Properties

Label 4009.2.a.c.1.15
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.98460 q^{2}\) \(+0.183292 q^{3}\) \(+1.93862 q^{4}\) \(-1.97615 q^{5}\) \(-0.363761 q^{6}\) \(-5.05020 q^{7}\) \(+0.121816 q^{8}\) \(-2.96640 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.98460 q^{2}\) \(+0.183292 q^{3}\) \(+1.93862 q^{4}\) \(-1.97615 q^{5}\) \(-0.363761 q^{6}\) \(-5.05020 q^{7}\) \(+0.121816 q^{8}\) \(-2.96640 q^{9}\) \(+3.92186 q^{10}\) \(-1.03522 q^{11}\) \(+0.355334 q^{12}\) \(-2.23925 q^{13}\) \(+10.0226 q^{14}\) \(-0.362212 q^{15}\) \(-4.11899 q^{16}\) \(+3.42668 q^{17}\) \(+5.88711 q^{18}\) \(+1.00000 q^{19}\) \(-3.83100 q^{20}\) \(-0.925661 q^{21}\) \(+2.05449 q^{22}\) \(+7.05983 q^{23}\) \(+0.0223278 q^{24}\) \(-1.09484 q^{25}\) \(+4.44401 q^{26}\) \(-1.09359 q^{27}\) \(-9.79041 q^{28}\) \(-5.16420 q^{29}\) \(+0.718845 q^{30}\) \(+10.3264 q^{31}\) \(+7.93090 q^{32}\) \(-0.189747 q^{33}\) \(-6.80058 q^{34}\) \(+9.97994 q^{35}\) \(-5.75073 q^{36}\) \(+1.06923 q^{37}\) \(-1.98460 q^{38}\) \(-0.410437 q^{39}\) \(-0.240726 q^{40}\) \(+2.33345 q^{41}\) \(+1.83706 q^{42}\) \(-7.22791 q^{43}\) \(-2.00689 q^{44}\) \(+5.86206 q^{45}\) \(-14.0109 q^{46}\) \(+6.90994 q^{47}\) \(-0.754979 q^{48}\) \(+18.5045 q^{49}\) \(+2.17281 q^{50}\) \(+0.628083 q^{51}\) \(-4.34106 q^{52}\) \(+3.02299 q^{53}\) \(+2.17034 q^{54}\) \(+2.04574 q^{55}\) \(-0.615193 q^{56}\) \(+0.183292 q^{57}\) \(+10.2489 q^{58}\) \(+11.7704 q^{59}\) \(-0.702192 q^{60}\) \(-5.86379 q^{61}\) \(-20.4937 q^{62}\) \(+14.9809 q^{63}\) \(-7.50165 q^{64}\) \(+4.42510 q^{65}\) \(+0.376571 q^{66}\) \(+9.91409 q^{67}\) \(+6.64303 q^{68}\) \(+1.29401 q^{69}\) \(-19.8061 q^{70}\) \(+0.176957 q^{71}\) \(-0.361354 q^{72}\) \(-14.5355 q^{73}\) \(-2.12198 q^{74}\) \(-0.200675 q^{75}\) \(+1.93862 q^{76}\) \(+5.22805 q^{77}\) \(+0.814552 q^{78}\) \(+4.79730 q^{79}\) \(+8.13974 q^{80}\) \(+8.69876 q^{81}\) \(-4.63094 q^{82}\) \(-10.0806 q^{83}\) \(-1.79450 q^{84}\) \(-6.77163 q^{85}\) \(+14.3445 q^{86}\) \(-0.946557 q^{87}\) \(-0.126106 q^{88}\) \(-12.1286 q^{89}\) \(-11.6338 q^{90}\) \(+11.3087 q^{91}\) \(+13.6863 q^{92}\) \(+1.89274 q^{93}\) \(-13.7134 q^{94}\) \(-1.97615 q^{95}\) \(+1.45367 q^{96}\) \(+9.93537 q^{97}\) \(-36.7239 q^{98}\) \(+3.07087 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98460 −1.40332 −0.701660 0.712511i \(-0.747558\pi\)
−0.701660 + 0.712511i \(0.747558\pi\)
\(3\) 0.183292 0.105824 0.0529119 0.998599i \(-0.483150\pi\)
0.0529119 + 0.998599i \(0.483150\pi\)
\(4\) 1.93862 0.969310
\(5\) −1.97615 −0.883761 −0.441880 0.897074i \(-0.645688\pi\)
−0.441880 + 0.897074i \(0.645688\pi\)
\(6\) −0.363761 −0.148505
\(7\) −5.05020 −1.90880 −0.954398 0.298538i \(-0.903501\pi\)
−0.954398 + 0.298538i \(0.903501\pi\)
\(8\) 0.121816 0.0430683
\(9\) −2.96640 −0.988801
\(10\) 3.92186 1.24020
\(11\) −1.03522 −0.312129 −0.156065 0.987747i \(-0.549881\pi\)
−0.156065 + 0.987747i \(0.549881\pi\)
\(12\) 0.355334 0.102576
\(13\) −2.23925 −0.621057 −0.310528 0.950564i \(-0.600506\pi\)
−0.310528 + 0.950564i \(0.600506\pi\)
\(14\) 10.0226 2.67865
\(15\) −0.362212 −0.0935228
\(16\) −4.11899 −1.02975
\(17\) 3.42668 0.831092 0.415546 0.909572i \(-0.363590\pi\)
0.415546 + 0.909572i \(0.363590\pi\)
\(18\) 5.88711 1.38761
\(19\) 1.00000 0.229416
\(20\) −3.83100 −0.856638
\(21\) −0.925661 −0.201996
\(22\) 2.05449 0.438018
\(23\) 7.05983 1.47208 0.736038 0.676941i \(-0.236695\pi\)
0.736038 + 0.676941i \(0.236695\pi\)
\(24\) 0.0223278 0.00455765
\(25\) −1.09484 −0.218967
\(26\) 4.44401 0.871542
\(27\) −1.09359 −0.210462
\(28\) −9.79041 −1.85021
\(29\) −5.16420 −0.958968 −0.479484 0.877551i \(-0.659176\pi\)
−0.479484 + 0.877551i \(0.659176\pi\)
\(30\) 0.718845 0.131243
\(31\) 10.3264 1.85467 0.927336 0.374229i \(-0.122093\pi\)
0.927336 + 0.374229i \(0.122093\pi\)
\(32\) 7.93090 1.40200
\(33\) −0.189747 −0.0330307
\(34\) −6.80058 −1.16629
\(35\) 9.97994 1.68692
\(36\) −5.75073 −0.958455
\(37\) 1.06923 0.175780 0.0878898 0.996130i \(-0.471988\pi\)
0.0878898 + 0.996130i \(0.471988\pi\)
\(38\) −1.98460 −0.321944
\(39\) −0.410437 −0.0657226
\(40\) −0.240726 −0.0380621
\(41\) 2.33345 0.364423 0.182211 0.983259i \(-0.441674\pi\)
0.182211 + 0.983259i \(0.441674\pi\)
\(42\) 1.83706 0.283465
\(43\) −7.22791 −1.10225 −0.551123 0.834424i \(-0.685801\pi\)
−0.551123 + 0.834424i \(0.685801\pi\)
\(44\) −2.00689 −0.302550
\(45\) 5.86206 0.873864
\(46\) −14.0109 −2.06579
\(47\) 6.90994 1.00792 0.503959 0.863728i \(-0.331876\pi\)
0.503959 + 0.863728i \(0.331876\pi\)
\(48\) −0.754979 −0.108972
\(49\) 18.5045 2.64350
\(50\) 2.17281 0.307281
\(51\) 0.628083 0.0879493
\(52\) −4.34106 −0.601997
\(53\) 3.02299 0.415239 0.207620 0.978210i \(-0.433428\pi\)
0.207620 + 0.978210i \(0.433428\pi\)
\(54\) 2.17034 0.295346
\(55\) 2.04574 0.275848
\(56\) −0.615193 −0.0822087
\(57\) 0.183292 0.0242776
\(58\) 10.2489 1.34574
\(59\) 11.7704 1.53237 0.766186 0.642618i \(-0.222152\pi\)
0.766186 + 0.642618i \(0.222152\pi\)
\(60\) −0.702192 −0.0906526
\(61\) −5.86379 −0.750782 −0.375391 0.926867i \(-0.622491\pi\)
−0.375391 + 0.926867i \(0.622491\pi\)
\(62\) −20.4937 −2.60270
