Properties

Label 4009.2.a.c.1.6
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 1.6
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61964 q^{2}\) \(-2.82043 q^{3}\) \(+4.86252 q^{4}\) \(-3.49446 q^{5}\) \(+7.38851 q^{6}\) \(+2.54132 q^{7}\) \(-7.49878 q^{8}\) \(+4.95481 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61964 q^{2}\) \(-2.82043 q^{3}\) \(+4.86252 q^{4}\) \(-3.49446 q^{5}\) \(+7.38851 q^{6}\) \(+2.54132 q^{7}\) \(-7.49878 q^{8}\) \(+4.95481 q^{9}\) \(+9.15424 q^{10}\) \(+3.23368 q^{11}\) \(-13.7144 q^{12}\) \(+5.10597 q^{13}\) \(-6.65735 q^{14}\) \(+9.85587 q^{15}\) \(+9.91908 q^{16}\) \(+3.26225 q^{17}\) \(-12.9798 q^{18}\) \(+1.00000 q^{19}\) \(-16.9919 q^{20}\) \(-7.16761 q^{21}\) \(-8.47108 q^{22}\) \(+0.140416 q^{23}\) \(+21.1498 q^{24}\) \(+7.21126 q^{25}\) \(-13.3758 q^{26}\) \(-5.51340 q^{27}\) \(+12.3572 q^{28}\) \(-7.46266 q^{29}\) \(-25.8189 q^{30}\) \(-7.63648 q^{31}\) \(-10.9869 q^{32}\) \(-9.12035 q^{33}\) \(-8.54593 q^{34}\) \(-8.88055 q^{35}\) \(+24.0929 q^{36}\) \(-1.59139 q^{37}\) \(-2.61964 q^{38}\) \(-14.4010 q^{39}\) \(+26.2042 q^{40}\) \(+0.548737 q^{41}\) \(+18.7766 q^{42}\) \(-1.07983 q^{43}\) \(+15.7238 q^{44}\) \(-17.3144 q^{45}\) \(-0.367839 q^{46}\) \(-2.92282 q^{47}\) \(-27.9760 q^{48}\) \(-0.541686 q^{49}\) \(-18.8909 q^{50}\) \(-9.20094 q^{51}\) \(+24.8279 q^{52}\) \(+14.3235 q^{53}\) \(+14.4431 q^{54}\) \(-11.3000 q^{55}\) \(-19.0568 q^{56}\) \(-2.82043 q^{57}\) \(+19.5495 q^{58}\) \(-7.74329 q^{59}\) \(+47.9244 q^{60}\) \(+10.3831 q^{61}\) \(+20.0048 q^{62}\) \(+12.5918 q^{63}\) \(+8.94349 q^{64}\) \(-17.8426 q^{65}\) \(+23.8921 q^{66}\) \(-0.497786 q^{67}\) \(+15.8628 q^{68}\) \(-0.396033 q^{69}\) \(+23.2639 q^{70}\) \(-14.8364 q^{71}\) \(-37.1550 q^{72}\) \(-4.71769 q^{73}\) \(+4.16886 q^{74}\) \(-20.3388 q^{75}\) \(+4.86252 q^{76}\) \(+8.21781 q^{77}\) \(+37.7255 q^{78}\) \(+0.388482 q^{79}\) \(-34.6618 q^{80}\) \(+0.685703 q^{81}\) \(-1.43750 q^{82}\) \(-2.18298 q^{83}\) \(-34.8527 q^{84}\) \(-11.3998 q^{85}\) \(+2.82878 q^{86}\) \(+21.0479 q^{87}\) \(-24.2486 q^{88}\) \(-4.22218 q^{89}\) \(+45.3575 q^{90}\) \(+12.9759 q^{91}\) \(+0.682776 q^{92}\) \(+21.5381 q^{93}\) \(+7.65673 q^{94}\) \(-3.49446 q^{95}\) \(+30.9877 q^{96}\) \(+4.05461 q^{97}\) \(+1.41902 q^{98}\) \(+16.0223 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61964 −1.85237 −0.926183 0.377074i \(-0.876930\pi\)
−0.926183 + 0.377074i \(0.876930\pi\)
\(3\) −2.82043 −1.62837 −0.814187 0.580603i \(-0.802817\pi\)
