) −2.40730 −0.138068
\(305\) −2.44556 −0.140033
\(306\) −12.8588 −0.735087
\(307\) 20.7049 1.18169 0.590846 0.806785i \(-0.298794\pi\)
0.590846 + 0.806785i \(0.298794\pi\)
\(308\) −6.11501 −0.348435
\(309\) −32.5249 −1.85028
\(310\) 8.50317 0.482947
\(311\) 24.9358 1.41398 0.706989 0.707224i \(-0.250053\pi\)
0.706989 + 0.707224i \(0.250053\pi\)
\(312\) −56.4834 −3.19774
\(313\) 21.6911 1.22605 0.613027 0.790062i \(-0.289952\pi\)
0.613027 + 0.790062i \(0.289952\pi\)
\(314\) −2.73725 −0.154472
\(315\) 7.84372 0.441944
\(316\) 12.6354 0.710799
\(317\) 9.40569 0.528276 0.264138 0.964485i \(-0.414913\pi\)
0.264138 + 0.964485i \(0.414913\pi\)
\(318\) −39.6038 −2.22087
\(319\) 48.8685 2.73611
\(320\) −7.21810 −0.403504
\(321\) −9.16844 −0.511732
\(322\) −2.27899 −0.127003
\(323\) 3.44451 0.191658
\(324\) −28.0595 −1.55886
\(325\) −5.68874 −0.315554
\(326\) −19.9744 −1.10628
\(327\) 24.0621 1.33064
\(328\) 15.0272 0.829739
\(329\) −1.87840 −0.103560
\(330\) −21.1386 −1.16364
\(331\) 18.9819 1.04334 0.521669 0.853148i \(-0.325310\pi\)
0.521669 + 0.853148i \(0.325310\pi\)
\(332\) 2.36481 0.129786
\(333\) 21.5639 1.18170
\(334\) 9.00631 0.492803
\(335\) 8.81817 0.481788
\(336\) 3.71356 0.202591
\(337\) −16.9403 −0.922800 −0.461400 0.887192i \(-0.652653\pi\)
−0.461400 + 0.887192i \(0.652653\pi\)
\(338\) −19.6709 −1.06996
\(339\) 31.6845 1.72086
\(340\) 1.56167 0.0846932
\(341\) −52.8819 −2.86372
\(342\) −17.0111 −0.919852
\(343\) −1.00000 −0.0539949
\(344\) −7.88085 −0.424907
\(345\) 7.38672 0.397688
\(346\) 5.12783 0.275674
\(347\) −32.9041 −1.76638 −0.883192 0.469011i \(-0.844610\pi\)
−0.883192 + 0.469011i \(0.844610\pi\)
\(348\) 24.6492 1.32133
\(349\) 10.3882 0.556070 0.278035 0.960571i \(-0.410317\pi\)
0.278035 + 0.960571i \(0.410317\pi\)
\(350\) 1.01597 0.0543057
\(351\) −90.7369 −4.84318
\(352\) 30.8632 1.64502
\(353\) 12.1743 0.647971 0.323986 0.946062i \(-0.394977\pi\)
0.323986 + 0.946062i \(0.394977\pi\)
\(354\) −3.03539 −0.161329
\(355\) 9.46632 0.502420
\(356\) −12.1802 −0.645549
\(357\) −5.31358 −0.281224
\(358\) −17.1433 −0.906049
\(359\) 7.28344 0.384405 0.192203 0.981355i \(-0.438437\pi\)
0.192203 + 0.981355i \(0.438437\pi\)
\(360\) −23.6504 −1.24648
\(361\) −14.4432 −0.760169
\(362\) −7.03260 −0.369625
\(363\) 95.2398 4.99879
\(364\) −5.50562 −0.288573
\(365\) −6.06503 −0.317458
\(366\) −8.18178 −0.427668
\(367\) −15.5822 −0.813383 −0.406692 0.913565i \(-0.633318\pi\)
−0.406692 + 0.913565i \(0.633318\pi\)
\(368\) 2.52967 0.131868
\(369\) 39.0917 2.03503
\(370\) 2.79309 0.145206
\(371\) −11.8377 −0.614583
\(372\) −26.6735 −1.38296
\(373\) −15.2450 −0.789355 −0.394677 0.918820i \(-0.629144\pi\)
−0.394677 + 0.918820i \(0.629144\pi\)
\(374\) 10.3582 0.535609
\(375\) −3.29298 −0.170049
\(376\) 5.66375 0.292086
\(377\) 43.9986 2.26604
\(378\) 16.2050 0.833493
\(379\) −33.0298 −1.69663 −0.848314 0.529494i \(-0.822382\pi\)
−0.848314 + 0.529494i \(0.822382\pi\)
\(380\) 2.06595 0.105981
\(381\) 66.2216 3.39263
\(382\) −17.2309 −0.881609
\(383\) −4.23856 −0.216580 −0.108290 0.994119i \(-0.534538\pi\)
−0.108290 + 0.994119i \(0.534538\pi\)
\(384\) 8.02164 0.409352
\(385\) −6.31839 −0.322015
\(386\) −20.3271 −1.03462
\(387\) −20.5012 −1.04214
\(388\) −13.1569 −0.667940
