Properties

Label 4033.2.a.d.1.10
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32027 q^{2}\) \(+1.35424 q^{3}\) \(+3.38367 q^{4}\) \(+2.79503 q^{5}\) \(-3.14221 q^{6}\) \(+4.55894 q^{7}\) \(-3.21050 q^{8}\) \(-1.16603 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32027 q^{2}\) \(+1.35424 q^{3}\) \(+3.38367 q^{4}\) \(+2.79503 q^{5}\) \(-3.14221 q^{6}\) \(+4.55894 q^{7}\) \(-3.21050 q^{8}\) \(-1.16603 q^{9}\) \(-6.48525 q^{10}\) \(-4.50751 q^{11}\) \(+4.58231 q^{12}\) \(-0.542954 q^{13}\) \(-10.5780 q^{14}\) \(+3.78515 q^{15}\) \(+0.681903 q^{16}\) \(-5.71836 q^{17}\) \(+2.70551 q^{18}\) \(-1.76426 q^{19}\) \(+9.45749 q^{20}\) \(+6.17391 q^{21}\) \(+10.4587 q^{22}\) \(-3.18066 q^{23}\) \(-4.34780 q^{24}\) \(+2.81222 q^{25}\) \(+1.25980 q^{26}\) \(-5.64181 q^{27}\) \(+15.4260 q^{28}\) \(-7.61112 q^{29}\) \(-8.78260 q^{30}\) \(-1.83148 q^{31}\) \(+4.83881 q^{32}\) \(-6.10426 q^{33}\) \(+13.2682 q^{34}\) \(+12.7424 q^{35}\) \(-3.94546 q^{36}\) \(-1.00000 q^{37}\) \(+4.09356 q^{38}\) \(-0.735291 q^{39}\) \(-8.97347 q^{40}\) \(-9.61850 q^{41}\) \(-14.3252 q^{42}\) \(+3.29074 q^{43}\) \(-15.2520 q^{44}\) \(-3.25909 q^{45}\) \(+7.38000 q^{46}\) \(+7.88287 q^{47}\) \(+0.923462 q^{48}\) \(+13.7839 q^{49}\) \(-6.52512 q^{50}\) \(-7.74405 q^{51}\) \(-1.83718 q^{52}\) \(-3.17321 q^{53}\) \(+13.0906 q^{54}\) \(-12.5987 q^{55}\) \(-14.6365 q^{56}\) \(-2.38923 q^{57}\) \(+17.6599 q^{58}\) \(+1.31889 q^{59}\) \(+12.8077 q^{60}\) \(+2.66774 q^{61}\) \(+4.24954 q^{62}\) \(-5.31585 q^{63}\) \(-12.5912 q^{64}\) \(-1.51758 q^{65}\) \(+14.1636 q^{66}\) \(-3.57012 q^{67}\) \(-19.3491 q^{68}\) \(-4.30738 q^{69}\) \(-29.5658 q^{70}\) \(-8.88574 q^{71}\) \(+3.74354 q^{72}\) \(+4.02855 q^{73}\) \(+2.32027 q^{74}\) \(+3.80842 q^{75}\) \(-5.96967 q^{76}\) \(-20.5495 q^{77}\) \(+1.70608 q^{78}\) \(-17.5481 q^{79}\) \(+1.90594 q^{80}\) \(-4.14229 q^{81}\) \(+22.3176 q^{82}\) \(+8.15290 q^{83}\) \(+20.8905 q^{84}\) \(-15.9830 q^{85}\) \(-7.63541 q^{86}\) \(-10.3073 q^{87}\) \(+14.4714 q^{88}\) \(-13.3217 q^{89}\) \(+7.56198 q^{90}\) \(-2.47529 q^{91}\) \(-10.7623 q^{92}\) \(-2.48027 q^{93}\) \(-18.2904 q^{94}\) \(-4.93116 q^{95}\) \(+6.55292 q^{96}\) \(+0.623333 q^{97}\) \(-31.9825 q^{98}\) \(+5.25589 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32027 −1.64068 −0.820341 0.571875i \(-0.806216\pi\)
−0.820341 + 0.571875i \(0.806216\pi\)
\(3\) 1.35424 0.781872 0.390936 0.920418i \(-0.372151\pi\)
0.390936 + 0.920418i \(0.372151\pi\)
\(4\) 3.38367 1.69184
\(5\) 2.79503 1.24998 0.624989 0.780634i \(-0.285104\pi\)
0.624989 + 0.780634i \(0.285104\pi\)
\(6\) −3.14221 −1.28280
\(7\) 4.55894 1.72312 0.861558 0.507659i \(-0.169489\pi\)
0.861558 + 0.507659i \(0.169489\pi\)
\(8\) −3.21050 −1.13508
\(9\) −1.16603 −0.388676
\(10\) −6.48525 −2.05082
\(11\) −4.50751 −1.35907 −0.679533 0.733645i \(-0.737818\pi\)
−0.679533 + 0.733645i \(0.737818\pi\)
\(12\) 4.58231 1.32280
\(13\) −0.542954 −0.150588 −0.0752942 0.997161i \(-0.523990\pi\)
−0.0752942 + 0.997161i \(0.523990\pi\)
\(14\) −10.5780 −2.82709
\(15\) 3.78515 0.977323
\(16\) 0.681903 0.170476
\(17\) −5.71836 −1.38691 −0.693453 0.720502i \(-0.743912\pi\)
−0.693453 + 0.720502i \(0.743912\pi\)
\(18\) 2.70551 0.637694
\(19\) −1.76426 −0.404748 −0.202374 0.979308i \(-0.564866\pi\)
−0.202374 + 0.979308i \(0.564866\pi\)
\(20\) 9.45749 2.11476
\(21\) 6.17391 1.34726
\(22\) 10.4587 2.22980
\(23\) −3.18066 −0.663213 −0.331607 0.943418i \(-0.607591\pi\)
−0.331607 + 0.943418i \(0.607591\pi\)
\(24\) −4.34780 −0.887491
\(25\) 2.81222 0.562444
\(26\) 1.25980 0.247068
\(27\) −5.64181 −1.08577
\(28\) 15.4260 2.91523
\(29\) −7.61112 −1.41335 −0.706675 0.707538i \(-0.749806\pi\)
−0.706675 + 0.707538i \(0.749806\pi\)
\(30\) −8.78260 −1.60348
\(31\) −1.83148 −0.328944 −0.164472 0.986382i \(-0.552592\pi\)
−0.164472 + 0.986382i \(0.552592\pi\)
\(32\) 4.83881 0.855388
\(33\) −6.10426 −1.06262
\(34\) 13.2682 2.27547
\(35\) 12.7424 2.15386
\(36\) −3.94546 −0.657577
\(37\) −1.00000 −0.164399
\(38\) 4.09356 0.664063
\(39\) −0.735291 −0.117741
\(40\) −8.97347 −1.41883
\(41\) −9.61850 −1.50216 −0.751079 0.660213i \(-0.770466\pi\)
−0.751079 + 0.660213i \(0.770466\pi\)
\(42\) −14.3252 −2.21042
\(43\) 3.29074 0.501833 0.250916 0.968009i \(-0.419268\pi\)
0.250916 + 0.968009i \(0.419268\pi\)
\(44\) −15.2520 −2.29932
\(45\) −3.25909 −0.485836
\(46\) 7.38000 1.08812
\(47\) 7.88287 1.14984 0.574918 0.818211i \(-0.305034\pi\)
0.574918 + 0.818211i \(0.305034\pi\)
\(48\) 0.923462 0.133290
\(49\) 13.7839 1.96913
\(50\) −6.52512 −0.922791
\(51\) −7.74405 −1.08438
\(52\) −1.83718 −0.254771
\(53\) −3.17321 −0.435874 −0.217937 0.975963i \(-0.569933\pi\)
−0.217937 + 0.975963i \(0.569933\pi\)
\(54\) 13.0906 1.78140
\(55\) −12.5987 −1.69880
\(56\) −14.6365 −1.95588
\(57\) −2.38923 −0.316461
\(58\) 17.6599 2.31886
\(59\) 1.31889 0.171705 0.0858526 0.996308i \(-0.472639\pi\)
0.0858526 + 0.996308i \(0.472639\pi\)
\(60\) 12.8077 1.65347
\(61\) 2.66774 0.341569 0.170784 0.985308i \(-0.445370\pi\)
0.170784 + 0.985308i \(0.445370\pi\)
\(62\) 4.24954 0.539692