\(63\) 14.9809 1.88742
\(64\) −7.50165 −0.937706
\(65\) 4.42510 0.548866
\(66\) 0.376571 0.0463527
\(67\) 9.91409 1.21120 0.605599 0.795770i \(-0.292933\pi\)
0.605599 + 0.795770i \(0.292933\pi\)
\(68\) 6.64303 0.805586
\(69\) 1.29401 0.155780
\(70\) −19.8061 −2.36729
\(71\) 0.176957 0.0210009 0.0105005 0.999945i \(-0.496658\pi\)
0.0105005 + 0.999945i \(0.496658\pi\)
\(72\) −0.361354 −0.0425860
\(73\) −14.5355 −1.70125 −0.850624 0.525774i \(-0.823776\pi\)
−0.850624 + 0.525774i \(0.823776\pi\)
\(74\) −2.12198 −0.246675
\(75\) −0.200675 −0.0231719
\(76\) 1.93862 0.222375
\(77\) 5.22805 0.595791
\(78\) 0.814552 0.0922298
\(79\) 4.79730 0.539738 0.269869 0.962897i \(-0.413020\pi\)
0.269869 + 0.962897i \(0.413020\pi\)
\(80\) 8.13974 0.910051
\(81\) 8.69876 0.966529
\(82\) −4.63094 −0.511402
\(83\) −10.0806 −1.10649 −0.553244 0.833019i \(-0.686610\pi\)
−0.553244 + 0.833019i \(0.686610\pi\)
\(84\) −1.79450 −0.195797
\(85\) −6.77163 −0.734486
\(86\) 14.3445 1.54681
\(87\) −0.946557 −0.101482
\(88\) −0.126106 −0.0134429
\(89\) −12.1286 −1.28563 −0.642816 0.766021i \(-0.722234\pi\)
−0.642816 + 0.766021i \(0.722234\pi\)
\(90\) −11.6338 −1.22631
\(91\) 11.3087 1.18547
\(92\) 13.6863 1.42690
\(93\) 1.89274 0.196268
\(94\) −13.7134 −1.41443
\(95\) −1.97615 −0.202749
\(96\) 1.45367 0.148365
\(97\) 9.93537 1.00878 0.504392 0.863475i \(-0.331717\pi\)
0.504392 + 0.863475i \(0.331717\pi\)
\(98\) −36.7239 −3.70968
\(99\) 3.07087 0.308634
\(100\) −2.12247 −0.212247
\(101\) −11.0117 −1.09571 −0.547853 0.836574i \(-0.684555\pi\)
−0.547853 + 0.836574i \(0.684555\pi\)
\(102\) −1.24649 −0.123421
\(103\) −11.5944 −1.14243 −0.571213 0.820802i \(-0.693527\pi\)
−0.571213 + 0.820802i \(0.693527\pi\)
\(104\) −0.272776 −0.0267479
\(105\) 1.82924 0.178516
\(106\) −5.99941 −0.582714
\(107\) 1.18854 0.114901 0.0574504 0.998348i \(-0.481703\pi\)
0.0574504 + 0.998348i \(0.481703\pi\)
\(108\) −2.12006 −0.204003
\(109\) 9.18440 0.879706 0.439853 0.898070i \(-0.355031\pi\)
0.439853 + 0.898070i \(0.355031\pi\)
\(110\) −4.05997 −0.387103
\(111\) 0.195980 0.0186016
\(112\) 20.8017 1.96558
\(113\) 7.83531 0.737084 0.368542 0.929611i \(-0.379857\pi\)
0.368542 + 0.929611i \(0.379857\pi\)
\(114\) −0.363761 −0.0340693
\(115\) −13.9513 −1.30096
\(116\) −10.0114 −0.929537
\(117\) 6.64253 0.614102
\(118\) −23.3594 −2.15041
\(119\) −17.3054 −1.58638
\(120\) −0.0441231 −0.00402787
\(121\) −9.92833 −0.902575
\(122\) 11.6373 1.05359
\(123\) 0.427702 0.0385646
\(124\) 20.0189 1.79775
\(125\) 12.0443 1.07728
\(126\) −29.7311 −2.64866
\(127\) 18.8489 1.67257 0.836285 0.548295i \(-0.184723\pi\)
0.836285 + 0.548295i \(0.184723\pi\)
\(128\) −0.974066 −0.0860961
\(129\) −1.32482 −0.116644
\(130\) −8.78203 −0.770235
\(131\) −9.09180 −0.794354 −0.397177 0.917742i \(-0.630010\pi\)
−0.397177 + 0.917742i \(0.630010\pi\)
\(132\) −0.367847 −0.0320170
\(133\) −5.05020 −0.437908
\(134\) −19.6755 −1.69970
\(135\) 2.16111 0.185998
\(136\) 0.417423 0.0357938
\(137\) −15.3139 −1.30835 −0.654177 0.756341i \(-0.726985\pi\)
−0.654177 + 0.756341i \(0.726985\pi\)
\(138\) −2.56809 −0.218610
\(139\) −7.61332 −0.645754 −0.322877 0.946441i \(-0.604650\pi\)
−0.322877 + 0.946441i \(0.604650\pi\)
\(140\) 19.3473 1.63515
\(141\) 1.26654 0.106662
\(142\) −0.351188 −0.0294710
\(143\) 2.31811 0.193850
\(144\) 12.2186 1.01822
\(145\) 10.2052 0.847498
\(146\) 28.8470 2.38740
\(147\) 3.39173 0.279745
\(148\) 2.07282 0.170385
\(149\) −13.2673 −1.08690 −0.543450 0.839442i \(-0.682882\pi\)
−0.543450 + 0.839442i \(0.682882\pi\)
\(150\) 0.398258 0.0325177
\(151\) 1.85102 0.150634 0.0753170 0.997160i \(-0.476003\pi\)
0.0753170 + 0.997160i \(0.476003\pi\)
\(152\) 0.121816 0.00988056
\(153\) −10.1649 −0.821785
\(154\) −10.3756 −0.836086
\(155\) −20.4065 −1.63909
\(156\) −0.795682 −0.0637055
\(157\) 3.98604 0.318121 0.159060 0.987269i \(-0.449154\pi\)
0.159060 + 0.987269i \(0.449154\pi\)
\(158\) −9.52069 −0.757426
\(159\) 0.554090 0.0439422
\(160\) −15.6726 −1.23903
\(161\) −35.6535 −2.80989
\(162\) −17.2635 −1.35635
\(163\) 23.1003 1.80935 0.904677 0.426098i \(-0.140112\pi\)
0.904677 + 0.426098i \(0.140112\pi\)
\(164\) 4.52366 0.353239
\(165\) 0.374968 0.0291912
\(166\) 20.0059 1.55276
\(167\) −17.6818 −1.36826 −0.684131 0.729359i \(-0.739818\pi\)
−0.684131 + 0.729359i \(0.739818\pi\)
\(168\) −0.112760 −0.00869963
\(169\) −7.98575 −0.614288
\(170\) 13.4389 1.03072
\(171\) −2.96640 −0.226847
\(172\) −14.0122 −1.06842
\(173\) 19.8141 1.50644 0.753219 0.657770i \(-0.228500\pi\)
0.753219 + 0.657770i \(0.228500\pi\)
\(174\) 1.87853 0.142411
\(175\) 5.52914 0.417964
\(176\) 4.26405 0.321415
\(177\) 2.15742 0.162161
\(178\) 24.0704 1.80415
\(179\) 6.83531 0.510895 0.255448 0.966823i \(-0.417777\pi\)
0.255448 + 0.966823i \(0.417777\pi\)
\(180\) 11.3643 0.847044
\(181\) 8.72166 0.648276 0.324138 0.946010i \(-0.394926\pi\)
0.324138 + 0.946010i \(0.394926\pi\)
\(182\) −22.4431 −1.66360
\(183\) −1.07479 −0.0794505
\(184\) 0.859997 0.0633998
\(185\) −2.11295 −0.155347
\(186\) −3.75633 −0.275427
\(187\) −3.54735 −0.259408
\(188\) 13.3957 0.976985
\(189\) 5.52287 0.401730
\(190\) 3.92186 0.284521
