Properties

Label 4009.2.a.c.1.1
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

Related objects

Downloads

Learn more about

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 1.1
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.82251 q^{2}\) \(+2.93474 q^{3}\) \(+5.96657 q^{4}\) \(+0.420997 q^{5}\) \(-8.28333 q^{6}\) \(-3.44749 q^{7}\) \(-11.1957 q^{8}\) \(+5.61269 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.82251 q^{2}\) \(+2.93474 q^{3}\) \(+5.96657 q^{4}\) \(+0.420997 q^{5}\) \(-8.28333 q^{6}\) \(-3.44749 q^{7}\) \(-11.1957 q^{8}\) \(+5.61269 q^{9}\) \(-1.18827 q^{10}\) \(-0.690697 q^{11}\) \(+17.5103 q^{12}\) \(-6.41936 q^{13}\) \(+9.73058 q^{14}\) \(+1.23552 q^{15}\) \(+19.6668 q^{16}\) \(+6.09680 q^{17}\) \(-15.8419 q^{18}\) \(+1.00000 q^{19}\) \(+2.51191 q^{20}\) \(-10.1175 q^{21}\) \(+1.94950 q^{22}\) \(+6.89386 q^{23}\) \(-32.8564 q^{24}\) \(-4.82276 q^{25}\) \(+18.1187 q^{26}\) \(+7.66757 q^{27}\) \(-20.5697 q^{28}\) \(-6.37730 q^{29}\) \(-3.48726 q^{30}\) \(-0.869751 q^{31}\) \(-33.1185 q^{32}\) \(-2.02701 q^{33}\) \(-17.2083 q^{34}\) \(-1.45138 q^{35}\) \(+33.4885 q^{36}\) \(+6.88837 q^{37}\) \(-2.82251 q^{38}\) \(-18.8391 q^{39}\) \(-4.71335 q^{40}\) \(-8.97979 q^{41}\) \(+28.5567 q^{42}\) \(+2.33166 q^{43}\) \(-4.12109 q^{44}\) \(+2.36293 q^{45}\) \(-19.4580 q^{46}\) \(-12.1493 q^{47}\) \(+57.7170 q^{48}\) \(+4.88519 q^{49}\) \(+13.6123 q^{50}\) \(+17.8925 q^{51}\) \(-38.3015 q^{52}\) \(-0.247210 q^{53}\) \(-21.6418 q^{54}\) \(-0.290781 q^{55}\) \(+38.5971 q^{56}\) \(+2.93474 q^{57}\) \(+18.0000 q^{58}\) \(-5.51539 q^{59}\) \(+7.37179 q^{60}\) \(-2.13549 q^{61}\) \(+2.45488 q^{62}\) \(-19.3497 q^{63}\) \(+54.1436 q^{64}\) \(-2.70253 q^{65}\) \(+5.72127 q^{66}\) \(+0.584061 q^{67}\) \(+36.3770 q^{68}\) \(+20.2317 q^{69}\) \(+4.09654 q^{70}\) \(-11.6130 q^{71}\) \(-62.8380 q^{72}\) \(+14.6875 q^{73}\) \(-19.4425 q^{74}\) \(-14.1535 q^{75}\) \(+5.96657 q^{76}\) \(+2.38117 q^{77}\) \(+53.1737 q^{78}\) \(-7.62708 q^{79}\) \(+8.27968 q^{80}\) \(+5.66423 q^{81}\) \(+25.3456 q^{82}\) \(+10.1726 q^{83}\) \(-60.3667 q^{84}\) \(+2.56673 q^{85}\) \(-6.58114 q^{86}\) \(-18.7157 q^{87}\) \(+7.73283 q^{88}\) \(-12.3693 q^{89}\) \(-6.66938 q^{90}\) \(+22.1307 q^{91}\) \(+41.1327 q^{92}\) \(-2.55249 q^{93}\) \(+34.2915 q^{94}\) \(+0.420997 q^{95}\) \(-97.1941 q^{96}\) \(-0.0438413 q^{97}\) \(-13.7885 q^{98}\) \(-3.87667 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82251 −1.99582 −0.997909 0.0646411i \(-0.979410\pi\)
−0.997909 + 0.0646411i \(0.979410\pi\)
\(3\) 2.93474 1.69437 0.847186 0.531296i \(-0.178295\pi\)
0.847186 + 0.531296i \(0.178295\pi\)
\(4\) 5.96657 2.98329
\(5\) 0.420997 0.188275 0.0941377 0.995559i \(-0.469991\pi\)
0.0941377 + 0.995559i \(0.469991\pi\)
\(6\) −8.28333 −3.38166
\(7\) −3.44749 −1.30303 −0.651515 0.758636i \(-0.725866\pi\)
−0.651515 + 0.758636i \(0.725866\pi\)
\(8\) −11.1957 −3.95828
\(9\) 5.61269 1.87090
\(10\) −1.18827 −0.375763
\(11\) −0.690697 −0.208253 −0.104126 0.994564i \(-0.533205\pi\)
−0.104126 + 0.994564i \(0.533205\pi\)
\(12\) 17.5103 5.05480
\(13\) −6.41936 −1.78041 −0.890204 0.455561i \(-0.849439\pi\)
−0.890204 + 0.455561i \(0.849439\pi\)
\(14\) 9.73058 2.60061
\(15\) 1.23552 0.319009
\(16\) 19.6668 4.91671
\(17\) 6.09680 1.47869 0.739346 0.673326i \(-0.235135\pi\)
0.739346 + 0.673326i \(0.235135\pi\)
\(18\) −15.8419 −3.73397
\(19\) 1.00000 0.229416
\(20\) 2.51191 0.561680
\(21\) −10.1175 −2.20782
\(22\) 1.94950 0.415635
\(23\) 6.89386 1.43747 0.718735 0.695284i \(-0.244721\pi\)
0.718735 + 0.695284i \(0.244721\pi\)
\(24\) −32.8564 −6.70679
\(25\) −4.82276 −0.964552
\(26\) 18.1187 3.55337
\(27\) 7.66757 1.47562
\(28\) −20.5697 −3.88731
\(29\) −6.37730 −1.18423 −0.592117 0.805852i \(-0.701708\pi\)
−0.592117 + 0.805852i \(0.701708\pi\)
\(30\) −3.48726 −0.636683
\(31\) −0.869751 −0.156212 −0.0781060 0.996945i \(-0.524887\pi\)
−0.0781060 + 0.996945i \(0.524887\pi\)
\(32\) −33.1185 −5.85458
\(33\) −2.02701 −0.352858
\(34\) −17.2083 −2.95120
\(35\) −1.45138 −0.245328
\(36\) 33.4885 5.58142
\(37\) 6.88837 1.13244 0.566220 0.824254i \(-0.308405\pi\)
0.566220 + 0.824254i \(0.308405\pi\)
\(38\) −2.82251 −0.457872
\(39\) −18.8391 −3.01668
\(40\) −4.71335 −0.745246
\(41\) −8.97979 −1.40241 −0.701204 0.712961i \(-0.747354\pi\)
−0.701204 + 0.712961i \(0.747354\pi\)
\(42\) 28.5567 4.40640
\(43\) 2.33166 0.355575 0.177787 0.984069i \(-0.443106\pi\)
0.177787 + 0.984069i \(0.443106\pi\)
\(44\) −4.12109 −0.621278
\(45\) 2.36293 0.352244
\(46\) −19.4580 −2.86893
\(47\) −12.1493 −1.77216 −0.886078 0.463536i \(-0.846580\pi\)
−0.886078 + 0.463536i \(0.846580\pi\)
\(48\) 57.7170 8.33074
\(49\) 4.88519 0.697885
\(50\) 13.6123 1.92507
\(51\) 17.8925 2.50545
\(52\) −38.3015 −5.31147
\(53\) −0.247210 −0.0339569 −0.0169784 0.999856i \(-0.505405\pi\)
−0.0169784 + 0.999856i \(0.505405\pi\)
\(54\) −21.6418 −2.94508
\(55\) −0.290781 −0.0392089
\(56\) 38.5971 5.15775
\(57\) 2.93474 0.388716
\(58\) 18.0000 2.36352
\(59\) −5.51539 −0.718043 −0.359021 0.933329i \(-0.616889\pi\)
−0.359021 + 0.933329i \(0.616889\pi\)
