Properties

Label 8041.2.a.j.1.12
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.25270 q^{2}\) \(+2.53862 q^{3}\) \(+3.07467 q^{4}\) \(-2.69802 q^{5}\) \(-5.71876 q^{6}\) \(-2.07248 q^{7}\) \(-2.42091 q^{8}\) \(+3.44461 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.25270 q^{2}\) \(+2.53862 q^{3}\) \(+3.07467 q^{4}\) \(-2.69802 q^{5}\) \(-5.71876 q^{6}\) \(-2.07248 q^{7}\) \(-2.42091 q^{8}\) \(+3.44461 q^{9}\) \(+6.07784 q^{10}\) \(+1.00000 q^{11}\) \(+7.80543 q^{12}\) \(+1.22220 q^{13}\) \(+4.66867 q^{14}\) \(-6.84926 q^{15}\) \(-0.695751 q^{16}\) \(+1.00000 q^{17}\) \(-7.75968 q^{18}\) \(+2.33904 q^{19}\) \(-8.29553 q^{20}\) \(-5.26124 q^{21}\) \(-2.25270 q^{22}\) \(+3.99896 q^{23}\) \(-6.14578 q^{24}\) \(+2.27933 q^{25}\) \(-2.75326 q^{26}\) \(+1.12870 q^{27}\) \(-6.37218 q^{28}\) \(-3.37911 q^{29}\) \(+15.4294 q^{30}\) \(+5.27548 q^{31}\) \(+6.40914 q^{32}\) \(+2.53862 q^{33}\) \(-2.25270 q^{34}\) \(+5.59159 q^{35}\) \(+10.5910 q^{36}\) \(-3.32932 q^{37}\) \(-5.26916 q^{38}\) \(+3.10272 q^{39}\) \(+6.53167 q^{40}\) \(-9.84032 q^{41}\) \(+11.8520 q^{42}\) \(+1.00000 q^{43}\) \(+3.07467 q^{44}\) \(-9.29364 q^{45}\) \(-9.00846 q^{46}\) \(+9.90673 q^{47}\) \(-1.76625 q^{48}\) \(-2.70484 q^{49}\) \(-5.13465 q^{50}\) \(+2.53862 q^{51}\) \(+3.75788 q^{52}\) \(+1.52330 q^{53}\) \(-2.54262 q^{54}\) \(-2.69802 q^{55}\) \(+5.01728 q^{56}\) \(+5.93794 q^{57}\) \(+7.61213 q^{58}\) \(+5.02001 q^{59}\) \(-21.0592 q^{60}\) \(-5.30301 q^{61}\) \(-11.8841 q^{62}\) \(-7.13888 q^{63}\) \(-13.0464 q^{64}\) \(-3.29754 q^{65}\) \(-5.71876 q^{66}\) \(-3.52986 q^{67}\) \(+3.07467 q^{68}\) \(+10.1519 q^{69}\) \(-12.5962 q^{70}\) \(-10.1166 q^{71}\) \(-8.33909 q^{72}\) \(-5.09905 q^{73}\) \(+7.49997 q^{74}\) \(+5.78635 q^{75}\) \(+7.19176 q^{76}\) \(-2.07248 q^{77}\) \(-6.98950 q^{78}\) \(+6.37136 q^{79}\) \(+1.87715 q^{80}\) \(-7.46849 q^{81}\) \(+22.1673 q^{82}\) \(+17.9066 q^{83}\) \(-16.1766 q^{84}\) \(-2.69802 q^{85}\) \(-2.25270 q^{86}\) \(-8.57829 q^{87}\) \(-2.42091 q^{88}\) \(+12.4966 q^{89}\) \(+20.9358 q^{90}\) \(-2.53299 q^{91}\) \(+12.2955 q^{92}\) \(+13.3925 q^{93}\) \(-22.3169 q^{94}\) \(-6.31078 q^{95}\) \(+16.2704 q^{96}\) \(+8.54706 q^{97}\) \(+6.09320 q^{98}\) \(+3.44461 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25270 −1.59290 −0.796451 0.604704i \(-0.793292\pi\)
−0.796451 + 0.604704i \(0.793292\pi\)
\(3\) 2.53862 1.46568 0.732838 0.680404i \(-0.238196\pi\)
0.732838 + 0.680404i \(0.238196\pi\)
\(4\) 3.07467 1.53733
\(5\) −2.69802 −1.20659 −0.603296 0.797517i \(-0.706146\pi\)
−0.603296 + 0.797517i \(0.706146\pi\)
\(6\) −5.71876 −2.33468
\(7\) −2.07248 −0.783323 −0.391661 0.920109i \(-0.628099\pi\)
−0.391661 + 0.920109i \(0.628099\pi\)
\(8\) −2.42091 −0.855920
\(9\) 3.44461 1.14820
\(10\) 6.07784 1.92198
\(11\) 1.00000 0.301511
\(12\) 7.80543 2.25323
\(13\) 1.22220 0.338979 0.169489 0.985532i \(-0.445788\pi\)
0.169489 + 0.985532i \(0.445788\pi\)
\(14\) 4.66867 1.24776
\(15\) −6.84926 −1.76847
\(16\) −0.695751 −0.173938
\(17\) 1.00000 0.242536
\(18\) −7.75968 −1.82897
\(19\) 2.33904 0.536612 0.268306 0.963334i \(-0.413536\pi\)
0.268306 + 0.963334i \(0.413536\pi\)
\(20\) −8.29553 −1.85494
\(21\) −5.26124 −1.14810
\(22\) −2.25270 −0.480278
\(23\) 3.99896 0.833840 0.416920 0.908943i \(-0.363109\pi\)
0.416920 + 0.908943i \(0.363109\pi\)
\(24\) −6.14578 −1.25450
\(25\) 2.27933 0.455865
\(26\) −2.75326 −0.539960
\(27\) 1.12870 0.217218
\(28\) −6.37218 −1.20423
\(29\) −3.37911 −0.627485 −0.313743 0.949508i \(-0.601583\pi\)
−0.313743 + 0.949508i \(0.601583\pi\)
\(30\) 15.4294 2.81700
\(31\) 5.27548 0.947504 0.473752 0.880658i \(-0.342899\pi\)
0.473752 + 0.880658i \(0.342899\pi\)
\(32\) 6.40914 1.13299
\(33\) 2.53862 0.441918
\(34\) −2.25270 −0.386335
\(35\) 5.59159 0.945151
\(36\) 10.5910 1.76517
\(37\) −3.32932 −0.547337 −0.273669 0.961824i \(-0.588237\pi\)
−0.273669 + 0.961824i \(0.588237\pi\)
\(38\) −5.26916 −0.854770
\(39\) 3.10272 0.496833
\(40\) 6.53167 1.03275
\(41\) −9.84032 −1.53680 −0.768400 0.639970i \(-0.778947\pi\)
−0.768400 + 0.639970i \(0.778947\pi\)
\(42\) 11.8520 1.82880
\(43\) 1.00000 0.152499
\(44\) 3.07467 0.463524
\(45\) −9.29364 −1.38541
\(46\) −9.00846 −1.32823
\(47\) 9.90673 1.44504 0.722522 0.691348i \(-0.242983\pi\)
0.722522 + 0.691348i \(0.242983\pi\)
\(48\) −1.76625 −0.254936
\(49\) −2.70484 −0.386406
\(50\) −5.13465 −0.726149
\(51\) 2.53862 0.355478
\(52\) 3.75788 0.521124
\(53\) 1.52330 0.209242 0.104621 0.994512i \(-0.466637\pi\)
0.104621 + 0.994512i \(0.466637\pi\)
\(54\) −2.54262 −0.346007
\(55\) −2.69802 −0.363801
\(56\) 5.01728 0.670462
\(57\) 5.93794 0.786499
\(58\) 7.61213 0.999522
\(59\) 5.02001 0.653550 0.326775 0.945102i \(-0.394038\pi\)
0.326775 + 0.945102i \(0.394038\pi\)
\(60\) −21.0592 −2.71873
\(61\) −5.30301 −0.678981 −0.339490 0.940610i \(-0.610255\pi\)
−0.339490 + 0.940610i \(0.610255\pi\)
\(62\) −11.8841 −1.50928
\(63\) −7.13888 −0.899414
\(64\) −13.0464 −1.63080
\(65\) −3.29754 −0.409009
\(66\) −5.71876 −0.703931
\(67\) −3.52986 −0.431241 −0.215621 0.976477i \(-0.569177\pi\)