\(191\) −13.2377 −0.957849 −0.478925 0.877856i \(-0.658973\pi\)
−0.478925 + 0.877856i \(0.658973\pi\)
\(192\) −1.37499 −0.0992316
\(193\) −20.2723 −1.45923 −0.729615 0.683858i \(-0.760301\pi\)
−0.729615 + 0.683858i \(0.760301\pi\)
\(194\) −19.7177 −1.41565
\(195\) 0.811085 0.0580830
\(196\) 35.8732 2.56237
\(197\) −18.2537 −1.30052 −0.650261 0.759711i \(-0.725341\pi\)
−0.650261 + 0.759711i \(0.725341\pi\)
\(198\) −6.09443 −0.433112
\(199\) 7.52021 0.533094 0.266547 0.963822i \(-0.414117\pi\)
0.266547 + 0.963822i \(0.414117\pi\)
\(200\) −0.133368 −0.00943056
\(201\) 1.81717 0.128174
\(202\) 21.8538 1.53763
\(203\) 26.0802 1.83047
\(204\) 1.21761 0.0852501
\(205\) −4.61123 −0.322063
\(206\) 23.0101 1.60319
\(207\) −20.9423 −1.45559
\(208\) 9.22347 0.639532
\(209\) −1.03522 −0.0716074
\(210\) −3.63031 −0.250515
\(211\) 1.00000 0.0688428
\(212\) 5.86042 0.402496
\(213\) 0.0324348 0.00222239
\(214\) −2.35878 −0.161243
\(215\) 14.2834 0.974122
\(216\) −0.133217 −0.00906427
\(217\) −52.1503 −3.54019
\(218\) −18.2273 −1.23451
\(219\) −2.66424 −0.180032
\(220\) 3.96591 0.267382
\(221\) −7.67320 −0.516156
\(222\) −0.388942 −0.0261041
\(223\) −27.0957 −1.81446 −0.907232 0.420631i \(-0.861809\pi\)
−0.907232 + 0.420631i \(0.861809\pi\)
\(224\) −40.0526 −2.67613
\(225\) 3.24773 0.216515
\(226\) −15.5499 −1.03437
\(227\) −6.51376 −0.432334 −0.216167 0.976356i \(-0.569356\pi\)
−0.216167 + 0.976356i \(0.569356\pi\)
\(228\) 0.355334 0.0235325
\(229\) 18.8408 1.24503 0.622516 0.782607i \(-0.286110\pi\)
0.622516 + 0.782607i \(0.286110\pi\)
\(230\) 27.6876 1.82567
\(231\) 0.958259 0.0630488
\(232\) −0.629081 −0.0413012
\(233\) 20.4575 1.34022 0.670108 0.742264i \(-0.266248\pi\)
0.670108 + 0.742264i \(0.266248\pi\)
\(234\) −13.1827 −0.861782
\(235\) −13.6551 −0.890758
\(236\) 22.8183 1.48534
\(237\) 0.879306 0.0571171
\(238\) 34.3443 2.22621
\(239\) −10.6829 −0.691021 −0.345511 0.938415i \(-0.612294\pi\)
−0.345511 + 0.938415i \(0.612294\pi\)
\(240\) 1.49195 0.0963050
\(241\) 26.1855 1.68676 0.843378 0.537321i \(-0.180564\pi\)
0.843378 + 0.537321i \(0.180564\pi\)
\(242\) 19.7037 1.26660
\(243\) 4.87520 0.312744
\(244\) −11.3677 −0.727740
\(245\) −36.5676 −2.33622
\(246\) −0.848815 −0.0541185
\(247\) −2.23925 −0.142480
\(248\) 1.25791 0.0798777
\(249\) −1.84769 −0.117093
\(250\) −23.9031 −1.51176
\(251\) 18.0663 1.14034 0.570168 0.821528i \(-0.306878\pi\)
0.570168 + 0.821528i \(0.306878\pi\)
\(252\) 29.0423 1.82949
\(253\) −7.30844 −0.459478
\(254\) −37.4075 −2.34715
\(255\) −1.24119 −0.0777261
\(256\) 16.9364 1.05853
\(257\) 28.4095 1.77213 0.886067 0.463558i \(-0.153427\pi\)
0.886067 + 0.463558i \(0.153427\pi\)
\(258\) 2.62923 0.163689
\(259\) −5.39980 −0.335527
\(260\) 8.57858 0.532021
\(261\) 15.3191 0.948229
\(262\) 18.0435 1.11473
\(263\) 7.70050 0.474833 0.237417 0.971408i \(-0.423699\pi\)
0.237417 + 0.971408i \(0.423699\pi\)
\(264\) −0.0231141 −0.00142258
\(265\) −5.97387 −0.366972
\(266\) 10.0226 0.614525
\(267\) −2.22308 −0.136050
\(268\) 19.2196 1.17403
\(269\) 22.9625 1.40005 0.700024 0.714119i \(-0.253173\pi\)
0.700024 + 0.714119i \(0.253173\pi\)
\(270\) −4.28892 −0.261015
\(271\) −6.78298 −0.412037 −0.206018 0.978548i \(-0.566051\pi\)
−0.206018 + 0.978548i \(0.566051\pi\)
\(272\) −14.1145 −0.855816
\(273\) 2.07279 0.125451
\(274\) 30.3919 1.83604
\(275\) 1.13339 0.0683461
\(276\) 2.50859 0.151000
\(277\) −3.03104 −0.182117 −0.0910587 0.995846i \(-0.529025\pi\)
−0.0910587 + 0.995846i \(0.529025\pi\)
\(278\) 15.1094 0.906200
\(279\) −30.6322 −1.83390
\(280\) 1.21571 0.0726528
\(281\) −19.1035 −1.13962 −0.569809 0.821777i \(-0.692983\pi\)
−0.569809 + 0.821777i \(0.692983\pi\)
\(282\) −2.51356 −0.149681
\(283\) 14.9169 0.886720 0.443360 0.896344i \(-0.353786\pi\)
0.443360 + 0.896344i \(0.353786\pi\)
\(284\) 0.343052 0.0203564
\(285\) −0.362212 −0.0214556
\(286\) −4.60051 −0.272034
\(287\) −11.7844 −0.695609
\(288\) −23.5263 −1.38630
\(289\) −5.25786 −0.309286
\(290\) −20.2533 −1.18931
\(291\) 1.82108 0.106753
\(292\) −28.1787 −1.64904
\(293\) 17.1529 1.00208 0.501041 0.865423i \(-0.332951\pi\)
0.501041 + 0.865423i \(0.332951\pi\)
\(294\) −6.73121 −0.392572
\(295\) −23.2600 −1.35425
\(296\) 0.130248 0.00757053
\(297\) 1.13211 0.0656915
\(298\) 26.3302 1.52527
\(299\) −15.8087 −0.914243
\(300\) −0.389032 −0.0224608
\(301\) 36.5024 2.10396
\(302\) −3.67353 −0.211388
\(303\) −2.01836 −0.115952
\(304\) −4.11899 −0.236240
\(305\) 11.5877 0.663511
\(306\) 20.1733 1.15323
\(307\) 34.0875 1.94548 0.972738 0.231907i \(-0.0744965\pi\)
0.972738 + 0.231907i \(0.0744965\pi\)
\(308\) 10.1352 0.577506
\(309\) −2.12515 −0.120896
\(310\) 40.4986 2.30016
\(311\) −19.7790 −1.12157 −0.560783 0.827963i \(-0.689500\pi\)
−0.560783 + 0.827963i \(0.689500\pi\)
\(312\) −0.0499977 −0.00283056
\(313\) −10.8051 −0.610740 −0.305370 0.952234i \(-0.598780\pi\)
−0.305370 + 0.952234i \(0.598780\pi\)
\(314\) −7.91068 −0.446425
\(315\) −29.6045 −1.66803
\(316\) 9.30013 0.523173
\(317\) 2.47587 0.139058 0.0695292 0.997580i \(-0.477850\pi\)
0.0695292 + 0.997580i \(0.477850\pi\)
\(318\) −1.09964 −0.0616650
\(319\) 5.34606 0.299322