\(60\) 7.37179 0.951694
\(61\) −2.13549 −0.273421 −0.136711 0.990611i \(-0.543653\pi\)
−0.136711 + 0.990611i \(0.543653\pi\)
\(62\) 2.45488 0.311770
\(63\) −19.3497 −2.43783
\(64\) 54.1436 6.76796
\(65\) −2.70253 −0.335207
\(66\) 5.72127 0.704240
\(67\) 0.584061 0.0713544 0.0356772 0.999363i \(-0.488641\pi\)
0.0356772 + 0.999363i \(0.488641\pi\)
\(68\) 36.3770 4.41136
\(69\) 20.2317 2.43561
\(70\) 4.09654 0.489631
\(71\) −11.6130 −1.37821 −0.689103 0.724663i \(-0.741995\pi\)
−0.689103 + 0.724663i \(0.741995\pi\)
\(72\) −62.8380 −7.40553
\(73\) 14.6875 1.71905 0.859523 0.511096i \(-0.170760\pi\)
0.859523 + 0.511096i \(0.170760\pi\)
\(74\) −19.4425 −2.26014
\(75\) −14.1535 −1.63431
\(76\) 5.96657 0.684413
\(77\) 2.38117 0.271360
\(78\) 53.1737 6.02073
\(79\) −7.62708 −0.858114 −0.429057 0.903277i \(-0.641154\pi\)
−0.429057 + 0.903277i \(0.641154\pi\)
\(80\) 8.27968 0.925696
\(81\) 5.66423 0.629359
\(82\) 25.3456 2.79895
\(83\) 10.1726 1.11659 0.558295 0.829643i \(-0.311456\pi\)
0.558295 + 0.829643i \(0.311456\pi\)
\(84\) −60.3667 −6.58655
\(85\) 2.56673 0.278401
\(86\) −6.58114 −0.709662
\(87\) −18.7157 −2.00653
\(88\) 7.73283 0.824323
\(89\) −12.3693 −1.31115 −0.655574 0.755131i \(-0.727573\pi\)
−0.655574 + 0.755131i \(0.727573\pi\)
\(90\) −6.66938 −0.703015
\(91\) 22.1307 2.31992
\(92\) 41.1327 4.28838
\(93\) −2.55249 −0.264681
\(94\) 34.2915 3.53690
\(95\) 0.420997 0.0431934
\(96\) −97.1941 −9.91983
\(97\) −0.0438413 −0.00445141 −0.00222571 0.999998i \(-0.500708\pi\)
−0.00222571 + 0.999998i \(0.500708\pi\)
\(98\) −13.7885 −1.39285
\(99\) −3.87667 −0.389620
\(100\) −28.7754 −2.87754
\(101\) 3.15007 0.313443 0.156722 0.987643i \(-0.449907\pi\)
0.156722 + 0.987643i \(0.449907\pi\)
\(102\) −50.5018 −5.00043
\(103\) −1.54513 −0.152247 −0.0761233 0.997098i \(-0.524254\pi\)
−0.0761233 + 0.997098i \(0.524254\pi\)
\(104\) 71.8692 7.04735
\(105\) −4.25943 −0.415678
\(106\) 0.697753 0.0677718
\(107\) −2.99572 −0.289607 −0.144803 0.989460i \(-0.546255\pi\)
−0.144803 + 0.989460i \(0.546255\pi\)
\(108\) 45.7491 4.40221
\(109\) −1.35462 −0.129749 −0.0648747 0.997893i \(-0.520665\pi\)
−0.0648747 + 0.997893i \(0.520665\pi\)
\(110\) 0.820733 0.0782538
\(111\) 20.2156 1.91878
\(112\) −67.8012 −6.40662
\(113\) −8.53263 −0.802683 −0.401341 0.915929i \(-0.631456\pi\)
−0.401341 + 0.915929i \(0.631456\pi\)
\(114\) −8.28333 −0.775805
\(115\) 2.90229 0.270640
\(116\) −38.0506 −3.53291
\(117\) −36.0299 −3.33096
\(118\) 15.5673 1.43308
\(119\) −21.0187 −1.92678
\(120\) −13.8325 −1.26272
\(121\) −10.5229 −0.956631
\(122\) 6.02744 0.545699
\(123\) −26.3534 −2.37620
\(124\) −5.18943 −0.466025
\(125\) −4.13535 −0.369877
\(126\) 54.6148 4.86547
\(127\) 19.6258 1.74151 0.870753 0.491720i \(-0.163632\pi\)
0.870753 + 0.491720i \(0.163632\pi\)
\(128\) −86.5841 −7.65303
\(129\) 6.84281 0.602476
\(130\) 7.62792 0.669013
\(131\) −2.64588 −0.231172 −0.115586 0.993297i \(-0.536875\pi\)
−0.115586 + 0.993297i \(0.536875\pi\)
\(132\) −12.0943 −1.05268
\(133\) −3.44749 −0.298935
\(134\) −1.64852 −0.142410
\(135\) 3.22802 0.277824
\(136\) −68.2579 −5.85307
\(137\) −4.38546 −0.374675 −0.187338 0.982296i \(-0.559986\pi\)
−0.187338 + 0.982296i \(0.559986\pi\)
\(138\) −57.1042 −4.86103
\(139\) −12.8484 −1.08979 −0.544894 0.838505i \(-0.683430\pi\)
−0.544894 + 0.838505i \(0.683430\pi\)
\(140\) −8.65978 −0.731885
\(141\) −35.6550 −3.00269
\(142\) 32.7778 2.75065
\(143\) 4.43383 0.370775
\(144\) 110.384 9.19866
\(145\) −2.68482 −0.222962
\(146\) −41.4558 −3.43090
\(147\) 14.3368 1.18248
\(148\) 41.1000 3.37840
\(149\) −3.29810 −0.270191 −0.135095 0.990833i \(-0.543134\pi\)
−0.135095 + 0.990833i \(0.543134\pi\)
\(150\) 39.9485 3.26179
\(151\) −2.85234 −0.232120 −0.116060 0.993242i \(-0.537027\pi\)
−0.116060 + 0.993242i \(0.537027\pi\)
\(152\) −11.1957 −0.908091
\(153\) 34.2195 2.76648
\(154\) −6.72088 −0.541584
\(155\) −0.366162 −0.0294109
\(156\) −112.405 −8.99961
\(157\) −21.8181 −1.74127 −0.870637 0.491927i \(-0.836293\pi\)
−0.870637 + 0.491927i \(0.836293\pi\)
\(158\) 21.5275 1.71264
\(159\) −0.725497 −0.0575356
\(160\) −13.9428 −1.10227
\(161\) −23.7665 −1.87307
\(162\) −15.9874 −1.25609
\(163\) 5.70997 0.447240 0.223620 0.974676i \(-0.428213\pi\)
0.223620 + 0.974676i \(0.428213\pi\)
\(164\) −53.5786 −4.18379
\(165\) −0.853367 −0.0664345
\(166\) −28.7123 −2.22851
\(167\) −12.5772 −0.973250 −0.486625 0.873611i \(-0.661772\pi\)
−0.486625 + 0.873611i \(0.661772\pi\)
\(168\) 113.272 8.73915
\(169\) 28.2081 2.16986
\(170\) −7.24464 −0.555638
\(171\) 5.61269 0.429213
\(172\) 13.9120 1.06078
\(173\) −4.90077 −0.372599 −0.186299 0.982493i \(-0.559649\pi\)
−0.186299 + 0.982493i \(0.559649\pi\)
\(174\) 52.8253 4.00468
\(175\) 16.6264 1.25684
\(176\) −13.5838 −1.02392
\(177\) −16.1862 −1.21663
\(178\) 34.9126 2.61681
\(179\) −9.62514 −0.719417 −0.359708 0.933065i \(-0.617124\pi\)
−0.359708 + 0.933065i \(0.617124\pi\)
\(180\) 14.0986 1.05084
\(181\) −9.16903 −0.681529 −0.340764 0.940149i \(-0.610686\pi\)
−0.340764 + 0.940149i \(0.610686\pi\)
\(182\) −62.4641 −4.63015
\(183\) −6.26710 −0.463277
