Properties

Label 4019.2.a.b.1.13
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56492 q^{2}\) \(-2.35383 q^{3}\) \(+4.57881 q^{4}\) \(+1.72936 q^{5}\) \(+6.03739 q^{6}\) \(-3.13382 q^{7}\) \(-6.61443 q^{8}\) \(+2.54053 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56492 q^{2}\) \(-2.35383 q^{3}\) \(+4.57881 q^{4}\) \(+1.72936 q^{5}\) \(+6.03739 q^{6}\) \(-3.13382 q^{7}\) \(-6.61443 q^{8}\) \(+2.54053 q^{9}\) \(-4.43566 q^{10}\) \(-4.23381 q^{11}\) \(-10.7777 q^{12}\) \(+2.84943 q^{13}\) \(+8.03799 q^{14}\) \(-4.07062 q^{15}\) \(+7.80786 q^{16}\) \(-1.50486 q^{17}\) \(-6.51625 q^{18}\) \(-1.85001 q^{19}\) \(+7.91840 q^{20}\) \(+7.37648 q^{21}\) \(+10.8594 q^{22}\) \(-7.40761 q^{23}\) \(+15.5693 q^{24}\) \(-2.00932 q^{25}\) \(-7.30855 q^{26}\) \(+1.08151 q^{27}\) \(-14.3491 q^{28}\) \(-1.18024 q^{29}\) \(+10.4408 q^{30}\) \(-7.01727 q^{31}\) \(-6.79766 q^{32}\) \(+9.96567 q^{33}\) \(+3.85985 q^{34}\) \(-5.41950 q^{35}\) \(+11.6326 q^{36}\) \(-0.469227 q^{37}\) \(+4.74514 q^{38}\) \(-6.70707 q^{39}\) \(-11.4387 q^{40}\) \(+3.60425 q^{41}\) \(-18.9201 q^{42}\) \(-10.0365 q^{43}\) \(-19.3858 q^{44}\) \(+4.39349 q^{45}\) \(+18.9999 q^{46}\) \(-11.2607 q^{47}\) \(-18.3784 q^{48}\) \(+2.82082 q^{49}\) \(+5.15374 q^{50}\) \(+3.54219 q^{51}\) \(+13.0470 q^{52}\) \(-6.26150 q^{53}\) \(-2.77400 q^{54}\) \(-7.32177 q^{55}\) \(+20.7284 q^{56}\) \(+4.35462 q^{57}\) \(+3.02722 q^{58}\) \(-8.36887 q^{59}\) \(-18.6386 q^{60}\) \(+14.3617 q^{61}\) \(+17.9987 q^{62}\) \(-7.96156 q^{63}\) \(+1.81973 q^{64}\) \(+4.92768 q^{65}\) \(-25.5611 q^{66}\) \(+14.3594 q^{67}\) \(-6.89047 q^{68}\) \(+17.4363 q^{69}\) \(+13.9006 q^{70}\) \(+12.7596 q^{71}\) \(-16.8042 q^{72}\) \(-12.7007 q^{73}\) \(+1.20353 q^{74}\) \(+4.72960 q^{75}\) \(-8.47086 q^{76}\) \(+13.2680 q^{77}\) \(+17.2031 q^{78}\) \(-0.827441 q^{79}\) \(+13.5026 q^{80}\) \(-10.1673 q^{81}\) \(-9.24461 q^{82}\) \(-12.6263 q^{83}\) \(+33.7755 q^{84}\) \(-2.60245 q^{85}\) \(+25.7429 q^{86}\) \(+2.77809 q^{87}\) \(+28.0042 q^{88}\) \(+16.1548 q^{89}\) \(-11.2689 q^{90}\) \(-8.92958 q^{91}\) \(-33.9180 q^{92}\) \(+16.5175 q^{93}\) \(+28.8828 q^{94}\) \(-3.19934 q^{95}\) \(+16.0006 q^{96}\) \(+5.98839 q^{97}\) \(-7.23516 q^{98}\) \(-10.7561 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56492 −1.81367 −0.906836 0.421484i \(-0.861509\pi\)
−0.906836 + 0.421484i \(0.861509\pi\)
\(3\) −2.35383 −1.35899 −0.679493 0.733682i \(-0.737800\pi\)
−0.679493 + 0.733682i \(0.737800\pi\)
\(4\) 4.57881 2.28940
\(5\) 1.72936 0.773393 0.386696 0.922207i \(-0.373616\pi\)
0.386696 + 0.922207i \(0.373616\pi\)
\(6\) 6.03739 2.46475
\(7\) −3.13382 −1.18447 −0.592236 0.805765i \(-0.701755\pi\)
−0.592236 + 0.805765i \(0.701755\pi\)
\(8\) −6.61443 −2.33855
\(9\) 2.54053 0.846844
\(10\) −4.43566 −1.40268
\(11\) −4.23381 −1.27654 −0.638270 0.769812i \(-0.720350\pi\)
−0.638270 + 0.769812i \(0.720350\pi\)
\(12\) −10.7777 −3.11127
\(13\) 2.84943 0.790289 0.395144 0.918619i \(-0.370695\pi\)
0.395144 + 0.918619i \(0.370695\pi\)
\(14\) 8.03799 2.14824
\(15\) −4.07062 −1.05103
\(16\) 7.80786 1.95196
\(17\) −1.50486 −0.364983 −0.182491 0.983207i \(-0.558416\pi\)
−0.182491 + 0.983207i \(0.558416\pi\)
\(18\) −6.51625 −1.53590
\(19\) −1.85001 −0.424422 −0.212211 0.977224i \(-0.568066\pi\)
−0.212211 + 0.977224i \(0.568066\pi\)
\(20\) 7.91840 1.77061
\(21\) 7.37648 1.60968
\(22\) 10.8594 2.31522
\(23\) −7.40761 −1.54459 −0.772297 0.635262i \(-0.780892\pi\)
−0.772297 + 0.635262i \(0.780892\pi\)
\(24\) 15.5693 3.17806
\(25\) −2.00932 −0.401864
\(26\) −7.30855 −1.43332
\(27\) 1.08151 0.208138
\(28\) −14.3491 −2.71173
\(29\) −1.18024 −0.219165 −0.109583 0.993978i \(-0.534951\pi\)
−0.109583 + 0.993978i \(0.534951\pi\)
\(30\) 10.4408 1.90622
\(31\) −7.01727 −1.26034 −0.630169 0.776458i \(-0.717015\pi\)
−0.630169 + 0.776458i \(0.717015\pi\)
\(32\) −6.79766 −1.20167
\(33\) 9.96567 1.73480
\(34\) 3.85985 0.661958
\(35\) −5.41950 −0.916062
\(36\) 11.6326 1.93877
\(37\) −0.469227 −0.0771404 −0.0385702 0.999256i \(-0.512280\pi\)
−0.0385702 + 0.999256i \(0.512280\pi\)
\(38\) 4.74514 0.769763
\(39\) −6.70707 −1.07399
\(40\) −11.4387 −1.80862
\(41\) 3.60425 0.562890 0.281445 0.959577i \(-0.409186\pi\)
0.281445 + 0.959577i \(0.409186\pi\)
\(42\) −18.9201 −2.91943
\(43\) −10.0365 −1.53055 −0.765277 0.643701i \(-0.777398\pi\)
−0.765277 + 0.643701i \(0.777398\pi\)
\(44\) −19.3858 −2.92252
\(45\) 4.39349 0.654943
\(46\) 18.9999 2.80138
\(47\) −11.2607 −1.64254 −0.821270 0.570539i \(-0.806734\pi\)
−0.821270 + 0.570539i \(0.806734\pi\)
\(48\) −18.3784 −2.65269
\(49\) 2.82082 0.402974
\(50\) 5.15374 0.728849
\(51\) 3.54219 0.496006
\(52\) 13.0470 1.80929
\(53\) −6.26150 −0.860083 −0.430042 0.902809i \(-0.641501\pi\)
−0.430042 + 0.902809i \(0.641501\pi\)
\(54\) −2.77400 −0.377493
\(55\) −7.32177 −0.987267
\(56\) 20.7284 2.76995
\(57\) 4.35462 0.576784
\(58\) 3.02722 0.397493
\(59\) −8.36887 −1.08953 −0.544767 0.838587i \(-0.683382\pi\)
−0.544767 + 0.838587i \(0.683382\pi\)
\(60\) −18.6386 −2.40623
\(61\) 14.3617 1.83883 0.919416 0.393286i \(-0.128662\pi\)