−0.215621 + 0.976477i \(0.569177\pi\)
\(68\) 3.07467 0.372858
\(69\) 10.1519 1.22214
\(70\) −12.5962 −1.50553
\(71\) −10.1166 −1.20062 −0.600311 0.799767i \(-0.704956\pi\)
−0.600311 + 0.799767i \(0.704956\pi\)
\(72\) −8.33909 −0.982771
\(73\) −5.09905 −0.596799 −0.298399 0.954441i \(-0.596453\pi\)
−0.298399 + 0.954441i \(0.596453\pi\)
\(74\) 7.49997 0.871854
\(75\) 5.78635 0.668151
\(76\) 7.19176 0.824952
\(77\) −2.07248 −0.236181
\(78\) −6.98950 −0.791405
\(79\) 6.37136 0.716834 0.358417 0.933562i \(-0.383317\pi\)
0.358417 + 0.933562i \(0.383317\pi\)
\(80\) 1.87715 0.209872
\(81\) −7.46849 −0.829832
\(82\) 22.1673 2.44797
\(83\) 17.9066 1.96550 0.982752 0.184928i \(-0.0592051\pi\)
0.982752 + 0.184928i \(0.0592051\pi\)
\(84\) −16.1766 −1.76501
\(85\) −2.69802 −0.292642
\(86\) −2.25270 −0.242915
\(87\) −8.57829 −0.919689
\(88\) −2.42091 −0.258070
\(89\) 12.4966 1.32464 0.662318 0.749223i \(-0.269573\pi\)
0.662318 + 0.749223i \(0.269573\pi\)
\(90\) 20.9358 2.20683
\(91\) −2.53299 −0.265530
\(92\) 12.2955 1.28189
\(93\) 13.3925 1.38873
\(94\) −22.3169 −2.30181
\(95\) −6.31078 −0.647472
\(96\) 16.2704 1.66059
\(97\) 8.54706 0.867822 0.433911 0.900956i \(-0.357133\pi\)
0.433911 + 0.900956i \(0.357133\pi\)
\(98\) 6.09320 0.615506
\(99\) 3.44461 0.346196
\(100\) 7.00817 0.700817
\(101\) 2.27426 0.226298 0.113149 0.993578i \(-0.463906\pi\)
0.113149 + 0.993578i \(0.463906\pi\)
\(102\) −5.71876 −0.566242
\(103\) 14.8724 1.46542 0.732712 0.680538i \(-0.238254\pi\)
0.732712 + 0.680538i \(0.238254\pi\)
\(104\) −2.95885 −0.290139
\(105\) 14.1949 1.38528
\(106\) −3.43155 −0.333301
\(107\) −0.832362 −0.0804675 −0.0402338 0.999190i \(-0.512810\pi\)
−0.0402338 + 0.999190i \(0.512810\pi\)
\(108\) 3.47037 0.333937
\(109\) 2.08727 0.199924 0.0999622 0.994991i \(-0.468128\pi\)
0.0999622 + 0.994991i \(0.468128\pi\)
\(110\) 6.07784 0.579500
\(111\) −8.45190 −0.802219
\(112\) 1.44193 0.136249
\(113\) 0.757367 0.0712471 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(114\) −13.3764 −1.25281
\(115\) −10.7893 −1.00611
\(116\) −10.3896 −0.964654
\(117\) 4.21002 0.389216
\(118\) −11.3086 −1.04104
\(119\) −2.07248 −0.189984
\(120\) 16.5814 1.51367
\(121\) 1.00000 0.0909091
\(122\) 11.9461 1.08155
\(123\) −24.9809 −2.25245
\(124\) 16.2203 1.45663
\(125\) 7.34044 0.656549
\(126\) 16.0818 1.43268
\(127\) −12.2963 −1.09112 −0.545560 0.838072i \(-0.683683\pi\)
−0.545560 + 0.838072i \(0.683683\pi\)
\(128\) 16.5713 1.46471
\(129\) 2.53862 0.223513
\(130\) 7.42837 0.651511
\(131\) −12.8405 −1.12188 −0.560939 0.827857i \(-0.689560\pi\)
−0.560939 + 0.827857i \(0.689560\pi\)
\(132\) 7.80543 0.679375
\(133\) −4.84760 −0.420340
\(134\) 7.95173 0.686925
\(135\) −3.04525 −0.262094
\(136\) −2.42091 −0.207591
\(137\) −4.39364 −0.375374 −0.187687 0.982229i \(-0.560099\pi\)
−0.187687 + 0.982229i \(0.560099\pi\)
\(138\) −22.8691 −1.94675
\(139\) −19.4582 −1.65042 −0.825211 0.564824i \(-0.808944\pi\)
−0.825211 + 0.564824i \(0.808944\pi\)
\(140\) 17.1923 1.45301
\(141\) 25.1495 2.11797
\(142\) 22.7897 1.91247
\(143\) 1.22220 0.102206
\(144\) −2.39659 −0.199716
\(145\) 9.11692 0.757119
\(146\) 11.4866 0.950642
\(147\) −6.86657 −0.566345
\(148\) −10.2366 −0.841440
\(149\) 10.4419 0.855433 0.427717 0.903913i \(-0.359318\pi\)
0.427717 + 0.903913i \(0.359318\pi\)
\(150\) −13.0349 −1.06430
\(151\) −0.944962 −0.0768999 −0.0384500 0.999261i \(-0.512242\pi\)
−0.0384500 + 0.999261i \(0.512242\pi\)
\(152\) −5.66260 −0.459297
\(153\) 3.44461 0.278480
\(154\) 4.66867 0.376212
\(155\) −14.2334 −1.14325
\(156\) 9.53983 0.763798
\(157\) 8.54009 0.681573 0.340787 0.940141i \(-0.389307\pi\)
0.340787 + 0.940141i \(0.389307\pi\)
\(158\) −14.3528 −1.14185
\(159\) 3.86709 0.306680
\(160\) −17.2920 −1.36705
\(161\) −8.28775 −0.653166
\(162\) 16.8243 1.32184
\(163\) −6.94489 −0.543966 −0.271983 0.962302i \(-0.587679\pi\)
−0.271983 + 0.962302i \(0.587679\pi\)
\(164\) −30.2557 −2.36258
\(165\) −6.84926 −0.533215
\(166\) −40.3382 −3.13085
\(167\) −13.2286 −1.02366 −0.511831 0.859086i \(-0.671033\pi\)
−0.511831 + 0.859086i \(0.671033\pi\)
\(168\) 12.7370 0.982679
\(169\) −11.5062 −0.885093
\(170\) 6.07784 0.466149
\(171\) 8.05707 0.616140
\(172\) 3.07467 0.234441
\(173\) 7.15541 0.544016 0.272008 0.962295i \(-0.412312\pi\)
0.272008 + 0.962295i \(0.412312\pi\)
\(174\) 19.3243 1.46497
\(175\) −4.72385 −0.357090
\(176\) −0.695751 −0.0524442
\(177\) 12.7439 0.957892
\(178\) −28.1511 −2.11001
\(179\) 12.1309 0.906708 0.453354 0.891331i \(-0.350227\pi\)
0.453354 + 0.891331i \(0.350227\pi\)
\(180\) −28.5749 −2.12984
\(181\) 0.219538 0.0163181 0.00815905 0.999967i \(-0.497403\pi\)
0.00815905 + 0.999967i \(0.497403\pi\)
\(182\) 5.70608 0.422963
\(183\) −13.4623 −0.995165
\(184\) −9.68111 −0.713701
\(185\) 8.98259 0.660413
\(186\) −30.1692 −2.21211
\(187\) 1.00000 0.0731272
\(188\) 30.4599 2.22152
\(189\) −2.33920 −0.170152
\(190\) 14.2163 1.03136
\(191\) −7.23933 −0.523820 −0.261910 0.965092i \(-0.584352\pi\)
−0.261910 + 0.965092i \(0.584352\pi\)
\(192\) −33.1198 −2.39022