\(184\) −77.1816 −5.68990
\(185\) 2.89998 0.213211
\(186\) 7.20444 0.528255
\(187\) −4.21104 −0.307942
\(188\) −72.4896 −5.28685
\(189\) −26.4339 −1.92278
\(190\) −1.18827 −0.0862060
\(191\) 1.25971 0.0911495 0.0455747 0.998961i \(-0.485488\pi\)
0.0455747 + 0.998961i \(0.485488\pi\)
\(192\) 158.897 11.4674
\(193\) 11.5044 0.828103 0.414052 0.910253i \(-0.364113\pi\)
0.414052 + 0.910253i \(0.364113\pi\)
\(194\) 0.123743 0.00888421
\(195\) −7.93121 −0.567966
\(196\) 29.1479 2.08199
\(197\) −12.1097 −0.862783 −0.431391 0.902165i \(-0.641977\pi\)
−0.431391 + 0.902165i \(0.641977\pi\)
\(198\) 10.9419 0.777610
\(199\) 5.90465 0.418569 0.209285 0.977855i \(-0.432886\pi\)
0.209285 + 0.977855i \(0.432886\pi\)
\(200\) 53.9942 3.81796
\(201\) 1.71407 0.120901
\(202\) −8.89110 −0.625576
\(203\) 21.9857 1.54309
\(204\) 106.757 7.47449
\(205\) −3.78046 −0.264039
\(206\) 4.36116 0.303856
\(207\) 38.6931 2.68936
\(208\) −126.248 −8.75375
\(209\) −0.690697 −0.0477765
\(210\) 12.0223 0.829617
\(211\) 1.00000 0.0688428
\(212\) −1.47500 −0.101303
\(213\) −34.0811 −2.33520
\(214\) 8.45545 0.578002
\(215\) 0.981621 0.0669460
\(216\) −85.8438 −5.84093
\(217\) 2.99846 0.203549
\(218\) 3.82344 0.258956
\(219\) 43.1041 2.91271
\(220\) −1.73497 −0.116971
\(221\) −39.1375 −2.63268
\(222\) −57.0587 −3.82953
\(223\) 15.6057 1.04503 0.522517 0.852629i \(-0.324993\pi\)
0.522517 + 0.852629i \(0.324993\pi\)
\(224\) 114.176 7.62868
\(225\) −27.0687 −1.80458
\(226\) 24.0835 1.60201
\(227\) 15.8817 1.05410 0.527051 0.849833i \(-0.323298\pi\)
0.527051 + 0.849833i \(0.323298\pi\)
\(228\) 17.5103 1.15965
\(229\) 5.37560 0.355229 0.177615 0.984100i \(-0.443162\pi\)
0.177615 + 0.984100i \(0.443162\pi\)
\(230\) −8.19176 −0.540149
\(231\) 6.98811 0.459784
\(232\) 71.3983 4.68753
\(233\) 13.3813 0.876640 0.438320 0.898819i \(-0.355574\pi\)
0.438320 + 0.898819i \(0.355574\pi\)
\(234\) 101.695 6.64799
\(235\) −5.11481 −0.333654
\(236\) −32.9080 −2.14213
\(237\) −22.3835 −1.45396
\(238\) 59.3254 3.84550
\(239\) 7.25161 0.469068 0.234534 0.972108i \(-0.424644\pi\)
0.234534 + 0.972108i \(0.424644\pi\)
\(240\) 24.2987 1.56847
\(241\) −0.0642279 −0.00413728 −0.00206864 0.999998i \(-0.500658\pi\)
−0.00206864 + 0.999998i \(0.500658\pi\)
\(242\) 29.7011 1.90926
\(243\) −6.37966 −0.409255
\(244\) −12.7415 −0.815694
\(245\) 2.05665 0.131395
\(246\) 74.3826 4.74246
\(247\) −6.41936 −0.408454
\(248\) 9.73747 0.618330
\(249\) 29.8540 1.89192
\(250\) 11.6721 0.738207
\(251\) −11.5298 −0.727751 −0.363876 0.931447i \(-0.618547\pi\)
−0.363876 + 0.931447i \(0.618547\pi\)
\(252\) −115.451 −7.27275
\(253\) −4.76157 −0.299357
\(254\) −55.3940 −3.47573
\(255\) 7.53269 0.471716
\(256\) 136.097 8.50608
\(257\) 12.2960 0.767002 0.383501 0.923540i \(-0.374718\pi\)
0.383501 + 0.923540i \(0.374718\pi\)
\(258\) −19.3139 −1.20243
\(259\) −23.7476 −1.47560
\(260\) −16.1248 −1.00002
\(261\) −35.7938 −2.21558
\(262\) 7.46803 0.461376
\(263\) −30.0825 −1.85497 −0.927483 0.373864i \(-0.878033\pi\)
−0.927483 + 0.373864i \(0.878033\pi\)
\(264\) 22.6938 1.39671
\(265\) −0.104075 −0.00639325
\(266\) 9.73058 0.596620
\(267\) −36.3008 −2.22157
\(268\) 3.48484 0.212871
\(269\) −25.8489 −1.57603 −0.788017 0.615654i \(-0.788892\pi\)
−0.788017 + 0.615654i \(0.788892\pi\)
\(270\) −9.11113 −0.554486
\(271\) −15.7209 −0.954976 −0.477488 0.878638i \(-0.658453\pi\)
−0.477488 + 0.878638i \(0.658453\pi\)
\(272\) 119.905 7.27030
\(273\) 64.9477 3.93082
\(274\) 12.3780 0.747783
\(275\) 3.33107 0.200871
\(276\) 120.714 7.26612
\(277\) −12.2223 −0.734367 −0.367184 0.930148i \(-0.619678\pi\)
−0.367184 + 0.930148i \(0.619678\pi\)
\(278\) 36.2648 2.17502
\(279\) −4.88165 −0.292256
\(280\) 16.2492 0.971078
\(281\) −17.3205 −1.03326 −0.516628 0.856210i \(-0.672813\pi\)
−0.516628 + 0.856210i \(0.672813\pi\)
\(282\) 100.637 5.99282
\(283\) −19.3883 −1.15251 −0.576256 0.817269i \(-0.695487\pi\)
−0.576256 + 0.817269i \(0.695487\pi\)
\(284\) −69.2897 −4.11159
\(285\) 1.23552 0.0731856
\(286\) −12.5145 −0.740000
\(287\) 30.9578 1.82738
\(288\) −185.884 −10.9533
\(289\) 20.1710 1.18653
\(290\) 7.57794 0.444992
\(291\) −0.128663 −0.00754235
\(292\) 87.6343 5.12841
\(293\) 21.4669 1.25411 0.627056 0.778974i \(-0.284260\pi\)
0.627056 + 0.778974i \(0.284260\pi\)
\(294\) −40.4657 −2.36001
\(295\) −2.32196 −0.135190
\(296\) −77.1201 −4.48251
\(297\) −5.29596 −0.307303
\(298\) 9.30892 0.539251
\(299\) −44.2542 −2.55928
\(300\) −84.4482 −4.87562
\(301\) −8.03837 −0.463324
\(302\) 8.05077 0.463270
\(303\) 9.24462 0.531090
\(304\) 19.6668 1.12797
\(305\) −0.899033 −0.0514785
\(306\) −96.5848 −5.52139
\(307\) 7.15175 0.408172 0.204086 0.978953i \(-0.434578\pi\)
0.204086 + 0.978953i \(0.434578\pi\)
\(308\) 14.2074 0.809543
\(309\) −4.53456 −0.257962
\(310\) 1.03350 0.0586987
\(311\) −5.72304 −0.324524 −0.162262 0.986748i \(-0.551879\pi\)
−0.162262 + 0.986748i \(0.551879\pi\)
\(312\) 210.917 11.9408
\(313\) −8.01417 −0.452988 −0.226494 0.974013i \(-0.572726\pi\)
−0.226494 + 0.974013i \(0.572726\pi\)
\(314\) 61.5818 3.47526
\(315\) −8.14616 −0.458984
\(316\) −45.5076 −2.56000