\(389\) −17.1906 −0.871600 −0.435800 0.900043i \(-0.643535\pi\)
−0.435800 + 0.900043i \(0.643535\pi\)
\(390\) −19.0320 −0.963723
\(391\) −3.61960 −0.183051
\(392\) 3.01520 0.152291
\(393\) −55.2459 −2.78679
\(394\) −10.2208 −0.514914
\(395\) 13.0557 0.656903
\(396\) 47.9644 2.41030
\(397\) −23.3017 −1.16948 −0.584740 0.811221i \(-0.698803\pi\)
−0.584740 + 0.811221i \(0.698803\pi\)
\(398\) 6.88922 0.345325
\(399\) −7.02941 −0.351910
\(400\) −1.12772 −0.0563860
\(401\) 29.6515 1.48073 0.740363 0.672207i \(-0.234654\pi\)
0.740363 + 0.672207i \(0.234654\pi\)
\(402\) 29.5017 1.47141
\(403\) −47.6120 −2.37173
\(404\) −5.04570 −0.251033
\(405\) −28.9928 −1.44066
\(406\) −7.85783 −0.389977
\(407\) −17.3705 −0.861023
\(408\) 16.0215 0.793182
\(409\) −5.58939 −0.276378 −0.138189 0.990406i \(-0.544128\pi\)
−0.138189 + 0.990406i \(0.544128\pi\)
\(410\) 5.06340 0.250064
\(411\) 30.3965 1.49935
\(412\) 9.55910 0.470943
\(413\) −0.907289 −0.0446448
\(414\) 17.8758 0.878545
\(415\) 2.44346 0.119945
\(416\) 27.7876 1.36240
\(417\) 50.7566 2.48556
\(418\) 13.7030 0.670236
\(419\) −18.0697 −0.882762 −0.441381 0.897320i \(-0.645511\pi\)
−0.441381 + 0.897320i \(0.645511\pi\)
\(420\) −3.18698 −0.155509
\(421\) 19.2290 0.937166 0.468583 0.883419i \(-0.344765\pi\)
0.468583 + 0.883419i \(0.344765\pi\)
\(422\) 6.36963 0.310069
\(423\) 14.7336 0.716375
\(424\) 35.6930 1.73341
\(425\) 1.61361 0.0782714
\(426\) 31.6702 1.53442
\(427\) −2.44556 −0.118349
\(428\) 2.69461 0.130249
\(429\) 118.362 5.71456
\(430\) −2.65544 −0.128057
\(431\) 11.7335 0.565181 0.282591 0.959241i \(-0.408806\pi\)
0.282591 + 0.959241i \(0.408806\pi\)
\(432\) −17.9875 −0.865422
\(433\) 7.41003 0.356103 0.178052 0.984021i \(-0.443021\pi\)
0.178052 + 0.984021i \(0.443021\pi\)
\(434\) 8.50317 0.408165
\(435\) 25.4690 1.22115
\(436\) −7.07187 −0.338681
\(437\) −4.78842 −0.229061
\(438\) −20.2909 −0.969537
\(439\) −7.88688 −0.376420 −0.188210 0.982129i \(-0.560269\pi\)
−0.188210 + 0.982129i \(0.560269\pi\)
\(440\) 19.0512 0.908230
\(441\) 7.84372 0.373511
\(442\) 9.32595 0.443590
\(443\) 37.6005 1.78645 0.893226 0.449607i \(-0.148436\pi\)
0.893226 + 0.449607i \(0.148436\pi\)
\(444\) −8.76163 −0.415809
\(445\) −12.5853 −0.596601
\(446\) 27.7099 1.31210
\(447\) −54.3865 −2.57239
\(448\) −7.21810 −0.341023
\(449\) 35.9048 1.69445 0.847226 0.531233i \(-0.178271\pi\)
0.847226 + 0.531233i \(0.178271\pi\)
\(450\) −7.96896 −0.375660
\(451\) −31.4897 −1.48279
\(452\) −9.31210 −0.438004
\(453\) 48.9038 2.29770
\(454\) 30.3499 1.42439
\(455\) −5.68874 −0.266692
\(456\) 21.1951 0.992549
\(457\) −11.7213 −0.548299 −0.274149 0.961687i \(-0.588396\pi\)
−0.274149 + 0.961687i \(0.588396\pi\)
\(458\) −1.01597 −0.0474730
\(459\) 25.7375 1.20132
\(460\) −2.17097 −0.101222
\(461\) −35.9816 −1.67583 −0.837916 0.545800i \(-0.816226\pi\)
−0.837916 + 0.545800i \(0.816226\pi\)
\(462\) −21.1386 −0.983454
\(463\) −3.76576 −0.175010 −0.0875049 0.996164i \(-0.527889\pi\)
−0.0875049 + 0.996164i \(0.527889\pi\)
\(464\) 8.72217 0.404916
\(465\) −27.5607 −1.27810
\(466\) −26.1784 −1.21269
\(467\) −15.5329 −0.718776 −0.359388 0.933188i \(-0.617014\pi\)
−0.359388 + 0.933188i \(0.617014\pi\)
\(468\) 43.1846 1.99621
\(469\) 8.81817 0.407185
\(470\) 1.90839 0.0880276
\(471\) 8.87206 0.408803