−0.814187 + 0.580603i \(0.802817\pi\)
\(4\) 4.86252 2.43126
\(5\) −3.49446 −1.56277 −0.781385 0.624049i \(-0.785487\pi\)
−0.781385 + 0.624049i \(0.785487\pi\)
\(6\) 7.38851 3.01635
\(7\) 2.54132 0.960529 0.480265 0.877124i \(-0.340541\pi\)
0.480265 + 0.877124i \(0.340541\pi\)
\(8\) −7.49878 −2.65122
\(9\) 4.95481 1.65160
\(10\) 9.15424 2.89482
\(11\) 3.23368 0.974990 0.487495 0.873126i \(-0.337911\pi\)
0.487495 + 0.873126i \(0.337911\pi\)
\(12\) −13.7144 −3.95900
\(13\) 5.10597 1.41614 0.708070 0.706142i \(-0.249566\pi\)
0.708070 + 0.706142i \(0.249566\pi\)
\(14\) −6.65735 −1.77925
\(15\) 9.85587 2.54478
\(16\) 9.91908 2.47977
\(17\) 3.26225 0.791212 0.395606 0.918420i \(-0.370535\pi\)
0.395606 + 0.918420i \(0.370535\pi\)
\(18\) −12.9798 −3.05937
\(19\) 1.00000 0.229416
\(20\) −16.9919 −3.79950
\(21\) −7.16761 −1.56410
\(22\) −8.47108 −1.80604
\(23\) 0.140416 0.0292787 0.0146394 0.999893i \(-0.495340\pi\)
0.0146394 + 0.999893i \(0.495340\pi\)
\(24\) 21.1498 4.31718
\(25\) 7.21126 1.44225
\(26\) −13.3758 −2.62321
\(27\) −5.51340 −1.06105
\(28\) 12.3572 2.33530
\(29\) −7.46266 −1.38578 −0.692891 0.721043i \(-0.743663\pi\)
−0.692891 + 0.721043i \(0.743663\pi\)
\(30\) −25.8189 −4.71386
\(31\) −7.63648 −1.37155 −0.685776 0.727813i \(-0.740537\pi\)
−0.685776 + 0.727813i \(0.740537\pi\)
\(32\) −10.9869 −1.94222
\(33\) −9.12035 −1.58765
\(34\) −8.54593 −1.46561
\(35\) −8.88055 −1.50109
\(36\) 24.0929 4.01548
\(37\) −1.59139 −0.261622 −0.130811 0.991407i \(-0.541758\pi\)
−0.130811 + 0.991407i \(0.541758\pi\)
\(38\) −2.61964 −0.424962
\(39\) −14.4010 −2.30601
\(40\) 26.2042 4.14325
\(41\) 0.548737 0.0856984 0.0428492 0.999082i \(-0.486357\pi\)
0.0428492 + 0.999082i \(0.486357\pi\)
\(42\) 18.7766 2.89729
\(43\) −1.07983 −0.164673 −0.0823366 0.996605i \(-0.526238\pi\)
−0.0823366 + 0.996605i \(0.526238\pi\)
\(44\) 15.7238 2.37046
\(45\) −17.3144 −2.58108
\(46\) −0.367839 −0.0542350
\(47\) −2.92282 −0.426336 −0.213168 0.977016i \(-0.568378\pi\)
−0.213168 + 0.977016i \(0.568378\pi\)
\(48\) −27.9760 −4.03799
\(49\) −0.541686 −0.0773837
\(50\) −18.8909 −2.67158
\(51\) −9.20094 −1.28839
\(52\) 24.8279 3.44301
\(53\) 14.3235 1.96748 0.983742 0.179588i \(-0.0574763\pi\)
0.983742 + 0.179588i \(0.0574763\pi\)
\(54\) 14.4431 1.96546
\(55\) −11.3000 −1.52369
\(56\) −19.0568 −2.54657
\(57\) −2.82043 −0.373575
\(58\) 19.5495 2.56697
\(59\) −7.74329 −1.00809 −0.504045 0.863677i \(-0.668156\pi\)
−0.504045 + 0.863677i \(0.668156\pi\)
\(60\) 47.9244 6.18701