\(317\) 19.8789 1.11651 0.558254 0.829670i \(-0.311471\pi\)
0.558254 + 0.829670i \(0.311471\pi\)
\(318\) 2.04772 0.114831
\(319\) 4.40478 0.246620
\(320\) 22.7943 1.27424
\(321\) −8.79165 −0.490702
\(322\) 67.0813 3.73830
\(323\) 6.09680 0.339235
\(324\) 33.7961 1.87756
\(325\) 30.9590 1.71730
\(326\) −16.1165 −0.892608
\(327\) −3.97547 −0.219844
\(328\) 100.535 5.55112
\(329\) 41.8846 2.30917
\(330\) 2.40864 0.132591
\(331\) 28.1032 1.54469 0.772347 0.635201i \(-0.219083\pi\)
0.772347 + 0.635201i \(0.219083\pi\)
\(332\) 60.6956 3.33111
\(333\) 38.6623 2.11868
\(334\) 35.4992 1.94243
\(335\) 0.245888 0.0134343
\(336\) −198.979 −10.8552
\(337\) 0.651770 0.0355042 0.0177521 0.999842i \(-0.494349\pi\)
0.0177521 + 0.999842i \(0.494349\pi\)
\(338\) −79.6178 −4.33064
\(339\) −25.0411 −1.36004
\(340\) 15.3146 0.830551
\(341\) 0.600734 0.0325316
\(342\) −15.8419 −0.856631
\(343\) 7.29078 0.393665
\(344\) −26.1045 −1.40746
\(345\) 8.51748 0.458566
\(346\) 13.8325 0.743639
\(347\) 3.04605 0.163521 0.0817604 0.996652i \(-0.473946\pi\)
0.0817604 + 0.996652i \(0.473946\pi\)
\(348\) −111.669 −5.98607
\(349\) 5.48867 0.293802 0.146901 0.989151i \(-0.453070\pi\)
0.146901 + 0.989151i \(0.453070\pi\)
\(350\) −46.9283 −2.50842
\(351\) −49.2208 −2.62721
\(352\) 22.8748 1.21923
\(353\) −16.3157 −0.868398 −0.434199 0.900817i \(-0.642969\pi\)
−0.434199 + 0.900817i \(0.642969\pi\)
\(354\) 45.6858 2.42817
\(355\) −4.88903 −0.259483
\(356\) −73.8026 −3.91153
\(357\) −61.6843 −3.26468
\(358\) 27.1671 1.43582
\(359\) −22.9094 −1.20911 −0.604556 0.796562i \(-0.706650\pi\)
−0.604556 + 0.796562i \(0.706650\pi\)
\(360\) −26.4546 −1.39428
\(361\) 1.00000 0.0526316
\(362\) 25.8797 1.36021
\(363\) −30.8821 −1.62089
\(364\) 132.044 6.92100
\(365\) 6.18341 0.323654
\(366\) 17.6890 0.924617
\(367\) −10.1724 −0.530992 −0.265496 0.964112i \(-0.585536\pi\)
−0.265496 + 0.964112i \(0.585536\pi\)
\(368\) 135.581 7.06762
\(369\) −50.4008 −2.62376
\(370\) −8.18523 −0.425530
\(371\) 0.852254 0.0442468
\(372\) −15.2296 −0.789620
\(373\) −24.2751 −1.25692 −0.628458 0.777843i \(-0.716314\pi\)
−0.628458 + 0.777843i \(0.716314\pi\)
\(374\) 11.8857 0.614596
\(375\) −12.1362 −0.626709
\(376\) 136.020 7.01468
\(377\) 40.9381 2.10842
\(378\) 74.6099 3.83752
\(379\) −21.7880 −1.11918 −0.559588 0.828771i \(-0.689041\pi\)
−0.559588 + 0.828771i \(0.689041\pi\)
\(380\) 2.51191 0.128858
\(381\) 57.5966 2.95076
\(382\) −3.55555 −0.181918
\(383\) 12.9552 0.661982 0.330991 0.943634i \(-0.392617\pi\)
0.330991 + 0.943634i \(0.392617\pi\)
\(384\) −254.102 −12.9671
\(385\) 1.00247 0.0510904
\(386\) −32.4712 −1.65274
\(387\) 13.0869 0.665244
\(388\) −0.261582 −0.0132798
\(389\) −23.2414 −1.17838 −0.589192 0.807993i \(-0.700554\pi\)
−0.589192 + 0.807993i \(0.700554\pi\)
\(390\) 22.3859 1.13356
\(391\) 42.0305 2.12558
\(392\) −54.6931 −2.76242
\(393\) −7.76497 −0.391691
\(394\) 34.1799 1.72196
\(395\) −3.21098 −0.161562
\(396\) −23.1304 −1.16235
\(397\) 18.7989 0.943489 0.471745 0.881735i \(-0.343624\pi\)
0.471745 + 0.881735i \(0.343624\pi\)
\(398\) −16.6659 −0.835388
\(399\) −10.1175 −0.506508
\(400\) −94.8485 −4.74242
\(401\) −30.5259 −1.52439 −0.762196 0.647346i \(-0.775879\pi\)
−0.762196 + 0.647346i \(0.775879\pi\)
\(402\) −4.83797 −0.241296
\(403\) 5.58324 0.278121
\(404\) 18.7951 0.935091
\(405\) 2.38462 0.118493
\(406\) −62.0548 −3.07973
\(407\) −4.75777 −0.235834
\(408\) −200.319 −9.91728
\(409\) 21.6876 1.07238 0.536190 0.844097i \(-0.319863\pi\)
0.536190 + 0.844097i \(0.319863\pi\)
\(410\) 10.6704 0.526974
\(411\) −12.8702 −0.634839
\(412\) −9.21915 −0.454195
\(413\) 19.0143 0.935631
\(414\) −109.212 −5.36747
\(415\) 4.28264 0.210226
\(416\) 212.599 10.4235
\(417\) −37.7067 −1.84651
\(418\) 1.94950 0.0953531
\(419\) 10.6826 0.521882 0.260941 0.965355i \(-0.415967\pi\)
0.260941 + 0.965355i \(0.415967\pi\)
\(420\) −25.4142 −1.24009
\(421\) −17.0064 −0.828839 −0.414419 0.910086i \(-0.636015\pi\)
−0.414419 + 0.910086i \(0.636015\pi\)
\(422\) −2.82251 −0.137398
\(423\) −68.1902 −3.31552
\(424\) 2.76769 0.134411
\(425\) −29.4034 −1.42628
\(426\) 96.1942 4.66062
\(427\) 7.36207 0.356276
\(428\) −17.8742 −0.863980
\(429\) 13.0121 0.628231
\(430\) −2.77064 −0.133612
\(431\) 6.43080 0.309761 0.154880 0.987933i \(-0.450501\pi\)
0.154880 + 0.987933i \(0.450501\pi\)
\(432\) 150.797 7.25522
\(433\) −7.96214 −0.382636 −0.191318 0.981528i \(-0.561276\pi\)
−0.191318 + 0.981528i \(0.561276\pi\)
\(434\) −8.46319 −0.406246
\(435\) −7.87925 −0.377781
\(436\) −8.08246 −0.387080
\(437\) 6.89386 0.329778
\(438\) −121.662 −5.81323
\(439\) 1.52263 0.0726714 0.0363357 0.999340i \(-0.488431\pi\)
0.0363357 + 0.999340i \(0.488431\pi\)
\(440\) 3.25550 0.155200
\(441\) 27.4191 1.30567
\(442\) 110.466 5.25434
\(443\) 9.83358 0.467207 0.233604 0.972332i \(-0.424948\pi\)
0.233604 + 0.972332i \(0.424948\pi\)
\(444\) 120.618 5.72426
\(445\) −5.20745 −0.246857
\(446\) −44.0472 −2.08570
\(447\) −9.67905 −0.457803
\(448\) −186.660 −8.81884
\(449\) 34.4302 1.62486 0.812430 0.583058i \(-0.198144\pi\)
0.812430 + 0.583058i \(0.198144\pi\)