\(472\) 2.73566 0.125919
\(473\) 16.5144 0.759335
\(474\) 43.6786 2.00622
\(475\) 2.13466 0.0979451
\(476\) 1.56167 0.0715788
\(477\) 92.8517 4.25139
\(478\) −10.2820 −0.470286
\(479\) 43.4103 1.98347 0.991733 0.128316i \(-0.0409573\pi\)
0.991733 + 0.128316i \(0.0409573\pi\)
\(480\) 16.0851 0.734182
\(481\) −15.6394 −0.713097
\(482\) 11.4044 0.519458
\(483\) 7.38672 0.336107
\(484\) −27.9911 −1.27232
\(485\) −13.5945 −0.617294
\(486\) −48.3822 −2.19466
\(487\) −0.771424 −0.0349566 −0.0174783 0.999847i \(-0.505564\pi\)
−0.0174783 + 0.999847i \(0.505564\pi\)
\(488\) 7.37386 0.333799
\(489\) 64.7415 2.92771
\(490\) 1.01597 0.0458967
\(491\) 1.25434 0.0566074 0.0283037 0.999599i \(-0.490989\pi\)
0.0283037 + 0.999599i \(0.490989\pi\)
\(492\) −15.8834 −0.716077
\(493\) −12.4802 −0.562079
\(494\) 12.3374 0.555088
\(495\) 49.5597 2.22754
\(496\) −9.43849 −0.423801
\(497\) 9.46632 0.424623
\(498\) 8.17474 0.366319
\(499\) 34.5239 1.54550 0.772750 0.634710i \(-0.218881\pi\)
0.772750 + 0.634710i \(0.218881\pi\)
\(500\) 0.967811 0.0432818
\(501\) −29.1915 −1.30418
\(502\) 18.1779 0.811321
\(503\) 10.2212 0.455741 0.227870 0.973691i \(-0.426824\pi\)
0.227870 + 0.973691i \(0.426824\pi\)
\(504\) −23.6504 −1.05347
\(505\) −5.21352 −0.231998
\(506\) −14.3995 −0.640138
\(507\) 63.7578 2.83158
\(508\) −19.4626 −0.863513
\(509\) 12.3039 0.545359 0.272680 0.962105i \(-0.412090\pi\)
0.272680 + 0.962105i \(0.412090\pi\)
\(510\) 5.39842 0.239046
\(511\) −6.06503 −0.268301
\(512\) 12.3091 0.543993
\(513\) 34.0485 1.50328
\(514\) −10.1571 −0.448011
\(515\) 9.87704 0.435234
\(516\) 8.32985 0.366701
\(517\) −11.8685 −0.521975
\(518\) 2.79309 0.122721
\(519\) −16.6204 −0.729557
\(520\) 17.1527 0.752194
\(521\) 17.8194 0.780682 0.390341 0.920670i \(-0.372357\pi\)
0.390341 + 0.920670i \(0.372357\pi\)
\(522\) 61.6346 2.69767
\(523\) 1.67232 0.0731254 0.0365627 0.999331i \(-0.488359\pi\)
0.0365627 + 0.999331i \(0.488359\pi\)
\(524\) 16.2368 0.709309
\(525\) −3.29298 −0.143717
\(526\) 16.5235 0.720459
\(527\) 13.5051 0.588293
\(528\) 23.4637 1.02113
\(529\) −17.9682 −0.781225
\(530\) 12.0267 0.522407
\(531\) 7.11652 0.308831
\(532\) 2.06595 0.0895703
\(533\) −28.3517 −1.22805
\(534\) −42.1049 −1.82206
\(535\) 2.78424 0.120373
\(536\) −26.5885 −1.14845
\(537\) 55.5652 2.39781
\(538\) 3.33948 0.143975
\(539\) −6.31839 −0.272152
\(540\) 15.4369 0.664296
\(541\) 27.7249 1.19199 0.595994 0.802989i \(-0.296758\pi\)
0.595994 + 0.802989i \(0.296758\pi\)
\(542\) −26.0093 −1.11720
\(543\) 22.7942 0.978195
\(544\) −7.88194 −0.337935
\(545\) −7.30708 −0.313001
\(546\) −19.0320 −0.814495
\(547\) −18.1333 −0.775323 −0.387662 0.921802i \(-0.626717\pi\)
−0.387662 + 0.921802i \(0.626717\pi\)
\(548\) −8.93356 −0.381623
\(549\) 19.1823 0.818681
\(550\) 6.41928 0.273719
\(551\) −16.5102 −0.703358
\(552\) −22.2724 −0.947978
\(553\) 13.0557 0.555184
\(554\) 5.17101 0.219695
\(555\) −9.05305 −0.384280
\(556\) −14.9174 −0.632640
\(557\) −25.3337 −1.07342 −0.536712 0.843765i \(-0.680334\pi\)
−0.536712 + 0.843765i \(0.680334\pi\)
\(558\) −66.6965 −2.82349
\(559\) 14.8687 0.628879
\(560\) −1.12772 −0.0476549
\(561\) −33.5732 −1.41746
\(562\) −13.3484 −0.563070
\(563\) −21.2954 −0.897492 −0.448746 0.893659i \(-0.648129\pi\)