\(61\) 10.3831 1.32942 0.664712 0.747099i \(-0.268554\pi\)
0.664712 + 0.747099i \(0.268554\pi\)
\(62\) 20.0048 2.54062
\(63\) 12.5918 1.58641
\(64\) 8.94349 1.11794
\(65\) −17.8426 −2.21310
\(66\) 23.8921 2.94091
\(67\) −0.497786 −0.0608142 −0.0304071 0.999538i \(-0.509680\pi\)
−0.0304071 + 0.999538i \(0.509680\pi\)
\(68\) 15.8628 1.92364
\(69\) −0.396033 −0.0476768
\(70\) 23.2639 2.78056
\(71\) −14.8364 −1.76076 −0.880380 0.474269i \(-0.842712\pi\)
−0.880380 + 0.474269i \(0.842712\pi\)
\(72\) −37.1550 −4.37876
\(73\) −4.71769 −0.552164 −0.276082 0.961134i \(-0.589036\pi\)
−0.276082 + 0.961134i \(0.589036\pi\)
\(74\) 4.16886 0.484620
\(75\) −20.3388 −2.34853
\(76\) 4.86252 0.557770
\(77\) 8.21781 0.936507
\(78\) 37.7255 4.27157
\(79\) 0.388482 0.0437076 0.0218538 0.999761i \(-0.493043\pi\)
0.0218538 + 0.999761i \(0.493043\pi\)
\(80\) −34.6618 −3.87531
\(81\) 0.685703 0.0761893
\(82\) −1.43750 −0.158745
\(83\) −2.18298 −0.239613 −0.119806 0.992797i \(-0.538227\pi\)
−0.119806 + 0.992797i \(0.538227\pi\)
\(84\) −34.8527 −3.80274
\(85\) −11.3998 −1.23648
\(86\) 2.82878 0.305035
\(87\) 21.0479 2.25657
\(88\) −24.2486 −2.58491
\(89\) −4.22218 −0.447550 −0.223775 0.974641i \(-0.571838\pi\)
−0.223775 + 0.974641i \(0.571838\pi\)
\(90\) 45.3575 4.78110
\(91\) 12.9759 1.36024
\(92\) 0.682776 0.0711843
\(93\) 21.5381 2.23340
\(94\) 7.65673 0.789731
\(95\) −3.49446 −0.358524
\(96\) 30.9877 3.16266
\(97\) 4.05461 0.411683 0.205842 0.978585i \(-0.434007\pi\)
0.205842 + 0.978585i \(0.434007\pi\)
\(98\) 1.41902 0.143343
\(99\) 16.0223 1.61030
\(100\) 35.0649 3.50649
\(101\) −14.3717 −1.43003 −0.715017 0.699107i \(-0.753581\pi\)
−0.715017 + 0.699107i \(0.753581\pi\)
\(102\) 24.1032 2.38657
\(103\) 10.9220 1.07618 0.538090 0.842887i \(-0.319146\pi\)
0.538090 + 0.842887i \(0.319146\pi\)
\(104\) −38.2885 −3.75450
\(105\) 25.0469 2.44433
\(106\) −37.5224 −3.64450
\(107\) 5.10147 0.493178 0.246589 0.969120i \(-0.420690\pi\)
0.246589 + 0.969120i \(0.420690\pi\)
\(108\) −26.8090 −2.57970
\(109\) −17.6997 −1.69533 −0.847664 0.530533i \(-0.821992\pi\)
−0.847664 + 0.530533i \(0.821992\pi\)
\(110\) 29.6018 2.82243
\(111\) 4.48839 0.426019
\(112\) 25.2076 2.38189
\(113\) −11.2553 −1.05881 −0.529404 0.848370i \(-0.677584\pi\)
−0.529404 + 0.848370i \(0.677584\pi\)
\(114\) 7.38851 0.691997
\(115\) −0.490678 −0.0457560
\(116\) −36.2873 −3.36920
\(117\) 25.2991 2.33890
\(118\) 20.2846 1.86735
\(119\) 8.29043 0.759982
\(120\) −73.9070 −6.74676