\(63\) −5.31585 −0.669734
\(64\) −12.5912 −1.57390
\(65\) −1.51758 −0.188232
\(66\) 14.1636 1.74341
\(67\) −3.57012 −0.436160 −0.218080 0.975931i \(-0.569979\pi\)
−0.218080 + 0.975931i \(0.569979\pi\)
\(68\) −19.3491 −2.34642
\(69\) −4.30738 −0.518548
\(70\) −29.5658 −3.53379
\(71\) −8.88574 −1.05454 −0.527272 0.849697i \(-0.676785\pi\)
−0.527272 + 0.849697i \(0.676785\pi\)
\(72\) 3.74354 0.441180
\(73\) 4.02855 0.471506 0.235753 0.971813i \(-0.424244\pi\)
0.235753 + 0.971813i \(0.424244\pi\)
\(74\) 2.32027 0.269726
\(75\) 3.80842 0.439759
\(76\) −5.96967 −0.684768
\(77\) −20.5495 −2.34183
\(78\) 1.70608 0.193175
\(79\) −17.5481 −1.97431 −0.987155 0.159763i \(-0.948927\pi\)
−0.987155 + 0.159763i \(0.948927\pi\)
\(80\) 1.90594 0.213091
\(81\) −4.14229 −0.460255
\(82\) 22.3176 2.46456
\(83\) 8.15290 0.894897 0.447448 0.894310i \(-0.352333\pi\)
0.447448 + 0.894310i \(0.352333\pi\)
\(84\) 20.8905 2.27934
\(85\) −15.9830 −1.73360
\(86\) −7.63541 −0.823348
\(87\) −10.3073 −1.10506
\(88\) 14.4714 1.54266
\(89\) −13.3217 −1.41210 −0.706051 0.708161i \(-0.749525\pi\)
−0.706051 + 0.708161i \(0.749525\pi\)
\(90\) 7.56198 0.797103
\(91\) −2.47529 −0.259481
\(92\) −10.7623 −1.12205
\(93\) −2.48027 −0.257192
\(94\) −18.2904 −1.88651
\(95\) −4.93116 −0.505926
\(96\) 6.55292 0.668804
\(97\) 0.623333 0.0632898 0.0316449 0.999499i \(-0.489925\pi\)
0.0316449 + 0.999499i \(0.489925\pi\)
\(98\) −31.9825 −3.23072
\(99\) 5.25589 0.528236
\(100\) 9.51563 0.951563
\(101\) −12.5441 −1.24818 −0.624090 0.781352i \(-0.714530\pi\)
−0.624090 + 0.781352i \(0.714530\pi\)
\(102\) 17.9683 1.77913
\(103\) −4.75597 −0.468620 −0.234310 0.972162i \(-0.575283\pi\)
−0.234310 + 0.972162i \(0.575283\pi\)
\(104\) 1.74316 0.170931
\(105\) 17.2563 1.68404
\(106\) 7.36273 0.715131
\(107\) 4.38886 0.424287 0.212143 0.977239i \(-0.431956\pi\)
0.212143 + 0.977239i \(0.431956\pi\)
\(108\) −19.0901 −1.83694
\(109\) −1.00000 −0.0957826
\(110\) 29.2323 2.78719
\(111\) −1.35424 −0.128539
\(112\) 3.10875 0.293750
\(113\) 10.6375 1.00069 0.500345 0.865826i \(-0.333207\pi\)
0.500345 + 0.865826i \(0.333207\pi\)
\(114\) 5.54367 0.519212
\(115\) −8.89005 −0.829002
\(116\) −25.7536 −2.39116
\(117\) 0.633100 0.0585301
\(118\) −3.06019 −0.281714
\(119\) −26.0697 −2.38980
\(120\) −12.1523 −1.10934
\(121\) 9.31766 0.847060
\(122\) −6.18988 −0.560405
\(123\) −13.0258 −1.17449
\(124\) −6.19714 −0.556519
\(125\) −6.11493 −0.546936
\(126\) 12.3342 1.09882
\(127\) 3.28276 0.291298 0.145649 0.989336i \(-0.453473\pi\)
0.145649 + 0.989336i \(0.453473\pi\)
\(128\) 19.5373 1.72687
\(129\) 4.45646 0.392369
\(130\) 3.52119 0.308829
\(131\) 5.19340 0.453749 0.226875 0.973924i \(-0.427149\pi\)
0.226875 + 0.973924i \(0.427149\pi\)
\(132\) −20.6548 −1.79777
\(133\) −8.04313 −0.697428
\(134\) 8.28367 0.715600
\(135\) −15.7691 −1.35718
\(136\) 18.3588 1.57426
\(137\) −2.60966 −0.222959 −0.111479 0.993767i \(-0.535559\pi\)
−0.111479 + 0.993767i \(0.535559\pi\)
\(138\) 9.99431 0.850772
\(139\) 15.8532 1.34465 0.672324 0.740257i \(-0.265296\pi\)
0.672324 + 0.740257i \(0.265296\pi\)
\(140\) 43.1161 3.64397
\(141\) 10.6753 0.899024
\(142\) 20.6174 1.73017
\(143\) 2.44737 0.204660
\(144\) −0.795118 −0.0662598
\(145\) −21.2733 −1.76666
\(146\) −9.34734 −0.773592
\(147\) 18.6668 1.53961
\(148\) −3.38367 −0.278136
\(149\) −7.20544 −0.590293 −0.295146 0.955452i \(-0.595368\pi\)
−0.295146 + 0.955452i \(0.595368\pi\)
\(150\) −8.83659 −0.721505
\(151\) 16.9066 1.37584 0.687920 0.725787i \(-0.258524\pi\)
0.687920 + 0.725787i \(0.258524\pi\)
\(152\) 5.66415 0.459423
\(153\) 6.66777 0.539057
\(154\) 47.6804 3.84220
\(155\) −5.11905 −0.411172
\(156\) −2.48799 −0.199198
\(157\) 12.4778 0.995835 0.497918 0.867224i \(-0.334098\pi\)
0.497918 + 0.867224i \(0.334098\pi\)
\(158\) 40.7163 3.23922
\(159\) −4.29730 −0.340798
\(160\) 13.5246 1.06922
\(161\) −14.5004 −1.14279
\(162\) 9.61126 0.755132
\(163\) −17.6605 −1.38328 −0.691638 0.722244i \(-0.743111\pi\)
−0.691638 + 0.722244i \(0.743111\pi\)
\(164\) −32.5459 −2.54141
\(165\) −17.0616 −1.32825
\(166\) −18.9170 −1.46824
\(167\) 18.3737 1.42180 0.710901 0.703292i \(-0.248287\pi\)
0.710901 + 0.703292i \(0.248287\pi\)
\(168\) −19.8214 −1.52925
\(169\) −12.7052 −0.977323
\(170\) 37.0850 2.84429
\(171\) 2.05717 0.157316
\(172\) 11.1348 0.849019
\(173\) 5.75232 0.437341 0.218671 0.975799i \(-0.429828\pi\)
0.218671 + 0.975799i \(0.429828\pi\)
\(174\) 23.9158 1.81305
\(175\) 12.8207 0.969156
\(176\) −3.07369 −0.231688
\(177\) 1.78610 0.134251
\(178\) 30.9101 2.31681
\(179\) −20.1054 −1.50275 −0.751375 0.659876i \(-0.770609\pi\)
−0.751375 + 0.659876i \(0.770609\pi\)
\(180\) −11.0277 −0.821956
\(181\) −7.62640 −0.566866 −0.283433 0.958992i \(-0.591473\pi\)
−0.283433 + 0.958992i \(0.591473\pi\)
\(182\) 5.74336 0.425726
\(183\) 3.61276 0.267063
\(184\) 10.2115 0.752803
\(185\) −2.79503 −0.205495
\(186\) 5.75491 0.421970
\(187\) 25.7756 1.88490
\(188\) 26.6731 1.94533
\(189\) −25.7207 −1.87090
\(190\) 11.4416 0.830063
\(191\) 12.2848 0.888897 0.444449 0.895804i \(-0.353400\pi\)