−0.448746 + 0.893659i \(0.648129\pi\)
\(564\) −5.98643 −0.252074
\(565\) −9.62182 −0.404793
\(566\) 5.39047 0.226578
\(567\) −28.9928 −1.21758
\(568\) −28.5428 −1.19763
\(569\) −35.1776 −1.47472 −0.737361 0.675499i \(-0.763928\pi\)
−0.737361 + 0.675499i \(0.763928\pi\)
\(570\) 7.14165 0.299131
\(571\) −33.5101 −1.40236 −0.701178 0.712987i \(-0.747342\pi\)
−0.701178 + 0.712987i \(0.747342\pi\)
\(572\) −34.7867 −1.45450
\(573\) 55.8492 2.33313
\(574\) 5.06340 0.211342
\(575\) −2.24317 −0.0935467
\(576\) 56.6168 2.35903
\(577\) −24.3175 −1.01235 −0.506176 0.862430i \(-0.668941\pi\)
−0.506176 + 0.862430i \(0.668941\pi\)
\(578\) 14.6261 0.608367
\(579\) 65.8849 2.73808
\(580\) −7.48537 −0.310813
\(581\) 2.44346 0.101372
\(582\) −45.4812 −1.88526
\(583\) −74.7952 −3.09770
\(584\) 18.2873 0.756732
\(585\) 44.6209 1.84485
\(586\) −16.8177 −0.694734
\(587\) 31.3520 1.29403 0.647017 0.762475i \(-0.276016\pi\)
0.647017 + 0.762475i \(0.276016\pi\)
\(588\) −3.18698 −0.131429
\(589\) 17.8661 0.736161
\(590\) 0.921776 0.0379489
\(591\) 33.1278 1.36270
\(592\) −3.10032 −0.127423
\(593\) −46.5771 −1.91269 −0.956346 0.292236i \(-0.905601\pi\)
−0.956346 + 0.292236i \(0.905601\pi\)
\(594\) 102.389 4.20108
\(595\) 1.61361 0.0661514
\(596\) 15.9842 0.654740
\(597\) −22.3295 −0.913887
\(598\) −12.9646 −0.530161
\(599\) −17.9722 −0.734323 −0.367161 0.930157i \(-0.619670\pi\)
−0.367161 + 0.930157i \(0.619670\pi\)
\(600\) 9.92899 0.405349
\(601\) 7.80235 0.318265 0.159132 0.987257i \(-0.449130\pi\)
0.159132 + 0.987257i \(0.449130\pi\)
\(602\) −2.65544 −0.108228
\(603\) −69.1673 −2.81671
\(604\) −14.3729 −0.584824
\(605\) −28.9221 −1.17585
\(606\) −17.4421 −0.708538
\(607\) 28.6507 1.16290 0.581449 0.813583i \(-0.302486\pi\)
0.581449 + 0.813583i \(0.302486\pi\)
\(608\) −10.4271 −0.422876
\(609\) 25.4690 1.03206
\(610\) 2.48461 0.100599
\(611\) −10.6857 −0.432298
\(612\) −12.2493 −0.495147
\(613\) 11.5405 0.466115 0.233058 0.972463i \(-0.425127\pi\)
0.233058 + 0.972463i \(0.425127\pi\)
\(614\) −21.0355 −0.848924
\(615\) −16.4116 −0.661781
\(616\) 19.0512 0.767595
\(617\) 43.4486 1.74917 0.874587 0.484869i \(-0.161133\pi\)
0.874587 + 0.484869i \(0.161133\pi\)
\(618\) 33.0442 1.32923
\(619\) 34.3689 1.38140 0.690702 0.723139i \(-0.257302\pi\)
0.690702 + 0.723139i \(0.257302\pi\)
\(620\) 8.10012 0.325309
\(621\) −35.7792 −1.43577
\(622\) −25.3339 −1.01580
\(623\) −12.5853 −0.504219
\(624\) 21.1255 0.845696
\(625\) 1.00000 0.0400000
\(626\) −22.0374 −0.880793
\(627\) −44.4145 −1.77375
\(628\) −2.60751 −0.104051
\(629\) 4.43612 0.176880
\(630\) −7.96896 −0.317491
\(631\) 28.1085 1.11898 0.559491 0.828836i \(-0.310996\pi\)
0.559491 + 0.828836i \(0.310996\pi\)
\(632\) −39.3655 −1.56588
\(633\) −20.6454 −0.820581
\(634\) −9.55587 −0.379512
\(635\) −20.1099 −0.798038
\(636\) −37.7266 −1.49596
\(637\) −5.68874 −0.225396
\(638\) −49.6488 −1.96562
\(639\) −74.2512 −2.93733
\(640\) −2.43598 −0.0962906
\(641\) 37.6643 1.48765 0.743826 0.668373i \(-0.233009\pi\)
0.743826 + 0.668373i \(0.233009\pi\)
\(642\) 9.31483 0.367627
\(643\) 18.5643 0.732106 0.366053 0.930594i \(-0.380709\pi\)
0.366053 + 0.930594i \(0.380709\pi\)
\(644\) −2.17097 −0.0855481
\(645\) 8.60690 0.338896
\(646\) −3.49951 −0.137686
\(647\) −44.5607 −1.75186 −0.875930 0.482438i \(-0.839751\pi\)