\(121\) −0.543330 −0.0493936
\(122\) −27.2001 −2.46258
\(123\) −1.54767 −0.139549
\(124\) −37.1325 −3.33460
\(125\) −7.72715 −0.691137
\(126\) −32.9859 −2.93862
\(127\) 4.67121 0.414503 0.207251 0.978288i \(-0.433548\pi\)
0.207251 + 0.978288i \(0.433548\pi\)
\(128\) −1.45502 −0.128607
\(129\) 3.04559 0.268150
\(130\) 46.7412 4.09948
\(131\) 18.3170 1.60036 0.800180 0.599759i \(-0.204737\pi\)
0.800180 + 0.599759i \(0.204737\pi\)
\(132\) −44.3479 −3.85999
\(133\) 2.54132 0.220361
\(134\) 1.30402 0.112650
\(135\) 19.2663 1.65818
\(136\) −24.4629 −2.09768
\(137\) −18.4773 −1.57863 −0.789313 0.613991i \(-0.789563\pi\)
−0.789313 + 0.613991i \(0.789563\pi\)
\(138\) 1.03746 0.0883148
\(139\) 3.22495 0.273537 0.136768 0.990603i \(-0.456328\pi\)
0.136768 + 0.990603i \(0.456328\pi\)
\(140\) −43.1819 −3.64953
\(141\) 8.24359 0.694235
\(142\) 38.8661 3.26157
\(143\) 16.5110 1.38072
\(144\) 49.1471 4.09559
\(145\) 26.0780 2.16566
\(146\) 12.3587 1.02281
\(147\) 1.52779 0.126010
\(148\) −7.73815 −0.636072
\(149\) 10.5860 0.867242 0.433621 0.901095i \(-0.357236\pi\)
0.433621 + 0.901095i \(0.357236\pi\)
\(150\) 53.2804 4.35033
\(151\) 9.09239 0.739928 0.369964 0.929046i \(-0.379370\pi\)
0.369964 + 0.929046i \(0.379370\pi\)
\(152\) −7.49878 −0.608232
\(153\) 16.1638 1.30677
\(154\) −21.5277 −1.73475
\(155\) 26.6854 2.14342
\(156\) −70.0252 −5.60650
\(157\) 21.9591 1.75252 0.876262 0.481835i \(-0.160030\pi\)
0.876262 + 0.481835i \(0.160030\pi\)
\(158\) −1.01768 −0.0809625
\(159\) −40.3984 −3.20380
\(160\) 38.3932 3.03525
\(161\) 0.356842 0.0281231
\(162\) −1.79630 −0.141130
\(163\) −8.51150 −0.666672 −0.333336 0.942808i \(-0.608174\pi\)
−0.333336 + 0.942808i \(0.608174\pi\)
\(164\) 2.66825 0.208355
\(165\) 31.8707 2.48113
\(166\) 5.71861 0.443851
\(167\) −22.2400 −1.72098 −0.860490 0.509468i \(-0.829842\pi\)
−0.860490 + 0.509468i \(0.829842\pi\)
\(168\) 53.7484 4.14678
\(169\) 13.0709 1.00545
\(170\) 29.8634 2.29042
\(171\) 4.95481 0.378904
\(172\) −5.25072 −0.400364
\(173\) 12.0437 0.915663 0.457831 0.889039i \(-0.348626\pi\)
0.457831 + 0.889039i \(0.348626\pi\)
\(174\) −55.1379 −4.17999
\(175\) 18.3261 1.38532
\(176\) 32.0751 2.41775
\(177\) 21.8394 1.64155
\(178\) 11.0606 0.829027
\(179\) −8.94236 −0.668383 −0.334192 0.942505i \(-0.608463\pi\)
−0.334192 + 0.942505i \(0.608463\pi\)
\(180\) −84.1916 −6.27527
\(181\) −18.5439 −1.37835 −0.689177 0.724593i \(-0.742028\pi\)
−0.689177 + 0.724593i \(0.742028\pi\)
\(182\) −33.9922 −2.51967
\(183\) −29.2849 −2.16480