\(193\) 12.1202 0.872430 0.436215 0.899842i \(-0.356319\pi\)
0.436215 + 0.899842i \(0.356319\pi\)
\(194\) −19.2540 −1.38235
\(195\) −8.37121 −0.599474
\(196\) −8.31649 −0.594035
\(197\) −5.79951 −0.413198 −0.206599 0.978426i \(-0.566240\pi\)
−0.206599 + 0.978426i \(0.566240\pi\)
\(198\) −7.75968 −0.551457
\(199\) 11.2251 0.795727 0.397864 0.917445i \(-0.369752\pi\)
0.397864 + 0.917445i \(0.369752\pi\)
\(200\) −5.51804 −0.390184
\(201\) −8.96099 −0.632059
\(202\) −5.12324 −0.360470
\(203\) 7.00313 0.491523
\(204\) 7.80543 0.546489
\(205\) 26.5494 1.85429
\(206\) −33.5032 −2.33428
\(207\) 13.7749 0.957419
\(208\) −0.850350 −0.0589612
\(209\) 2.33904 0.161795
\(210\) −31.9770 −2.20662
\(211\) −16.3880 −1.12820 −0.564098 0.825708i \(-0.690776\pi\)
−0.564098 + 0.825708i \(0.690776\pi\)
\(212\) 4.68365 0.321674
\(213\) −25.6823 −1.75972
\(214\) 1.87506 0.128177
\(215\) −2.69802 −0.184004
\(216\) −2.73248 −0.185921
\(217\) −10.9333 −0.742201
\(218\) −4.70200 −0.318460
\(219\) −12.9446 −0.874713
\(220\) −8.29553 −0.559284
\(221\) 1.22220 0.0822144
\(222\) 19.0396 1.27785
\(223\) −5.50360 −0.368548 −0.184274 0.982875i \(-0.558993\pi\)
−0.184274 + 0.982875i \(0.558993\pi\)
\(224\) −13.2828 −0.887493
\(225\) 7.85139 0.523426
\(226\) −1.70612 −0.113490
\(227\) −12.6639 −0.840534 −0.420267 0.907401i \(-0.638064\pi\)
−0.420267 + 0.907401i \(0.638064\pi\)
\(228\) 18.2572 1.20911
\(229\) 4.79412 0.316804 0.158402 0.987375i \(-0.449366\pi\)
0.158402 + 0.987375i \(0.449366\pi\)
\(230\) 24.3050 1.60263
\(231\) −5.26124 −0.346164
\(232\) 8.18052 0.537077
\(233\) 3.27279 0.214408 0.107204 0.994237i \(-0.465810\pi\)
0.107204 + 0.994237i \(0.465810\pi\)
\(234\) −9.48392 −0.619983
\(235\) −26.7286 −1.74358
\(236\) 15.4349 1.00472
\(237\) 16.1745 1.05065
\(238\) 4.66867 0.302625
\(239\) 25.8317 1.67091 0.835457 0.549556i \(-0.185203\pi\)
0.835457 + 0.549556i \(0.185203\pi\)
\(240\) 4.76538 0.307604
\(241\) −8.71206 −0.561193 −0.280597 0.959826i \(-0.590532\pi\)
−0.280597 + 0.959826i \(0.590532\pi\)
\(242\) −2.25270 −0.144809
\(243\) −22.3458 −1.43348
\(244\) −16.3050 −1.04382
\(245\) 7.29772 0.466234
\(246\) 56.2745 3.58793
\(247\) 2.85878 0.181900
\(248\) −12.7714 −0.810988
\(249\) 45.4581 2.88079
\(250\) −16.5358 −1.04582
\(251\) 14.4717 0.913443 0.456721 0.889610i \(-0.349024\pi\)
0.456721 + 0.889610i \(0.349024\pi\)
\(252\) −21.9497 −1.38270
\(253\) 3.99896 0.251412
\(254\) 27.6999 1.73805
\(255\) −6.84926 −0.428918
\(256\) −11.2375 −0.702345
\(257\) 28.1495 1.75592 0.877960 0.478734i \(-0.158904\pi\)
0.877960 + 0.478734i \(0.158904\pi\)
\(258\) −5.71876 −0.356035
\(259\) 6.89994 0.428742
\(260\) −10.1388 −0.628784
\(261\) −11.6397 −0.720481
\(262\) 28.9258 1.78704
\(263\) 0.766205 0.0472462 0.0236231 0.999721i \(-0.492480\pi\)
0.0236231 + 0.999721i \(0.492480\pi\)
\(264\) −6.14578 −0.378246
\(265\) −4.10990 −0.252469
\(266\) 10.9202 0.669561
\(267\) 31.7241 1.94149
\(268\) −10.8532 −0.662962
\(269\) 13.9161 0.848477 0.424238 0.905551i \(-0.360542\pi\)
0.424238 + 0.905551i \(0.360542\pi\)
\(270\) 6.86005 0.417489
\(271\) 26.2183 1.59265 0.796325 0.604869i \(-0.206774\pi\)
0.796325 + 0.604869i \(0.206774\pi\)
\(272\) −0.695751 −0.0421861
\(273\) −6.43031 −0.389180
\(274\) 9.89755 0.597933
\(275\) 2.27933 0.137449
\(276\) 31.2136 1.87884
\(277\) −15.5451 −0.934015 −0.467008 0.884253i \(-0.654668\pi\)
−0.467008 + 0.884253i \(0.654668\pi\)
\(278\) 43.8335 2.62896
\(279\) 18.1720 1.08793
\(280\) −13.5367 −0.808974
\(281\) 21.4381 1.27889 0.639446 0.768836i \(-0.279164\pi\)
0.639446 + 0.768836i \(0.279164\pi\)
\(282\) −56.6542 −3.37371
\(283\) −6.83917 −0.406547 −0.203273 0.979122i \(-0.565158\pi\)
−0.203273 + 0.979122i \(0.565158\pi\)
\(284\) −31.1052 −1.84576
\(285\) −16.0207 −0.948984
\(286\) −2.75326 −0.162804
\(287\) 20.3938 1.20381
\(288\) 22.0770 1.30090
\(289\) 1.00000 0.0588235
\(290\) −20.5377 −1.20602
\(291\) 21.6978 1.27195
\(292\) −15.6779 −0.917479
\(293\) 24.3396 1.42193 0.710966 0.703226i \(-0.248258\pi\)
0.710966 + 0.703226i \(0.248258\pi\)
\(294\) 15.4683 0.902132
\(295\) −13.5441 −0.788569
\(296\) 8.05998 0.468477
\(297\) 1.12870 0.0654937
\(298\) −23.5225 −1.36262
\(299\) 4.88755 0.282654
\(300\) 17.7911 1.02717
\(301\) −2.07248 −0.119456
\(302\) 2.12872 0.122494
\(303\) 5.77350 0.331679
\(304\) −1.62739 −0.0933370
\(305\) 14.3076 0.819253
\(306\) −7.75968 −0.443592
\(307\) −4.88601 −0.278859 −0.139430 0.990232i \(-0.544527\pi\)
−0.139430 + 0.990232i \(0.544527\pi\)
\(308\) −6.37218 −0.363089
\(309\) 37.7555 2.14784
\(310\) 32.0635 1.82109
\(311\) 8.28068 0.469554 0.234777 0.972049i \(-0.424564\pi\)
0.234777 + 0.972049i \(0.424564\pi\)
\(312\) −7.51140 −0.425249
\(313\) 18.0872 1.02235 0.511174 0.859477i \(-0.329211\pi\)
0.511174 + 0.859477i \(0.329211\pi\)
\(314\) −19.2383 −1.08568
\(315\) 19.2608 1.08523
\(316\) 19.5898 1.10201
\(317\) 6.61130 0.371327 0.185664 0.982613i \(-0.440556\pi\)
0.185664 + 0.982613i \(0.440556\pi\)
\(318\) −8.71141 −0.488511
\(319\) −3.37911 −0.189194
\(320\) 35.1994 1.96771
\(321\) −2.11306 −0.117939