0.444449 + 0.895804i \(0.353400\pi\)
\(192\) −17.0515 −1.23059
\(193\) 10.4966 0.755558 0.377779 0.925896i \(-0.376688\pi\)
0.377779 + 0.925896i \(0.376688\pi\)
\(194\) −1.44630 −0.103838
\(195\) −2.05516 −0.147173
\(196\) 46.6403 3.33145
\(197\) 20.5025 1.46075 0.730373 0.683049i \(-0.239346\pi\)
0.730373 + 0.683049i \(0.239346\pi\)
\(198\) −12.1951 −0.866668
\(199\) 19.8362 1.40615 0.703075 0.711116i \(-0.251810\pi\)
0.703075 + 0.711116i \(0.251810\pi\)
\(200\) −9.02864 −0.638421
\(201\) −4.83481 −0.341021
\(202\) 29.1057 2.04787
\(203\) −34.6986 −2.43537
\(204\) −26.2033 −1.83460
\(205\) −26.8840 −1.87766
\(206\) 11.0352 0.768856
\(207\) 3.70874 0.257775
\(208\) −0.370242 −0.0256717
\(209\) 7.95240 0.550079
\(210\) −40.0393 −2.76297
\(211\) −9.91613 −0.682654 −0.341327 0.939945i \(-0.610876\pi\)
−0.341327 + 0.939945i \(0.610876\pi\)
\(212\) −10.7371 −0.737428
\(213\) −12.0334 −0.824518
\(214\) −10.1834 −0.696120
\(215\) 9.19772 0.627280
\(216\) 18.1131 1.23244
\(217\) −8.34961 −0.566808
\(218\) 2.32027 0.157149
\(219\) 5.45563 0.368657
\(220\) −42.6297 −2.87410
\(221\) 3.10481 0.208852
\(222\) 3.14221 0.210892
\(223\) −4.75550 −0.318452 −0.159226 0.987242i \(-0.550900\pi\)
−0.159226 + 0.987242i \(0.550900\pi\)
\(224\) 22.0598 1.47393
\(225\) −3.27913 −0.218608
\(226\) −24.6819 −1.64181
\(227\) −11.6726 −0.774740 −0.387370 0.921924i \(-0.626616\pi\)
−0.387370 + 0.921924i \(0.626616\pi\)
\(228\) −8.08437 −0.535401
\(229\) −2.28055 −0.150703 −0.0753516 0.997157i \(-0.524008\pi\)
−0.0753516 + 0.997157i \(0.524008\pi\)
\(230\) 20.6274 1.36013
\(231\) −27.8290 −1.83101
\(232\) 24.4355 1.60427
\(233\) −9.09780 −0.596017 −0.298008 0.954563i \(-0.596322\pi\)
−0.298008 + 0.954563i \(0.596322\pi\)
\(234\) −1.46896 −0.0960292
\(235\) 22.0329 1.43727
\(236\) 4.46270 0.290497
\(237\) −23.7643 −1.54366
\(238\) 60.4888 3.92090
\(239\) −4.65691 −0.301231 −0.150615 0.988592i \(-0.548126\pi\)
−0.150615 + 0.988592i \(0.548126\pi\)
\(240\) 2.58111 0.166610
\(241\) −22.8884 −1.47437 −0.737187 0.675689i \(-0.763846\pi\)
−0.737187 + 0.675689i \(0.763846\pi\)
\(242\) −21.6195 −1.38976
\(243\) 11.3158 0.725907
\(244\) 9.02675 0.577878
\(245\) 38.5265 2.46137
\(246\) 30.2234 1.92697
\(247\) 0.957910 0.0609503
\(248\) 5.87998 0.373379
\(249\) 11.0410 0.699695
\(250\) 14.1883 0.897347
\(251\) 13.7361 0.867014 0.433507 0.901150i \(-0.357276\pi\)
0.433507 + 0.901150i \(0.357276\pi\)
\(252\) −17.9871 −1.13308
\(253\) 14.3369 0.901351
\(254\) −7.61690 −0.477927
\(255\) −21.6449 −1.35545
\(256\) −20.1497 −1.25936
\(257\) 12.3695 0.771590 0.385795 0.922585i \(-0.373927\pi\)
0.385795 + 0.922585i \(0.373927\pi\)
\(258\) −10.3402 −0.643753
\(259\) −4.55894 −0.283279
\(260\) −5.13498 −0.318458
\(261\) 8.87478 0.549335
\(262\) −12.0501 −0.744458
\(263\) 30.9483 1.90835 0.954177 0.299244i \(-0.0967345\pi\)
0.954177 + 0.299244i \(0.0967345\pi\)
\(264\) 19.5978 1.20616
\(265\) −8.86924 −0.544833
\(266\) 18.6623 1.14426
\(267\) −18.0409 −1.10408
\(268\) −12.0801 −0.737912
\(269\) 5.77611 0.352176 0.176088 0.984374i \(-0.443656\pi\)
0.176088 + 0.984374i \(0.443656\pi\)
\(270\) 36.5885 2.22671
\(271\) 3.48402 0.211639 0.105819 0.994385i \(-0.466253\pi\)
0.105819 + 0.994385i \(0.466253\pi\)
\(272\) −3.89937 −0.236434
\(273\) −3.35215 −0.202881
\(274\) 6.05514 0.365804
\(275\) −12.6761 −0.764398
\(276\) −14.5748 −0.877299
\(277\) 15.6447 0.940000 0.470000 0.882666i \(-0.344254\pi\)
0.470000 + 0.882666i \(0.344254\pi\)
\(278\) −36.7837 −2.20614
\(279\) 2.13556 0.127853
\(280\) −40.9095 −2.44481
\(281\) −0.0847937 −0.00505837 −0.00252918 0.999997i \(-0.500805\pi\)
−0.00252918 + 0.999997i \(0.500805\pi\)
\(282\) −24.7697 −1.47501
\(283\) 20.0758 1.19338 0.596690 0.802472i \(-0.296482\pi\)
0.596690 + 0.802472i \(0.296482\pi\)
\(284\) −30.0665 −1.78412
\(285\) −6.67798 −0.395569
\(286\) −5.67857 −0.335781
\(287\) −43.8501 −2.58839
\(288\) −5.64218 −0.332469
\(289\) 15.6997 0.923509
\(290\) 49.3600 2.89852
\(291\) 0.844143 0.0494845
\(292\) 13.6313 0.797712
\(293\) 5.53254 0.323215 0.161607 0.986855i \(-0.448332\pi\)
0.161607 + 0.986855i \(0.448332\pi\)
\(294\) −43.3120 −2.52601
\(295\) 3.68635 0.214628
\(296\) 3.21050 0.186607
\(297\) 25.4305 1.47563
\(298\) 16.7186 0.968483
\(299\) 1.72695 0.0998722
\(300\) 12.8865 0.744001
\(301\) 15.0023 0.864716
\(302\) −39.2280 −2.25732
\(303\) −16.9877 −0.975917
\(304\) −1.20305 −0.0689997
\(305\) 7.45641 0.426953
\(306\) −15.4711 −0.884422
\(307\) −9.62765 −0.549479 −0.274740 0.961519i \(-0.588592\pi\)
−0.274740 + 0.961519i \(0.588592\pi\)
\(308\) −69.5327 −3.96199
\(309\) −6.44074 −0.366401
\(310\) 11.8776 0.674603
\(311\) −28.3753 −1.60901 −0.804507 0.593943i \(-0.797570\pi\)
−0.804507 + 0.593943i \(0.797570\pi\)
\(312\) 2.36066 0.133646
\(313\) 2.52731 0.142852 0.0714260 0.997446i \(-0.477245\pi\)
0.0714260 + 0.997446i \(0.477245\pi\)
\(314\) −28.9519 −1.63385
\(315\) −14.8580 −0.837152
\(316\) −59.3769 −3.34021
\(317\) 10.9461 0.614792 0.307396 0.951582i \(-0.400542\pi\)
0.307396 + 0.951582i \(0.400542\pi\)
\(318\) 9.97091 0.559141
\(319\) 34.3072 1.92084