\(184\) −1.05295 −0.0776244
\(185\) 5.56103 0.408855
\(186\) −56.4222 −4.13707
\(187\) 10.5491 0.771424
\(188\) −14.2123 −1.03654
\(189\) −14.0113 −1.01917
\(190\) 9.15424 0.664118
\(191\) −4.36184 −0.315612 −0.157806 0.987470i \(-0.550442\pi\)
−0.157806 + 0.987470i \(0.550442\pi\)
\(192\) −25.2245 −1.82042
\(193\) −21.7113 −1.56281 −0.781406 0.624023i \(-0.785497\pi\)
−0.781406 + 0.624023i \(0.785497\pi\)
\(194\) −10.6216 −0.762589
\(195\) 50.3237 3.60376
\(196\) −2.63396 −0.188140
\(197\) −0.956526 −0.0681496 −0.0340748 0.999419i \(-0.510848\pi\)
−0.0340748 + 0.999419i \(0.510848\pi\)
\(198\) −41.9726 −2.98286
\(199\) 4.57302 0.324173 0.162086 0.986777i \(-0.448178\pi\)
0.162086 + 0.986777i \(0.448178\pi\)
\(200\) −54.0756 −3.82373
\(201\) 1.40397 0.0990283
\(202\) 37.6486 2.64895
\(203\) −18.9650 −1.33108
\(204\) −44.7398 −3.13241
\(205\) −1.91754 −0.133927
\(206\) −28.6118 −1.99348
\(207\) 0.695734 0.0483569
\(208\) 50.6465 3.51170
\(209\) 3.23368 0.223678
\(210\) −65.6140 −4.52780
\(211\) 1.00000 0.0688428
\(212\) 69.6483 4.78347
\(213\) 41.8451 2.86718
\(214\) −13.3640 −0.913546
\(215\) 3.77344 0.257346
\(216\) 41.3438 2.81309
\(217\) −19.4067 −1.31742
\(218\) 46.3670 3.14037
\(219\) 13.3059 0.899130
\(220\) −54.9463 −3.70448
\(221\) 16.6569 1.12047
\(222\) −11.7580 −0.789143
\(223\) −15.1464 −1.01428 −0.507138 0.861865i \(-0.669296\pi\)
−0.507138 + 0.861865i \(0.669296\pi\)
\(224\) −27.9212 −1.86556
\(225\) 35.7304 2.38203
\(226\) 29.4848 1.96130
\(227\) −2.48470 −0.164915 −0.0824577 0.996595i \(-0.526277\pi\)
−0.0824577 + 0.996595i \(0.526277\pi\)
\(228\) −13.7144 −0.908258
\(229\) 12.6784 0.837812 0.418906 0.908030i \(-0.362414\pi\)
0.418906 + 0.908030i \(0.362414\pi\)
\(230\) 1.28540 0.0847568
\(231\) −23.1777 −1.52498
\(232\) 55.9609 3.67401
\(233\) −17.2086 −1.12737 −0.563687 0.825988i \(-0.690618\pi\)
−0.563687 + 0.825988i \(0.690618\pi\)
\(234\) −66.2745 −4.33250
\(235\) 10.2137 0.666266
\(236\) −37.6519 −2.45093
\(237\) −1.09568 −0.0711723
\(238\) −21.7180 −1.40777
\(239\) 4.23894 0.274194 0.137097 0.990558i \(-0.456223\pi\)
0.137097 + 0.990558i \(0.456223\pi\)
\(240\) 97.7612 6.31046
\(241\) −10.8967 −0.701918 −0.350959 0.936391i \(-0.614144\pi\)
−0.350959 + 0.936391i \(0.614144\pi\)
\(242\) 1.42333 0.0914950
\(243\) 14.6062 0.936989
\(244\) 50.4882 3.23218
\(245\) 1.89290 0.120933
\(246\) 4.05435 0.258496
\(247\) 5.10597 0.324885
\(248\) 57.2643 3.63629
\(249\) 6.15692 0.390179
\(250\) 20.2424 1.28024