\(322\) 18.6698 1.04043
\(323\) 2.33904 0.130148
\(324\) −22.9631 −1.27573
\(325\) 2.78580 0.154529
\(326\) 15.6448 0.866483
\(327\) 5.29880 0.293024
\(328\) 23.8225 1.31538
\(329\) −20.5315 −1.13194
\(330\) 15.4294 0.849358
\(331\) −29.5351 −1.62340 −0.811698 0.584077i \(-0.801457\pi\)
−0.811698 + 0.584077i \(0.801457\pi\)
\(332\) 55.0568 3.02164
\(333\) −11.4682 −0.628455
\(334\) 29.8002 1.63059
\(335\) 9.52365 0.520332
\(336\) 3.66051 0.199697
\(337\) −28.3966 −1.54686 −0.773431 0.633880i \(-0.781461\pi\)
−0.773431 + 0.633880i \(0.781461\pi\)
\(338\) 25.9201 1.40987
\(339\) 1.92267 0.104425
\(340\) −8.29553 −0.449888
\(341\) 5.27548 0.285683
\(342\) −18.1502 −0.981450
\(343\) 20.1131 1.08600
\(344\) −2.42091 −0.130527
\(345\) −27.3899 −1.47462
\(346\) −16.1190 −0.866564
\(347\) −9.40481 −0.504877 −0.252438 0.967613i \(-0.581232\pi\)
−0.252438 + 0.967613i \(0.581232\pi\)
\(348\) −26.3754 −1.41387
\(349\) 34.5889 1.85150 0.925750 0.378136i \(-0.123435\pi\)
0.925750 + 0.378136i \(0.123435\pi\)
\(350\) 10.6414 0.568809
\(351\) 1.37950 0.0736323
\(352\) 6.40914 0.341608
\(353\) 1.60975 0.0856783 0.0428391 0.999082i \(-0.486360\pi\)
0.0428391 + 0.999082i \(0.486360\pi\)
\(354\) −28.7083 −1.52583
\(355\) 27.2949 1.44866
\(356\) 38.4229 2.03641
\(357\) −5.26124 −0.278454
\(358\) −27.3274 −1.44430
\(359\) −31.1633 −1.64474 −0.822368 0.568956i \(-0.807347\pi\)
−0.822368 + 0.568956i \(0.807347\pi\)
\(360\) 22.4990 1.18580
\(361\) −13.5289 −0.712048
\(362\) −0.494553 −0.0259931
\(363\) 2.53862 0.133243
\(364\) −7.78811 −0.408208
\(365\) 13.7574 0.720093
\(366\) 30.3267 1.58520
\(367\) 28.1321 1.46848 0.734242 0.678888i \(-0.237538\pi\)
0.734242 + 0.678888i \(0.237538\pi\)
\(368\) −2.78228 −0.145036
\(369\) −33.8961 −1.76456
\(370\) −20.2351 −1.05197
\(371\) −3.15701 −0.163904
\(372\) 41.1774 2.13495
\(373\) 10.0689 0.521347 0.260674 0.965427i \(-0.416055\pi\)
0.260674 + 0.965427i \(0.416055\pi\)
\(374\) −2.25270 −0.116484
\(375\) 18.6346 0.962287
\(376\) −23.9833 −1.23684
\(377\) −4.12997 −0.212704
\(378\) 5.26952 0.271035
\(379\) 15.4194 0.792040 0.396020 0.918242i \(-0.370391\pi\)
0.396020 + 0.918242i \(0.370391\pi\)
\(380\) −19.4035 −0.995381
\(381\) −31.2157 −1.59923
\(382\) 16.3081 0.834393
\(383\) 15.6070 0.797483 0.398741 0.917063i \(-0.369447\pi\)
0.398741 + 0.917063i \(0.369447\pi\)
\(384\) 42.0684 2.14679
\(385\) 5.59159 0.284974
\(386\) −27.3032 −1.38970
\(387\) 3.44461 0.175099
\(388\) 26.2794 1.33413
\(389\) 31.2811 1.58601 0.793006 0.609214i \(-0.208515\pi\)
0.793006 + 0.609214i \(0.208515\pi\)
\(390\) 18.8578 0.954904
\(391\) 3.99896 0.202236
\(392\) 6.54817 0.330733
\(393\) −32.5971 −1.64431
\(394\) 13.0646 0.658183
\(395\) −17.1901 −0.864926
\(396\) 10.5910 0.532220
\(397\) 23.5654 1.18271 0.591357 0.806410i \(-0.298592\pi\)
0.591357 + 0.806410i \(0.298592\pi\)
\(398\) −25.2868 −1.26751
\(399\) −12.3062 −0.616082
\(400\) −1.58584 −0.0792922
\(401\) 2.46060 0.122877 0.0614383 0.998111i \(-0.480431\pi\)
0.0614383 + 0.998111i \(0.480431\pi\)
\(402\) 20.1864 1.00681
\(403\) 6.44772 0.321184
\(404\) 6.99261 0.347895
\(405\) 20.1502 1.00127
\(406\) −15.7760 −0.782948
\(407\) −3.32932 −0.165028
\(408\) −6.14578 −0.304261
\(409\) 18.0781 0.893907 0.446953 0.894557i \(-0.352509\pi\)
0.446953 + 0.894557i \(0.352509\pi\)
\(410\) −59.8079 −2.95370
\(411\) −11.1538 −0.550176
\(412\) 45.7278 2.25285
\(413\) −10.4039 −0.511940
\(414\) −31.0306 −1.52507
\(415\) −48.3124 −2.37156
\(416\) 7.83328 0.384058
\(417\) −49.3970 −2.41898
\(418\) −5.26916 −0.257723
\(419\) 9.24303 0.451552 0.225776 0.974179i \(-0.427508\pi\)
0.225776 + 0.974179i \(0.427508\pi\)
\(420\) 43.6447 2.12965
\(421\) 30.9745 1.50960 0.754802 0.655953i \(-0.227733\pi\)
0.754802 + 0.655953i \(0.227733\pi\)
\(422\) 36.9173 1.79710
\(423\) 34.1248 1.65921
\(424\) −3.68778 −0.179094
\(425\) 2.27933 0.110564
\(426\) 57.8545 2.80306
\(427\) 10.9904 0.531861
\(428\) −2.55924 −0.123705
\(429\) 3.10272 0.149801
\(430\) 6.07784 0.293100
\(431\) 4.28745 0.206519 0.103260 0.994654i \(-0.467073\pi\)
0.103260 + 0.994654i \(0.467073\pi\)
\(432\) −0.785293 −0.0377824
\(433\) −12.2719 −0.589748 −0.294874 0.955536i \(-0.595278\pi\)
−0.294874 + 0.955536i \(0.595278\pi\)
\(434\) 24.6295 1.18225
\(435\) 23.1444 1.10969
\(436\) 6.41767 0.307351
\(437\) 9.35371 0.447449
\(438\) 29.1603 1.39333
\(439\) 11.3644 0.542392 0.271196 0.962524i \(-0.412581\pi\)
0.271196 + 0.962524i \(0.412581\pi\)
\(440\) 6.53167 0.311385
\(441\) −9.31712 −0.443672
\(442\) −2.75326 −0.130959
\(443\) 36.1347 1.71681 0.858407 0.512970i \(-0.171455\pi\)
0.858407 + 0.512970i \(0.171455\pi\)
\(444\) −25.9868 −1.23328
\(445\) −33.7161 −1.59830
\(446\) 12.3980 0.587061
\(447\) 26.5080 1.25379
\(448\) 27.0383 1.27744
\(449\) −12.1611 −0.573916 −0.286958 0.957943i \(-0.592644\pi\)
−0.286958 + 0.957943i \(0.592644\pi\)
\(450\) −17.6869 −0.833766
\(451\) −9.84032 −0.463363
\(452\) 2.32865 0.109531
\(453\) −2.39890 −0.112710
\(454\) 28.5280 1.33889
\(455\) 6.83407 0.320386
\(456\) −14.3752 −0.673180