\(320\) 14.8244 0.828708
\(321\) 0.217851 0.0121592
\(322\) 70.7578 3.94318
\(323\) 3.42668 0.190666
\(324\) 16.8636 0.936866
\(325\) 2.45162 0.135991
\(326\) −45.8447 −2.53910
\(327\) 1.68343 0.0930938
\(328\) 0.284250 0.0156951
\(329\) −34.8966 −1.92391
\(330\) −0.744160 −0.0409647
\(331\) 18.0143 0.990154 0.495077 0.868849i \(-0.335140\pi\)
0.495077 + 0.868849i \(0.335140\pi\)
\(332\) −19.5424 −1.07253
\(333\) −3.17175 −0.173811
\(334\) 35.0913 1.92011
\(335\) −19.5917 −1.07041
\(336\) 3.81279 0.208005
\(337\) 17.9903 0.979995 0.489997 0.871724i \(-0.336998\pi\)
0.489997 + 0.871724i \(0.336998\pi\)
\(338\) 15.8485 0.862044
\(339\) 1.43615 0.0780010
\(340\) −13.1276 −0.711945
\(341\) −10.6900 −0.578898
\(342\) 5.88711 0.318339
\(343\) −58.1000 −3.13710
\(344\) −0.880473 −0.0474719
\(345\) −2.55716 −0.137673
\(346\) −39.3230 −2.11402
\(347\) 0.0527141 0.00282984 0.00141492 0.999999i \(-0.499550\pi\)
0.00141492 + 0.999999i \(0.499550\pi\)
\(348\) −1.83501 −0.0983671
\(349\) −34.1048 −1.82559 −0.912795 0.408418i \(-0.866081\pi\)
−0.912795 + 0.408418i \(0.866081\pi\)
\(350\) −10.9731 −0.586537
\(351\) 2.44883 0.130709
\(352\) −8.21020 −0.437605
\(353\) 20.0799 1.06875 0.534373 0.845249i \(-0.320548\pi\)
0.534373 + 0.845249i \(0.320548\pi\)
\(354\) −4.28160 −0.227564
\(355\) −0.349693 −0.0185598
\(356\) −23.5128 −1.24618
\(357\) −3.17195 −0.167877
\(358\) −13.5653 −0.716950
\(359\) 6.82176 0.360039 0.180019 0.983663i \(-0.442384\pi\)
0.180019 + 0.983663i \(0.442384\pi\)
\(360\) 0.714090 0.0376359
\(361\) 1.00000 0.0526316
\(362\) −17.3090 −0.909739
\(363\) −1.81978 −0.0955139
\(364\) 21.9232 1.14909
\(365\) 28.7242 1.50350
\(366\) 2.13302 0.111495
\(367\) −31.0974 −1.62327 −0.811634 0.584166i \(-0.801422\pi\)
−0.811634 + 0.584166i \(0.801422\pi\)
\(368\) −29.0794 −1.51587
\(369\) −6.92194 −0.360342
\(370\) 4.19335 0.218002
\(371\) −15.2667 −0.792607
\(372\) 3.66931 0.190245
\(373\) −5.72994 −0.296685 −0.148342 0.988936i \(-0.547394\pi\)
−0.148342 + 0.988936i \(0.547394\pi\)
\(374\) 7.04006 0.364033
\(375\) 2.20763 0.114001
\(376\) 0.841739 0.0434094
\(377\) 11.5640 0.595574
\(378\) −10.9607 −0.563756
\(379\) −19.2301 −0.987784 −0.493892 0.869523i \(-0.664426\pi\)
−0.493892 + 0.869523i \(0.664426\pi\)
\(380\) −3.83100 −0.196526
\(381\) 3.45486 0.176998
\(382\) 26.2716 1.34417
\(383\) −18.8960 −0.965540 −0.482770 0.875747i \(-0.660369\pi\)
−0.482770 + 0.875747i \(0.660369\pi\)
\(384\) −0.178539 −0.00911101
\(385\) −10.3314 −0.526537
\(386\) 40.2323 2.04777
\(387\) 21.4409 1.08990
\(388\) 19.2609 0.977824
\(389\) −23.6568 −1.19945 −0.599725 0.800207i \(-0.704723\pi\)
−0.599725 + 0.800207i \(0.704723\pi\)
\(390\) −1.60968 −0.0815091
\(391\) 24.1918 1.22343
\(392\) 2.25414 0.113851
\(393\) −1.66645 −0.0840615
\(394\) 36.2262 1.82505
\(395\) −9.48017 −0.476999
\(396\) 5.95325 0.299162
\(397\) −14.5261 −0.729046 −0.364523 0.931194i \(-0.618768\pi\)
−0.364523 + 0.931194i \(0.618768\pi\)
\(398\) −14.9246 −0.748102
\(399\) −0.925661 −0.0463410
\(400\) 4.50963 0.225481
\(401\) 0.0826359 0.00412664 0.00206332 0.999998i \(-0.499343\pi\)
0.00206332 + 0.999998i \(0.499343\pi\)
\(402\) −3.60635 −0.179869
\(403\) −23.1234 −1.15186
\(404\) −21.3475 −1.06208
\(405\) −17.1901 −0.854181
\(406\) −51.7587 −2.56874
\(407\) −1.10688 −0.0548660
\(408\) 0.0765104 0.00378783
\(409\) −10.6563 −0.526922 −0.263461 0.964670i \(-0.584864\pi\)
−0.263461 + 0.964670i \(0.584864\pi\)
\(410\) 9.15144 0.451957
\(411\) −2.80692 −0.138455
\(412\) −22.4771 −1.10736
\(413\) −59.4427 −2.92499
\(414\) 41.5620 2.04266
\(415\) 19.9207 0.977871
\(416\) −17.7593 −0.870721
\(417\) −1.39546 −0.0683361
\(418\) 2.05449 0.100488
\(419\) −40.4095 −1.97413 −0.987065 0.160318i \(-0.948748\pi\)
−0.987065 + 0.160318i \(0.948748\pi\)
\(420\) 3.54621 0.173037
\(421\) 23.6456 1.15241 0.576207 0.817303i \(-0.304532\pi\)
0.576207 + 0.817303i \(0.304532\pi\)
\(422\) −1.98460 −0.0966086
\(423\) −20.4977 −0.996631
\(424\) 0.368247 0.0178837
\(425\) −3.75166 −0.181982
\(426\) −0.0643699 −0.00311873
\(427\) 29.6133 1.43309
\(428\) 2.30413 0.111374
\(429\) 0.424891 0.0205139
\(430\) −28.3468 −1.36701
\(431\) −17.4242 −0.839293 −0.419647 0.907688i \(-0.637846\pi\)
−0.419647 + 0.907688i \(0.637846\pi\)
\(432\) 4.50451 0.216723
\(433\) 38.9863 1.87356 0.936781 0.349917i \(-0.113790\pi\)
0.936781 + 0.349917i \(0.113790\pi\)
\(434\) 103.497 4.96802
\(435\) 1.87054 0.0896854
\(436\) 17.8051 0.852708
\(437\) 7.05983 0.337717
\(438\) 5.28743 0.252643
\(439\) 13.4354 0.641237 0.320619 0.947208i \(-0.396109\pi\)
0.320619 + 0.947208i \(0.396109\pi\)
\(440\) 0.249203 0.0118803
\(441\) −54.8918 −2.61390
\(442\) 15.2282 0.724332
\(443\) 9.51570 0.452104 0.226052 0.974115i \(-0.427418\pi\)
0.226052 + 0.974115i \(0.427418\pi\)
\(444\) 0.379932 0.0180308
\(445\) 23.9680 1.13619
\(446\) 53.7740 2.54627
\(447\) −2.43179 −0.115020
\(448\) 37.8848 1.78989
\(449\) −24.5849 −1.16024 −0.580118 0.814533i \(-0.696993\pi\)
−0.580118 + 0.814533i \(0.696993\pi\)
\(450\) −6.44543 −0.303840
\(451\) −2.41562 −0.113747
\(452\) 15.1897 0.714463
\(453\) 0.339277 0.0159406