0.919416 + 0.393286i \(0.128662\pi\)
\(62\) 17.9987 2.28584
\(63\) −7.96156 −1.00306
\(64\) 1.81973 0.227466
\(65\) 4.92768 0.611203
\(66\) −25.5611 −3.14636
\(67\) 14.3594 1.75429 0.877143 0.480230i \(-0.159447\pi\)
0.877143 + 0.480230i \(0.159447\pi\)
\(68\) −6.89047 −0.835592
\(69\) 17.4363 2.09908
\(70\) 13.9006 1.66144
\(71\) 12.7596 1.51429 0.757144 0.653248i \(-0.226594\pi\)
0.757144 + 0.653248i \(0.226594\pi\)
\(72\) −16.8042 −1.98039
\(73\) −12.7007 −1.48651 −0.743253 0.669010i \(-0.766718\pi\)
−0.743253 + 0.669010i \(0.766718\pi\)
\(74\) 1.20353 0.139907
\(75\) 4.72960 0.546127
\(76\) −8.47086 −0.971674
\(77\) 13.2680 1.51203
\(78\) 17.2031 1.94787
\(79\) −0.827441 −0.0930944 −0.0465472 0.998916i \(-0.514822\pi\)
−0.0465472 + 0.998916i \(0.514822\pi\)
\(80\) 13.5026 1.50963
\(81\) −10.1673 −1.12970
\(82\) −9.24461 −1.02090
\(83\) −12.6263 −1.38592 −0.692959 0.720977i \(-0.743694\pi\)
−0.692959 + 0.720977i \(0.743694\pi\)
\(84\) 33.7755 3.68521
\(85\) −2.60245 −0.282275
\(86\) 25.7429 2.77592
\(87\) 2.77809 0.297842
\(88\) 28.0042 2.98526
\(89\) 16.1548 1.71241 0.856205 0.516636i \(-0.172816\pi\)
0.856205 + 0.516636i \(0.172816\pi\)
\(90\) −11.2689 −1.18785
\(91\) −8.92958 −0.936075
\(92\) −33.9180 −3.53620
\(93\) 16.5175 1.71278
\(94\) 28.8828 2.97903
\(95\) −3.19934 −0.328245
\(96\) 16.0006 1.63305
\(97\) 5.98839 0.608029 0.304015 0.952667i \(-0.401673\pi\)
0.304015 + 0.952667i \(0.401673\pi\)
\(98\) −7.23516 −0.730862
\(99\) −10.7561 −1.08103
\(100\) −9.20028 −0.920028
\(101\) −9.67112 −0.962313 −0.481156 0.876635i \(-0.659783\pi\)
−0.481156 + 0.876635i \(0.659783\pi\)
\(102\) −9.08544 −0.899592
\(103\) 14.9180 1.46991 0.734955 0.678116i \(-0.237203\pi\)
0.734955 + 0.678116i \(0.237203\pi\)
\(104\) −18.8473 −1.84813
\(105\) 12.7566 1.24492
\(106\) 16.0602 1.55991
\(107\) −14.4129 −1.39335 −0.696673 0.717388i \(-0.745337\pi\)
−0.696673 + 0.717388i \(0.745337\pi\)
\(108\) 4.95205 0.476511
\(109\) −3.42377 −0.327938 −0.163969 0.986465i \(-0.552430\pi\)
−0.163969 + 0.986465i \(0.552430\pi\)
\(110\) 18.7797 1.79058
\(111\) 1.10448 0.104833
\(112\) −24.4684 −2.31205
\(113\) −20.0631 −1.88738 −0.943690 0.330831i \(-0.892671\pi\)
−0.943690 + 0.330831i \(0.892671\pi\)
\(114\) −11.1693 −1.04610
\(115\) −12.8104 −1.19458
\(116\) −5.40409 −0.501757
\(117\) 7.23905 0.669251
\(118\) 21.4655 1.97606
\(119\) 4.71596 0.432312
\(120\) 26.9248 2.45789
\(121\) 6.92511 0.629555
\(122\) −36.8367 −3.33504
\(123\) −8.48381 −0.764959
\(124\) −32.1307 −2.88542
\(125\) −12.1216 −1.08419
\(126\) 20.4208 1.81923
\(127\) −0.833610 −0.0739709 −0.0369854 0.999316i \(-0.511776\pi\)
−0.0369854 + 0.999316i \(0.511776\pi\)
\(128\) 8.92787 0.789120
\(129\) 23.6243 2.08000
\(130\) −12.6391 −1.10852
\(131\) 13.5317 1.18227 0.591136 0.806572i \(-0.298680\pi\)
0.591136 + 0.806572i \(0.298680\pi\)
\(132\) 45.6309 3.97166
\(133\) 5.79761 0.502716
\(134\) −36.8308 −3.18170
\(135\) 1.87033 0.160972
\(136\) 9.95380 0.853531
\(137\) 6.36466 0.543770 0.271885 0.962330i \(-0.412353\pi\)
0.271885 + 0.962330i \(0.412353\pi\)
\(138\) −44.7226 −3.80704
\(139\) 0.239341 0.0203006 0.0101503 0.999948i \(-0.496769\pi\)
0.0101503 + 0.999948i \(0.496769\pi\)
\(140\) −24.8148 −2.09724
\(141\) 26.5058 2.23219
\(142\) −32.7274 −2.74642
\(143\) −12.0639 −1.00884
\(144\) 19.8361 1.65301
\(145\) −2.04106 −0.169501
\(146\) 32.5763 2.69603
\(147\) −6.63973 −0.547636
\(148\) −2.14850 −0.176606
\(149\) −14.3535 −1.17588 −0.587942 0.808903i \(-0.700062\pi\)
−0.587942 + 0.808903i \(0.700062\pi\)
\(150\) −12.1310 −0.990495
\(151\) −8.54922 −0.695725 −0.347863 0.937546i \(-0.613092\pi\)
−0.347863 + 0.937546i \(0.613092\pi\)
\(152\) 12.2368 0.992534
\(153\) −3.82315 −0.309083
\(154\) −34.0313 −2.74232
\(155\) −12.1354 −0.974737
\(156\) −30.7104 −2.45880
\(157\) −11.7819 −0.940299 −0.470150 0.882587i \(-0.655800\pi\)
−0.470150 + 0.882587i \(0.655800\pi\)
\(158\) 2.12232 0.168843
\(159\) 14.7385 1.16884
\(160\) −11.7556 −0.929361
\(161\) 23.2141 1.82953
\(162\) 26.0783 2.04890
\(163\) −17.7086 −1.38705 −0.693523 0.720435i \(-0.743942\pi\)
−0.693523 + 0.720435i \(0.743942\pi\)
\(164\) 16.5032 1.28868
\(165\) 17.2342 1.34168
\(166\) 32.3855 2.51360
\(167\) −14.8486 −1.14902 −0.574508 0.818499i \(-0.694807\pi\)
−0.574508 + 0.818499i \(0.694807\pi\)
\(168\) −48.7912 −3.76433
\(169\) −4.88077 −0.375444
\(170\) 6.67506 0.511954
\(171\) −4.70002 −0.359419
\(172\) −45.9553 −3.50406
\(173\) −7.43849 −0.565538 −0.282769 0.959188i \(-0.591253\pi\)
−0.282769 + 0.959188i \(0.591253\pi\)
\(174\) −7.12557 −0.540188
\(175\) 6.29684 0.475996
\(176\) −33.0569 −2.49176
\(177\) 19.6989 1.48066
\(178\) −41.4359 −3.10575
\(179\) 12.3096 0.920063 0.460031 0.887903i \(-0.347838\pi\)
0.460031 + 0.887903i \(0.347838\pi\)
\(180\) 20.1169 1.49943
\(181\) −24.0222 −1.78556 −0.892780 0.450493i \(-0.851248\pi\)
−0.892780 + 0.450493i \(0.851248\pi\)
\(182\) 22.9037 1.69773
\(183\) −33.8051 −2.49895
\(184\) 48.9971 3.61212
\(185\) −0.811462 −0.0596598
\(186\) −42.3660 −3.10642
\(187\) 6.37129 0.465915
\(188\) −51.5605 −3.76044