−0.875930 + 0.482438i \(0.839751\pi\)
\(648\) 87.4190 3.43414
\(649\) −5.73261 −0.225025
\(650\) 5.77957 0.226693
\(651\) −27.5607 −1.08019
\(652\) −19.0276 −0.745179
\(653\) 26.8931 1.05241 0.526204 0.850359i \(-0.323615\pi\)
0.526204 + 0.850359i \(0.323615\pi\)
\(654\) −24.4463 −0.955925
\(655\) 16.7769 0.655526
\(656\) −5.62036 −0.219438
\(657\) 47.5724 1.85598
\(658\) 1.90839 0.0743969
\(659\) 4.68623 0.182549 0.0912747 0.995826i \(-0.470906\pi\)
0.0912747 + 0.995826i \(0.470906\pi\)
\(660\) −20.1366 −0.783816
\(661\) 5.91209 0.229954 0.114977 0.993368i \(-0.463321\pi\)
0.114977 + 0.993368i \(0.463321\pi\)
\(662\) −19.2849 −0.749531
\(663\) −30.2275 −1.17394
\(664\) −7.36751 −0.285915
\(665\) 2.13466 0.0827787
\(666\) −21.9082 −0.848927
\(667\) 17.3494 0.671773
\(668\) 8.57942 0.331948
\(669\) −89.8140 −3.47241
\(670\) −8.95897 −0.346115
\(671\) −15.4520 −0.596519
\(672\) 16.0851 0.620497
\(673\) 37.3520 1.43981 0.719907 0.694070i \(-0.244184\pi\)
0.719907 + 0.694070i \(0.244184\pi\)
\(674\) 17.2108 0.662937
\(675\) 15.9503 0.613926
\(676\) −18.7385 −0.720711
\(677\) 16.3677 0.629063 0.314532 0.949247i \(-0.398153\pi\)
0.314532 + 0.949247i \(0.398153\pi\)
\(678\) −32.1904 −1.23626
\(679\) −13.5945 −0.521709
\(680\) −4.86534 −0.186577
\(681\) −98.3709 −3.76958
\(682\) 53.7263 2.05729
\(683\) −37.6564 −1.44088 −0.720441 0.693516i \(-0.756061\pi\)
−0.720441 + 0.693516i \(0.756061\pi\)
\(684\) −16.2047 −0.619604
\(685\) −9.23069 −0.352686
\(686\) 1.01597 0.0387898
\(687\) 3.29298 0.125635
\(688\) 2.94754 0.112374
\(689\) −67.3416 −2.56551
\(690\) −7.50467 −0.285698
\(691\) −15.3103 −0.582431 −0.291215 0.956657i \(-0.594060\pi\)
−0.291215 + 0.956657i \(0.594060\pi\)
\(692\) 4.88477 0.185691
\(693\) 49.5597 1.88262
\(694\) 33.4295 1.26897
\(695\) −15.4136 −0.584671
\(696\) −76.7941 −2.91087
\(697\) 8.04193 0.304610
\(698\) −10.5541 −0.399479
\(699\) 84.8500 3.20932
\(700\) 0.967811 0.0365798
\(701\) 47.9878 1.81248 0.906238 0.422769i \(-0.138942\pi\)
0.906238 + 0.422769i \(0.138942\pi\)
\(702\) 92.1857 3.47933
\(703\) 5.86861 0.221339
\(704\) −45.6068 −1.71887
\(705\) −6.18554 −0.232961
\(706\) −12.3687 −0.465501
\(707\) −5.21352 −0.196074
\(708\) −2.89151 −0.108670
\(709\) −3.73742 −0.140362 −0.0701808 0.997534i \(-0.522358\pi\)
−0.0701808 + 0.997534i \(0.522358\pi\)
\(710\) −9.61748 −0.360937
\(711\) −102.405 −3.84049
\(712\) 37.9472 1.42213
\(713\) −18.7743 −0.703103
\(714\) 5.39842 0.202031
\(715\) −35.9437 −1.34422
\(716\) −16.3307 −0.610306
\(717\) 33.3262 1.24459
\(718\) −7.39973 −0.276156
\(719\) 3.52836 0.131586 0.0657929 0.997833i \(-0.479042\pi\)
0.0657929 + 0.997833i \(0.479042\pi\)
\(720\) 8.84553 0.329653
\(721\) 9.87704 0.367840
\(722\) 14.6738 0.546103
\(723\) −36.9644 −1.37472
\(724\) −6.69925 −0.248976
\(725\) −7.73433 −0.287246
\(726\) −96.7605 −3.59112
\(727\) −1.70109 −0.0630898 −0.0315449 0.999502i \(-0.510043\pi\)
−0.0315449 + 0.999502i \(0.510043\pi\)
\(728\) 17.1527 0.635720
\(729\) 69.8395 2.58665
\(730\) 6.16187 0.228061
\(731\) −4.21750 −0.155990
\(732\) −7.79396 −0.288073
\(733\) 18.6527 0.688955 0.344477 0.938795i \(-0.388056\pi\)
0.344477 + 0.938795i \(0.388056\pi\)
\(734\) 15.8310 0.584332
\(735\) −3.29298 −0.121463