\(454\) 12.9272 0.606703
\(455\) −22.3476 −1.04767
\(456\) 0.0223278 0.00104560
\(457\) 22.8354 1.06820 0.534099 0.845422i \(-0.320651\pi\)
0.534099 + 0.845422i \(0.320651\pi\)
\(458\) −37.3913 −1.74718
\(459\) −3.74740 −0.174914
\(460\) −27.0462 −1.26104
\(461\) −5.50773 −0.256521 −0.128260 0.991741i \(-0.540939\pi\)
−0.128260 + 0.991741i \(0.540939\pi\)
\(462\) −1.90176 −0.0884777
\(463\) −23.4931 −1.09182 −0.545908 0.837845i \(-0.683815\pi\)
−0.545908 + 0.837845i \(0.683815\pi\)
\(464\) 21.2713 0.987496
\(465\) −3.74034 −0.173454
\(466\) −40.5999 −1.88075
\(467\) 25.3861 1.17473 0.587364 0.809323i \(-0.300166\pi\)
0.587364 + 0.809323i \(0.300166\pi\)
\(468\) 12.8773 0.595255
\(469\) −50.0681 −2.31193
\(470\) 27.0998 1.25002
\(471\) 0.730609 0.0336647
\(472\) 1.43382 0.0659968
\(473\) 7.48245 0.344043
\(474\) −1.74507 −0.0801536
\(475\) −1.09484 −0.0502346
\(476\) −33.5486 −1.53770
\(477\) −8.96741 −0.410589
\(478\) 21.2013 0.969724
\(479\) −18.2520 −0.833953 −0.416977 0.908917i \(-0.636910\pi\)
−0.416977 + 0.908917i \(0.636910\pi\)
\(480\) −2.87267 −0.131119
\(481\) −2.39427 −0.109169
\(482\) −51.9676 −2.36706
\(483\) −6.53501 −0.297353
\(484\) −19.2472 −0.874875
\(485\) −19.6338 −0.891524
\(486\) −9.67530 −0.438880
\(487\) −3.11860 −0.141317 −0.0706585 0.997501i \(-0.522510\pi\)
−0.0706585 + 0.997501i \(0.522510\pi\)
\(488\) −0.714302 −0.0323349
\(489\) 4.23410 0.191473
\(490\) 72.5720 3.27847
\(491\) −11.7998 −0.532518 −0.266259 0.963902i \(-0.585788\pi\)
−0.266259 + 0.963902i \(0.585788\pi\)
\(492\) 0.829151 0.0373810
\(493\) −17.6961 −0.796991
\(494\) 4.44401 0.199945
\(495\) −6.06849 −0.272758
\(496\) −42.5343 −1.90985
\(497\) −0.893667 −0.0400864
\(498\) 3.66692 0.164319
\(499\) −22.0648 −0.987758 −0.493879 0.869531i \(-0.664421\pi\)
−0.493879 + 0.869531i \(0.664421\pi\)
\(500\) 23.3493 1.04421
\(501\) −3.24094 −0.144795
\(502\) −35.8544 −1.60026
\(503\) −31.8720 −1.42110 −0.710550 0.703647i \(-0.751554\pi\)
−0.710550 + 0.703647i \(0.751554\pi\)
\(504\) 1.82491 0.0812880
\(505\) 21.7608 0.968343
\(506\) 14.5043 0.644795
\(507\) −1.46372 −0.0650063
\(508\) 36.5409 1.62124
\(509\) −33.4009 −1.48047 −0.740234 0.672350i \(-0.765285\pi\)
−0.740234 + 0.672350i \(0.765285\pi\)
\(510\) 2.46325 0.109075
\(511\) 73.4070 3.24733
\(512\) −31.6638 −1.39936
\(513\) −1.09359 −0.0482834
\(514\) −56.3813 −2.48687
\(515\) 22.9122 1.00963
\(516\) −2.56832 −0.113064
\(517\) −7.15328 −0.314601
\(518\) 10.7164 0.470852
\(519\) 3.63177 0.159417
\(520\) 0.539046 0.0236387
\(521\) −20.3064 −0.889639 −0.444819 0.895620i \(-0.646732\pi\)
−0.444819 + 0.895620i \(0.646732\pi\)
\(522\) −30.4022 −1.33067
\(523\) −11.1373 −0.487000 −0.243500 0.969901i \(-0.578296\pi\)
−0.243500 + 0.969901i \(0.578296\pi\)
\(524\) −17.6255 −0.769975
\(525\) 1.01345 0.0442305
\(526\) −15.2824 −0.666343
\(527\) 35.3852 1.54140
\(528\) 0.781566 0.0340133
\(529\) 26.8411 1.16701
\(530\) 11.8557 0.514980
\(531\) −34.9157 −1.51521
\(532\) −9.79041 −0.424468
\(533\) −5.22517 −0.226327
\(534\) 4.41192 0.190922
\(535\) −2.34874 −0.101545
\(536\) 1.20769 0.0521643
\(537\) 1.25286 0.0540648
\(538\) −45.5713 −1.96472
\(539\) −19.1562 −0.825114
\(540\) 4.18956 0.180290
\(541\) 26.9609 1.15914 0.579569 0.814923i \(-0.303221\pi\)
0.579569 + 0.814923i \(0.303221\pi\)
\(542\) 13.4615 0.578220
\(543\) 1.59861 0.0686030
\(544\) 27.1767 1.16519
\(545\) −18.1497 −0.777449
\(546\) −4.11365 −0.176048
\(547\) 16.2978 0.696845 0.348422 0.937338i \(-0.386717\pi\)
0.348422 + 0.937338i \(0.386717\pi\)
\(548\) −29.6878 −1.26820
\(549\) 17.3944 0.742374
\(550\) −2.24933 −0.0959116
\(551\) −5.16420 −0.220002
\(552\) 0.157631 0.00670921
\(553\) −24.2273 −1.03025
\(554\) 6.01539 0.255569
\(555\) −0.387287 −0.0164394
\(556\) −14.7593 −0.625935
\(557\) −15.0286 −0.636781 −0.318390 0.947960i \(-0.603142\pi\)
−0.318390 + 0.947960i \(0.603142\pi\)
\(558\) 60.7925 2.57355
\(559\) 16.1851 0.684558
\(560\) −41.1073 −1.73710
\(561\) −0.650202 −0.0274516
\(562\) 37.9127 1.59925
\(563\) −44.2606 −1.86536 −0.932681 0.360702i \(-0.882537\pi\)
−0.932681 + 0.360702i \(0.882537\pi\)
\(564\) 2.45533 0.103388
\(565\) −15.4837 −0.651406
\(566\) −29.6041 −1.24435
\(567\) −43.9305 −1.84491
\(568\) 0.0215561 0.000904475 0
\(569\) 8.79078 0.368529 0.184264 0.982877i \(-0.441010\pi\)
0.184264 + 0.982877i \(0.441010\pi\)
\(570\) 0.718845 0.0301091
\(571\) 26.7878 1.12103 0.560517 0.828143i \(-0.310602\pi\)
0.560517 + 0.828143i \(0.310602\pi\)
\(572\) 4.49393 0.187901
\(573\) −2.42637 −0.101363
\(574\) 23.3872 0.976162
\(575\) −7.72936 −0.322336
\(576\) 22.2529 0.927205
\(577\) 33.0688 1.37667 0.688336 0.725392i \(-0.258341\pi\)
0.688336 + 0.725392i \(0.258341\pi\)
\(578\) 10.4347 0.434027
\(579\) −3.71575 −0.154421
\(580\) 19.7841 0.821488
\(581\) 50.9090 2.11206
\(582\) −3.61410 −0.149809
\(583\) −3.12945 −0.129608
\(584\) −1.77065 −0.0732699
\(585\) −13.1266 −0.542719
\(586\) −34.0415 −1.40624
\(587\) 17.1216 0.706686 0.353343 0.935494i \(-0.385045\pi\)
0.353343 + 0.935494i \(0.385045\pi\)
\(588\) 6.57527 0.271160
\(589\) 10.3264 0.425491
\(590\) 46.1617 1.90045