\(189\) −3.38927 −0.246533
\(190\) 8.20604 0.595329
\(191\) 21.9545 1.58857 0.794286 0.607544i \(-0.207845\pi\)
0.794286 + 0.607544i \(0.207845\pi\)
\(192\) −4.28333 −0.309123
\(193\) 14.9290 1.07461 0.537306 0.843387i \(-0.319442\pi\)
0.537306 + 0.843387i \(0.319442\pi\)
\(194\) −15.3597 −1.10276
\(195\) −11.5989 −0.830617
\(196\) 12.9160 0.922569
\(197\) −11.1127 −0.791748 −0.395874 0.918305i \(-0.629558\pi\)
−0.395874 + 0.918305i \(0.629558\pi\)
\(198\) 27.5886 1.96063
\(199\) −9.01753 −0.639236 −0.319618 0.947547i \(-0.603555\pi\)
−0.319618 + 0.947547i \(0.603555\pi\)
\(200\) 13.2905 0.939780
\(201\) −33.7997 −2.38405
\(202\) 24.8056 1.74532
\(203\) 3.69866 0.259595
\(204\) 16.2190 1.13556
\(205\) 6.23304 0.435335
\(206\) −38.2633 −2.66593
\(207\) −18.8193 −1.30803
\(208\) 22.2479 1.54262
\(209\) 7.83260 0.541792
\(210\) −32.7196 −2.25787
\(211\) 25.4175 1.74981 0.874906 0.484292i \(-0.160923\pi\)
0.874906 + 0.484292i \(0.160923\pi\)
\(212\) −28.6702 −1.96908
\(213\) −30.0340 −2.05790
\(214\) 36.9679 2.52707
\(215\) −17.3567 −1.18372
\(216\) −7.15360 −0.486741
\(217\) 21.9908 1.49284
\(218\) 8.78170 0.594772
\(219\) 29.8954 2.02014
\(220\) −33.5250 −2.26025
\(221\) −4.28799 −0.288442
\(222\) −2.83291 −0.190132
\(223\) −8.35112 −0.559232 −0.279616 0.960112i \(-0.590207\pi\)
−0.279616 + 0.960112i \(0.590207\pi\)
\(224\) 21.3026 1.42334
\(225\) −5.10473 −0.340316
\(226\) 51.4603 3.42309
\(227\) −22.2708 −1.47816 −0.739082 0.673616i \(-0.764740\pi\)
−0.739082 + 0.673616i \(0.764740\pi\)
\(228\) 19.9390 1.32049
\(229\) 5.03103 0.332460 0.166230 0.986087i \(-0.446841\pi\)
0.166230 + 0.986087i \(0.446841\pi\)
\(230\) 32.8577 2.16657
\(231\) −31.2306 −2.05482
\(232\) 7.80661 0.512529
\(233\) 0.216936 0.0142119 0.00710597 0.999975i \(-0.497738\pi\)
0.00710597 + 0.999975i \(0.497738\pi\)
\(234\) −18.5676 −1.21380
\(235\) −19.4738 −1.27033
\(236\) −38.3194 −2.49438
\(237\) 1.94766 0.126514
\(238\) −12.0961 −0.784071
\(239\) 4.06053 0.262654 0.131327 0.991339i \(-0.458076\pi\)
0.131327 + 0.991339i \(0.458076\pi\)
\(240\) −31.7828 −2.05157
\(241\) 3.31497 0.213536 0.106768 0.994284i \(-0.465950\pi\)
0.106768 + 0.994284i \(0.465950\pi\)
\(242\) −17.7623 −1.14181
\(243\) 20.6876 1.32711
\(244\) 65.7596 4.20983
\(245\) 4.87820 0.311657
\(246\) 21.7603 1.38738
\(247\) −5.27148 −0.335416
\(248\) 46.4152 2.94737
\(249\) 29.7203 1.88344
\(250\) 31.0910 1.96637
\(251\) −24.0627 −1.51883 −0.759413 0.650609i \(-0.774514\pi\)
−0.759413 + 0.650609i \(0.774514\pi\)
\(252\) −36.4544 −2.29641
\(253\) 31.3624 1.97174
\(254\) 2.13814 0.134159
\(255\) 6.12572 0.383608
\(256\) −26.5387 −1.65867
\(257\) −13.2377 −0.825747 −0.412874 0.910788i \(-0.635475\pi\)
−0.412874 + 0.910788i \(0.635475\pi\)
\(258\) −60.5944 −3.77244
\(259\) 1.47047 0.0913707
\(260\) 22.5629 1.39929
\(261\) −2.99844 −0.185599
\(262\) −34.7078 −2.14425
\(263\) 22.3921 1.38075 0.690377 0.723450i \(-0.257445\pi\)
0.690377 + 0.723450i \(0.257445\pi\)
\(264\) −65.9172 −4.05692
\(265\) −10.8284 −0.665182
\(266\) −14.8704 −0.911762
\(267\) −38.0258 −2.32714
\(268\) 65.7491 4.01627
\(269\) −11.6268 −0.708897 −0.354449 0.935075i \(-0.615331\pi\)
−0.354449 + 0.935075i \(0.615331\pi\)
\(270\) −4.79723 −0.291950
\(271\) 20.3251 1.23466 0.617331 0.786704i \(-0.288214\pi\)
0.617331 + 0.786704i \(0.288214\pi\)
\(272\) −11.7497 −0.712433
\(273\) 21.0187 1.27211
\(274\) −16.3248 −0.986219
\(275\) 8.50706 0.512995
\(276\) 79.8374 4.80564
\(277\) −22.8110 −1.37058 −0.685291 0.728269i \(-0.740325\pi\)
−0.685291 + 0.728269i \(0.740325\pi\)
\(278\) −0.613889 −0.0368186
\(279\) −17.8276 −1.06731
\(280\) 35.8469 2.14226
\(281\) −27.8052 −1.65872 −0.829361 0.558713i \(-0.811295\pi\)
−0.829361 + 0.558713i \(0.811295\pi\)
\(282\) −67.9852 −4.04846
\(283\) 2.11607 0.125787 0.0628937 0.998020i \(-0.479967\pi\)
0.0628937 + 0.998020i \(0.479967\pi\)
\(284\) 58.4238 3.46682
\(285\) 7.53071 0.446081
\(286\) 30.9430 1.82970
\(287\) −11.2951 −0.666727
\(288\) −17.2697 −1.01762
\(289\) −14.7354 −0.866788
\(290\) 5.23515 0.307419
\(291\) −14.0957 −0.826303
\(292\) −58.1541 −3.40321
\(293\) 2.87678 0.168063 0.0840317 0.996463i \(-0.473220\pi\)
0.0840317 + 0.996463i \(0.473220\pi\)
\(294\) 17.0304 0.993231
\(295\) −14.4728 −0.842638
\(296\) 3.10367 0.180397
\(297\) −4.57892 −0.265696
\(298\) 36.8155 2.13267
\(299\) −21.1074 −1.22067
\(300\) 21.6559 1.25031
\(301\) 31.4526 1.81290
\(302\) 21.9280 1.26182
\(303\) 22.7642 1.30777
\(304\) −14.4446 −0.828457
\(305\) 24.8366 1.42214
\(306\) 9.80606 0.560575
\(307\) 25.2953 1.44368 0.721840 0.692060i \(-0.243297\pi\)
0.721840 + 0.692060i \(0.243297\pi\)
\(308\) 60.7515 3.46164
\(309\) −35.1144 −1.99759
\(310\) 31.1262 1.76785
\(311\) 0.219709 0.0124585 0.00622927 0.999981i \(-0.498017\pi\)
0.00622927 + 0.999981i \(0.498017\pi\)
\(312\) 44.3635 2.51159
\(313\) 30.9954 1.75197 0.875983 0.482342i \(-0.160214\pi\)
0.875983 + 0.482342i \(0.160214\pi\)
\(314\) 30.2197 1.70539
\(315\) −13.7684 −0.775761
\(316\) −3.78869 −0.213131
\(317\) 19.5578 1.09848 0.549238 0.835666i \(-0.314918\pi\)