\(320\) −35.1927 −1.96733
\(321\) 5.94358 0.331738
\(322\) 33.6450 1.87496
\(323\) 10.0887 0.561348
\(324\) −14.0162 −0.778676
\(325\) −1.52691 −0.0846975
\(326\) 40.9772 2.26952
\(327\) −1.35424 −0.0748898
\(328\) 30.8802 1.70508
\(329\) 35.9375 1.98130
\(330\) 39.5877 2.17923
\(331\) −6.37333 −0.350310 −0.175155 0.984541i \(-0.556043\pi\)
−0.175155 + 0.984541i \(0.556043\pi\)
\(332\) 27.5867 1.51402
\(333\) 1.16603 0.0638979
\(334\) −42.6321 −2.33273
\(335\) −9.97862 −0.545190
\(336\) 4.21000 0.229675
\(337\) −24.9949 −1.36156 −0.680780 0.732488i \(-0.738359\pi\)
−0.680780 + 0.732488i \(0.738359\pi\)
\(338\) 29.4796 1.60348
\(339\) 14.4057 0.782412
\(340\) −54.0813 −2.93297
\(341\) 8.25542 0.447056
\(342\) −4.77320 −0.258105
\(343\) 30.9274 1.66992
\(344\) −10.5649 −0.569623
\(345\) −12.0393 −0.648173
\(346\) −13.3470 −0.717538
\(347\) −21.9289 −1.17720 −0.588601 0.808423i \(-0.700321\pi\)
−0.588601 + 0.808423i \(0.700321\pi\)
\(348\) −34.8766 −1.86958
\(349\) 2.11353 0.113135 0.0565675 0.998399i \(-0.481984\pi\)
0.0565675 + 0.998399i \(0.481984\pi\)
\(350\) −29.7476 −1.59008
\(351\) 3.06324 0.163504
\(352\) −21.8110 −1.16253
\(353\) 13.5606 0.721759 0.360879 0.932613i \(-0.382477\pi\)
0.360879 + 0.932613i \(0.382477\pi\)
\(354\) −4.14424 −0.220264
\(355\) −24.8360 −1.31816
\(356\) −45.0764 −2.38905
\(357\) −35.3046 −1.86852
\(358\) 46.6501 2.46553
\(359\) −8.79154 −0.464000 −0.232000 0.972716i \(-0.574527\pi\)
−0.232000 + 0.972716i \(0.574527\pi\)
\(360\) 10.4633 0.551465
\(361\) −15.8874 −0.836179
\(362\) 17.6953 0.930046
\(363\) 12.6184 0.662293
\(364\) −8.37559 −0.439000
\(365\) 11.2599 0.589372
\(366\) −8.38260 −0.438165
\(367\) 19.6485 1.02564 0.512821 0.858496i \(-0.328601\pi\)
0.512821 + 0.858496i \(0.328601\pi\)
\(368\) −2.16890 −0.113062
\(369\) 11.2154 0.583853
\(370\) 6.48525 0.337152
\(371\) −14.4665 −0.751062
\(372\) −8.39242 −0.435127
\(373\) −21.0622 −1.09056 −0.545280 0.838254i \(-0.683577\pi\)
−0.545280 + 0.838254i \(0.683577\pi\)
\(374\) −59.8064 −3.09252
\(375\) −8.28109 −0.427634
\(376\) −25.3080 −1.30516
\(377\) 4.13249 0.212834
\(378\) 59.6790 3.06956
\(379\) −29.5015 −1.51539 −0.757696 0.652608i \(-0.773675\pi\)
−0.757696 + 0.652608i \(0.773675\pi\)
\(380\) −16.6854 −0.855944
\(381\) 4.44565 0.227758
\(382\) −28.5041 −1.45840
\(383\) −1.80978 −0.0924754 −0.0462377 0.998930i \(-0.514723\pi\)
−0.0462377 + 0.998930i \(0.514723\pi\)
\(384\) 26.4583 1.35019
\(385\) −57.4365 −2.92723
\(386\) −24.3549 −1.23963
\(387\) −3.83709 −0.195050
\(388\) 2.10915 0.107076
\(389\) 11.9716 0.606984 0.303492 0.952834i \(-0.401847\pi\)
0.303492 + 0.952834i \(0.401847\pi\)
\(390\) 4.76855 0.241465
\(391\) 18.1882 0.919815
\(392\) −44.2533 −2.23513
\(393\) 7.03312 0.354774
\(394\) −47.5715 −2.39662
\(395\) −49.0474 −2.46784
\(396\) 17.7842 0.893690
\(397\) 16.7828 0.842305 0.421152 0.906990i \(-0.361626\pi\)
0.421152 + 0.906990i \(0.361626\pi\)
\(398\) −46.0254 −2.30704
\(399\) −10.8923 −0.545299
\(400\) 1.91766 0.0958830
\(401\) −6.20959 −0.310092 −0.155046 0.987907i \(-0.549553\pi\)
−0.155046 + 0.987907i \(0.549553\pi\)
\(402\) 11.2181 0.559508
\(403\) 0.994410 0.0495351
\(404\) −42.4450 −2.11172
\(405\) −11.5779 −0.575308
\(406\) 80.5103 3.99566
\(407\) 4.50751 0.223429
\(408\) 24.8623 1.23087
\(409\) 26.2955 1.30023 0.650115 0.759836i \(-0.274721\pi\)
0.650115 + 0.759836i \(0.274721\pi\)
\(410\) 62.3784 3.08065
\(411\) −3.53412 −0.174325
\(412\) −16.0927 −0.792828
\(413\) 6.01275 0.295868
\(414\) −8.60529 −0.422927
\(415\) 22.7876 1.11860
\(416\) −2.62725 −0.128811
\(417\) 21.4690 1.05134
\(418\) −18.4518 −0.902505
\(419\) 20.8439 1.01829 0.509145 0.860681i \(-0.329962\pi\)
0.509145 + 0.860681i \(0.329962\pi\)
\(420\) 58.3896 2.84912
\(421\) −18.8063 −0.916564 −0.458282 0.888807i \(-0.651535\pi\)
−0.458282 + 0.888807i \(0.651535\pi\)
\(422\) 23.0081 1.12002
\(423\) −9.19165 −0.446913
\(424\) 10.1876 0.494754
\(425\) −16.0813 −0.780057
\(426\) 27.9209 1.35277
\(427\) 12.1620 0.588562
\(428\) 14.8505 0.717824
\(429\) 3.31433 0.160018
\(430\) −21.3412 −1.02917
\(431\) −14.2075 −0.684352 −0.342176 0.939636i \(-0.611164\pi\)
−0.342176 + 0.939636i \(0.611164\pi\)
\(432\) −3.84717 −0.185097
\(433\) 35.2815 1.69552 0.847760 0.530379i \(-0.177951\pi\)
0.847760 + 0.530379i \(0.177951\pi\)
\(434\) 19.3734 0.929952
\(435\) −28.8093 −1.38130
\(436\) −3.38367 −0.162049
\(437\) 5.61150 0.268434
\(438\) −12.6586 −0.604850
\(439\) 4.61054 0.220049 0.110025 0.993929i \(-0.464907\pi\)
0.110025 + 0.993929i \(0.464907\pi\)
\(440\) 40.4480 1.92828
\(441\) −16.0724 −0.765354
\(442\) −7.20401 −0.342660
\(443\) 20.1239 0.956114 0.478057 0.878329i \(-0.341341\pi\)
0.478057 + 0.878329i \(0.341341\pi\)
\(444\) −4.58231 −0.217467
\(445\) −37.2347 −1.76510
\(446\) 11.0341 0.522478
\(447\) −9.75791 −0.461533
\(448\) −57.4023 −2.71201
\(449\) 7.15537 0.337683 0.168841 0.985643i \(-0.445997\pi\)
0.168841 + 0.985643i \(0.445997\pi\)
\(450\) 7.60847 0.358667
\(451\) 43.3555 2.04153
\(452\) 35.9938 1.69300
\(453\) 22.8956 1.07573
\(454\) 27.0837 1.27110