\(457\) 13.2266 0.618713 0.309357 0.950946i \(-0.399886\pi\)
0.309357 + 0.950946i \(0.399886\pi\)
\(458\) −10.7997 −0.504638
\(459\) 1.12870 0.0526831
\(460\) −33.1735 −1.54672
\(461\) 18.3851 0.856282 0.428141 0.903712i \(-0.359169\pi\)
0.428141 + 0.903712i \(0.359169\pi\)
\(462\) 11.8520 0.551405
\(463\) −22.0656 −1.02547 −0.512737 0.858546i \(-0.671368\pi\)
−0.512737 + 0.858546i \(0.671368\pi\)
\(464\) 2.35102 0.109143
\(465\) −36.1331 −1.67563
\(466\) −7.37263 −0.341530
\(467\) 9.77489 0.452328 0.226164 0.974089i \(-0.427381\pi\)
0.226164 + 0.974089i \(0.427381\pi\)
\(468\) 12.9444 0.598356
\(469\) 7.31556 0.337801
\(470\) 60.2115 2.77735
\(471\) 21.6801 0.998965
\(472\) −12.1530 −0.559387
\(473\) 1.00000 0.0459800
\(474\) −36.4363 −1.67357
\(475\) 5.33143 0.244623
\(476\) −6.37218 −0.292068
\(477\) 5.24718 0.240252
\(478\) −58.1911 −2.66160
\(479\) 33.3551 1.52403 0.762017 0.647557i \(-0.224209\pi\)
0.762017 + 0.647557i \(0.224209\pi\)
\(480\) −43.8979 −2.00365
\(481\) −4.06911 −0.185536
\(482\) 19.6257 0.893925
\(483\) −21.0395 −0.957329
\(484\) 3.07467 0.139758
\(485\) −23.0601 −1.04711
\(486\) 50.3384 2.28340
\(487\) 28.2469 1.27999 0.639994 0.768380i \(-0.278937\pi\)
0.639994 + 0.768380i \(0.278937\pi\)
\(488\) 12.8381 0.581153
\(489\) −17.6305 −0.797277
\(490\) −16.4396 −0.742665
\(491\) 22.0923 0.997014 0.498507 0.866886i \(-0.333882\pi\)
0.498507 + 0.866886i \(0.333882\pi\)
\(492\) −76.8079 −3.46277
\(493\) −3.37911 −0.152188
\(494\) −6.43999 −0.289749
\(495\) −9.29364 −0.417718
\(496\) −3.67042 −0.164807
\(497\) 20.9664 0.940474
\(498\) −102.404 −4.58881
\(499\) 29.3635 1.31449 0.657245 0.753677i \(-0.271722\pi\)
0.657245 + 0.753677i \(0.271722\pi\)
\(500\) 22.5694 1.00933
\(501\) −33.5825 −1.50036
\(502\) −32.6003 −1.45502
\(503\) −11.5657 −0.515691 −0.257846 0.966186i \(-0.583013\pi\)
−0.257846 + 0.966186i \(0.583013\pi\)
\(504\) 17.2826 0.769827
\(505\) −6.13602 −0.273049
\(506\) −9.00846 −0.400475
\(507\) −29.2100 −1.29726
\(508\) −37.8070 −1.67742
\(509\) 16.0722 0.712386 0.356193 0.934412i \(-0.384075\pi\)
0.356193 + 0.934412i \(0.384075\pi\)
\(510\) 15.4294 0.683223
\(511\) 10.5677 0.467486
\(512\) −7.82786 −0.345946
\(513\) 2.64007 0.116562
\(514\) −63.4125 −2.79701
\(515\) −40.1262 −1.76817
\(516\) 7.80543 0.343615
\(517\) 9.90673 0.435697
\(518\) −15.5435 −0.682943
\(519\) 18.1649 0.797351
\(520\) 7.98303 0.350079
\(521\) 26.8079 1.17447 0.587237 0.809415i \(-0.300216\pi\)
0.587237 + 0.809415i \(0.300216\pi\)
\(522\) 26.2208 1.14765
\(523\) 1.14213 0.0499420 0.0249710 0.999688i \(-0.492051\pi\)
0.0249710 + 0.999688i \(0.492051\pi\)
\(524\) −39.4802 −1.72470
\(525\) −11.9921 −0.523377
\(526\) −1.72603 −0.0752586
\(527\) 5.27548 0.229803
\(528\) −1.76625 −0.0768661
\(529\) −7.00833 −0.304710
\(530\) 9.25839 0.402159
\(531\) 17.2920 0.750408
\(532\) −14.9048 −0.646204
\(533\) −12.0269 −0.520942
\(534\) −71.4650 −3.09259
\(535\) 2.24573 0.0970915
\(536\) 8.54547 0.369108
\(537\) 30.7959 1.32894
\(538\) −31.3487 −1.35154
\(539\) −2.70484 −0.116506
\(540\) −9.36315 −0.402926
\(541\) 7.97118 0.342708 0.171354 0.985210i \(-0.445186\pi\)
0.171354 + 0.985210i \(0.445186\pi\)
\(542\) −59.0621 −2.53693
\(543\) 0.557323 0.0239170
\(544\) 6.40914 0.274789
\(545\) −5.63151 −0.241227
\(546\) 14.4856 0.619926
\(547\) −28.4476 −1.21633 −0.608165 0.793811i \(-0.708094\pi\)
−0.608165 + 0.793811i \(0.708094\pi\)
\(548\) −13.5090 −0.577075
\(549\) −18.2668 −0.779608
\(550\) −5.13465 −0.218942
\(551\) −7.90387 −0.336716
\(552\) −24.5767 −1.04605
\(553\) −13.2045 −0.561512
\(554\) 35.0185 1.48779
\(555\) 22.8034 0.967951
\(556\) −59.8275 −2.53725
\(557\) −38.2834 −1.62212 −0.811059 0.584964i \(-0.801109\pi\)
−0.811059 + 0.584964i \(0.801109\pi\)
\(558\) −40.9360 −1.73296
\(559\) 1.22220 0.0516938
\(560\) −3.89035 −0.164397
\(561\) 2.53862 0.107181
\(562\) −48.2937 −2.03715
\(563\) −43.6484 −1.83956 −0.919781 0.392432i \(-0.871634\pi\)
−0.919781 + 0.392432i \(0.871634\pi\)
\(564\) 77.3262 3.25602
\(565\) −2.04339 −0.0859662
\(566\) 15.4066 0.647589
\(567\) 15.4783 0.650026
\(568\) 24.4914 1.02764
\(569\) −28.2975 −1.18629 −0.593147 0.805094i \(-0.702115\pi\)
−0.593147 + 0.805094i \(0.702115\pi\)
\(570\) 36.0898 1.51164
\(571\) −15.1814 −0.635320 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(572\) 3.75788 0.157125
\(573\) −18.3779 −0.767749
\(574\) −45.9412 −1.91755
\(575\) 9.11493 0.380119
\(576\) −44.9397 −1.87249
\(577\) 40.3111 1.67817 0.839087 0.543997i \(-0.183090\pi\)
0.839087 + 0.543997i \(0.183090\pi\)
\(578\) −2.25270 −0.0937001
\(579\) 30.7686 1.27870
\(580\) 28.0315 1.16394
\(581\) −37.1110 −1.53962
\(582\) −48.8786 −2.02608
\(583\) 1.52330 0.0630887
\(584\) 12.3443 0.510812
\(585\) −11.3587 −0.469626
\(586\) −54.8298 −2.26500
\(587\) 23.6597 0.976539 0.488269 0.872693i \(-0.337628\pi\)
0.488269 + 0.872693i \(0.337628\pi\)
\(588\) −21.1124 −0.870662
\(589\) 12.3395 0.508442
\(590\) 30.5108 1.25611
\(591\) −14.7228 −0.605614
\(592\) 2.31638 0.0952026
\(593\) −3.34731 −0.137458 −0.0687288 0.997635i \(-0.521894\pi\)