0.549238 + 0.835666i \(0.314918\pi\)
\(318\) −37.8031 −2.11989
\(319\) 4.99691 0.279773
\(320\) 3.14696 0.175920
\(321\) 33.9255 1.89354
\(322\) −59.5423 −3.31816
\(323\) 2.78402 0.154907
\(324\) −46.5541 −2.58634
\(325\) −5.72540 −0.317588
\(326\) 45.4211 2.51564
\(327\) 8.05899 0.445663
\(328\) −23.8401 −1.31635
\(329\) 35.2890 1.94554
\(330\) −44.2044 −2.43337
\(331\) 0.257369 0.0141463 0.00707314 0.999975i \(-0.497749\pi\)
0.00707314 + 0.999975i \(0.497749\pi\)
\(332\) −57.8135 −3.17293
\(333\) −1.19209 −0.0653259
\(334\) 38.0854 2.08394
\(335\) 24.8326 1.35675
\(336\) 57.5945 3.14204
\(337\) 13.2799 0.723400 0.361700 0.932295i \(-0.382196\pi\)
0.361700 + 0.932295i \(0.382196\pi\)
\(338\) 12.5188 0.680932
\(339\) 47.2252 2.56492
\(340\) −11.9161 −0.646241
\(341\) 29.7098 1.60887
\(342\) 12.0552 0.651868
\(343\) 13.0968 0.707161
\(344\) 66.3858 3.57928
\(345\) 30.1536 1.62341
\(346\) 19.0791 1.02570
\(347\) 9.05813 0.486266 0.243133 0.969993i \(-0.421825\pi\)
0.243133 + 0.969993i \(0.421825\pi\)
\(348\) 12.7203 0.681881
\(349\) −1.78507 −0.0955525 −0.0477763 0.998858i \(-0.515213\pi\)
−0.0477763 + 0.998858i \(0.515213\pi\)
\(350\) −16.1509 −0.863301
\(351\) 3.08170 0.164489
\(352\) 28.7800 1.53398
\(353\) −10.4495 −0.556172 −0.278086 0.960556i \(-0.589700\pi\)
−0.278086 + 0.960556i \(0.589700\pi\)
\(354\) −50.5261 −2.68543
\(355\) 22.0660 1.17114
\(356\) 73.9699 3.92040
\(357\) −11.1006 −0.587505
\(358\) −31.5731 −1.66869
\(359\) 25.1178 1.32567 0.662833 0.748768i \(-0.269354\pi\)
0.662833 + 0.748768i \(0.269354\pi\)
\(360\) −29.0604 −1.53162
\(361\) −15.5774 −0.819866
\(362\) 61.6151 3.23842
\(363\) −16.3006 −0.855557
\(364\) −40.8868 −2.14305
\(365\) −21.9641 −1.14965
\(366\) 86.7074 4.53227
\(367\) 15.7527 0.822284 0.411142 0.911571i \(-0.365130\pi\)
0.411142 + 0.911571i \(0.365130\pi\)
\(368\) −57.8376 −3.01499
\(369\) 9.15671 0.476679
\(370\) 2.08133 0.108203
\(371\) 19.6224 1.01874
\(372\) 75.6303 3.92125
\(373\) 8.45360 0.437711 0.218855 0.975757i \(-0.429768\pi\)
0.218855 + 0.975757i \(0.429768\pi\)
\(374\) −16.3418 −0.845017
\(375\) 28.5323 1.47340
\(376\) 74.4830 3.84117
\(377\) −3.36301 −0.173204
\(378\) 8.69320 0.447130
\(379\) 22.5437 1.15799 0.578996 0.815330i \(-0.303445\pi\)
0.578996 + 0.815330i \(0.303445\pi\)
\(380\) −14.6491 −0.751486
\(381\) 1.96218 0.100525
\(382\) −56.3115 −2.88115
\(383\) −29.1214 −1.48803 −0.744017 0.668161i \(-0.767082\pi\)
−0.744017 + 0.668161i \(0.767082\pi\)
\(384\) −21.0147 −1.07240
\(385\) 22.9451 1.16939
\(386\) −38.2916 −1.94899
\(387\) −25.4981 −1.29614
\(388\) 27.4197 1.39202
\(389\) 27.9047 1.41483 0.707413 0.706800i \(-0.249862\pi\)
0.707413 + 0.706800i \(0.249862\pi\)
\(390\) 29.7503 1.50647
\(391\) 11.1474 0.563750
\(392\) −18.6581 −0.942375
\(393\) −31.8514 −1.60669
\(394\) 28.5032 1.43597
\(395\) −1.43094 −0.0719985
\(396\) −49.2502 −2.47491
\(397\) 0.653695 0.0328080 0.0164040 0.999865i \(-0.494778\pi\)
0.0164040 + 0.999865i \(0.494778\pi\)
\(398\) 23.1292 1.15936
\(399\) −13.6466 −0.683185
\(400\) −15.6885 −0.784423
\(401\) −11.4916 −0.573861 −0.286930 0.957951i \(-0.592635\pi\)
−0.286930 + 0.957951i \(0.592635\pi\)
\(402\) 86.6936 4.32388
\(403\) −19.9952 −0.996031
\(404\) −44.2822 −2.20312
\(405\) −17.5829 −0.873701
\(406\) −9.48676 −0.470820
\(407\) 1.98662 0.0984729
\(408\) −23.4296 −1.15994
\(409\) −17.6216 −0.871334 −0.435667 0.900108i \(-0.643488\pi\)
−0.435667 + 0.900108i \(0.643488\pi\)
\(410\) −15.9873 −0.789554
\(411\) −14.9813 −0.738975
\(412\) 68.3064 3.36522
\(413\) 26.2265 1.29052
\(414\) 48.2699 2.37233
\(415\) −21.8354 −1.07186
\(416\) −19.3694 −0.949664
\(417\) −0.563368 −0.0275882
\(418\) −20.0900 −0.982633
\(419\) 29.9448 1.46290 0.731450 0.681896i \(-0.238844\pi\)
0.731450 + 0.681896i \(0.238844\pi\)
\(420\) 58.4100 2.85011
\(421\) 12.5826 0.613238 0.306619 0.951832i \(-0.400802\pi\)
0.306619 + 0.951832i \(0.400802\pi\)
\(422\) −65.1938 −3.17359
\(423\) −28.6081 −1.39098
\(424\) 41.4162 2.01135
\(425\) 3.02375 0.146673
\(426\) 77.0348 3.73235
\(427\) −45.0071 −2.17804
\(428\) −65.9939 −3.18993
\(429\) 28.3964 1.37099
\(430\) 44.5186 2.14688
\(431\) 4.02343 0.193802 0.0969010 0.995294i \(-0.469107\pi\)
0.0969010 + 0.995294i \(0.469107\pi\)
\(432\) 8.44431 0.406277
\(433\) 3.50484 0.168432 0.0842159 0.996448i \(-0.473161\pi\)
0.0842159 + 0.996448i \(0.473161\pi\)
\(434\) −56.4047 −2.70751
\(435\) 4.80431 0.230349
\(436\) −15.6768 −0.750782
\(437\) 13.7042 0.655560
\(438\) −76.6792 −3.66387
\(439\) 26.2372 1.25223 0.626116 0.779730i \(-0.284644\pi\)
0.626116 + 0.779730i \(0.284644\pi\)
\(440\) 48.4293 2.30878
\(441\) 7.16637 0.341256
\(442\) 10.9983 0.523138
\(443\) 0.516363 0.0245331 0.0122666 0.999925i \(-0.496095\pi\)
0.0122666 + 0.999925i \(0.496095\pi\)
\(444\) 5.05721 0.240004
\(445\) 27.9375 1.32437
\(446\) 21.4199 1.01426
\(447\) 33.7857 1.59801
\(448\) −5.70269 −0.269427
\(449\) −18.1358 −0.855882 −0.427941 0.903807i \(-0.640761\pi\)
−0.427941 + 0.903807i \(0.640761\pi\)
\(450\) 13.0932 0.617221
\(451\) −15.2597 −0.718551