\(455\) −6.91853 −0.324346
\(456\) 7.67063 0.359210
\(457\) −2.31265 −0.108181 −0.0540907 0.998536i \(-0.517226\pi\)
−0.0540907 + 0.998536i \(0.517226\pi\)
\(458\) 5.29151 0.247256
\(459\) 32.2619 1.50586
\(460\) −30.0810 −1.40254
\(461\) −7.36287 −0.342923 −0.171462 0.985191i \(-0.554849\pi\)
−0.171462 + 0.985191i \(0.554849\pi\)
\(462\) 64.5708 3.00411
\(463\) −7.39672 −0.343755 −0.171877 0.985118i \(-0.554983\pi\)
−0.171877 + 0.985118i \(0.554983\pi\)
\(464\) −5.19005 −0.240942
\(465\) −6.93244 −0.321484
\(466\) 21.1094 0.977874
\(467\) −34.1617 −1.58082 −0.790408 0.612580i \(-0.790132\pi\)
−0.790408 + 0.612580i \(0.790132\pi\)
\(468\) 2.14220 0.0990234
\(469\) −16.2760 −0.751555
\(470\) −51.1224 −2.35810
\(471\) 16.8979 0.778616
\(472\) −4.23431 −0.194900
\(473\) −14.8330 −0.682024
\(474\) 55.1397 2.53265
\(475\) −4.96147 −0.227648
\(476\) −88.2112 −4.04315
\(477\) 3.70006 0.169414
\(478\) 10.8053 0.494224
\(479\) −36.8577 −1.68407 −0.842036 0.539421i \(-0.818643\pi\)
−0.842036 + 0.539421i \(0.818643\pi\)
\(480\) 18.3156 0.835990
\(481\) 0.542954 0.0247566
\(482\) 53.1074 2.41898
\(483\) −19.6371 −0.893518
\(484\) 31.5279 1.43309
\(485\) 1.74224 0.0791109
\(486\) −26.2557 −1.19098
\(487\) 24.7483 1.12145 0.560727 0.828001i \(-0.310522\pi\)
0.560727 + 0.828001i \(0.310522\pi\)
\(488\) −8.56478 −0.387709
\(489\) −23.9166 −1.08154
\(490\) −89.3921 −4.03832
\(491\) 5.94814 0.268436 0.134218 0.990952i \(-0.457148\pi\)
0.134218 + 0.990952i \(0.457148\pi\)
\(492\) −44.0750 −1.98705
\(493\) 43.5231 1.96018
\(494\) −2.22261 −0.100000
\(495\) 14.6904 0.660284
\(496\) −1.24889 −0.0560769
\(497\) −40.5095 −1.81710
\(498\) −25.6181 −1.14798
\(499\) 9.74237 0.436128 0.218064 0.975934i \(-0.430026\pi\)
0.218064 + 0.975934i \(0.430026\pi\)
\(500\) −20.6909 −0.925326
\(501\) 24.8825 1.11167
\(502\) −31.8715 −1.42249
\(503\) −23.3427 −1.04080 −0.520400 0.853923i \(-0.674217\pi\)
−0.520400 + 0.853923i \(0.674217\pi\)
\(504\) 17.0666 0.760205
\(505\) −35.0611 −1.56020
\(506\) −33.2654 −1.47883
\(507\) −17.2059 −0.764142
\(508\) 11.1078 0.492828
\(509\) 16.0759 0.712551 0.356275 0.934381i \(-0.384046\pi\)
0.356275 + 0.934381i \(0.384046\pi\)
\(510\) 50.2221 2.22387
\(511\) 18.3659 0.812460
\(512\) 7.67810 0.339327
\(513\) 9.95360 0.439462
\(514\) −28.7007 −1.26593
\(515\) −13.2931 −0.585764
\(516\) 15.0792 0.663824
\(517\) −35.5322 −1.56270
\(518\) 10.5780 0.464770
\(519\) 7.79004 0.341945
\(520\) 4.87218 0.213659
\(521\) −34.9058 −1.52925 −0.764625 0.644476i \(-0.777076\pi\)
−0.764625 + 0.644476i \(0.777076\pi\)
\(522\) −20.5919 −0.901284
\(523\) 39.8219 1.74129 0.870646 0.491911i \(-0.163701\pi\)
0.870646 + 0.491911i \(0.163701\pi\)
\(524\) 17.5728 0.767670
\(525\) 17.3624 0.757756
\(526\) −71.8085 −3.13100
\(527\) 10.4731 0.456214
\(528\) −4.16252 −0.181150
\(529\) −12.8834 −0.560148
\(530\) 20.5791 0.893898
\(531\) −1.53787 −0.0667377
\(532\) −27.2153 −1.17993
\(533\) 5.22240 0.226207
\(534\) 41.8598 1.81145
\(535\) 12.2670 0.530349
\(536\) 11.4619 0.495079
\(537\) −27.2276 −1.17496
\(538\) −13.4022 −0.577808
\(539\) −62.1311 −2.67618
\(540\) −53.3574 −2.29613
\(541\) −31.8027 −1.36731 −0.683653 0.729807i \(-0.739610\pi\)
−0.683653 + 0.729807i \(0.739610\pi\)
\(542\) −8.08387 −0.347232
\(543\) −10.3280 −0.443216
\(544\) −27.6700 −1.18634
\(545\) −2.79503 −0.119726
\(546\) 7.77790 0.332863
\(547\) 0.572452 0.0244763 0.0122381 0.999925i \(-0.496104\pi\)
0.0122381 + 0.999925i \(0.496104\pi\)
\(548\) −8.83025 −0.377210
\(549\) −3.11065 −0.132760
\(550\) 29.4121 1.25413
\(551\) 13.4280 0.572050
\(552\) 13.8289 0.588596
\(553\) −80.0005 −3.40197
\(554\) −36.3000 −1.54224
\(555\) −3.78515 −0.160671
\(556\) 53.6419 2.27492
\(557\) −17.8864 −0.757872 −0.378936 0.925423i \(-0.623710\pi\)
−0.378936 + 0.925423i \(0.623710\pi\)
\(558\) −4.95508 −0.209765
\(559\) −1.78672 −0.0755702
\(560\) 8.68907 0.367180
\(561\) 34.9064 1.47375
\(562\) 0.196745 0.00829917
\(563\) −19.1333 −0.806371 −0.403186 0.915118i \(-0.632097\pi\)
−0.403186 + 0.915118i \(0.632097\pi\)
\(564\) 36.1218 1.52100
\(565\) 29.7321 1.25084
\(566\) −46.5813 −1.95796
\(567\) −18.8845 −0.793073
\(568\) 28.5277 1.19700
\(569\) −29.5091 −1.23708 −0.618542 0.785751i \(-0.712277\pi\)
−0.618542 + 0.785751i \(0.712277\pi\)
\(570\) 15.4947 0.649003
\(571\) 6.93007 0.290014 0.145007 0.989431i \(-0.453679\pi\)
0.145007 + 0.989431i \(0.453679\pi\)
\(572\) 8.28111 0.346251
\(573\) 16.6366 0.695004
\(574\) 101.744 4.24673
\(575\) −8.94471 −0.373020
\(576\) 14.6817 0.611736
\(577\) −25.9680 −1.08106 −0.540531 0.841324i \(-0.681777\pi\)
−0.540531 + 0.841324i \(0.681777\pi\)
\(578\) −36.4275 −1.51519
\(579\) 14.2149 0.590750
\(580\) −71.9821 −2.98889
\(581\) 37.1685 1.54201
\(582\) −1.95864 −0.0811884
\(583\) 14.3033 0.592382
\(584\) −12.9337 −0.535199
\(585\) 1.76954 0.0731613
\(586\) −12.8370 −0.530292
\(587\) −30.4304 −1.25600 −0.627999 0.778214i \(-0.716126\pi\)
−0.627999 + 0.778214i \(0.716126\pi\)
\(588\) 63.1622 2.60477
\(589\) 3.23120 0.133139
\(590\) −8.55334 −0.352136
\(591\) 27.7654 1.14212