\(736\) 10.9572 0.403886
\(737\) 55.7166 2.05235
\(738\) −39.7159 −1.46196
\(739\) −23.6173 −0.868777 −0.434389 0.900726i \(-0.643036\pi\)
−0.434389 + 0.900726i \(0.643036\pi\)
\(740\) 2.66070 0.0978093
\(741\) −39.9884 −1.46901
\(742\) 12.0267 0.441515
\(743\) −5.26847 −0.193281 −0.0966406 0.995319i \(-0.530810\pi\)
−0.0966406 + 0.995319i \(0.530810\pi\)
\(744\) 83.1010 3.04663
\(745\) 16.5159 0.605095
\(746\) 15.4884 0.567070
\(747\) −19.1658 −0.701240
\(748\) 9.86722 0.360781
\(749\) 2.78424 0.101734
\(750\) 3.34556 0.122163
\(751\) −26.6578 −0.972758 −0.486379 0.873748i \(-0.661683\pi\)
−0.486379 + 0.873748i \(0.661683\pi\)
\(752\) −2.11831 −0.0772469
\(753\) −58.9188 −2.14712
\(754\) −44.7011 −1.62792
\(755\) −14.8509 −0.540480
\(756\) 15.4369 0.561433
\(757\) 9.05913 0.329260 0.164630 0.986355i \(-0.447357\pi\)
0.164630 + 0.986355i \(0.447357\pi\)
\(758\) 33.5572 1.21885
\(759\) 46.6722 1.69409
\(760\) −6.43643 −0.233474
\(761\) −18.8796 −0.684384 −0.342192 0.939630i \(-0.611169\pi\)
−0.342192 + 0.939630i \(0.611169\pi\)
\(762\) −67.2789 −2.43726
\(763\) −7.30708 −0.264534
\(764\) −16.4141 −0.593843
\(765\) −12.6567 −0.457603
\(766\) 4.30623 0.155591
\(767\) −5.16133 −0.186365
\(768\) −55.6879 −2.00946
\(769\) −43.9318 −1.58422 −0.792110 0.610379i \(-0.791017\pi\)
−0.792110 + 0.610379i \(0.791017\pi\)
\(770\) 6.41928 0.231335
\(771\) 32.9215 1.18564
\(772\) −19.3636 −0.696913
\(773\) −30.9174 −1.11202 −0.556012 0.831174i \(-0.687669\pi\)
−0.556012 + 0.831174i \(0.687669\pi\)
\(774\) 20.8286 0.748667
\(775\) 8.36953 0.300642
\(776\) 40.9901 1.47146
\(777\) −9.05305 −0.324776
\(778\) 17.4651 0.626155
\(779\) 10.6388 0.381174
\(780\) −18.1299 −0.649155
\(781\) 59.8119 2.14024
\(782\) 3.67739 0.131503
\(783\) −123.365 −4.40870
\(784\) −1.12772 −0.0402757
\(785\) −2.69423 −0.0961614
\(786\) 56.1280 2.00202
\(787\) 38.8018 1.38314 0.691568 0.722312i \(-0.256920\pi\)
0.691568 + 0.722312i \(0.256920\pi\)
\(788\) −9.73630 −0.346841
\(789\) −53.5564 −1.90666
\(790\) −13.2642 −0.471917
\(791\) −9.62182 −0.342113
\(792\) −149.432 −5.30984
\(793\) −13.9122 −0.494035
\(794\) 23.6738 0.840151
\(795\) −38.9813 −1.38253
\(796\) 6.56267 0.232608
\(797\) −33.5262 −1.18756 −0.593780 0.804628i \(-0.702365\pi\)
−0.593780 + 0.804628i \(0.702365\pi\)
\(798\) 7.14165 0.252812
\(799\) 3.03100 0.107229
\(800\) −4.88467 −0.172699
\(801\) 98.7156 3.48794
\(802\) −30.1250 −1.06375
\(803\) −38.3212 −1.35233
\(804\) 28.1034 0.991129
\(805\) −2.24317 −0.0790614
\(806\) 48.3723 1.70384
\(807\) −10.8240 −0.381023
\(808\) 15.7198 0.553020
\(809\) 10.3643 0.364390 0.182195 0.983262i \(-0.441680\pi\)
0.182195 + 0.983262i \(0.441680\pi\)
\(810\) 29.4557 1.03497
\(811\) 23.3528 0.820029 0.410015 0.912079i \(-0.365524\pi\)
0.410015 + 0.912079i \(0.365524\pi\)
\(812\) −7.48537 −0.262685
\(813\) 84.3021 2.95660
\(814\) 17.6478 0.618557
\(815\) −19.6605 −0.688676
\(816\) −5.99223 −0.209770
\(817\) −5.57939 −0.195198
\(818\) 5.67864 0.198549
\(819\) 44.6209 1.55918
\(820\) 4.82340 0.168440
\(821\) −15.3408 −0.535399 −0.267699 0.963502i \(-0.586263\pi\)
−0.267699 + 0.963502i \(0.586263\pi\)
\(822\) −30.8818 −1.07713
\(823\) −27.6997 −0.965549 −0.482775 0.875745i \(-0.660371\pi\)
−0.482775 + 0.875745i \(0.660371\pi\)