\(450\) 76.4017 3.60161
\(451\) 6.20231 0.292056
\(452\) −50.9106 −2.39463
\(453\) −8.37089 −0.393298
\(454\) −44.8262 −2.10380
\(455\) 9.31694 0.436785
\(456\) −32.8564 −1.53864
\(457\) −17.7814 −0.831780 −0.415890 0.909415i \(-0.636530\pi\)
−0.415890 + 0.909415i \(0.636530\pi\)
\(458\) −15.1727 −0.708973
\(459\) 46.7476 2.18199
\(460\) 17.3168 0.807398
\(461\) 7.65333 0.356451 0.178226 0.983990i \(-0.442964\pi\)
0.178226 + 0.983990i \(0.442964\pi\)
\(462\) −19.7240 −0.917645
\(463\) −14.4561 −0.671833 −0.335916 0.941892i \(-0.609046\pi\)
−0.335916 + 0.941892i \(0.609046\pi\)
\(464\) −125.421 −5.82254
\(465\) −1.07459 −0.0498330
\(466\) −37.7689 −1.74961
\(467\) 15.9899 0.739926 0.369963 0.929047i \(-0.379370\pi\)
0.369963 + 0.929047i \(0.379370\pi\)
\(468\) −214.975 −9.93721
\(469\) −2.01355 −0.0929769
\(470\) 14.4366 0.665911
\(471\) −64.0304 −2.95036
\(472\) 61.7486 2.84221
\(473\) −1.61047 −0.0740495
\(474\) 63.1777 2.90185
\(475\) −4.82276 −0.221283
\(476\) −125.409 −5.74813
\(477\) −1.38751 −0.0635299
\(478\) −20.4678 −0.936174
\(479\) 4.20152 0.191973 0.0959863 0.995383i \(-0.469400\pi\)
0.0959863 + 0.995383i \(0.469400\pi\)
\(480\) −40.9184 −1.86766
\(481\) −44.2189 −2.01621
\(482\) 0.181284 0.00825725
\(483\) −69.7486 −3.17367
\(484\) −62.7859 −2.85390
\(485\) −0.0184571 −0.000838092 0
\(486\) 18.0067 0.816799
\(487\) 14.9208 0.676125 0.338063 0.941124i \(-0.390228\pi\)
0.338063 + 0.941124i \(0.390228\pi\)
\(488\) 23.9083 1.08228
\(489\) 16.7573 0.757790
\(490\) −5.80492 −0.262240
\(491\) −34.1756 −1.54232 −0.771162 0.636639i \(-0.780324\pi\)
−0.771162 + 0.636639i \(0.780324\pi\)
\(492\) −157.239 −7.08889
\(493\) −38.8811 −1.75112
\(494\) 18.1187 0.815199
\(495\) −1.63206 −0.0733558
\(496\) −17.1053 −0.768049
\(497\) 40.0356 1.79584
\(498\) −84.2632 −3.77592
\(499\) −35.3665 −1.58322 −0.791612 0.611024i \(-0.790758\pi\)
−0.791612 + 0.611024i \(0.790758\pi\)
\(500\) −24.6739 −1.10345
\(501\) −36.9107 −1.64905
\(502\) 32.5429 1.45246
\(503\) −36.3428 −1.62044 −0.810222 0.586123i \(-0.800654\pi\)
−0.810222 + 0.586123i \(0.800654\pi\)
\(504\) 216.633 9.64962
\(505\) 1.32617 0.0590137
\(506\) 13.4396 0.597462
\(507\) 82.7835 3.67654
\(508\) 117.099 5.19541
\(509\) 14.9231 0.661454 0.330727 0.943726i \(-0.392706\pi\)
0.330727 + 0.943726i \(0.392706\pi\)
\(510\) −21.2611 −0.941458
\(511\) −50.6352 −2.23997
\(512\) −210.968 −9.32356
\(513\) 7.66757 0.338531
\(514\) −34.7055 −1.53080
\(515\) −0.650496 −0.0286643
\(516\) 40.8281 1.79736
\(517\) 8.39147 0.369057
\(518\) 67.0278 2.94503
\(519\) −14.3825 −0.631321
\(520\) 30.2567 1.32684
\(521\) 1.35926 0.0595504 0.0297752 0.999557i \(-0.490521\pi\)
0.0297752 + 0.999557i \(0.490521\pi\)
\(522\) 101.028 4.42190
\(523\) −21.6227 −0.945493 −0.472746 0.881198i \(-0.656737\pi\)
−0.472746 + 0.881198i \(0.656737\pi\)
\(524\) −15.7868 −0.689651
\(525\) 48.7942 2.12955
\(526\) 84.9082 3.70217
\(527\) −5.30270 −0.230989
\(528\) −39.8650 −1.73490
\(529\) 24.5254 1.06632
\(530\) 0.293752 0.0127598
\(531\) −30.9562 −1.34338
\(532\) −20.5697 −0.891810
\(533\) 57.6445 2.49686
\(534\) 102.459 4.43385
\(535\) −1.26119 −0.0545259
\(536\) −6.53897 −0.282441
\(537\) −28.2473 −1.21896
\(538\) 72.9587 3.14547
\(539\) −3.37419 −0.145337
\(540\) 19.2602 0.828828
\(541\) −2.82574 −0.121488 −0.0607440 0.998153i \(-0.519347\pi\)
−0.0607440 + 0.998153i \(0.519347\pi\)
\(542\) 44.3724 1.90596
\(543\) −26.9087 −1.15476
\(544\) −201.917 −8.65711
\(545\) −0.570292 −0.0244286
\(546\) −183.316 −7.84519
\(547\) 5.27972 0.225745 0.112872 0.993609i \(-0.463995\pi\)
0.112872 + 0.993609i \(0.463995\pi\)
\(548\) −26.1662 −1.11776
\(549\) −11.9858 −0.511543
\(550\) −9.40197 −0.400901
\(551\) −6.37730 −0.271682
\(552\) −226.508 −9.64082
\(553\) 26.2943 1.11815
\(554\) 34.4976 1.46566
\(555\) 8.51069 0.361259
\(556\) −76.6609 −3.25115
\(557\) 19.0028 0.805175 0.402587 0.915382i \(-0.368111\pi\)
0.402587 + 0.915382i \(0.368111\pi\)
\(558\) 13.7785 0.583290
\(559\) −14.9677 −0.633068
\(560\) −28.5441 −1.20621
\(561\) −12.3583 −0.521768
\(562\) 48.8874 2.06219
\(563\) 35.7761 1.50778 0.753891 0.657000i \(-0.228175\pi\)
0.753891 + 0.657000i \(0.228175\pi\)
\(564\) −212.738 −8.95789
\(565\) −3.59221 −0.151125
\(566\) 54.7236 2.30020
\(567\) −19.5274 −0.820073
\(568\) 130.015 5.45532
\(569\) 39.3100 1.64796 0.823980 0.566618i \(-0.191749\pi\)
0.823980 + 0.566618i \(0.191749\pi\)
\(570\) −3.48726 −0.146065
\(571\) 32.3918 1.35556 0.677778 0.735267i \(-0.262943\pi\)
0.677778 + 0.735267i \(0.262943\pi\)
\(572\) 26.4548 1.10613
\(573\) 3.69692 0.154441
\(574\) −87.3786 −3.64711
\(575\) −33.2475 −1.38652
\(576\) 303.892 12.6622
\(577\) −2.95608 −0.123063 −0.0615317 0.998105i \(-0.519599\pi\)
−0.0615317 + 0.998105i \(0.519599\pi\)
\(578\) −56.9329 −2.36809
\(579\) 33.7623 1.40311
\(580\) −16.0192 −0.665160
\(581\) −35.0700 −1.45495
\(582\) 0.363152 0.0150532
\(583\) 0.170747 0.00707162
\(584\) −164.437 −6.80446
\(585\) −15.1685 −0.627138
\(586\) −60.5907 −2.50298
\(587\) 13.6580 0.563725 0.281863 0.959455i \(-0.409048\pi\)
0.281863 + 0.959455i \(0.409048\pi\)