\(251\) 19.3873 1.22372 0.611859 0.790967i \(-0.290422\pi\)
0.611859 + 0.790967i \(0.290422\pi\)
\(252\) 61.2277 3.85698
\(253\) 0.454060 0.0285465
\(254\) −12.2369 −0.767811
\(255\) 32.1523 2.01346
\(256\) −14.0754 −0.879710
\(257\) −18.3122 −1.14228 −0.571141 0.820852i \(-0.693499\pi\)
−0.571141 + 0.820852i \(0.693499\pi\)
\(258\) −7.97837 −0.496711
\(259\) −4.04422 −0.251296
\(260\) −86.7600 −5.38063
\(261\) −36.9760 −2.28876
\(262\) −47.9839 −2.96445
\(263\) 4.34806 0.268113 0.134057 0.990974i \(-0.457200\pi\)
0.134057 + 0.990974i \(0.457200\pi\)
\(264\) 68.3915 4.20921
\(265\) −50.0529 −3.07473
\(266\) −6.65735 −0.408188
\(267\) 11.9084 0.728780
\(268\) −2.42049 −0.147855
\(269\) −4.64805 −0.283397 −0.141698 0.989910i \(-0.545256\pi\)
−0.141698 + 0.989910i \(0.545256\pi\)
\(270\) −50.4709 −3.07156
\(271\) 21.5938 1.31173 0.655865 0.754878i \(-0.272304\pi\)
0.655865 + 0.754878i \(0.272304\pi\)
\(272\) 32.3585 1.96202
\(273\) −36.5976 −2.21499
\(274\) 48.4040 2.92419
\(275\) 23.3189 1.40618
\(276\) −1.92572 −0.115915
\(277\) −13.9013 −0.835250 −0.417625 0.908619i \(-0.637137\pi\)
−0.417625 + 0.908619i \(0.637137\pi\)
\(278\) −8.44822 −0.506690
\(279\) −37.8373 −2.26526
\(280\) 66.5933 3.97971
\(281\) 20.0441 1.19573 0.597865 0.801597i \(-0.296016\pi\)
0.597865 + 0.801597i \(0.296016\pi\)
\(282\) −21.5952 −1.28598
\(283\) −1.86018 −0.110576 −0.0552882 0.998470i \(-0.517608\pi\)
−0.0552882 + 0.998470i \(0.517608\pi\)
\(284\) −72.1424 −4.28087
\(285\) 9.85587 0.583811
\(286\) −43.2530 −2.55761
\(287\) 1.39452 0.0823158
\(288\) −54.4378 −3.20778
\(289\) −6.35771 −0.373983
\(290\) −68.3149 −4.01159
\(291\) −11.4357 −0.670375
\(292\) −22.9399 −1.34245
\(293\) 32.2980 1.88687 0.943435 0.331558i \(-0.107574\pi\)
0.943435 + 0.331558i \(0.107574\pi\)
\(294\) −4.00225 −0.233416
\(295\) 27.0586 1.57541
\(296\) 11.9335 0.693618
\(297\) −17.8285 −1.03452
\(298\) −27.7316 −1.60645
\(299\) 0.716959 0.0414628
\(300\) −98.8980 −5.70988
\(301\) −2.74421 −0.158173
\(302\) −23.8188 −1.37062
\(303\) 40.5342 2.32863
\(304\) 9.91908 0.568898
\(305\) −36.2835 −2.07759
\(306\) −42.3434 −2.42061
\(307\) −16.3508 −0.933191 −0.466595 0.884471i \(-0.654520\pi\)
−0.466595 + 0.884471i \(0.654520\pi\)
\(308\) 39.9593 2.27689
\(309\) −30.8048 −1.75242
\(310\) −69.9061 −3.97040
\(311\) −26.0022 −1.47445 −0.737223 0.675649i \(-0.763863\pi\)
−0.737223 + 0.675649i \(0.763863\pi\)
\(312\) 107.990 6.11373
\(313\) 5.37721 0.303938 0.151969 0.988385i \(-0.451439\pi\)