−0.0687288 + 0.997635i \(0.521894\pi\)
\(594\) −2.54262 −0.104325
\(595\) 5.59159 0.229233
\(596\) 32.1054 1.31509
\(597\) 28.4963 1.16628
\(598\) −11.0102 −0.450240
\(599\) 19.1550 0.782652 0.391326 0.920252i \(-0.372017\pi\)
0.391326 + 0.920252i \(0.372017\pi\)
\(600\) −14.0082 −0.571884
\(601\) 8.23332 0.335844 0.167922 0.985800i \(-0.446294\pi\)
0.167922 + 0.985800i \(0.446294\pi\)
\(602\) 4.66867 0.190281
\(603\) −12.1590 −0.495153
\(604\) −2.90544 −0.118221
\(605\) −2.69802 −0.109690
\(606\) −13.0060 −0.528332
\(607\) −21.7263 −0.881845 −0.440923 0.897545i \(-0.645349\pi\)
−0.440923 + 0.897545i \(0.645349\pi\)
\(608\) 14.9912 0.607974
\(609\) 17.7783 0.720413
\(610\) −32.2309 −1.30499
\(611\) 12.1081 0.489839
\(612\) 10.5910 0.428117
\(613\) 29.0227 1.17222 0.586108 0.810233i \(-0.300659\pi\)
0.586108 + 0.810233i \(0.300659\pi\)
\(614\) 11.0067 0.444196
\(615\) 67.3990 2.71779
\(616\) 5.01728 0.202152
\(617\) −32.0365 −1.28974 −0.644871 0.764291i \(-0.723089\pi\)
−0.644871 + 0.764291i \(0.723089\pi\)
\(618\) −85.0520 −3.42129
\(619\) −20.3053 −0.816138 −0.408069 0.912951i \(-0.633798\pi\)
−0.408069 + 0.912951i \(0.633798\pi\)
\(620\) −43.7629 −1.75756
\(621\) 4.51362 0.181125
\(622\) −18.6539 −0.747954
\(623\) −25.8989 −1.03762
\(624\) −2.15872 −0.0864179
\(625\) −31.2013 −1.24805
\(626\) −40.7451 −1.62850
\(627\) 5.93794 0.237138
\(628\) 26.2579 1.04781
\(629\) −3.32932 −0.132749
\(630\) −43.3890 −1.72866
\(631\) 1.88309 0.0749647 0.0374823 0.999297i \(-0.488066\pi\)
0.0374823 + 0.999297i \(0.488066\pi\)
\(632\) −15.4245 −0.613553
\(633\) −41.6029 −1.65357
\(634\) −14.8933 −0.591488
\(635\) 33.1757 1.31654
\(636\) 11.8900 0.471470
\(637\) −3.30587 −0.130983
\(638\) 7.61213 0.301367
\(639\) −34.8478 −1.37856
\(640\) −44.7098 −1.76731
\(641\) 27.3336 1.07961 0.539807 0.841789i \(-0.318497\pi\)
0.539807 + 0.841789i \(0.318497\pi\)
\(642\) 4.76008 0.187866
\(643\) −31.0099 −1.22291 −0.611455 0.791279i \(-0.709416\pi\)
−0.611455 + 0.791279i \(0.709416\pi\)
\(644\) −25.4821 −1.00413
\(645\) −6.84926 −0.269690
\(646\) −5.26916 −0.207312
\(647\) 8.92462 0.350863 0.175431 0.984492i \(-0.443868\pi\)
0.175431 + 0.984492i \(0.443868\pi\)
\(648\) 18.0805 0.710270
\(649\) 5.02001 0.197053
\(650\) −6.27559 −0.246149
\(651\) −27.7556 −1.08783
\(652\) −21.3532 −0.836257
\(653\) −3.73419 −0.146130 −0.0730651 0.997327i \(-0.523278\pi\)
−0.0730651 + 0.997327i \(0.523278\pi\)
\(654\) −11.9366 −0.466759
\(655\) 34.6439 1.35365
\(656\) 6.84641 0.267307
\(657\) −17.5642 −0.685247
\(658\) 46.2513 1.80306
\(659\) −2.38540 −0.0929221 −0.0464610 0.998920i \(-0.514794\pi\)
−0.0464610 + 0.998920i \(0.514794\pi\)
\(660\) −21.0592 −0.819729
\(661\) −14.0868 −0.547912 −0.273956 0.961742i \(-0.588332\pi\)
−0.273956 + 0.961742i \(0.588332\pi\)
\(662\) 66.5338 2.58591
\(663\) 3.10272 0.120500
\(664\) −43.3502 −1.68232
\(665\) 13.0789 0.507179
\(666\) 25.8345 1.00107
\(667\) −13.5129 −0.523223
\(668\) −40.6736 −1.57371
\(669\) −13.9716 −0.540172
\(670\) −21.4539 −0.828838
\(671\) −5.30301 −0.204720
\(672\) −33.7200 −1.30078
\(673\) −1.19080 −0.0459022 −0.0229511 0.999737i \(-0.507306\pi\)
−0.0229511 + 0.999737i \(0.507306\pi\)
\(674\) 63.9691 2.46400
\(675\) 2.57267 0.0990222
\(676\) −35.3778 −1.36068
\(677\) −6.80576 −0.261567 −0.130783 0.991411i \(-0.541749\pi\)
−0.130783 + 0.991411i \(0.541749\pi\)
\(678\) −4.33120 −0.166339
\(679\) −17.7136 −0.679785
\(680\) 6.53167 0.250478
\(681\) −32.1489 −1.23195
\(682\) −11.8841 −0.455065
\(683\) 46.2536 1.76985 0.884923 0.465737i \(-0.154211\pi\)
0.884923 + 0.465737i \(0.154211\pi\)
\(684\) 24.7728 0.947213
\(685\) 11.8541 0.452923
\(686\) −45.3087 −1.72990
\(687\) 12.1705 0.464332
\(688\) −0.695751 −0.0265252
\(689\) 1.86179 0.0709285
\(690\) 61.7014 2.34893
\(691\) −13.4198 −0.510515 −0.255258 0.966873i \(-0.582160\pi\)
−0.255258 + 0.966873i \(0.582160\pi\)
\(692\) 22.0005 0.836334
\(693\) −7.13888 −0.271183
\(694\) 21.1862 0.804219
\(695\) 52.4987 1.99139
\(696\) 20.7673 0.787181
\(697\) −9.84032 −0.372729
\(698\) −77.9185 −2.94926
\(699\) 8.30839 0.314252
\(700\) −14.5243 −0.548966
\(701\) −15.8949 −0.600343 −0.300171 0.953885i \(-0.597044\pi\)
−0.300171 + 0.953885i \(0.597044\pi\)
\(702\) −3.10761 −0.117289
\(703\) −7.78741 −0.293708
\(704\) −13.0464 −0.491704
\(705\) −67.8538 −2.55552
\(706\) −3.62629 −0.136477
\(707\) −4.71336 −0.177264
\(708\) 39.1833 1.47260
\(709\) 23.6411 0.887862 0.443931 0.896061i \(-0.353584\pi\)
0.443931 + 0.896061i \(0.353584\pi\)
\(710\) −61.4872 −2.30757
\(711\) 21.9468 0.823071
\(712\) −30.2531 −1.13378
\(713\) 21.0964 0.790067
\(714\) 11.8520 0.443550
\(715\) −3.29754 −0.123321
\(716\) 37.2986 1.39391
\(717\) 65.5769 2.44902
\(718\) 70.2016 2.61990
\(719\) −26.2428 −0.978692 −0.489346 0.872090i \(-0.662764\pi\)
−0.489346 + 0.872090i \(0.662764\pi\)
\(720\) 6.46605 0.240976
\(721\) −30.8228 −1.14790
\(722\) 30.4766 1.13422
\(723\) −22.1166 −0.822527
\(724\) 0.675005 0.0250864
\(725\) −7.70210 −0.286049
\(726\) −5.71876 −0.212243
\(727\) 16.9405 0.628289 0.314144 0.949375i \(-0.398282\pi\)