\(588\) 85.5413 3.52767
\(589\) −0.869751 −0.0358375
\(590\) 6.55376 0.269814
\(591\) −35.5389 −1.46188
\(592\) 135.472 5.56788
\(593\) 11.2049 0.460130 0.230065 0.973175i \(-0.426106\pi\)
0.230065 + 0.973175i \(0.426106\pi\)
\(594\) 14.9479 0.613321
\(595\) −8.84879 −0.362765
\(596\) −19.6783 −0.806056
\(597\) 17.3286 0.709212
\(598\) 124.908 5.10786
\(599\) 9.16037 0.374282 0.187141 0.982333i \(-0.440078\pi\)
0.187141 + 0.982333i \(0.440078\pi\)
\(600\) 158.459 6.46905
\(601\) 38.7626 1.58116 0.790579 0.612360i \(-0.209780\pi\)
0.790579 + 0.612360i \(0.209780\pi\)
\(602\) 22.6884 0.924710
\(603\) 3.27816 0.133497
\(604\) −17.0187 −0.692482
\(605\) −4.43012 −0.180110
\(606\) −26.0931 −1.05996
\(607\) −25.6614 −1.04156 −0.520782 0.853690i \(-0.674360\pi\)
−0.520782 + 0.853690i \(0.674360\pi\)
\(608\) −33.1185 −1.34313
\(609\) 64.5222 2.61457
\(610\) 2.53753 0.102742
\(611\) 77.9906 3.15516
\(612\) 204.173 8.25320
\(613\) 23.4250 0.946127 0.473063 0.881028i \(-0.343148\pi\)
0.473063 + 0.881028i \(0.343148\pi\)
\(614\) −20.1859 −0.814637
\(615\) −11.0947 −0.447381
\(616\) −26.6589 −1.07412
\(617\) −10.0293 −0.403765 −0.201883 0.979410i \(-0.564706\pi\)
−0.201883 + 0.979410i \(0.564706\pi\)
\(618\) 12.7989 0.514846
\(619\) 11.4897 0.461811 0.230906 0.972976i \(-0.425831\pi\)
0.230906 + 0.972976i \(0.425831\pi\)
\(620\) −2.18473 −0.0877411
\(621\) 52.8592 2.12117
\(622\) 16.1533 0.647690
\(623\) 42.6432 1.70846
\(624\) −370.506 −14.8321
\(625\) 22.3728 0.894914
\(626\) 22.6201 0.904081
\(627\) −2.02701 −0.0809512
\(628\) −130.179 −5.19472
\(629\) 41.9970 1.67453
\(630\) 22.9926 0.916049
\(631\) 21.1201 0.840779 0.420390 0.907344i \(-0.361893\pi\)
0.420390 + 0.907344i \(0.361893\pi\)
\(632\) 85.3905 3.39665
\(633\) 2.93474 0.116645
\(634\) −56.1083 −2.22835
\(635\) 8.26239 0.327883
\(636\) −4.32873 −0.171645
\(637\) −31.3598 −1.24252
\(638\) −12.4325 −0.492209
\(639\) −65.1801 −2.57848
\(640\) −36.4516 −1.44088
\(641\) −13.8403 −0.546658 −0.273329 0.961921i \(-0.588125\pi\)
−0.273329 + 0.961921i \(0.588125\pi\)
\(642\) 24.8145 0.979351
\(643\) −18.1373 −0.715265 −0.357633 0.933862i \(-0.616416\pi\)
−0.357633 + 0.933862i \(0.616416\pi\)
\(644\) −141.805 −5.58789
\(645\) 2.88080 0.113431
\(646\) −17.2083 −0.677051
\(647\) −18.3540 −0.721569 −0.360785 0.932649i \(-0.617491\pi\)
−0.360785 + 0.932649i \(0.617491\pi\)
\(648\) −63.4150 −2.49118
\(649\) 3.80946 0.149534
\(650\) −87.3822 −3.42741
\(651\) 8.79970 0.344887
\(652\) 34.0690 1.33424
\(653\) 3.48619 0.136425 0.0682126 0.997671i \(-0.478270\pi\)
0.0682126 + 0.997671i \(0.478270\pi\)
\(654\) 11.2208 0.438768
\(655\) −1.11391 −0.0435239
\(656\) −176.604 −6.89523
\(657\) 82.4366 3.21616
\(658\) −118.220 −4.60868
\(659\) 27.5969 1.07502 0.537512 0.843256i \(-0.319364\pi\)
0.537512 + 0.843256i \(0.319364\pi\)
\(660\) −5.09167 −0.198193
\(661\) 10.4583 0.406782 0.203391 0.979098i \(-0.434804\pi\)
0.203391 + 0.979098i \(0.434804\pi\)
\(662\) −79.3217 −3.08293
\(663\) −114.858 −4.46073
\(664\) −113.889 −4.41977
\(665\) −1.45138 −0.0562822
\(666\) −109.125 −4.22850
\(667\) −43.9642 −1.70230
\(668\) −75.0425 −2.90348
\(669\) 45.7986 1.77068
\(670\) −0.694021 −0.0268124
\(671\) 1.47497 0.0569408
\(672\) 335.076 12.9258
\(673\) 15.2269 0.586953 0.293476 0.955966i \(-0.405188\pi\)
0.293476 + 0.955966i \(0.405188\pi\)
\(674\) −1.83963 −0.0708599
\(675\) −36.9789 −1.42332
\(676\) 168.306 6.47330
\(677\) −15.5958 −0.599395 −0.299697 0.954034i \(-0.596886\pi\)
−0.299697 + 0.954034i \(0.596886\pi\)
\(678\) 70.6787 2.71440
\(679\) 0.151143 0.00580032
\(680\) −28.7364 −1.10199
\(681\) 46.6085 1.78604
\(682\) −1.69558 −0.0649271
\(683\) 39.7788 1.52209 0.761047 0.648697i \(-0.224686\pi\)
0.761047 + 0.648697i \(0.224686\pi\)
\(684\) 33.4885 1.28047
\(685\) −1.84626 −0.0705421
\(686\) −20.5783 −0.785683
\(687\) 15.7760 0.601891
\(688\) 45.8564 1.74826
\(689\) 1.58693 0.0604572
\(690\) −24.0407 −0.915213
\(691\) 6.35208 0.241644 0.120822 0.992674i \(-0.461447\pi\)
0.120822 + 0.992674i \(0.461447\pi\)
\(692\) −29.2408 −1.11157
\(693\) 13.3648 0.507686
\(694\) −8.59752 −0.326357
\(695\) −5.40914 −0.205180
\(696\) 209.535 7.94242
\(697\) −54.7480 −2.07373
\(698\) −15.4918 −0.586375
\(699\) 39.2707 1.48535
\(700\) 99.2028 3.74951
\(701\) −30.1226 −1.13772 −0.568858 0.822436i \(-0.692615\pi\)
−0.568858 + 0.822436i \(0.692615\pi\)
\(702\) 138.926 5.24344
\(703\) 6.88837 0.259800
\(704\) −37.3968 −1.40945
\(705\) −15.0106 −0.565333
\(706\) 46.0513 1.73316
\(707\) −10.8598 −0.408426
\(708\) −96.5763 −3.62956
\(709\) 20.1582 0.757056 0.378528 0.925590i \(-0.376430\pi\)
0.378528 + 0.925590i \(0.376430\pi\)
\(710\) 13.7993 0.517880
\(711\) −42.8085 −1.60544
\(712\) 138.483 5.18988
\(713\) −5.99595 −0.224550
\(714\) 174.105 6.51570
\(715\) 1.86663 0.0698079
\(716\) −57.4291 −2.14623
\(717\) 21.2816 0.794776
\(718\) 64.6621 2.41317
\(719\) 48.5936 1.81223 0.906117 0.423027i \(-0.139033\pi\)
0.906117 + 0.423027i \(0.139033\pi\)
\(720\) 46.4713 1.73188
\(721\) 5.32683 0.198382
\(722\) −2.82251 −0.105043
\(723\) −0.188492 −0.00701009