\(592\) −0.681903 −0.0280260
\(593\) 4.03002 0.165493 0.0827466 0.996571i \(-0.473631\pi\)
0.0827466 + 0.996571i \(0.473631\pi\)
\(594\) −59.0058 −2.42104
\(595\) −72.8656 −2.98720
\(596\) −24.3809 −0.998679
\(597\) 26.8630 1.09943
\(598\) −4.00700 −0.163858
\(599\) 47.9874 1.96071 0.980355 0.197239i \(-0.0631975\pi\)
0.980355 + 0.197239i \(0.0631975\pi\)
\(600\) −12.2270 −0.499164
\(601\) 12.5769 0.513022 0.256511 0.966541i \(-0.417427\pi\)
0.256511 + 0.966541i \(0.417427\pi\)
\(602\) −34.8094 −1.41872
\(603\) 4.16287 0.169525
\(604\) 57.2064 2.32770
\(605\) 26.0432 1.05881
\(606\) 39.4161 1.60117
\(607\) 3.74591 0.152042 0.0760208 0.997106i \(-0.475778\pi\)
0.0760208 + 0.997106i \(0.475778\pi\)
\(608\) −8.53689 −0.346217
\(609\) −46.9903 −1.90414
\(610\) −17.3009 −0.700494
\(611\) −4.28004 −0.173152
\(612\) 22.5616 0.911997
\(613\) 16.5359 0.667880 0.333940 0.942594i \(-0.391622\pi\)
0.333940 + 0.942594i \(0.391622\pi\)
\(614\) 22.3388 0.901520
\(615\) −36.4075 −1.46809
\(616\) 65.9741 2.65817
\(617\) −17.3833 −0.699824 −0.349912 0.936783i \(-0.613789\pi\)
−0.349912 + 0.936783i \(0.613789\pi\)
\(618\) 14.9443 0.601147
\(619\) −11.5692 −0.465005 −0.232503 0.972596i \(-0.574691\pi\)
−0.232503 + 0.972596i \(0.574691\pi\)
\(620\) −17.3212 −0.695637
\(621\) 17.9447 0.720095
\(622\) 65.8384 2.63988
\(623\) −60.7330 −2.43322
\(624\) −0.501397 −0.0200720
\(625\) −31.1525 −1.24610
\(626\) −5.86406 −0.234375
\(627\) 10.7695 0.430092
\(628\) 42.2207 1.68479
\(629\) 5.71836 0.228006
\(630\) 34.4746 1.37350
\(631\) 28.6251 1.13955 0.569774 0.821801i \(-0.307031\pi\)
0.569774 + 0.821801i \(0.307031\pi\)
\(632\) 56.3381 2.24101
\(633\) −13.4288 −0.533748
\(634\) −25.3979 −1.00868
\(635\) 9.17542 0.364116
\(636\) −14.5407 −0.576575
\(637\) −7.48403 −0.296528
\(638\) −79.6022 −3.15148
\(639\) 10.3610 0.409876
\(640\) 54.6076 2.15855
\(641\) 5.31302 0.209852 0.104926 0.994480i \(-0.466539\pi\)
0.104926 + 0.994480i \(0.466539\pi\)
\(642\) −13.7907 −0.544277
\(643\) −31.1406 −1.22806 −0.614032 0.789281i \(-0.710453\pi\)
−0.614032 + 0.789281i \(0.710453\pi\)
\(644\) −49.0647 −1.93342
\(645\) 12.4559 0.490452
\(646\) −23.4084 −0.920993
\(647\) 5.32709 0.209430 0.104715 0.994502i \(-0.466607\pi\)
0.104715 + 0.994502i \(0.466607\pi\)
\(648\) 13.2989 0.522428
\(649\) −5.94492 −0.233359
\(650\) 3.54284 0.138962
\(651\) −11.3074 −0.443172
\(652\) −59.7573 −2.34028
\(653\) −40.5221 −1.58575 −0.792877 0.609382i \(-0.791417\pi\)
−0.792877 + 0.609382i \(0.791417\pi\)
\(654\) 3.14221 0.122870
\(655\) 14.5157 0.567176
\(656\) −6.55888 −0.256081
\(657\) −4.69740 −0.183263
\(658\) −83.3849 −3.25068
\(659\) 45.0757 1.75590 0.877950 0.478752i \(-0.158911\pi\)
0.877950 + 0.478752i \(0.158911\pi\)
\(660\) −57.7310 −2.24718
\(661\) 27.7112 1.07784 0.538921 0.842356i \(-0.318832\pi\)
0.538921 + 0.842356i \(0.318832\pi\)
\(662\) 14.7879 0.574747
\(663\) 4.20466 0.163296
\(664\) −26.1749 −1.01578
\(665\) −22.4808 −0.871769
\(666\) −2.70551 −0.104836
\(667\) 24.2084 0.937352
\(668\) 62.1707 2.40546
\(669\) −6.44009 −0.248988
\(670\) 23.1531 0.894484
\(671\) −12.0249 −0.464214
\(672\) 29.8743 1.15243
\(673\) 28.4810 1.09786 0.548930 0.835868i \(-0.315035\pi\)
0.548930 + 0.835868i \(0.315035\pi\)
\(674\) 57.9951 2.23389
\(675\) −15.8660 −0.610683
\(676\) −42.9903 −1.65347
\(677\) −16.5157 −0.634750 −0.317375 0.948300i \(-0.602801\pi\)
−0.317375 + 0.948300i \(0.602801\pi\)
\(678\) −33.4252 −1.28369
\(679\) 2.84173 0.109056
\(680\) 51.3135 1.96778
\(681\) −15.8076 −0.605748
\(682\) −19.1549 −0.733477
\(683\) −15.6304 −0.598082 −0.299041 0.954240i \(-0.596667\pi\)
−0.299041 + 0.954240i \(0.596667\pi\)
\(684\) 6.96080 0.266153
\(685\) −7.29410 −0.278693
\(686\) −71.7601 −2.73981
\(687\) −3.08842 −0.117831
\(688\) 2.24396 0.0855503
\(689\) 1.72291 0.0656376
\(690\) 27.9344 1.06345
\(691\) −36.1910 −1.37677 −0.688385 0.725346i \(-0.741680\pi\)
−0.688385 + 0.725346i \(0.741680\pi\)
\(692\) 19.4640 0.739910
\(693\) 23.9613 0.910213
\(694\) 50.8810 1.93142
\(695\) 44.3101 1.68078
\(696\) 33.0916 1.25434
\(697\) 55.0021 2.08335
\(698\) −4.90398 −0.185618
\(699\) −12.3206 −0.466009
\(700\) 43.3812 1.63965
\(701\) 3.47540 0.131264 0.0656320 0.997844i \(-0.479094\pi\)
0.0656320 + 0.997844i \(0.479094\pi\)
\(702\) −7.10757 −0.268258
\(703\) 1.76426 0.0665402
\(704\) 56.7548 2.13903
\(705\) 29.8379 1.12376
\(706\) −31.4643 −1.18418
\(707\) −57.1876 −2.15076
\(708\) 6.04358 0.227132
\(709\) 1.15906 0.0435295 0.0217647 0.999763i \(-0.493072\pi\)
0.0217647 + 0.999763i \(0.493072\pi\)
\(710\) 57.6262 2.16267
\(711\) 20.4615 0.767367
\(712\) 42.7695 1.60286
\(713\) 5.82532 0.218160
\(714\) 81.9164 3.06565
\(715\) 6.84049 0.255820
\(716\) −68.0302 −2.54241
\(717\) −6.30659 −0.235524
\(718\) 20.3988 0.761276
\(719\) −5.92839 −0.221092 −0.110546 0.993871i \(-0.535260\pi\)
−0.110546 + 0.993871i \(0.535260\pi\)
\(720\) −2.22238 −0.0828233
\(721\) −21.6822 −0.807487
\(722\) 36.8631 1.37190
\(723\) −30.9965 −1.15277
\(724\) −25.8052 −0.959044
\(725\) −21.4041 −0.794930
\(726\) −29.2781 −1.08661