0.314144 + 0.949375i \(0.398282\pi\)
\(728\) 6.13214 0.227272
\(729\) −34.3221 −1.27119
\(730\) −30.9912 −1.14704
\(731\) 1.00000 0.0369863
\(732\) −41.3922 −1.52990
\(733\) −46.6879 −1.72446 −0.862228 0.506521i \(-0.830931\pi\)
−0.862228 + 0.506521i \(0.830931\pi\)
\(734\) −63.3732 −2.33915
\(735\) 18.5262 0.683348
\(736\) 25.6299 0.944729
\(737\) −3.52986 −0.130024
\(738\) 76.3578 2.81077
\(739\) 44.8070 1.64825 0.824126 0.566406i \(-0.191667\pi\)
0.824126 + 0.566406i \(0.191667\pi\)
\(740\) 27.6185 1.01528
\(741\) 7.25737 0.266606
\(742\) 7.11180 0.261082
\(743\) 8.45192 0.310071 0.155035 0.987909i \(-0.450451\pi\)
0.155035 + 0.987909i \(0.450451\pi\)
\(744\) −32.4219 −1.18864
\(745\) −28.1725 −1.03216
\(746\) −22.6822 −0.830455
\(747\) 61.6812 2.25680
\(748\) 3.07467 0.112421
\(749\) 1.72505 0.0630320
\(750\) −41.9782 −1.53283
\(751\) −38.5382 −1.40628 −0.703140 0.711052i \(-0.748219\pi\)
−0.703140 + 0.711052i \(0.748219\pi\)
\(752\) −6.89261 −0.251348
\(753\) 36.7381 1.33881
\(754\) 9.30359 0.338817
\(755\) 2.54953 0.0927869
\(756\) −7.19227 −0.261580
\(757\) 0.975598 0.0354587 0.0177294 0.999843i \(-0.494356\pi\)
0.0177294 + 0.999843i \(0.494356\pi\)
\(758\) −34.7353 −1.26164
\(759\) 10.1519 0.368489
\(760\) 15.2778 0.554184
\(761\) 24.0879 0.873187 0.436593 0.899659i \(-0.356185\pi\)
0.436593 + 0.899659i \(0.356185\pi\)
\(762\) 70.3196 2.54741
\(763\) −4.32582 −0.156605
\(764\) −22.2585 −0.805286
\(765\) −9.29364 −0.336012
\(766\) −35.1580 −1.27031
\(767\) 6.13548 0.221540
\(768\) −28.5278 −1.02941
\(769\) 15.0132 0.541391 0.270696 0.962665i \(-0.412746\pi\)
0.270696 + 0.962665i \(0.412746\pi\)
\(770\) −12.5962 −0.453935
\(771\) 71.4611 2.57361
\(772\) 37.2656 1.34122
\(773\) −10.0063 −0.359903 −0.179952 0.983675i \(-0.557594\pi\)
−0.179952 + 0.983675i \(0.557594\pi\)
\(774\) −7.75968 −0.278916
\(775\) 12.0245 0.431934
\(776\) −20.6916 −0.742786
\(777\) 17.5164 0.628396
\(778\) −70.4669 −2.52636
\(779\) −23.0169 −0.824665
\(780\) −25.7387 −0.921593
\(781\) −10.1166 −0.362001
\(782\) −9.00846 −0.322142
\(783\) −3.81400 −0.136301
\(784\) 1.88189 0.0672105
\(785\) −23.0413 −0.822381
\(786\) 73.4317 2.61922
\(787\) −20.6709 −0.736839 −0.368420 0.929660i \(-0.620101\pi\)
−0.368420 + 0.929660i \(0.620101\pi\)
\(788\) −17.8316 −0.635223
\(789\) 1.94511 0.0692476
\(790\) 38.7241 1.37774
\(791\) −1.56963 −0.0558095
\(792\) −8.33909 −0.296317
\(793\) −6.48136 −0.230160
\(794\) −53.0859 −1.88395
\(795\) −10.4335 −0.370038
\(796\) 34.5135 1.22330
\(797\) −8.22826 −0.291460 −0.145730 0.989324i \(-0.546553\pi\)
−0.145730 + 0.989324i \(0.546553\pi\)
\(798\) 27.7223 0.981358
\(799\) 9.90673 0.350475
\(800\) 14.6085 0.516489
\(801\) 43.0459 1.52095
\(802\) −5.54300 −0.195730
\(803\) −5.09905 −0.179942
\(804\) −27.5521 −0.971687
\(805\) 22.3605 0.788105
\(806\) −14.5248 −0.511614
\(807\) 35.3276 1.24359
\(808\) −5.50578 −0.193693
\(809\) 50.7744 1.78513 0.892567 0.450915i \(-0.148902\pi\)
0.892567 + 0.450915i \(0.148902\pi\)
\(810\) −45.3923 −1.59492
\(811\) −5.39691 −0.189511 −0.0947556 0.995501i \(-0.530207\pi\)
−0.0947556 + 0.995501i \(0.530207\pi\)
\(812\) 21.5323 0.755636
\(813\) 66.5585 2.33431
\(814\) 7.49997 0.262874
\(815\) 18.7375 0.656345
\(816\) −1.76625 −0.0618311
\(817\) 2.33904 0.0818326
\(818\) −40.7247 −1.42391
\(819\) −8.72517 −0.304882
\(820\) 81.6306 2.85067
\(821\) 4.24978 0.148318 0.0741591 0.997246i \(-0.476373\pi\)
0.0741591 + 0.997246i \(0.476373\pi\)
\(822\) 25.1262 0.876376
\(823\) 12.1155 0.422319 0.211160 0.977452i \(-0.432276\pi\)
0.211160 + 0.977452i \(0.432276\pi\)
\(824\) −36.0048 −1.25429
\(825\) 5.78635 0.201455
\(826\) 23.4368 0.815471
\(827\) 19.0989 0.664135 0.332068 0.943256i \(-0.392254\pi\)
0.332068 + 0.943256i \(0.392254\pi\)
\(828\) 42.3531 1.47187
\(829\) 27.1789 0.943963 0.471981 0.881609i \(-0.343539\pi\)
0.471981 + 0.881609i \(0.343539\pi\)
\(830\) 108.833 3.77767
\(831\) −39.4632 −1.36896
\(832\) −15.9453 −0.552805
\(833\) −2.70484 −0.0937171
\(834\) 111.277 3.85320
\(835\) 35.6911 1.23514
\(836\) 7.19176 0.248732
\(837\) 5.95442 0.205815
\(838\) −20.8218 −0.719277
\(839\) 26.7474 0.923424 0.461712 0.887030i \(-0.347235\pi\)
0.461712 + 0.887030i \(0.347235\pi\)
\(840\) −34.3647 −1.18569
\(841\) −17.5816 −0.606262
\(842\) −69.7763 −2.40465
\(843\) 54.4234 1.87444
\(844\) −50.3876 −1.73441
\(845\) 31.0440 1.06795
\(846\) −76.8731 −2.64295
\(847\) −2.07248 −0.0712111
\(848\) −1.05984 −0.0363950
\(849\) −17.3621 −0.595865
\(850\) −5.13465 −0.176117
\(851\) −13.3138 −0.456392
\(852\) −78.9645 −2.70528
\(853\) 25.5588 0.875118 0.437559 0.899190i \(-0.355843\pi\)
0.437559 + 0.899190i \(0.355843\pi\)
\(854\) −24.7580 −0.847202
\(855\) −21.7382 −0.743430
\(856\) 2.01507 0.0688738
\(857\) 22.8162 0.779386 0.389693 0.920945i \(-0.372581\pi\)
0.389693 + 0.920945i \(0.372581\pi\)
\(858\) −6.98950 −0.238618
\(859\) −38.4709 −1.31261 −0.656304 0.754496i \(-0.727881\pi\)
−0.656304 + 0.754496i \(0.727881\pi\)
\(860\) −8.29553 −0.282875
\(861\) 51.7723 1.76439
\(862\) −9.65834 −0.328964