\(452\) −91.8652 −4.32097
\(453\) 20.1234 0.945481
\(454\) 57.1227 2.68090
\(455\) −15.4425 −0.723953
\(456\) −28.8034 −1.34884
\(457\) 13.9130 0.650825 0.325412 0.945572i \(-0.394497\pi\)
0.325412 + 0.945572i \(0.394497\pi\)
\(458\) −12.9042 −0.602973
\(459\) −1.62753 −0.0759666
\(460\) −58.6564 −2.73487
\(461\) −41.6907 −1.94173 −0.970865 0.239626i \(-0.922975\pi\)
−0.970865 + 0.239626i \(0.922975\pi\)
\(462\) 80.1040 3.72677
\(463\) 8.96811 0.416783 0.208392 0.978045i \(-0.433177\pi\)
0.208392 + 0.978045i \(0.433177\pi\)
\(464\) −9.21515 −0.427802
\(465\) 28.5646 1.32465
\(466\) −0.556423 −0.0257758
\(467\) −40.1977 −1.86013 −0.930064 0.367397i \(-0.880249\pi\)
−0.930064 + 0.367397i \(0.880249\pi\)
\(468\) 33.1462 1.53218
\(469\) −44.9999 −2.07790
\(470\) 49.9487 2.30396
\(471\) 27.7327 1.27785
\(472\) 55.3553 2.54793
\(473\) 42.4927 1.95381
\(474\) −4.99559 −0.229455
\(475\) 3.71727 0.170560
\(476\) 21.5935 0.989736
\(477\) −15.9075 −0.728356
\(478\) −10.4149 −0.476367
\(479\) 3.64681 0.166627 0.0833134 0.996523i \(-0.473450\pi\)
0.0833134 + 0.996523i \(0.473450\pi\)
\(480\) 27.6707 1.26299
\(481\) −1.33703 −0.0609632
\(482\) −8.50262 −0.387284
\(483\) −54.6421 −2.48630
\(484\) 31.7087 1.44131
\(485\) 10.3561 0.470245
\(486\) −53.0619 −2.40694
\(487\) 14.1341 0.640479 0.320239 0.947337i \(-0.396237\pi\)
0.320239 + 0.947337i \(0.396237\pi\)
\(488\) −94.9947 −4.30021
\(489\) 41.6831 1.88498
\(490\) −12.5122 −0.565243
\(491\) −7.46697 −0.336980 −0.168490 0.985703i \(-0.553889\pi\)
−0.168490 + 0.985703i \(0.553889\pi\)
\(492\) −38.8457 −1.75130
\(493\) 1.77610 0.0799914
\(494\) 13.5209 0.608335
\(495\) −18.6012 −0.836061
\(496\) −54.7898 −2.46014
\(497\) −39.9863 −1.79363
\(498\) −76.2300 −3.41595
\(499\) 40.3277 1.80531 0.902657 0.430360i \(-0.141613\pi\)
0.902657 + 0.430360i \(0.141613\pi\)
\(500\) −55.5026 −2.48215
\(501\) 34.9510 1.56150
\(502\) 61.7189 2.75465
\(503\) −17.4210 −0.776765 −0.388383 0.921498i \(-0.626966\pi\)
−0.388383 + 0.921498i \(0.626966\pi\)
\(504\) 52.6612 2.34572
\(505\) −16.7248 −0.744246
\(506\) −80.4420 −3.57608
\(507\) 11.4885 0.510223
\(508\) −3.81694 −0.169349
\(509\) 7.67650 0.340255 0.170127 0.985422i \(-0.445582\pi\)
0.170127 + 0.985422i \(0.445582\pi\)
\(510\) −15.7120 −0.695738
\(511\) 39.8017 1.76073
\(512\) 50.2139 2.21916
\(513\) −2.00082 −0.0883382
\(514\) 33.9537 1.49763
\(515\) 25.7985 1.13682
\(516\) 108.171 4.76197
\(517\) 47.6756 2.09677
\(518\) −3.77164 −0.165716
\(519\) 17.5090 0.768558
\(520\) −32.5938 −1.42933
\(521\) −25.6705 −1.12465 −0.562323 0.826918i \(-0.690092\pi\)
−0.562323 + 0.826918i \(0.690092\pi\)
\(522\) 7.69074 0.336615
\(523\) 10.3769 0.453749 0.226874 0.973924i \(-0.427149\pi\)
0.226874 + 0.973924i \(0.427149\pi\)
\(524\) 61.9591 2.70670
\(525\) −14.8217 −0.646872
\(526\) −57.4338 −2.50423
\(527\) 10.5600 0.460002
\(528\) 77.8105 3.38627
\(529\) 31.8727 1.38577
\(530\) 27.7739 1.20642
\(531\) −21.2614 −0.922665
\(532\) 26.5461 1.15092
\(533\) 10.2700 0.444845
\(534\) 97.5331 4.22067
\(535\) −24.9251 −1.07760
\(536\) −94.9795 −4.10249
\(537\) −28.9747 −1.25035
\(538\) 29.8218 1.28571
\(539\) −11.9428 −0.514412
\(540\) 8.56386 0.368530
\(541\) −33.8666 −1.45604 −0.728018 0.685558i \(-0.759558\pi\)
−0.728018 + 0.685558i \(0.759558\pi\)
\(542\) −52.1322 −2.23927
\(543\) 56.5444 2.42655
\(544\) 10.2295 0.438588
\(545\) −5.92093 −0.253625
\(546\) −53.9114 −2.30719
\(547\) −28.0498 −1.19932 −0.599662 0.800254i \(-0.704698\pi\)
−0.599662 + 0.800254i \(0.704698\pi\)
\(548\) 29.1425 1.24491
\(549\) 36.4864 1.55720
\(550\) −21.8199 −0.930405
\(551\) 2.18346 0.0930186
\(552\) −115.331 −4.90881
\(553\) 2.59305 0.110268
\(554\) 58.5085 2.48579
\(555\) 1.91005 0.0810769
\(556\) 1.09589 0.0464763
\(557\) 9.44587 0.400234 0.200117 0.979772i \(-0.435868\pi\)
0.200117 + 0.979772i \(0.435868\pi\)
\(558\) 45.7263 1.93575
\(559\) −28.5983 −1.20958
\(560\) −42.3146 −1.78812
\(561\) −14.9970 −0.633172
\(562\) 71.3182 3.00838
\(563\) 20.5234 0.864960 0.432480 0.901643i \(-0.357639\pi\)
0.432480 + 0.901643i \(0.357639\pi\)
\(564\) 121.365 5.11038
\(565\) −34.6963 −1.45969
\(566\) −5.42755 −0.228137
\(567\) 31.8625 1.33810
\(568\) −84.3976 −3.54124
\(569\) −36.4038 −1.52613 −0.763064 0.646323i \(-0.776306\pi\)
−0.763064 + 0.646323i \(0.776306\pi\)
\(570\) −19.3157 −0.809044
\(571\) −1.13713 −0.0475872 −0.0237936 0.999717i \(-0.507574\pi\)
−0.0237936 + 0.999717i \(0.507574\pi\)
\(572\) −55.2383 −2.30963
\(573\) −51.6773 −2.15885
\(574\) 28.9709 1.20922
\(575\) 14.8842 0.620716
\(576\) 4.62307 0.192628
\(577\) 5.13363 0.213716 0.106858 0.994274i \(-0.465921\pi\)
0.106858 + 0.994274i \(0.465921\pi\)
\(578\) 37.7951 1.57207
\(579\) −35.1404 −1.46038
\(580\) −9.34561 −0.388055
\(581\) 39.5686 1.64158
\(582\) 36.1543 1.49864
\(583\) 26.5100 1.09793
\(584\) 84.0080 3.47628
\(585\) 12.5189 0.517594
\(586\) −7.37871 −0.304812
\(587\) 19.5210 0.805716 0.402858 0.915263i \(-0.368017\pi\)
0.402858 + 0.915263i \(0.368017\pi\)
\(588\) −30.4020 −1.25376
\(589\) 12.9820 0.534916
\(590\) 37.1215 1.52827
\(591\) 26.1575 1.07597