\(824\) −29.7812 −1.03748
\(825\) −20.8063 −0.724384
\(826\) 0.921776 0.0320727
\(827\) 12.0039 0.417415 0.208708 0.977978i \(-0.433074\pi\)
0.208708 + 0.977978i \(0.433074\pi\)
\(828\) 17.0285 0.591780
\(829\) −2.56630 −0.0891314 −0.0445657 0.999006i \(-0.514190\pi\)
−0.0445657 + 0.999006i \(0.514190\pi\)
\(830\) −2.48247 −0.0861679
\(831\) −16.7604 −0.581413
\(832\) −41.0619 −1.42357
\(833\) 1.61361 0.0559082
\(834\) −51.5671 −1.78562
\(835\) 8.86477 0.306778
\(836\) 13.0535 0.451464
\(837\) 133.496 4.61431
\(838\) 18.3582 0.634174
\(839\) 1.41712 0.0489245 0.0244623 0.999701i \(-0.492213\pi\)
0.0244623 + 0.999701i \(0.492213\pi\)
\(840\) 9.92899 0.342583
\(841\) 30.8199 1.06275
\(842\) −19.5361 −0.673258
\(843\) 43.2653 1.49014
\(844\) 6.06771 0.208859
\(845\) −19.3617 −0.666064
\(846\) −14.9689 −0.514641
\(847\) −28.9221 −0.993774
\(848\) −13.3496 −0.458428
\(849\) −17.4717 −0.599629
\(850\) −1.63937 −0.0562300
\(851\) −6.16692 −0.211399
\(852\) 30.1690 1.03357
\(853\) −4.92765 −0.168720 −0.0843598 0.996435i \(-0.526885\pi\)
−0.0843598 + 0.996435i \(0.526885\pi\)
\(854\) 2.48461 0.0850217
\(855\) −16.7437 −0.572623
\(856\) −8.39502 −0.286936
\(857\) 30.7269 1.04961 0.524805 0.851223i \(-0.324138\pi\)
0.524805 + 0.851223i \(0.324138\pi\)
\(858\) −120.252 −4.10532
\(859\) 10.5675 0.360557 0.180279 0.983616i \(-0.442300\pi\)
0.180279 + 0.983616i \(0.442300\pi\)
\(860\) −2.52958 −0.0862578
\(861\) −16.4116 −0.559307
\(862\) −11.9208 −0.406025
\(863\) −47.6106 −1.62068 −0.810342 0.585957i \(-0.800719\pi\)
−0.810342 + 0.585957i \(0.800719\pi\)
\(864\) −77.9118 −2.65061
\(865\) 5.04724 0.171611
\(866\) −7.52835 −0.255824
\(867\) −47.4066 −1.61001
\(868\) 8.10012 0.274936
\(869\) 82.4909 2.79831
\(870\) −25.8757 −0.877267
\(871\) 50.1643 1.69975
\(872\) 22.0323 0.746107
\(873\) 106.631 3.60893
\(874\) 4.86488 0.164557
\(875\) 1.00000 0.0338062
\(876\) −19.3291 −0.653071
\(877\) −16.7822 −0.566694 −0.283347 0.959017i \(-0.591445\pi\)
−0.283347 + 0.959017i \(0.591445\pi\)
\(878\) 8.01281 0.270419
\(879\) 54.5101 1.83858
\(880\) −7.12538 −0.240197
\(881\) 9.77832 0.329440 0.164720 0.986340i \(-0.447328\pi\)
0.164720 + 0.986340i \(0.447328\pi\)
\(882\) −7.96896 −0.268329
\(883\) 36.9449 1.24330 0.621648 0.783297i \(-0.286464\pi\)
0.621648 + 0.783297i \(0.286464\pi\)
\(884\) 8.88391 0.298798
\(885\) −2.98769 −0.100430
\(886\) −38.2009 −1.28338
\(887\) −38.1648 −1.28145 −0.640725 0.767771i \(-0.721366\pi\)
−0.640725 + 0.767771i \(0.721366\pi\)
\(888\) 27.2967 0.916018
\(889\) −20.1099 −0.674465
\(890\) 12.7863 0.428596
\(891\) −183.188 −6.13702
\(892\) 26.3964 0.883818
\(893\) 4.00975 0.134181
\(894\) 55.2549 1.84800
\(895\) −16.8738 −0.564030
\(896\) −2.43598 −0.0813804
\(897\) 42.0211 1.40304
\(898\) −36.4781 −1.21729
\(899\) −64.7327 −2.15896
\(900\) −7.59124 −0.253041
\(901\) 19.1014 0.636360
\(902\) 31.9925 1.06524
\(903\) 8.60690 0.286420
\(904\) 29.0117 0.964915
\(905\) −6.92207 −0.230097
\(906\) −49.6846 −1.65066
\(907\) 48.9170 1.62426 0.812131 0.583475i \(-0.198307\pi\)
0.812131 + 0.583475i \(0.198307\pi\)
\(908\) 28.9113 0.959456
\(909\) 40.8934 1.35635
\(910\) 5.77957 0.191591
\(911\) −5.11665 −0.169522 −0.0847611 0.996401i \(-0.527013\pi\)
−0.0847611 + 0.996401i \(0.527013\pi\)