\(727\) 4.15447 0.154081 0.0770404 0.997028i \(-0.475453\pi\)
0.0770404 + 0.997028i \(0.475453\pi\)
\(728\) 7.94694 0.294533
\(729\) 27.7512 1.02782
\(730\) −26.1261 −0.966972
\(731\) −18.8176 −0.695995
\(732\) 12.2244 0.451827
\(733\) 45.0288 1.66318 0.831589 0.555391i \(-0.187431\pi\)
0.831589 + 0.555391i \(0.187431\pi\)
\(734\) −45.5898 −1.68275
\(735\) 52.1742 1.92448
\(736\) −15.3906 −0.567305
\(737\) 16.0924 0.592770
\(738\) −26.0229 −0.957916
\(739\) −14.9696 −0.550667 −0.275334 0.961349i \(-0.588788\pi\)
−0.275334 + 0.961349i \(0.588788\pi\)
\(740\) −9.45749 −0.347664
\(741\) 1.29724 0.0476554
\(742\) 33.5662 1.23225
\(743\) 38.8332 1.42465 0.712327 0.701848i \(-0.247641\pi\)
0.712327 + 0.701848i \(0.247641\pi\)
\(744\) 7.96292 0.291935
\(745\) −20.1395 −0.737853
\(746\) 48.8701 1.78926
\(747\) −9.50651 −0.347825
\(748\) 87.2162 3.18894
\(749\) 20.0085 0.731096
\(750\) 19.2144 0.701611
\(751\) 6.56896 0.239705 0.119852 0.992792i \(-0.461758\pi\)
0.119852 + 0.992792i \(0.461758\pi\)
\(752\) 5.37536 0.196019
\(753\) 18.6020 0.677894
\(754\) −9.58851 −0.349193
\(755\) 47.2545 1.71977
\(756\) −87.0303 −3.16526
\(757\) −30.2955 −1.10111 −0.550555 0.834799i \(-0.685584\pi\)
−0.550555 + 0.834799i \(0.685584\pi\)
\(758\) 68.4517 2.48628
\(759\) 19.4156 0.704741
\(760\) 15.8315 0.574269
\(761\) 39.6992 1.43910 0.719548 0.694443i \(-0.244349\pi\)
0.719548 + 0.694443i \(0.244349\pi\)
\(762\) −10.3151 −0.373678
\(763\) −4.55894 −0.165045
\(764\) 41.5678 1.50387
\(765\) 18.6366 0.673809
\(766\) 4.19919 0.151723
\(767\) −0.716098 −0.0258568
\(768\) −27.2876 −0.984655
\(769\) −28.0237 −1.01056 −0.505280 0.862955i \(-0.668611\pi\)
−0.505280 + 0.862955i \(0.668611\pi\)
\(770\) 133.268 4.80266
\(771\) 16.7513 0.603285
\(772\) 35.5169 1.27828
\(773\) 27.1559 0.976730 0.488365 0.872639i \(-0.337593\pi\)
0.488365 + 0.872639i \(0.337593\pi\)
\(774\) 8.90311 0.320016
\(775\) −5.15053 −0.185012
\(776\) −2.00121 −0.0718393
\(777\) −6.17391 −0.221488
\(778\) −27.7774 −0.995867
\(779\) 16.9695 0.607995
\(780\) −6.95401 −0.248993
\(781\) 40.0526 1.43319
\(782\) −42.2015 −1.50912
\(783\) 42.9405 1.53457
\(784\) 9.39929 0.335689
\(785\) 34.8758 1.24477
\(786\) −16.3188 −0.582071
\(787\) 9.59642 0.342075 0.171038 0.985264i \(-0.445288\pi\)
0.171038 + 0.985264i \(0.445288\pi\)
\(788\) 69.3739 2.47134
\(789\) 41.9115 1.49209
\(790\) 113.804 4.04895
\(791\) 48.4956 1.72431
\(792\) −16.8740 −0.599593
\(793\) −1.44846 −0.0514362
\(794\) −38.9407 −1.38195
\(795\) −12.0111 −0.425990
\(796\) 67.1192 2.37898
\(797\) 6.74808 0.239029 0.119515 0.992832i \(-0.461866\pi\)
0.119515 + 0.992832i \(0.461866\pi\)
\(798\) 25.2732 0.894663
\(799\) −45.0771 −1.59471
\(800\) 13.6078 0.481108
\(801\) 15.5335 0.548850
\(802\) 14.4080 0.508763
\(803\) −18.1587 −0.640808
\(804\) −16.3594 −0.576953
\(805\) −40.5292 −1.42847
\(806\) −2.30730 −0.0812713
\(807\) 7.82226 0.275356
\(808\) 40.2727 1.41679
\(809\) −35.2446 −1.23913 −0.619567 0.784944i \(-0.712692\pi\)
−0.619567 + 0.784944i \(0.712692\pi\)
\(810\) 26.8638 0.943898
\(811\) −45.9002 −1.61177 −0.805886 0.592070i \(-0.798311\pi\)
−0.805886 + 0.592070i \(0.798311\pi\)
\(812\) −117.409 −4.12024
\(813\) 4.71820 0.165475
\(814\) −10.4587 −0.366576
\(815\) −49.3617 −1.72906
\(816\) −5.28069 −0.184861
\(817\) −5.80570 −0.203116
\(818\) −61.0128 −2.13326
\(819\) 2.88626 0.100854
\(820\) −90.9668 −3.17670
\(821\) 18.1215 0.632445 0.316223 0.948685i \(-0.397585\pi\)
0.316223 + 0.948685i \(0.397585\pi\)
\(822\) 8.20012 0.286012
\(823\) −52.8759 −1.84314 −0.921568 0.388216i \(-0.873091\pi\)
−0.921568 + 0.388216i \(0.873091\pi\)
\(824\) 15.2691 0.531923
\(825\) −17.1665 −0.597662
\(826\) −13.9512 −0.485425
\(827\) −39.5266 −1.37448 −0.687238 0.726432i \(-0.741177\pi\)
−0.687238 + 0.726432i \(0.741177\pi\)
\(828\) 12.5492 0.436113
\(829\) −6.48153 −0.225113 −0.112556 0.993645i \(-0.535904\pi\)
−0.112556 + 0.993645i \(0.535904\pi\)
\(830\) −52.8736 −1.83527
\(831\) 21.1867 0.734960
\(832\) 6.83642 0.237010
\(833\) −78.8214 −2.73100
\(834\) −49.8140 −1.72492
\(835\) 51.3552 1.77722
\(836\) 26.9083 0.930645
\(837\) 10.3329 0.357156
\(838\) −48.3635 −1.67069
\(839\) 19.2899 0.665961 0.332980 0.942934i \(-0.391946\pi\)
0.332980 + 0.942934i \(0.391946\pi\)
\(840\) −55.4014 −1.91153
\(841\) 28.9292 0.997557
\(842\) 43.6358 1.50379
\(843\) −0.114831 −0.00395500
\(844\) −33.5529 −1.15494
\(845\) −35.5115 −1.22163
\(846\) 21.3272 0.733243
\(847\) 42.4787 1.45958
\(848\) −2.16382 −0.0743060
\(849\) 27.1874 0.933071
\(850\) 37.3130 1.27982
\(851\) 3.18066 0.109032
\(852\) −40.7173 −1.39495
\(853\) 57.7687 1.97796 0.988981 0.148041i \(-0.0472966\pi\)
0.988981 + 0.148041i \(0.0472966\pi\)
\(854\) −28.2193 −0.965644
\(855\) 5.74987 0.196641
\(856\) −14.0904 −0.481602
\(857\) −18.4445 −0.630051 −0.315026 0.949083i \(-0.602013\pi\)
−0.315026 + 0.949083i \(0.602013\pi\)
\(858\) −7.69016 −0.262538
\(859\) −5.57626 −0.190260 −0.0951298 0.995465i \(-0.530327\pi\)
−0.0951298 + 0.995465i \(0.530327\pi\)
\(860\) 31.1221 1.06125
\(861\) −59.3837 −2.02379