\(592\) −3.66366 −0.150575
\(593\) 36.7443 1.50891 0.754453 0.656354i \(-0.227902\pi\)
0.754453 + 0.656354i \(0.227902\pi\)
\(594\) 11.7446 0.481885
\(595\) 8.15559 0.334347
\(596\) −65.7219 −2.69207
\(597\) 21.2258 0.868712
\(598\) 54.1389 2.21390
\(599\) −15.2825 −0.624425 −0.312212 0.950012i \(-0.601070\pi\)
−0.312212 + 0.950012i \(0.601070\pi\)
\(600\) −31.2836 −1.27715
\(601\) 30.3715 1.23888 0.619440 0.785044i \(-0.287360\pi\)
0.619440 + 0.785044i \(0.287360\pi\)
\(602\) −80.6734 −3.28800
\(603\) 36.4806 1.48561
\(604\) −39.1452 −1.59280
\(605\) 11.9760 0.486894
\(606\) −58.3883 −2.37186
\(607\) 33.1723 1.34642 0.673212 0.739450i \(-0.264914\pi\)
0.673212 + 0.739450i \(0.264914\pi\)
\(608\) 12.5758 0.510015
\(609\) −8.70602 −0.352786
\(610\) −63.7038 −2.57929
\(611\) −32.0865 −1.29808
\(612\) −17.5055 −0.707616
\(613\) 2.52504 0.101985 0.0509927 0.998699i \(-0.483761\pi\)
0.0509927 + 0.998699i \(0.483761\pi\)
\(614\) −64.8804 −2.61836
\(615\) −14.6715 −0.591614
\(616\) −87.7601 −3.53595
\(617\) 12.3309 0.496424 0.248212 0.968706i \(-0.420157\pi\)
0.248212 + 0.968706i \(0.420157\pi\)
\(618\) 90.0655 3.62297
\(619\) −3.69101 −0.148354 −0.0741771 0.997245i \(-0.523633\pi\)
−0.0741771 + 0.997245i \(0.523633\pi\)
\(620\) −55.5655 −2.23157
\(621\) −8.01144 −0.321488
\(622\) −0.563535 −0.0225957
\(623\) −50.6263 −2.02830
\(624\) −52.3679 −2.09639
\(625\) −10.9160 −0.436642
\(626\) −79.5008 −3.17749
\(627\) −18.4366 −0.736288
\(628\) −53.9471 −2.15272
\(629\) 0.706121 0.0281549
\(630\) 35.3148 1.40698
\(631\) 28.4517 1.13264 0.566321 0.824185i \(-0.308366\pi\)
0.566321 + 0.824185i \(0.308366\pi\)
\(632\) 5.47305 0.217706
\(633\) −59.8286 −2.37797
\(634\) −50.1642 −1.99227
\(635\) −1.44161 −0.0572086
\(636\) 67.4849 2.67595
\(637\) 8.03771 0.318465
\(638\) −12.8167 −0.507416
\(639\) 32.4162 1.28237
\(640\) 15.4395 0.610299
\(641\) 25.8084 1.01937 0.509684 0.860361i \(-0.329762\pi\)
0.509684 + 0.860361i \(0.329762\pi\)
\(642\) −87.0163 −3.43426
\(643\) 21.3973 0.843828 0.421914 0.906636i \(-0.361358\pi\)
0.421914 + 0.906636i \(0.361358\pi\)
\(644\) 106.293 4.18853
\(645\) 40.8549 1.60866
\(646\) −7.14077 −0.280950
\(647\) −15.4759 −0.608419 −0.304210 0.952605i \(-0.598392\pi\)
−0.304210 + 0.952605i \(0.598392\pi\)
\(648\) 67.2509 2.64186
\(649\) 35.4322 1.39083
\(650\) 14.6852 0.576001
\(651\) −51.7628 −2.02874
\(652\) −81.0843 −3.17551
\(653\) 19.5037 0.763238 0.381619 0.924320i \(-0.375367\pi\)
0.381619 + 0.924320i \(0.375367\pi\)
\(654\) −20.6706 −0.808286
\(655\) 23.4012 0.914361
\(656\) 28.1415 1.09874
\(657\) −32.2666 −1.25884
\(658\) −90.5133 −3.52858
\(659\) 0.261503 0.0101867 0.00509336 0.999987i \(-0.498379\pi\)
0.00509336 + 0.999987i \(0.498379\pi\)
\(660\) 78.9122 3.07165
\(661\) −3.09137 −0.120240 −0.0601202 0.998191i \(-0.519148\pi\)
−0.0601202 + 0.998191i \(0.519148\pi\)
\(662\) −0.660131 −0.0256567
\(663\) 10.0932 0.391988
\(664\) 83.5159 3.24105
\(665\) 10.0261 0.388797
\(666\) 3.05760 0.118480
\(667\) 8.74276 0.338521
\(668\) −67.9887 −2.63056
\(669\) 19.6571 0.759989
\(670\) −63.6937 −2.46070
\(671\) −60.8048 −2.34734
\(672\) −50.1428 −1.93430
\(673\) 33.6025 1.29528 0.647640 0.761946i \(-0.275756\pi\)
0.647640 + 0.761946i \(0.275756\pi\)
\(674\) −34.0617 −1.31201
\(675\) −2.17311 −0.0836429
\(676\) −22.3481 −0.859543
\(677\) 0.107883 0.00414628 0.00207314 0.999998i \(-0.499340\pi\)
0.00207314 + 0.999998i \(0.499340\pi\)
\(678\) −121.129 −4.65193
\(679\) −18.7665 −0.720193
\(680\) 17.2137 0.660115
\(681\) 52.4217 2.00880
\(682\) −76.2031 −2.91797
\(683\) −41.5019 −1.58802 −0.794012 0.607902i \(-0.792011\pi\)
−0.794012 + 0.607902i \(0.792011\pi\)
\(684\) −21.5205 −0.822856
\(685\) 11.0068 0.420548
\(686\) −33.5922 −1.28256
\(687\) −11.8422 −0.451808
\(688\) −78.3637 −2.98759
\(689\) −17.8417 −0.679714
\(690\) −77.3415 −2.94434
\(691\) −29.4036 −1.11856 −0.559282 0.828977i \(-0.688923\pi\)
−0.559282 + 0.828977i \(0.688923\pi\)
\(692\) −34.0594 −1.29474
\(693\) 33.7077 1.28045
\(694\) −23.2334 −0.881926
\(695\) 0.413906 0.0157003
\(696\) −18.3755 −0.696520
\(697\) −5.42390 −0.205445
\(698\) 4.57856 0.173301
\(699\) −0.510631 −0.0193138
\(700\) 28.8320 1.08975
\(701\) 32.0049 1.20881 0.604404 0.796678i \(-0.293411\pi\)
0.604404 + 0.796678i \(0.293411\pi\)
\(702\) −7.90430 −0.298328
\(703\) 0.868076 0.0327401
\(704\) −7.70437 −0.290369
\(705\) 45.8380 1.72636
\(706\) 26.8022 1.00871
\(707\) 30.3075 1.13983
\(708\) 90.1976 3.38983
\(709\) 16.2222 0.609238 0.304619 0.952474i \(-0.401471\pi\)
0.304619 + 0.952474i \(0.401471\pi\)
\(710\) −56.5974 −2.12406
\(711\) −2.10214 −0.0788364
\(712\) −106.855 −4.00456
\(713\) 51.9812 1.94671
\(714\) 28.4721 1.06554
\(715\) −20.8628 −0.780226
\(716\) 56.3633 2.10639
\(717\) −9.55780 −0.356943
\(718\) −64.4250 −2.40432
\(719\) −27.5372 −1.02696 −0.513482 0.858101i \(-0.671645\pi\)
−0.513482 + 0.858101i \(0.671645\pi\)
\(720\) 34.3037 1.27842
\(721\) −46.7502 −1.74107
\(722\) 39.9549 1.48697
\(723\) −7.80288 −0.290192
\(724\) −109.993 −4.08787
\(725\) 2.37148 0.0880745