\(912\) −7.92721 −0.262496
\(913\) 15.4387 0.510947
\(914\) 11.9084 0.393896
\(915\) −8.05319 −0.266230
\(916\) −0.967811 −0.0319774
\(917\) 16.7769 0.554021
\(918\) −26.1484 −0.863027
\(919\) −11.9663 −0.394731 −0.197366 0.980330i \(-0.563239\pi\)
−0.197366 + 0.980330i \(0.563239\pi\)
\(920\) 6.76361 0.222990
\(921\) 68.1809 2.24664
\(922\) 36.5561 1.20391
\(923\) 53.8514 1.77254
\(924\) −20.1366 −0.662445
\(925\) 2.74919 0.0903930
\(926\) 3.82589 0.125727
\(927\) −77.4727 −2.54454
\(928\) 37.7797 1.24018
\(929\) −42.2904 −1.38750 −0.693751 0.720215i \(-0.744043\pi\)
−0.693751 + 0.720215i \(0.744043\pi\)
\(930\) 28.0008 0.918181
\(931\) 2.13466 0.0699608
\(932\) −24.9375 −0.816855
\(933\) 82.1131 2.68826
\(934\) 15.7809 0.516366
\(935\) 10.1954 0.333425
\(936\) −134.541 −4.39760
\(937\) 5.27378 0.172287 0.0861434 0.996283i \(-0.472546\pi\)
0.0861434 + 0.996283i \(0.472546\pi\)
\(938\) −8.95897 −0.292521
\(939\) 71.4284 2.33098
\(940\) 1.81794 0.0592945
\(941\) −3.18610 −0.103864 −0.0519319 0.998651i \(-0.516538\pi\)
−0.0519319 + 0.998651i \(0.516538\pi\)
\(942\) −9.01372 −0.293683
\(943\) −11.1796 −0.364057
\(944\) −1.02317 −0.0333013
\(945\) 15.9503 0.518863
\(946\) −16.7781 −0.545504
\(947\) 23.0059 0.747592 0.373796 0.927511i \(-0.378056\pi\)
0.373796 + 0.927511i \(0.378056\pi\)
\(948\) 41.6082 1.35137
\(949\) −34.5023 −1.11999
\(950\) −2.16875 −0.0703635
\(951\) 30.9728 1.00436
\(952\) −4.86534 −0.157687
\(953\) −0.254204 −0.00823449 −0.00411725 0.999992i \(-0.501311\pi\)
−0.00411725 + 0.999992i \(0.501311\pi\)
\(954\) −94.3342 −3.05418
\(955\) −16.9601 −0.548815
\(956\) −9.79461 −0.316780
\(957\) 160.923 5.20191
\(958\) −44.1034 −1.42492
\(959\) −9.23069 −0.298074
\(960\) −23.7691 −0.767144
\(961\) 39.0490 1.25965
\(962\) 15.8892 0.512287
\(963\) −21.8388 −0.703745
\(964\) 10.8639 0.349902
\(965\) −20.0077 −0.644070
\(966\) −7.50467 −0.241459
\(967\) 17.4491 0.561126 0.280563 0.959836i \(-0.409479\pi\)
0.280563 + 0.959836i \(0.409479\pi\)
\(968\) 87.2057 2.80290
\(969\) 11.3427 0.364380
\(970\) 13.8116 0.443462
\(971\) −46.4827 −1.49170 −0.745851 0.666113i \(-0.767957\pi\)
−0.745851 + 0.666113i \(0.767957\pi\)
\(972\) −46.0890 −1.47830
\(973\) −15.4136 −0.494137
\(974\) 0.783742 0.0251127
\(975\) −18.7329 −0.599933
\(976\) −2.75791 −0.0882786
\(977\) 1.25071 0.0400136 0.0200068 0.999800i \(-0.493631\pi\)
0.0200068 + 0.999800i \(0.493631\pi\)
\(978\) −65.7753 −2.10326
\(979\) −79.5188 −2.54143
\(980\) 0.967811 0.0309156
\(981\) 57.3147 1.82992
\(982\) −1.27436 −0.0406666
\(983\) 23.1933 0.739752 0.369876 0.929081i \(-0.379400\pi\)
0.369876 + 0.929081i \(0.379400\pi\)
\(984\) 49.4843 1.57750
\(985\) −10.0601 −0.320542
\(986\) 12.6794 0.403796
\(987\) −6.18554 −0.196888
\(988\) 11.7527 0.373902
\(989\) 5.86300 0.186433
\(990\) −50.3510 −1.60026
\(991\) 13.4093 0.425960 0.212980 0.977057i \(-0.431683\pi\)
0.212980 + 0.977057i \(0.431683\pi\)
\(992\) −40.8824 −1.29802
\(993\) 62.5069 1.98360
\(994\) −9.61748 −0.305048
\(995\) 6.78095 0.214970
\(996\) 7.78726 0.246749
\(997\) 12.8080 0.405635 0.202817 0.979217i \(-0.434990\pi\)
0.202817 + 0.979217i \(0.434990\pi\)
\(998\) −35.0751 −1.11028
\(999\) 43.8504 1.38737
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 \(a_p\))