\(724\) −54.7077 −2.03319
\(725\) 30.7562 1.14226
\(726\) 87.1650 3.23500
\(727\) −12.4327 −0.461102 −0.230551 0.973060i \(-0.574053\pi\)
−0.230551 + 0.973060i \(0.574053\pi\)
\(728\) −247.768 −9.18290
\(729\) −35.7153 −1.32279
\(730\) −17.4527 −0.645955
\(731\) 14.2157 0.525785
\(732\) −37.3931 −1.38209
\(733\) 9.65456 0.356599 0.178300 0.983976i \(-0.442940\pi\)
0.178300 + 0.983976i \(0.442940\pi\)
\(734\) 28.7116 1.05976
\(735\) 6.03573 0.222631
\(736\) −228.314 −8.41578
\(737\) −0.403409 −0.0148598
\(738\) 142.257 5.23655
\(739\) 16.9923 0.625072 0.312536 0.949906i \(-0.398822\pi\)
0.312536 + 0.949906i \(0.398822\pi\)
\(740\) 17.3029 0.636069
\(741\) −18.8391 −0.692073
\(742\) −2.40550 −0.0883086
\(743\) −12.0555 −0.442273 −0.221137 0.975243i \(-0.570977\pi\)
−0.221137 + 0.975243i \(0.570977\pi\)
\(744\) 28.5769 1.04768
\(745\) −1.38849 −0.0508703
\(746\) 68.5167 2.50858
\(747\) 57.0957 2.08902
\(748\) −25.1255 −0.918679
\(749\) 10.3277 0.377366
\(750\) 34.2545 1.25080
\(751\) −16.2218 −0.591943 −0.295971 0.955197i \(-0.595643\pi\)
−0.295971 + 0.955197i \(0.595643\pi\)
\(752\) −238.938 −8.71318
\(753\) −33.8368 −1.23308
\(754\) −115.548 −4.20802
\(755\) −1.20083 −0.0437026
\(756\) −157.720 −5.73621
\(757\) 51.8528 1.88462 0.942311 0.334740i \(-0.108648\pi\)
0.942311 + 0.334740i \(0.108648\pi\)
\(758\) 61.4970 2.23367
\(759\) −13.9740 −0.507223
\(760\) −4.71335 −0.170971
\(761\) 12.6680 0.459214 0.229607 0.973283i \(-0.426256\pi\)
0.229607 + 0.973283i \(0.426256\pi\)
\(762\) −162.567 −5.88918
\(763\) 4.67005 0.169067
\(764\) 7.51616 0.271925
\(765\) 14.4063 0.520860
\(766\) −36.5663 −1.32119
\(767\) 35.4053 1.27841
\(768\) 399.410 14.4125
\(769\) 11.8069 0.425768 0.212884 0.977077i \(-0.431714\pi\)
0.212884 + 0.977077i \(0.431714\pi\)
\(770\) −2.82947 −0.101967
\(771\) 36.0855 1.29959
\(772\) 68.6417 2.47047
\(773\) 0.366113 0.0131682 0.00658409 0.999978i \(-0.497904\pi\)
0.00658409 + 0.999978i \(0.497904\pi\)
\(774\) −36.9379 −1.32770
\(775\) 4.19460 0.150675
\(776\) 0.490834 0.0176199
\(777\) −69.6930 −2.50022
\(778\) 65.5991 2.35184
\(779\) −8.97979 −0.321735
\(780\) −47.3222 −1.69441
\(781\) 8.02105 0.287016
\(782\) −118.632 −4.24226
\(783\) −48.8984 −1.74749
\(784\) 96.0763 3.43130
\(785\) −9.18535 −0.327839
\(786\) 21.9167 0.781743
\(787\) 17.3834 0.619650 0.309825 0.950794i \(-0.399729\pi\)
0.309825 + 0.950794i \(0.399729\pi\)
\(788\) −72.2536 −2.57393
\(789\) −88.2843 −3.14300
\(790\) 9.06302 0.322448
\(791\) 29.4162 1.04592
\(792\) 43.4020 1.54222
\(793\) 13.7085 0.486802
\(794\) −53.0601 −1.88303
\(795\) −0.305432 −0.0108325
\(796\) 35.2305 1.24871
\(797\) 2.59713 0.0919952 0.0459976 0.998942i \(-0.485353\pi\)
0.0459976 + 0.998942i \(0.485353\pi\)
\(798\) 28.5567 1.01090
\(799\) −74.0718 −2.62047
\(800\) 159.723 5.64705
\(801\) −69.4253 −2.45302
\(802\) 86.1598 3.04241
\(803\) −10.1446 −0.357996
\(804\) 10.2271 0.360682
\(805\) −10.0056 −0.352652
\(806\) −15.7588 −0.555079
\(807\) −75.8597 −2.67039
\(808\) −35.2672 −1.24070
\(809\) −10.9044 −0.383379 −0.191690 0.981456i \(-0.561397\pi\)
−0.191690 + 0.981456i \(0.561397\pi\)
\(810\) −6.73063 −0.236490
\(811\) 30.7678 1.08040 0.540202 0.841535i \(-0.318348\pi\)
0.540202 + 0.841535i \(0.318348\pi\)
\(812\) 131.179 4.60349
\(813\) −46.1367 −1.61808
\(814\) 13.4289 0.470682
\(815\) 2.40388 0.0842042
\(816\) 351.889 12.3186
\(817\) 2.33166 0.0815744
\(818\) −61.2134 −2.14028
\(819\) 124.213 4.34034
\(820\) −22.5564 −0.787704
\(821\) −39.7355 −1.38678 −0.693390 0.720563i \(-0.743884\pi\)
−0.693390 + 0.720563i \(0.743884\pi\)
\(822\) 36.3262 1.26702
\(823\) 32.0151 1.11598 0.557989 0.829848i \(-0.311573\pi\)
0.557989 + 0.829848i \(0.311573\pi\)
\(824\) 17.2988 0.602634
\(825\) 9.77581 0.340350
\(826\) −53.6680 −1.86735
\(827\) 13.8659 0.482166 0.241083 0.970504i \(-0.422497\pi\)
0.241083 + 0.970504i \(0.422497\pi\)
\(828\) 230.865 8.02313
\(829\) 2.23297 0.0775542 0.0387771 0.999248i \(-0.487654\pi\)
0.0387771 + 0.999248i \(0.487654\pi\)
\(830\) −12.0878 −0.419573
\(831\) −35.8693 −1.24429
\(832\) −347.567 −12.0497
\(833\) 29.7841 1.03196
\(834\) 106.428 3.68529
\(835\) −5.29494 −0.183239
\(836\) −4.12109 −0.142531
\(837\) −6.66888 −0.230510
\(838\) −30.1519 −1.04158
\(839\) 33.5557 1.15847 0.579236 0.815160i \(-0.303351\pi\)
0.579236 + 0.815160i \(0.303351\pi\)
\(840\) 47.6873 1.64537
\(841\) 11.6699 0.402412
\(842\) 48.0006 1.65421
\(843\) −50.8313 −1.75072
\(844\) 5.96657 0.205378
\(845\) 11.8755 0.408531
\(846\) 192.468 6.61717
\(847\) 36.2777 1.24652
\(848\) −4.86184 −0.166956
\(849\) −56.8995 −1.95278
\(850\) 82.9915 2.84659
\(851\) 47.4875 1.62785
\(852\) −203.347 −6.96656
\(853\) −40.9089 −1.40069 −0.700347 0.713802i \(-0.746972\pi\)
−0.700347 + 0.713802i \(0.746972\pi\)
\(854\) −20.7795 −0.711061
\(855\) 2.36293 0.0808103
\(856\) 33.5391 1.14634
\(857\) −57.8252 −1.97527 −0.987636 0.156763i \(-0.949894\pi\)
−0.987636 + 0.156763i \(0.949894\pi\)
\(858\) −36.7269 −1.25383
\(859\) −5.77724 −0.197117 −0.0985585 0.995131i \(-0.531423\pi\)
−0.0985585 + 0.995131i \(0.531423\pi\)