\(726\) 41.8096 1.55170
\(727\) 2.58108 0.0957268 0.0478634 0.998854i \(-0.484759\pi\)
0.0478634 + 0.998854i \(0.484759\pi\)
\(728\) 59.0641 2.18906
\(729\) −18.1932 −0.673823
\(730\) 56.3361 2.08509
\(731\) 15.1036 0.558626
\(732\) −154.787 −5.72110
\(733\) −20.2967 −0.749675 −0.374837 0.927091i \(-0.622301\pi\)
−0.374837 + 0.927091i \(0.622301\pi\)
\(734\) −40.4044 −1.49135
\(735\) −11.4825 −0.423537
\(736\) 50.3544 1.85609
\(737\) −60.7951 −2.23942
\(738\) −23.4862 −0.864540
\(739\) −32.4696 −1.19441 −0.597207 0.802087i \(-0.703723\pi\)
−0.597207 + 0.802087i \(0.703723\pi\)
\(740\) −3.71553 −0.136585
\(741\) 12.4082 0.455826
\(742\) −50.3299 −1.84767
\(743\) −4.23816 −0.155483 −0.0777416 0.996974i \(-0.524771\pi\)
−0.0777416 + 0.996974i \(0.524771\pi\)
\(744\) −109.254 −4.00543
\(745\) −24.8223 −0.909420
\(746\) −21.6828 −0.793863
\(747\) −32.0776 −1.17366
\(748\) 29.1729 1.06667
\(749\) 45.1674 1.65038
\(750\) −73.1830 −2.67226
\(751\) −43.3553 −1.58206 −0.791028 0.611780i \(-0.790454\pi\)
−0.791028 + 0.611780i \(0.790454\pi\)
\(752\) −87.9219 −3.20618
\(753\) 56.6397 2.06406
\(754\) 8.62584 0.314135
\(755\) −14.7847 −0.538069
\(756\) −15.5188 −0.564414
\(757\) 21.8697 0.794867 0.397434 0.917631i \(-0.369901\pi\)
0.397434 + 0.917631i \(0.369901\pi\)
\(758\) −57.8227 −2.10022
\(759\) −73.8218 −2.67956
\(760\) 21.1618 0.767619
\(761\) 1.57884 0.0572328 0.0286164 0.999590i \(-0.490890\pi\)
0.0286164 + 0.999590i \(0.490890\pi\)
\(762\) −5.03283 −0.182320
\(763\) 10.7295 0.388433
\(764\) 100.525 3.63688
\(765\) −6.61159 −0.239043
\(766\) 74.6940 2.69880
\(767\) −23.8465 −0.861046
\(768\) 62.4677 2.25411
\(769\) 24.0855 0.868545 0.434272 0.900782i \(-0.357006\pi\)
0.434272 + 0.900782i \(0.357006\pi\)
\(770\) −58.8523 −2.12089
\(771\) 31.1594 1.12218
\(772\) 68.3570 2.46022
\(773\) −28.4294 −1.02253 −0.511266 0.859422i \(-0.670823\pi\)
−0.511266 + 0.859422i \(0.670823\pi\)
\(774\) 65.4005 2.35077
\(775\) 14.0999 0.506484
\(776\) −39.6098 −1.42191
\(777\) −3.46124 −0.124171
\(778\) −71.5734 −2.56603
\(779\) −6.66792 −0.238903
\(780\) −53.1093 −1.90162
\(781\) −54.0217 −1.93305
\(782\) −28.5922 −1.02246
\(783\) −1.27645 −0.0456165
\(784\) 22.0245 0.786590
\(785\) −20.3752 −0.727221
\(786\) 81.6963 2.91401
\(787\) 10.3541 0.369083 0.184541 0.982825i \(-0.440920\pi\)
0.184541 + 0.982825i \(0.440920\pi\)
\(788\) −50.8830 −1.81263
\(789\) −52.7072 −1.87643
\(790\) 3.67025 0.130582
\(791\) 62.8742 2.23555
\(792\) 71.1455 2.52805
\(793\) 40.9227 1.45321
\(794\) −1.67667 −0.0595029
\(795\) 25.4882 0.903973
\(796\) −41.2895 −1.46347
\(797\) 17.6804 0.626273 0.313137 0.949708i \(-0.398620\pi\)
0.313137 + 0.949708i \(0.398620\pi\)
\(798\) 35.0024 1.23907
\(799\) 16.9458 0.599499
\(800\) 13.6587 0.482907
\(801\) 41.0419 1.45014
\(802\) 29.4749 1.04079
\(803\) 53.7724 1.89759
\(804\) −154.762 −5.45805
\(805\) 40.1455 1.41494
\(806\) 51.2860 1.80647
\(807\) 27.3675 0.963382
\(808\) 63.9690 2.25042
\(809\) −2.30859 −0.0811657 −0.0405829 0.999176i \(-0.512921\pi\)
−0.0405829 + 0.999176i \(0.512921\pi\)
\(810\) 45.0987 1.58461
\(811\) −32.7612 −1.15040 −0.575201 0.818012i \(-0.695076\pi\)
−0.575201 + 0.818012i \(0.695076\pi\)
\(812\) 16.9354 0.594317
\(813\) −47.8419 −1.67789
\(814\) −5.09551 −0.178597
\(815\) −30.6245 −1.07273
\(816\) 27.6569 0.968186
\(817\) 18.5677 0.649602
\(818\) 45.1981 1.58031
\(819\) −22.6859 −0.792709
\(820\) 28.5399 0.996657
\(821\) 38.2226 1.33398 0.666989 0.745068i \(-0.267583\pi\)
0.666989 + 0.745068i \(0.267583\pi\)
\(822\) 38.4259 1.34026
\(823\) 21.1413 0.736940 0.368470 0.929640i \(-0.379882\pi\)
0.368470 + 0.929640i \(0.379882\pi\)
\(824\) −98.6738 −3.43746
\(825\) −20.0242 −0.697153
\(826\) −67.2689 −2.34058
\(827\) 29.9798 1.04250 0.521250 0.853404i \(-0.325466\pi\)
0.521250 + 0.853404i \(0.325466\pi\)
\(828\) −86.1698 −2.99461
\(829\) 7.93885 0.275728 0.137864 0.990451i \(-0.455976\pi\)
0.137864 + 0.990451i \(0.455976\pi\)
\(830\) 56.0061 1.94400
\(831\) 53.6934 1.86260
\(832\) 5.18517 0.179764
\(833\) −4.24494 −0.147078
\(834\) 1.44499 0.0500360
\(835\) −25.6785 −0.888641
\(836\) 35.8640 1.24038
\(837\) −7.58928 −0.262324
\(838\) −76.8060 −2.65322
\(839\) 42.6530 1.47254 0.736272 0.676686i \(-0.236584\pi\)
0.736272 + 0.676686i \(0.236584\pi\)
\(840\) −84.3775 −2.91130
\(841\) −27.6070 −0.951967
\(842\) −32.2733 −1.11221
\(843\) 65.4489 2.25418
\(844\) 116.382 4.00603
\(845\) −8.44060 −0.290366
\(846\) 73.3775 2.52277
\(847\) −21.7020 −0.745691
\(848\) −48.8889 −1.67885
\(849\) −4.98088 −0.170943
\(850\) −7.75566 −0.266017
\(851\) 3.47585 0.119151
\(852\) −137.520 −4.71136
\(853\) 46.8850 1.60531 0.802657 0.596442i \(-0.203419\pi\)
0.802657 + 0.596442i \(0.203419\pi\)
\(854\) 115.439 3.95026
\(855\) −8.12802 −0.277972
\(856\) 95.3331 3.25842
\(857\) 0.963805 0.0329230 0.0164615 0.999865i \(-0.494760\pi\)
0.0164615 + 0.999865i \(0.494760\pi\)
\(858\) −72.8346 −2.48653
\(859\) 4.46872 0.152471 0.0762353 0.997090i \(-0.475710\pi\)
0.0762353 + 0.997090i \(0.475710\pi\)
\(860\) −79.4732 −2.71001
\(861\) 26.5867 0.906073