\(591\) −3.34576 −0.137626
\(592\) −4.40413 −0.181009
\(593\) −11.9614 −0.491197 −0.245598 0.969372i \(-0.578984\pi\)
−0.245598 + 0.969372i \(0.578984\pi\)
\(594\) −2.24677 −0.0921862
\(595\) 34.1981 1.40198
\(596\) −25.7202 −1.05354
\(597\) 1.37840 0.0564140
\(598\) 31.3739 1.28298
\(599\) −25.6444 −1.04780 −0.523900 0.851780i \(-0.675523\pi\)
−0.523900 + 0.851780i \(0.675523\pi\)
\(600\) −0.0244453 −0.000997977 0
\(601\) −13.8425 −0.564646 −0.282323 0.959319i \(-0.591105\pi\)
−0.282323 + 0.959319i \(0.591105\pi\)
\(602\) −72.4425 −2.95253
\(603\) −29.4092 −1.19763
\(604\) 3.58842 0.146011
\(605\) 19.6199 0.797660
\(606\) 4.00563 0.162718
\(607\) −33.6896 −1.36742 −0.683710 0.729754i \(-0.739635\pi\)
−0.683710 + 0.729754i \(0.739635\pi\)
\(608\) 7.93090 0.321641
\(609\) 4.78030 0.193708
\(610\) −22.9969 −0.931119
\(611\) −15.4731 −0.625975
\(612\) −19.7059 −0.796564
\(613\) −8.02097 −0.323964 −0.161982 0.986794i \(-0.551789\pi\)
−0.161982 + 0.986794i \(0.551789\pi\)
\(614\) −67.6499 −2.73013
\(615\) −0.845203 −0.0340819
\(616\) 0.636858 0.0256597
\(617\) 4.45711 0.179437 0.0897183 0.995967i \(-0.471403\pi\)
0.0897183 + 0.995967i \(0.471403\pi\)
\(618\) 4.21757 0.169656
\(619\) 22.8836 0.919768 0.459884 0.887979i \(-0.347891\pi\)
0.459884 + 0.887979i \(0.347891\pi\)
\(620\) −39.5604 −1.58878
\(621\) −7.72059 −0.309816
\(622\) 39.2534 1.57392
\(623\) 61.2520 2.45401
\(624\) 1.69059 0.0676777
\(625\) −18.3271 −0.733086
\(626\) 21.4437 0.857064
\(627\) −0.189747 −0.00757776
\(628\) 7.72741 0.308357
\(629\) 3.66389 0.146089
\(630\) 58.7530 2.34078
\(631\) −39.3805 −1.56771 −0.783856 0.620942i \(-0.786750\pi\)
−0.783856 + 0.620942i \(0.786750\pi\)
\(632\) 0.584386 0.0232456
\(633\) 0.183292 0.00728521
\(634\) −4.91359 −0.195144
\(635\) −37.2483 −1.47815
\(636\) 1.07417 0.0425936
\(637\) −41.4362 −1.64176
\(638\) −10.6098 −0.420045
\(639\) −0.524926 −0.0207657
\(640\) 1.92490 0.0760884
\(641\) −29.8672 −1.17968 −0.589841 0.807519i \(-0.700810\pi\)
−0.589841 + 0.807519i \(0.700810\pi\)
\(642\) −0.432345 −0.0170633
\(643\) 32.5415 1.28331 0.641655 0.766993i \(-0.278248\pi\)
0.641655 + 0.766993i \(0.278248\pi\)
\(644\) −69.1186 −2.72365
\(645\) 2.61804 0.103085
\(646\) −6.80058 −0.267565
\(647\) −6.52497 −0.256523 −0.128261 0.991740i \(-0.540940\pi\)
−0.128261 + 0.991740i \(0.540940\pi\)
\(648\) 1.05965 0.0416268
\(649\) −12.1849 −0.478299
\(650\) −4.86547 −0.190839
\(651\) −9.55873 −0.374636
\(652\) 44.7827 1.75382
\(653\) 50.7498 1.98599 0.992997 0.118138i \(-0.0376925\pi\)
0.992997 + 0.118138i \(0.0376925\pi\)
\(654\) −3.34092 −0.130640
\(655\) 17.9667 0.702019
\(656\) −9.61145 −0.375264
\(657\) 43.1181 1.68220
\(658\) 69.2555 2.69986
\(659\) −10.4815 −0.408301 −0.204150 0.978940i \(-0.565443\pi\)
−0.204150 + 0.978940i \(0.565443\pi\)
\(660\) 0.726920 0.0282953
\(661\) −22.7687 −0.885600 −0.442800 0.896620i \(-0.646015\pi\)
−0.442800 + 0.896620i \(0.646015\pi\)
\(662\) −35.7510 −1.38950
\(663\) −1.40644 −0.0546215
\(664\) −1.22797 −0.0476546
\(665\) 9.97994 0.387006
\(666\) 6.29465 0.243913
\(667\) −36.4584 −1.41167
\(668\) −34.2784 −1.32627
\(669\) −4.96643 −0.192013
\(670\) 38.8816 1.50213
\(671\) 6.07029 0.234341
\(672\) −7.34133 −0.283198
\(673\) 22.6890 0.874597 0.437299 0.899316i \(-0.355935\pi\)
0.437299 + 0.899316i \(0.355935\pi\)
\(674\) −35.7035 −1.37525
\(675\) 1.19731 0.0460844
\(676\) −15.4813 −0.595436
\(677\) 12.0734 0.464017 0.232009 0.972714i \(-0.425470\pi\)
0.232009 + 0.972714i \(0.425470\pi\)
\(678\) −2.85018 −0.109460
\(679\) −50.1756 −1.92556
\(680\) −0.824891 −0.0316331
\(681\) −1.19392 −0.0457512
\(682\) 21.2154 0.812379
\(683\) −9.53261 −0.364755 −0.182378 0.983229i \(-0.558379\pi\)
−0.182378 + 0.983229i \(0.558379\pi\)
\(684\) −5.75073 −0.219885
\(685\) 30.2625 1.15627
\(686\) 115.305 4.40237
\(687\) 3.45336 0.131754
\(688\) 29.7717 1.13504
\(689\) −6.76924 −0.257887
\(690\) 5.07492 0.193199
\(691\) 17.9810 0.684029 0.342014 0.939695i \(-0.388891\pi\)
0.342014 + 0.939695i \(0.388891\pi\)
\(692\) 38.4120 1.46020
\(693\) −15.5085 −0.589119
\(694\) −0.104616 −0.00397117
\(695\) 15.0451 0.570692
\(696\) −0.115305 −0.00437064
\(697\) 7.99597 0.302869
\(698\) 67.6843 2.56189
\(699\) 3.74970 0.141827
\(700\) 10.7189 0.405136
\(701\) 30.6817 1.15883 0.579416 0.815032i \(-0.303280\pi\)
0.579416 + 0.815032i \(0.303280\pi\)
\(702\) −4.85995 −0.183427
\(703\) 1.06923 0.0403266
\(704\) 7.76583 0.292686
\(705\) −2.50287 −0.0942634
\(706\) −39.8505 −1.49979
\(707\) 55.6114 2.09148
\(708\) 4.18241 0.157185
\(709\) −50.8685 −1.91041 −0.955203 0.295951i \(-0.904363\pi\)
−0.955203 + 0.295951i \(0.904363\pi\)
\(710\) 0.693999 0.0260453
\(711\) −14.2307 −0.533694
\(712\) −1.47746 −0.0553700
\(713\) 72.9024 2.73022
\(714\) 6.29503 0.235586
\(715\) −4.58093 −0.171317
\(716\) 13.2511 0.495216
\(717\) −1.95810 −0.0731264
\(718\) −13.5384 −0.505250
\(719\) −24.1338 −0.900039 −0.450019 0.893019i \(-0.648583\pi\)
−0.450019 + 0.893019i \(0.648583\pi\)
\(720\) −24.1458 −0.899860
\(721\) 58.5538 2.18066
\(722\) −1.98460 −0.0738590
\(723\) 4.79959 0.178499
\(724\) 16.9080 0.628380
\(725\) 5.65396 0.209983