\(862\) 32.9653 1.12280
\(863\) −4.39475 −0.149599 −0.0747996 0.997199i \(-0.523832\pi\)
−0.0747996 + 0.997199i \(0.523832\pi\)
\(864\) −27.2996 −0.928752
\(865\) 16.0779 0.546666
\(866\) −81.8628 −2.78181
\(867\) 21.2611 0.722066
\(868\) −28.2524 −0.958948
\(869\) 79.0981 2.68322
\(870\) 66.8454 2.26627
\(871\) 1.93841 0.0656806
\(872\) 3.21050 0.108721
\(873\) −0.726823 −0.0245992
\(874\) −13.0202 −0.440415
\(875\) −27.8776 −0.942434
\(876\) 18.4601 0.623708
\(877\) 22.8025 0.769986 0.384993 0.922920i \(-0.374204\pi\)
0.384993 + 0.922920i \(0.374204\pi\)
\(878\) −10.6977 −0.361031
\(879\) 7.49240 0.252713
\(880\) −8.59106 −0.289605
\(881\) −43.2800 −1.45814 −0.729070 0.684439i \(-0.760047\pi\)
−0.729070 + 0.684439i \(0.760047\pi\)
\(882\) 37.2924 1.25570
\(883\) −54.9047 −1.84769 −0.923845 0.382767i \(-0.874971\pi\)
−0.923845 + 0.382767i \(0.874971\pi\)
\(884\) 10.5057 0.353343
\(885\) 4.99221 0.167811
\(886\) −46.6929 −1.56868
\(887\) −34.8669 −1.17072 −0.585358 0.810775i \(-0.699046\pi\)
−0.585358 + 0.810775i \(0.699046\pi\)
\(888\) 4.34780 0.145903
\(889\) 14.9659 0.501940
\(890\) 86.3948 2.89596
\(891\) 18.6714 0.625517
\(892\) −16.0911 −0.538768
\(893\) −13.9074 −0.465394
\(894\) 22.6410 0.757229
\(895\) −56.1953 −1.87840
\(896\) 89.0696 2.97560
\(897\) 2.33871 0.0780873
\(898\) −16.6024 −0.554030
\(899\) 13.9396 0.464913
\(900\) −11.0955 −0.369850
\(901\) 18.1456 0.604517
\(902\) −100.597 −3.34950
\(903\) 20.3167 0.676097
\(904\) −34.1517 −1.13587
\(905\) −21.3160 −0.708569
\(906\) −53.1242 −1.76493
\(907\) 55.4376 1.84077 0.920387 0.391008i \(-0.127874\pi\)
0.920387 + 0.391008i \(0.127874\pi\)
\(908\) −39.4964 −1.31073
\(909\) 14.6267 0.485138
\(910\) 16.0529 0.532148
\(911\) −5.96738 −0.197708 −0.0988541 0.995102i \(-0.531518\pi\)
−0.0988541 + 0.995102i \(0.531518\pi\)
\(912\) −1.62922 −0.0539490
\(913\) −36.7493 −1.21622
\(914\) 5.36599 0.177491
\(915\) 10.0978 0.333823
\(916\) −7.71665 −0.254965
\(917\) 23.6764 0.781863
\(918\) −74.8565 −2.47063
\(919\) 26.2471 0.865812 0.432906 0.901439i \(-0.357488\pi\)
0.432906 + 0.901439i \(0.357488\pi\)
\(920\) 28.5416 0.940987
\(921\) −13.0382 −0.429622
\(922\) 17.0839 0.562628
\(923\) 4.82455 0.158802
\(924\) −94.1641 −3.09777
\(925\) −2.81222 −0.0924652
\(926\) 17.1624 0.563992
\(927\) 5.54560 0.182141
\(928\) −36.8287 −1.20896
\(929\) −13.2520 −0.434785 −0.217392 0.976084i \(-0.569755\pi\)
−0.217392 + 0.976084i \(0.569755\pi\)
\(930\) 16.0852 0.527453
\(931\) −24.3183 −0.797001
\(932\) −30.7840 −1.00836
\(933\) −38.4270 −1.25804
\(934\) 79.2646 2.59362
\(935\) 72.0436 2.35608
\(936\) −2.03257 −0.0664366
\(937\) 56.5819 1.84845 0.924225 0.381849i \(-0.124713\pi\)
0.924225 + 0.381849i \(0.124713\pi\)
\(938\) 37.7647 1.23306
\(939\) 3.42259 0.111692
\(940\) 74.5522 2.43162
\(941\) −23.2216 −0.757001 −0.378501 0.925601i \(-0.623560\pi\)
−0.378501 + 0.925601i \(0.623560\pi\)
\(942\) −39.2078 −1.27746
\(943\) 30.5932 0.996251
\(944\) 0.899357 0.0292716
\(945\) −71.8901 −2.33859
\(946\) 34.4167 1.11898
\(947\) 48.0255 1.56062 0.780310 0.625393i \(-0.215061\pi\)
0.780310 + 0.625393i \(0.215061\pi\)
\(948\) −80.4107 −2.61162
\(949\) −2.18732 −0.0710033
\(950\) 11.5120 0.373498
\(951\) 14.8236 0.480689
\(952\) 83.6967 2.71263
\(953\) −12.6050 −0.408316 −0.204158 0.978938i \(-0.565446\pi\)
−0.204158 + 0.978938i \(0.565446\pi\)
\(954\) −8.58515 −0.277954
\(955\) 34.3365 1.11110
\(956\) −15.7575 −0.509633
\(957\) 46.4603 1.50185
\(958\) 85.5200 2.76303
\(959\) −11.8973 −0.384184
\(960\) −47.6595 −1.53820
\(961\) −27.6457 −0.891796
\(962\) −1.25980 −0.0406177
\(963\) −5.11753 −0.164910
\(964\) −77.4470 −2.49440
\(965\) 29.3382 0.944431
\(966\) 45.5634 1.46598
\(967\) 13.1586 0.423153 0.211577 0.977361i \(-0.432140\pi\)
0.211577 + 0.977361i \(0.432140\pi\)
\(968\) −29.9144 −0.961485
\(969\) 13.6625 0.438902
\(970\) −4.04247 −0.129796
\(971\) −10.0381 −0.322138 −0.161069 0.986943i \(-0.551494\pi\)
−0.161069 + 0.986943i \(0.551494\pi\)
\(972\) 38.2889 1.22812
\(973\) 72.2736 2.31698
\(974\) −57.4229 −1.83995
\(975\) −2.06780 −0.0662226
\(976\) 1.81914 0.0582292
\(977\) −33.9704 −1.08681 −0.543404 0.839471i \(-0.682865\pi\)
−0.543404 + 0.839471i \(0.682865\pi\)
\(978\) 55.4930 1.77447
\(979\) 60.0479 1.91914
\(980\) 130.361 4.16423
\(981\) 1.16603 0.0372284
\(982\) −13.8013 −0.440418
\(983\) −23.0476 −0.735105 −0.367553 0.930003i \(-0.619804\pi\)
−0.367553 + 0.930003i \(0.619804\pi\)
\(984\) 41.8193 1.33315
\(985\) 57.3053 1.82590
\(986\) −100.986 −3.21604
\(987\) 48.6681 1.54912
\(988\) 3.24125 0.103118
\(989\) −10.4667 −0.332822
\(990\) −34.0857 −1.08332
\(991\) 49.0958 1.55958 0.779790 0.626041i \(-0.215326\pi\)
0.779790 + 0.626041i \(0.215326\pi\)
\(992\) −8.86218 −0.281375
\(993\) −8.63103 −0.273897
\(994\) 93.9933 2.98129
\(995\) 55.4428 1.75765
\(996\) 37.3591 1.18377
\(997\) −4.09217 −0.129600 −0.0648001 0.997898i \(-0.520641\pi\)
−0.0648001 + 0.997898i \(0.520641\pi\)
\(998\) −22.6050 −0.715548
\(999\) 5.64181 0.178499
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 \(a_p\))