\(862\) −10.3198 −0.351493
\(863\) 13.6613 0.465038 0.232519 0.972592i \(-0.425303\pi\)
0.232519 + 0.972592i \(0.425303\pi\)
\(864\) −7.35177 −0.250112
\(865\) −12.8638 −0.437383
\(866\) −8.98963 −0.305480
\(867\) 34.6847 1.17795
\(868\) 100.692 3.41770
\(869\) 3.50323 0.118839
\(870\) −12.3227 −0.417778
\(871\) 40.9162 1.38639
\(872\) 22.6463 0.766900
\(873\) 15.2137 0.514905
\(874\) −35.1501 −1.18897
\(875\) 37.9870 1.28419
\(876\) 136.885 4.62492
\(877\) −2.14149 −0.0723129 −0.0361565 0.999346i \(-0.511511\pi\)
−0.0361565 + 0.999346i \(0.511511\pi\)
\(878\) −67.2962 −2.27114
\(879\) −6.77146 −0.228396
\(880\) −57.1673 −1.92711
\(881\) 7.40246 0.249395 0.124698 0.992195i \(-0.460204\pi\)
0.124698 + 0.992195i \(0.460204\pi\)
\(882\) −18.3811 −0.618925
\(883\) −35.5025 −1.19476 −0.597378 0.801960i \(-0.703791\pi\)
−0.597378 + 0.801960i \(0.703791\pi\)
\(884\) −19.6339 −0.660359
\(885\) 34.0665 1.14513
\(886\) −1.32443 −0.0444950
\(887\) −37.9021 −1.27263 −0.636314 0.771430i \(-0.719542\pi\)
−0.636314 + 0.771430i \(0.719542\pi\)
\(888\) −7.30552 −0.245157
\(889\) 2.61238 0.0876164
\(890\) −71.6575 −2.40196
\(891\) 43.0464 1.44211
\(892\) −38.2381 −1.28031
\(893\) 20.8324 0.697131
\(894\) −86.6576 −2.89826
\(895\) 21.2877 0.711570
\(896\) −27.9783 −0.934690
\(897\) 49.6834 1.65888
\(898\) 46.5169 1.55229
\(899\) 8.28206 0.276222
\(900\) −23.3736 −0.779120
\(901\) 9.42269 0.313915
\(902\) 39.1399 1.30322
\(903\) −74.0342 −2.46370
\(904\) 132.706 4.41374
\(905\) −41.5431 −1.38094
\(906\) −51.6149 −1.71479
\(907\) 33.0502 1.09741 0.548707 0.836015i \(-0.315120\pi\)
0.548707 + 0.836015i \(0.315120\pi\)
\(908\) −101.974 −3.38411
\(909\) −24.5698 −0.814928
\(910\) 39.6086 1.31301
\(911\) −16.3806 −0.542715 −0.271357 0.962479i \(-0.587473\pi\)
−0.271357 + 0.962479i \(0.587473\pi\)
\(912\) 34.0003 1.12586
\(913\) 53.4574 1.76918
\(914\) −35.6858 −1.18038
\(915\) −58.4612 −1.93267
\(916\) 23.0361 0.761135
\(917\) −42.4060 −1.40037
\(918\) 4.17448 0.137778
\(919\) 11.4723 0.378436 0.189218 0.981935i \(-0.439405\pi\)
0.189218 + 0.981935i \(0.439405\pi\)
\(920\) 84.7336 2.79358
\(921\) −59.5409 −1.96194
\(922\) 106.933 3.52166
\(923\) 36.3576 1.19672
\(924\) −142.999 −4.70432
\(925\) 0.942826 0.0309999
\(926\) −23.0025 −0.755908
\(927\) 37.8995 1.24478
\(928\) 8.02287 0.263364
\(929\) −34.0419 −1.11688 −0.558439 0.829545i \(-0.688600\pi\)
−0.558439 + 0.829545i \(0.688600\pi\)
\(930\) −73.2660 −2.40249
\(931\) −5.21855 −0.171031
\(932\) 0.993307 0.0325369
\(933\) −0.517158 −0.0169310
\(934\) 103.104 3.37366
\(935\) 11.0182 0.360335
\(936\) −47.8822 −1.56508
\(937\) −32.5403 −1.06305 −0.531523 0.847044i \(-0.678380\pi\)
−0.531523 + 0.847044i \(0.678380\pi\)
\(938\) 115.421 3.76863
\(939\) −72.9581 −2.38090
\(940\) −89.1667 −2.90830
\(941\) 12.8669 0.419449 0.209724 0.977761i \(-0.432743\pi\)
0.209724 + 0.977761i \(0.432743\pi\)
\(942\) −71.1320 −2.31761
\(943\) −26.6989 −0.869436
\(944\) −65.3429 −2.12673
\(945\) −5.86126 −0.190667
\(946\) −108.990 −3.54358
\(947\) −8.06349 −0.262028 −0.131014 0.991381i \(-0.541823\pi\)
−0.131014 + 0.991381i \(0.541823\pi\)
\(948\) 8.91795 0.289642
\(949\) −36.1898 −1.17477
\(950\) −9.53449 −0.309340
\(951\) −46.0358 −1.49281
\(952\) −31.1934 −1.01098
\(953\) −16.7651 −0.543075 −0.271537 0.962428i \(-0.587532\pi\)
−0.271537 + 0.962428i \(0.587532\pi\)
\(954\) 40.8015 1.32100
\(955\) 37.9672 1.22859
\(956\) 18.5924 0.601320
\(957\) −11.7619 −0.380208
\(958\) −9.35376 −0.302206
\(959\) −19.9457 −0.644080
\(960\) −7.40742 −0.239073
\(961\) 18.2421 0.588453
\(962\) 3.42937 0.110567
\(963\) −36.6164 −1.17995
\(964\) 15.1786 0.488870
\(965\) 25.8176 0.831097
\(966\) 140.153 4.50934
\(967\) −21.4038 −0.688301 −0.344150 0.938915i \(-0.611833\pi\)
−0.344150 + 0.938915i \(0.611833\pi\)
\(968\) −45.8056 −1.47225
\(969\) −6.55311 −0.210516
\(970\) −26.5625 −0.852870
\(971\) 28.5292 0.915546 0.457773 0.889069i \(-0.348647\pi\)
0.457773 + 0.889069i \(0.348647\pi\)
\(972\) 94.7244 3.03829
\(973\) −0.750050 −0.0240455
\(974\) −36.2529 −1.16162
\(975\) 13.4766 0.431598
\(976\) 112.134 3.58933
\(977\) −27.9594 −0.894501 −0.447250 0.894409i \(-0.647597\pi\)
−0.447250 + 0.894409i \(0.647597\pi\)
\(978\) −106.914 −3.41873
\(979\) −68.3965 −2.18596
\(980\) 22.3363 0.713508
\(981\) −8.69820 −0.277712
\(982\) 19.1522 0.611171
\(983\) −27.2372 −0.868730 −0.434365 0.900737i \(-0.643027\pi\)
−0.434365 + 0.900737i \(0.643027\pi\)
\(984\) 56.1155 1.78890
\(985\) −19.2179 −0.612332
\(986\) −4.55555 −0.145078
\(987\) −83.0643 −2.64397
\(988\) −24.1371 −0.767903
\(989\) 74.3466 2.36408
\(990\) 47.7105 1.51634
\(991\) −36.4980 −1.15940 −0.579698 0.814831i \(-0.696830\pi\)
−0.579698 + 0.814831i \(0.696830\pi\)
\(992\) 47.7010 1.51451
\(993\) −0.605804 −0.0192246
\(994\) 102.562 3.25306
\(995\) −15.5945 −0.494380
\(996\) 136.083 4.31196
\(997\) 43.9585 1.39218 0.696091 0.717954i \(-0.254921\pi\)
0.696091 + 0.717954i \(0.254921\pi\)
\(998\) −103.437 −3.27425
\(999\) −0.507476 −0.0160558
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 \(a_p\))