\(726\) 3.61153 0.134037
\(727\) 31.1050 1.15362 0.576810 0.816878i \(-0.304297\pi\)
0.576810 + 0.816878i \(0.304297\pi\)
\(728\) 1.37757 0.0510563
\(729\) −25.2027 −0.933434
\(730\) −57.0060 −2.10989
\(731\) −24.7677 −0.916068
\(732\) −2.08360 −0.0770121
\(733\) 12.2211 0.451398 0.225699 0.974197i \(-0.427533\pi\)
0.225699 + 0.974197i \(0.427533\pi\)
\(734\) 61.7157 2.27797
\(735\) −6.70256 −0.247228
\(736\) 55.9908 2.06385
\(737\) −10.2632 −0.378051
\(738\) 13.7373 0.505675
\(739\) −27.5409 −1.01311 −0.506554 0.862208i \(-0.669081\pi\)
−0.506554 + 0.862208i \(0.669081\pi\)
\(740\) −4.09620 −0.150579
\(741\) −0.410437 −0.0150778
\(742\) 30.2982 1.11228
\(743\) 25.0627 0.919459 0.459730 0.888059i \(-0.347946\pi\)
0.459730 + 0.888059i \(0.347946\pi\)
\(744\) 0.230566 0.00845295
\(745\) 26.2182 0.960559
\(746\) 11.3716 0.416344
\(747\) 29.9031 1.09410
\(748\) −6.87697 −0.251447
\(749\) −6.00238 −0.219322
\(750\) −4.38124 −0.159980
\(751\) 5.36830 0.195892 0.0979460 0.995192i \(-0.468773\pi\)
0.0979460 + 0.995192i \(0.468773\pi\)
\(752\) −28.4620 −1.03790
\(753\) 3.31142 0.120675
\(754\) −22.9498 −0.835781
\(755\) −3.65789 −0.133124
\(756\) 10.7067 0.389400
\(757\) −22.2032 −0.806990 −0.403495 0.914982i \(-0.632205\pi\)
−0.403495 + 0.914982i \(0.632205\pi\)
\(758\) 38.1640 1.38618
\(759\) −1.33958 −0.0486237
\(760\) −0.240726 −0.00873204
\(761\) −22.9976 −0.833661 −0.416830 0.908984i \(-0.636859\pi\)
−0.416830 + 0.908984i \(0.636859\pi\)
\(762\) −6.85649 −0.248385
\(763\) −46.3830 −1.67918
\(764\) −25.6629 −0.928453
\(765\) 20.0874 0.726261
\(766\) 37.5009 1.35496
\(767\) −26.3569 −0.951691
\(768\) 3.10431 0.112017
\(769\) −34.7753 −1.25403 −0.627015 0.779007i \(-0.715724\pi\)
−0.627015 + 0.779007i \(0.715724\pi\)
\(770\) 20.5036 0.738900
\(771\) 5.20723 0.187534
\(772\) −39.3002 −1.41445
\(773\) −11.9074 −0.428281 −0.214140 0.976803i \(-0.568695\pi\)
−0.214140 + 0.976803i \(0.568695\pi\)
\(774\) −42.5515 −1.52948
\(775\) −11.3057 −0.406113
\(776\) 1.21028 0.0434467
\(777\) −0.989740 −0.0355067
\(778\) 46.9492 1.68321
\(779\) 2.33345 0.0836044
\(780\) 1.57239 0.0563004
\(781\) −0.183189 −0.00655500
\(782\) −48.0109 −1.71687
\(783\) 5.64754 0.201827
\(784\) −76.2199 −2.72214
\(785\) −7.87701 −0.281142
\(786\) 3.30724 0.117965
\(787\) 35.9964 1.28313 0.641566 0.767068i \(-0.278285\pi\)
0.641566 + 0.767068i \(0.278285\pi\)
\(788\) −35.3870 −1.26061
\(789\) 1.41144 0.0502486
\(790\) 18.8143 0.669383
\(791\) −39.5699 −1.40694
\(792\) 0.374080 0.0132924
\(793\) 13.1305 0.466278
\(794\) 28.8285 1.02309
\(795\) −1.09496 −0.0388344
\(796\) 14.5788 0.516733
\(797\) 1.93637 0.0685897 0.0342948 0.999412i \(-0.489081\pi\)
0.0342948 + 0.999412i \(0.489081\pi\)
\(798\) 1.83706 0.0650313
\(799\) 23.6782 0.837673
\(800\) −8.68305 −0.306992
\(801\) 35.9784 1.27123
\(802\) −0.163999 −0.00579100
\(803\) 15.0474 0.531009
\(804\) 3.52281 0.124240
\(805\) 70.4566 2.48327
\(806\) 45.8905 1.61643
\(807\) 4.20884 0.148158
\(808\) −1.34140 −0.0471903
\(809\) 39.9490 1.40453 0.702267 0.711914i \(-0.252171\pi\)
0.702267 + 0.711914i \(0.252171\pi\)
\(810\) 34.1153 1.19869
\(811\) −51.8907 −1.82213 −0.911064 0.412266i \(-0.864738\pi\)
−0.911064 + 0.412266i \(0.864738\pi\)
\(812\) 50.5597 1.77430
\(813\) −1.24327 −0.0436033
\(814\) 2.19671 0.0769945
\(815\) −45.6496 −1.59904
\(816\) −2.58707 −0.0905656
\(817\) −7.22791 −0.252873
\(818\) 21.1485 0.739441
\(819\) −33.5461 −1.17219
\(820\) −8.93943 −0.312178
\(821\) 40.0103 1.39637 0.698184 0.715918i \(-0.253992\pi\)
0.698184 + 0.715918i \(0.253992\pi\)
\(822\) 5.57059 0.194297
\(823\) 26.5451 0.925305 0.462652 0.886540i \(-0.346898\pi\)
0.462652 + 0.886540i \(0.346898\pi\)
\(824\) −1.41237 −0.0492024
\(825\) 0.207742 0.00723264
\(826\) 117.970 4.10469
\(827\) 14.9343 0.519316 0.259658 0.965701i \(-0.416390\pi\)
0.259658 + 0.965701i \(0.416390\pi\)
\(828\) −40.5991 −1.41092
\(829\) 14.0711 0.488711 0.244356 0.969686i \(-0.421424\pi\)
0.244356 + 0.969686i \(0.421424\pi\)
\(830\) −39.5346 −1.37227
\(831\) −0.555565 −0.0192724
\(832\) 16.7981 0.582369
\(833\) 63.4090 2.19699
\(834\) 2.76943 0.0958974
\(835\) 34.9419 1.20922
\(836\) −2.00689 −0.0694097
\(837\) −11.2929 −0.390339
\(838\) 80.1964 2.77034
\(839\) 22.3229 0.770673 0.385337 0.922776i \(-0.374085\pi\)
0.385337 + 0.922776i \(0.374085\pi\)
\(840\) 0.222831 0.00768839
\(841\) −2.33102 −0.0803800
\(842\) −46.9269 −1.61721
\(843\) −3.50152 −0.120599
\(844\) 1.93862 0.0667300
\(845\) 15.7810 0.542884
\(846\) 40.6796 1.39859
\(847\) 50.1400 1.72283
\(848\) −12.4517 −0.427592
\(849\) 2.73416 0.0938361
\(850\) 7.44552 0.255379
\(851\) 7.54854 0.258761
\(852\) 0.0628787 0.00215419
\(853\) −21.6475 −0.741196 −0.370598 0.928793i \(-0.620847\pi\)
−0.370598 + 0.928793i \(0.620847\pi\)
\(854\) −58.7704 −2.01108
\(855\) 5.86206 0.200478
\(856\) 0.144783 0.00494859
\(857\) 20.4736 0.699364 0.349682 0.936868i \(-0.386290\pi\)
0.349682 + 0.936868i \(0.386290\pi\)
\(858\) −0.843237 −0.0287876
\(859\) −44.9662 −1.53423 −0.767114 0.641511i \(-0.778308\pi\)
−0.767114 + 0.641511i \(0.778308\pi\)
\(860\) 27.6901 0.944226