\(863\) −32.5189 −1.10696 −0.553478 0.832864i \(-0.686700\pi\)
−0.553478 + 0.832864i \(0.686700\pi\)
\(864\) 7.23398 0.246105
\(865\) −19.3055 −0.656406
\(866\) 27.6449 0.939411
\(867\) 2.53862 0.0862162
\(868\) −33.6163 −1.14101
\(869\) 6.37136 0.216134
\(870\) −52.1375 −1.76763
\(871\) −4.31421 −0.146182
\(872\) −5.05309 −0.171119
\(873\) 29.4413 0.996436
\(874\) −21.0711 −0.712742
\(875\) −15.2129 −0.514289
\(876\) −39.8003 −1.34473
\(877\) 0.292773 0.00988623 0.00494312 0.999988i \(-0.498427\pi\)
0.00494312 + 0.999988i \(0.498427\pi\)
\(878\) −25.6006 −0.863978
\(879\) 61.7890 2.08409
\(880\) 1.87715 0.0632788
\(881\) 46.2265 1.55741 0.778706 0.627389i \(-0.215876\pi\)
0.778706 + 0.627389i \(0.215876\pi\)
\(882\) 20.9887 0.706726
\(883\) 1.37310 0.0462085 0.0231043 0.999733i \(-0.492645\pi\)
0.0231043 + 0.999733i \(0.492645\pi\)
\(884\) 3.75788 0.126391
\(885\) −34.3834 −1.15579
\(886\) −81.4008 −2.73471
\(887\) 16.0227 0.537990 0.268995 0.963142i \(-0.413308\pi\)
0.268995 + 0.963142i \(0.413308\pi\)
\(888\) 20.4613 0.686635
\(889\) 25.4838 0.854699
\(890\) 75.9523 2.54593
\(891\) −7.46849 −0.250204
\(892\) −16.9217 −0.566582
\(893\) 23.1722 0.775428
\(894\) −59.7147 −1.99716
\(895\) −32.7295 −1.09403
\(896\) −34.3437 −1.14734
\(897\) 12.4076 0.414279
\(898\) 27.3953 0.914192
\(899\) −17.8264 −0.594545
\(900\) 24.1404 0.804681
\(901\) 1.52330 0.0507486
\(902\) 22.1673 0.738091
\(903\) −5.26124 −0.175083
\(904\) −1.83352 −0.0609818
\(905\) −0.592317 −0.0196893
\(906\) 5.40401 0.179536
\(907\) 9.61190 0.319158 0.159579 0.987185i \(-0.448986\pi\)
0.159579 + 0.987185i \(0.448986\pi\)
\(908\) −38.9374 −1.29218
\(909\) 7.83395 0.259836
\(910\) −15.3951 −0.510343
\(911\) 29.8926 0.990385 0.495193 0.868783i \(-0.335097\pi\)
0.495193 + 0.868783i \(0.335097\pi\)
\(912\) −4.13132 −0.136802
\(913\) 17.9066 0.592622
\(914\) −29.7956 −0.985549
\(915\) 36.3217 1.20076
\(916\) 14.7403 0.487034
\(917\) 26.6116 0.878792
\(918\) −2.54262 −0.0839190
\(919\) −28.3193 −0.934166 −0.467083 0.884213i \(-0.654695\pi\)
−0.467083 + 0.884213i \(0.654695\pi\)
\(920\) 26.1199 0.861146
\(921\) −12.4037 −0.408717
\(922\) −41.4163 −1.36397
\(923\) −12.3646 −0.406985
\(924\) −16.1766 −0.532170
\(925\) −7.58861 −0.249512
\(926\) 49.7071 1.63348
\(927\) 51.2297 1.68261
\(928\) −21.6572 −0.710932
\(929\) −4.37703 −0.143606 −0.0718029 0.997419i \(-0.522875\pi\)
−0.0718029 + 0.997419i \(0.522875\pi\)
\(930\) 81.3972 2.66912
\(931\) −6.32672 −0.207350
\(932\) 10.0628 0.329616
\(933\) 21.0215 0.688214
\(934\) −22.0199 −0.720514
\(935\) −2.69802 −0.0882348
\(936\) −10.1921 −0.333138
\(937\) −17.3124 −0.565570 −0.282785 0.959183i \(-0.591258\pi\)
−0.282785 + 0.959183i \(0.591258\pi\)
\(938\) −16.4798 −0.538084
\(939\) 45.9166 1.49843
\(940\) −82.1815 −2.68047
\(941\) 35.1224 1.14496 0.572479 0.819920i \(-0.305982\pi\)
0.572479 + 0.819920i \(0.305982\pi\)
\(942\) −48.8387 −1.59125
\(943\) −39.3510 −1.28145
\(944\) −3.49268 −0.113677
\(945\) 6.31122 0.205304
\(946\) −2.25270 −0.0732417
\(947\) 41.0402 1.33363 0.666813 0.745225i \(-0.267658\pi\)
0.666813 + 0.745225i \(0.267658\pi\)
\(948\) 49.7312 1.61519
\(949\) −6.23209 −0.202302
\(950\) −12.0101 −0.389660
\(951\) 16.7836 0.544245
\(952\) 5.01728 0.162611
\(953\) 34.0470 1.10289 0.551445 0.834211i \(-0.314077\pi\)
0.551445 + 0.834211i \(0.314077\pi\)
\(954\) −11.8203 −0.382698
\(955\) 19.5319 0.632037
\(956\) 79.4239 2.56875
\(957\) −8.57829 −0.277297
\(958\) −75.1392 −2.42764
\(959\) 9.10571 0.294039
\(960\) 89.3581 2.88402
\(961\) −3.16933 −0.102236
\(962\) 9.16650 0.295540
\(963\) −2.86716 −0.0923931
\(964\) −26.7867 −0.862741
\(965\) −32.7005 −1.05267
\(966\) 47.3957 1.52493
\(967\) 16.8578 0.542110 0.271055 0.962564i \(-0.412628\pi\)
0.271055 + 0.962564i \(0.412628\pi\)
\(968\) −2.42091 −0.0778109
\(969\) 5.93794 0.190754
\(970\) 51.9477 1.66794
\(971\) 24.9096 0.799387 0.399694 0.916649i \(-0.369117\pi\)
0.399694 + 0.916649i \(0.369117\pi\)
\(972\) −68.7059 −2.20374
\(973\) 40.3267 1.29281
\(974\) −63.6318 −2.03889
\(975\) 7.07211 0.226489
\(976\) 3.68957 0.118100
\(977\) −38.2055 −1.22230 −0.611150 0.791515i \(-0.709293\pi\)
−0.611150 + 0.791515i \(0.709293\pi\)
\(978\) 39.7162 1.26998
\(979\) 12.4966 0.399393
\(980\) 22.4381 0.716758
\(981\) 7.18984 0.229554
\(982\) −49.7675 −1.58814
\(983\) −20.6473 −0.658547 −0.329273 0.944235i \(-0.606804\pi\)
−0.329273 + 0.944235i \(0.606804\pi\)
\(984\) 60.4764 1.92792
\(985\) 15.6472 0.498561
\(986\) 7.61213 0.242420
\(987\) −52.1217 −1.65905
\(988\) 8.78981 0.279641
\(989\) 3.99896 0.127159
\(990\) 20.9358 0.665383
\(991\) −10.5298 −0.334490 −0.167245 0.985915i \(-0.553487\pi\)
−0.167245 + 0.985915i \(0.553487\pi\)
\(992\) 33.8113 1.07351
\(993\) −74.9785 −2.37937
\(994\) −47.2312 −1.49808
\(995\) −30.2856 −0.960118
\(996\) 139.769 4.42874
\(997\) −19.6324 −0.621766 −0.310883 0.950448i \(-0.600625\pi\)
−0.310883 + 0.950448i \(0.600625\pi\)
\(998\) −66.1472 −2.09385
\(999\) −3.75780 −0.118892
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 \(a_p\))