\(860\) 5.85691 0.199719
\(861\) 90.8529 3.09626
\(862\) −18.1510 −0.618226
\(863\) 10.4135 0.354481 0.177241 0.984168i \(-0.443283\pi\)
0.177241 + 0.984168i \(0.443283\pi\)
\(864\) −253.938 −8.63916
\(865\) −2.06321 −0.0701512
\(866\) 22.4732 0.763672
\(867\) 59.1966 2.01042
\(868\) 17.8905 0.607244
\(869\) 5.26800 0.178705
\(870\) 22.2393 0.753982
\(871\) −3.74930 −0.127040
\(872\) 15.1660 0.513584
\(873\) −0.246068 −0.00832814
\(874\) −19.4580 −0.658177
\(875\) 14.2566 0.481961
\(876\) 257.184 8.68943
\(877\) −11.4111 −0.385325 −0.192663 0.981265i \(-0.561712\pi\)
−0.192663 + 0.981265i \(0.561712\pi\)
\(878\) −4.29765 −0.145039
\(879\) 62.9998 2.12493
\(880\) −5.71874 −0.192779
\(881\) 45.0574 1.51802 0.759012 0.651077i \(-0.225682\pi\)
0.759012 + 0.651077i \(0.225682\pi\)
\(882\) −77.3907 −2.60588
\(883\) −51.0951 −1.71949 −0.859744 0.510726i \(-0.829377\pi\)
−0.859744 + 0.510726i \(0.829377\pi\)
\(884\) −233.517 −7.85402
\(885\) −6.81435 −0.229062
\(886\) −27.7554 −0.932460
\(887\) 4.89146 0.164239 0.0821195 0.996622i \(-0.473831\pi\)
0.0821195 + 0.996622i \(0.473831\pi\)
\(888\) −226.327 −7.59505
\(889\) −67.6597 −2.26923
\(890\) 14.6981 0.492681
\(891\) −3.91227 −0.131066
\(892\) 93.1125 3.11764
\(893\) −12.1493 −0.406560
\(894\) 27.3192 0.913692
\(895\) −4.05215 −0.135449
\(896\) 298.498 9.97211
\(897\) −129.874 −4.33638
\(898\) −97.1796 −3.24292
\(899\) 5.54666 0.184992
\(900\) −161.507 −5.38357
\(901\) −1.50719 −0.0502118
\(902\) −17.5061 −0.582890
\(903\) −23.5905 −0.785044
\(904\) 95.5288 3.17724
\(905\) −3.86013 −0.128315
\(906\) 23.6269 0.784952
\(907\) −45.7022 −1.51752 −0.758758 0.651373i \(-0.774193\pi\)
−0.758758 + 0.651373i \(0.774193\pi\)
\(908\) 94.7591 3.14469
\(909\) 17.6804 0.586420
\(910\) −26.2972 −0.871743
\(911\) 28.2317 0.935358 0.467679 0.883898i \(-0.345090\pi\)
0.467679 + 0.883898i \(0.345090\pi\)
\(912\) 57.7170 1.91120
\(913\) −7.02619 −0.232533
\(914\) 50.1883 1.66008
\(915\) −2.63843 −0.0872238
\(916\) 32.0739 1.05975
\(917\) 9.12165 0.301223
\(918\) −131.946 −4.35486
\(919\) 15.0963 0.497982 0.248991 0.968506i \(-0.419901\pi\)
0.248991 + 0.968506i \(0.419901\pi\)
\(920\) −32.4932 −1.07127
\(921\) 20.9885 0.691595
\(922\) −21.6016 −0.711412
\(923\) 74.5478 2.45377
\(924\) 41.6951 1.37167
\(925\) −33.2210 −1.09230
\(926\) 40.8026 1.34086
\(927\) −8.67236 −0.284838
\(928\) 211.207 6.93319
\(929\) 20.6539 0.677631 0.338816 0.940853i \(-0.389974\pi\)
0.338816 + 0.940853i \(0.389974\pi\)
\(930\) 3.03305 0.0994575
\(931\) 4.88519 0.160106
\(932\) 79.8406 2.61527
\(933\) −16.7956 −0.549864
\(934\) −45.1318 −1.47676
\(935\) −1.77283 −0.0579779
\(936\) 403.379 13.1849
\(937\) 32.1069 1.04889 0.524443 0.851446i \(-0.324274\pi\)
0.524443 + 0.851446i \(0.324274\pi\)
\(938\) 5.68326 0.185565
\(939\) −23.5195 −0.767530
\(940\) −30.5179 −0.995384
\(941\) 45.7400 1.49108 0.745541 0.666459i \(-0.232191\pi\)
0.745541 + 0.666459i \(0.232191\pi\)
\(942\) 180.727 5.88839
\(943\) −61.9055 −2.01592
\(944\) −108.470 −3.53041
\(945\) −11.1286 −0.362013
\(946\) 4.54557 0.147789
\(947\) −38.0423 −1.23621 −0.618104 0.786096i \(-0.712099\pi\)
−0.618104 + 0.786096i \(0.712099\pi\)
\(948\) −133.553 −4.33759
\(949\) −94.2846 −3.06061
\(950\) 13.6123 0.441641
\(951\) 58.3393 1.89178
\(952\) 235.319 7.62672
\(953\) 55.0605 1.78359 0.891793 0.452444i \(-0.149448\pi\)
0.891793 + 0.452444i \(0.149448\pi\)
\(954\) 3.91627 0.126794
\(955\) 0.530334 0.0171612
\(956\) 43.2673 1.39936
\(957\) 12.9269 0.417867
\(958\) −11.8589 −0.383142
\(959\) 15.1188 0.488212
\(960\) 66.8953 2.15904
\(961\) −30.2435 −0.975598
\(962\) 124.808 4.02398
\(963\) −16.8140 −0.541825
\(964\) −0.383220 −0.0123427
\(965\) 4.84330 0.155911
\(966\) 196.866 6.33407
\(967\) −22.8863 −0.735975 −0.367987 0.929831i \(-0.619953\pi\)
−0.367987 + 0.929831i \(0.619953\pi\)
\(968\) 117.812 3.78661
\(969\) 17.8925 0.574791
\(970\) 0.0520953 0.00167268
\(971\) −56.2640 −1.80560 −0.902799 0.430064i \(-0.858491\pi\)
−0.902799 + 0.430064i \(0.858491\pi\)
\(972\) −38.0647 −1.22093
\(973\) 44.2948 1.42002
\(974\) −42.1141 −1.34942
\(975\) 90.8566 2.90974
\(976\) −41.9983 −1.34433
\(977\) 28.5026 0.911878 0.455939 0.890011i \(-0.349303\pi\)
0.455939 + 0.890011i \(0.349303\pi\)
\(978\) −47.2976 −1.51241
\(979\) 8.54346 0.273050
\(980\) 12.2712 0.391988
\(981\) −7.60308 −0.242748
\(982\) 96.4610 3.07820
\(983\) −41.3832 −1.31992 −0.659959 0.751302i \(-0.729426\pi\)
−0.659959 + 0.751302i \(0.729426\pi\)
\(984\) 295.044 9.40566
\(985\) −5.09816 −0.162441
\(986\) 109.742 3.49491
\(987\) 122.920 3.91259
\(988\) −38.3015 −1.21853
\(989\) 16.0741 0.511128
\(990\) 4.60652 0.146405
\(991\) 49.9187 1.58572 0.792860 0.609404i \(-0.208591\pi\)
0.792860 + 0.609404i \(0.208591\pi\)
\(992\) 28.8048 0.914555
\(993\) 82.4757 2.61729
\(994\) −113.001 −3.58418
\(995\) 2.48584 0.0788063
\(996\) 178.126 5.64413
\(997\) 19.2470 0.609559 0.304780 0.952423i \(-0.401417\pi\)
0.304780 + 0.952423i \(0.401417\pi\)
\(998\) 99.8225 3.15983
\(999\) 52.8170 1.67106
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 \(a_p\))