\(861\) −2.15998 −0.0736119
\(862\) 34.5800 1.17780
\(863\) 15.5290 0.528612 0.264306 0.964439i \(-0.414857\pi\)
0.264306 + 0.964439i \(0.414857\pi\)
\(864\) −8.67319 −0.295068
\(865\) −39.1556 −1.33133
\(866\) −77.3720 −2.62921
\(867\) −0.963724 −0.0327298
\(868\) −101.099 −3.43154
\(869\) −4.96624 −0.168468
\(870\) −3.71226 −0.125857
\(871\) −22.2001 −0.752223
\(872\) 1.11880 0.0378875
\(873\) −29.4723 −0.997487
\(874\) −14.0109 −0.473926
\(875\) −60.8261 −2.05630
\(876\) −5.16494 −0.174507
\(877\) 30.5561 1.03181 0.515903 0.856647i \(-0.327456\pi\)
0.515903 + 0.856647i \(0.327456\pi\)
\(878\) −26.6639 −0.899862
\(879\) 3.14399 0.106044
\(880\) −8.42639 −0.284054
\(881\) 14.0321 0.472753 0.236376 0.971662i \(-0.424040\pi\)
0.236376 + 0.971662i \(0.424040\pi\)
\(882\) 108.938 3.66814
\(883\) 35.2712 1.18697 0.593485 0.804845i \(-0.297751\pi\)
0.593485 + 0.804845i \(0.297751\pi\)
\(884\) −14.8754 −0.500315
\(885\) −4.26338 −0.143312
\(886\) −18.8848 −0.634448
\(887\) −28.3299 −0.951226 −0.475613 0.879655i \(-0.657774\pi\)
−0.475613 + 0.879655i \(0.657774\pi\)
\(888\) 0.0238735 0.000801142 0
\(889\) −95.1907 −3.19260
\(890\) −47.5667 −1.59444
\(891\) −9.00510 −0.301682
\(892\) −52.5283 −1.75878
\(893\) 6.90994 0.231232
\(894\) 4.82612 0.161410
\(895\) −13.5076 −0.451509
\(896\) 4.91923 0.164340
\(897\) −2.89762 −0.0967486
\(898\) 48.7912 1.62818
\(899\) −53.3275 −1.77857
\(900\) 6.29611 0.209870
\(901\) 10.3588 0.345102
\(902\) 4.79403 0.159624
\(903\) 6.69060 0.222649
\(904\) 0.954464 0.0317450
\(905\) −17.2353 −0.572921
\(906\) −0.673328 −0.0223698
\(907\) 45.0034 1.49431 0.747157 0.664647i \(-0.231418\pi\)
0.747157 + 0.664647i \(0.231418\pi\)
\(908\) −12.6277 −0.419065
\(909\) 32.6652 1.08344
\(910\) 44.3510 1.47022
\(911\) 52.7922 1.74908 0.874542 0.484951i \(-0.161162\pi\)
0.874542 + 0.484951i \(0.161162\pi\)
\(912\) −0.754979 −0.0249998
\(913\) 10.4356 0.345368
\(914\) −45.3191 −1.49902
\(915\) 2.12394 0.0702152
\(916\) 36.5251 1.20682
\(917\) 45.9154 1.51626
\(918\) 7.43707 0.245460
\(919\) 27.9022 0.920409 0.460205 0.887813i \(-0.347776\pi\)
0.460205 + 0.887813i \(0.347776\pi\)
\(920\) −1.69948 −0.0560303
\(921\) 6.24797 0.205878
\(922\) 10.9306 0.359981
\(923\) −0.396251 −0.0130428
\(924\) 1.85770 0.0611138
\(925\) −1.17063 −0.0384900
\(926\) 46.6243 1.53217
\(927\) 34.3936 1.12963
\(928\) −40.9568 −1.34447
\(929\) −44.0144 −1.44407 −0.722033 0.691859i \(-0.756792\pi\)
−0.722033 + 0.691859i \(0.756792\pi\)
\(930\) 7.42307 0.243412
\(931\) 18.5045 0.606460
\(932\) 39.6593 1.29908
\(933\) −3.62534 −0.118688
\(934\) −50.3811 −1.64852
\(935\) 7.01010 0.229255
\(936\) 0.809164 0.0264484
\(937\) 38.5904 1.26069 0.630347 0.776314i \(-0.282913\pi\)
0.630347 + 0.776314i \(0.282913\pi\)
\(938\) 99.3649 3.24438
\(939\) −1.98049 −0.0646308
\(940\) −26.4720 −0.863421
\(941\) −5.87135 −0.191400 −0.0957002 0.995410i \(-0.530509\pi\)
−0.0957002 + 0.995410i \(0.530509\pi\)
\(942\) −1.44996 −0.0472424
\(943\) 16.4737 0.536458
\(944\) −48.4821 −1.57796
\(945\) −10.9140 −0.355033
\(946\) −14.8496 −0.482803
\(947\) −43.4887 −1.41319 −0.706597 0.707616i \(-0.749771\pi\)
−0.706597 + 0.707616i \(0.749771\pi\)
\(948\) 1.70464 0.0553641
\(949\) 32.5486 1.05657
\(950\) 2.17281 0.0704952
\(951\) 0.453806 0.0147157
\(952\) −2.10807 −0.0683230
\(953\) 36.2193 1.17326 0.586630 0.809855i \(-0.300454\pi\)
0.586630 + 0.809855i \(0.300454\pi\)
\(954\) 17.7967 0.576189
\(955\) 26.1597 0.846509
\(956\) −20.7101 −0.669813
\(957\) 0.979891 0.0316754
\(958\) 36.2228 1.17030
\(959\) 77.3382 2.49738
\(960\) 2.71719 0.0876970
\(961\) 75.6341 2.43981
\(962\) 4.75165 0.153199
\(963\) −3.52570 −0.113614
\(964\) 50.7637 1.63499
\(965\) 40.0610 1.28961
\(966\) 12.9693 0.417282
\(967\) −31.3258 −1.00737 −0.503685 0.863887i \(-0.668023\pi\)
−0.503685 + 0.863887i \(0.668023\pi\)
\(968\) −1.20943 −0.0388724
\(969\) 0.628083 0.0201769
\(970\) 38.9651 1.25109
\(971\) 25.3805 0.814501 0.407250 0.913317i \(-0.366488\pi\)
0.407250 + 0.913317i \(0.366488\pi\)
\(972\) 9.45115 0.303146
\(973\) 38.4488 1.23261
\(974\) 6.18915 0.198313
\(975\) 0.449362 0.0143911
\(976\) 24.1529 0.773116
\(977\) −32.1047 −1.02712 −0.513561 0.858053i \(-0.671674\pi\)
−0.513561 + 0.858053i \(0.671674\pi\)
\(978\) −8.40297 −0.268697
\(979\) 12.5557 0.401283
\(980\) −70.8907 −2.26452
\(981\) −27.2446 −0.869854
\(982\) 23.4178 0.747293
\(983\) −6.79007 −0.216570 −0.108285 0.994120i \(-0.534536\pi\)
−0.108285 + 0.994120i \(0.534536\pi\)
\(984\) 0.0521008 0.00166091
\(985\) 36.0720 1.14935
\(986\) 35.1195 1.11843
\(987\) −6.39626 −0.203595
\(988\) −4.34106 −0.138107
\(989\) −51.0278 −1.62259
\(990\) 12.0435 0.382768
\(991\) 2.61060 0.0829283 0.0414642 0.999140i \(-0.486798\pi\)
0.0414642 + 0.999140i \(0.486798\pi\)
\(992\) 81.8975 2.60025
\(993\) 3.30187 0.104782
\(994\) 1.77357 0.0562542
\(995\) −14.8611 −0.471127
\(996\) −3.58197 −0.113499
\(997\) −9.16613 −0.290294 −0.145147 0.989410i \(-0.546366\pi\)
−0.145147 + 0.989410i \(0.546366\pi\)
\(998\) 43.7898 1.38614
\(999\) −1.16930 −0.0369950
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 \(a_p\))