0.151969 + 0.988385i \(0.451439\pi\)
\(314\) −57.5249 −3.24632
\(315\) −44.0014 −2.47920
\(316\) 1.88900 0.106265
\(317\) 31.0435 1.74358 0.871788 0.489883i \(-0.162961\pi\)
0.871788 + 0.489883i \(0.162961\pi\)
\(318\) 105.829 5.93461
\(319\) −24.1318 −1.35112
\(320\) −31.2527 −1.74708
\(321\) −14.3883 −0.803078
\(322\) −0.934798 −0.0520943
\(323\) 3.26225 0.181517
\(324\) 3.33425 0.185236
\(325\) 36.8204 2.04243
\(326\) 22.2971 1.23492
\(327\) 49.9208 2.76063
\(328\) −4.11486 −0.227205
\(329\) −7.42781 −0.409509
\(330\) −83.4898 −4.59596
\(331\) −23.8215 −1.30935 −0.654674 0.755912i \(-0.727194\pi\)
−0.654674 + 0.755912i \(0.727194\pi\)
\(332\) −10.6148 −0.582561
\(333\) −7.88501 −0.432096
\(334\) 58.2607 3.18788
\(335\) 1.73949 0.0950387
\(336\) −71.0961 −3.87861
\(337\) 28.6715 1.56184 0.780919 0.624633i \(-0.214751\pi\)
0.780919 + 0.624633i \(0.214751\pi\)
\(338\) −34.2410 −1.86247
\(339\) 31.7447 1.72414
\(340\) −55.4318 −3.00621
\(341\) −24.6939 −1.33725
\(342\) −12.9798 −0.701868
\(343\) −19.1658 −1.03486
\(344\) 8.09744 0.436585
\(345\) 1.38392 0.0745078
\(346\) −31.5501 −1.69614
\(347\) −15.4470 −0.829238 −0.414619 0.909995i \(-0.636085\pi\)
−0.414619 + 0.909995i \(0.636085\pi\)
\(348\) 102.346 5.48631
\(349\) −28.4809 −1.52455 −0.762273 0.647256i \(-0.775917\pi\)
−0.762273 + 0.647256i \(0.775917\pi\)
\(350\) −48.0079 −2.56613
\(351\) −28.1512 −1.50260
\(352\) −35.5280 −1.89365
\(353\) 26.1593 1.39232 0.696160 0.717886i \(-0.254890\pi\)
0.696160 + 0.717886i \(0.254890\pi\)
\(354\) −57.2114 −3.04075
\(355\) 51.8453 2.75166
\(356\) −20.5305 −1.08811
\(357\) −23.3826 −1.23754
\(358\) 23.4258 1.23809
\(359\) −10.4251 −0.550216 −0.275108 0.961413i \(-0.588714\pi\)
−0.275108 + 0.961413i \(0.588714\pi\)
\(360\) 129.837 6.84300
\(361\) 1.00000 0.0526316
\(362\) 48.5783 2.55322
\(363\) 1.53242 0.0804313
\(364\) 63.0956 3.30711
\(365\) 16.4858 0.862905
\(366\) 76.7159 4.01000
\(367\) −31.0491 −1.62075 −0.810376 0.585910i \(-0.800737\pi\)
−0.810376 + 0.585910i \(0.800737\pi\)
\(368\) 1.39280 0.0726045
\(369\) 2.71889 0.141540
\(370\) −14.5679 −0.757350
\(371\) 36.4006 1.88983
\(372\) 104.730 5.42998
\(373\) 19.4727 1.00826 0.504130 0.863628i \(-0.331813\pi\)
0.504130 + 0.863628i \(0.331813\pi\)
\(374\) −27.6348 −1.42896
\(375\) 21.7939 1.12543
\(376\) 21.9176 1.13031
\(377\) −38.1041 −1.96246
\(378\) 36.7046 1.88788
\(379\) 6.99458 0.359288 0.179644 0.983732i \(-0.442505\pi\)
0.179644 + 0.983732i \(0.442505\pi\)
\(380\) −16.9919 −0.871666
\(381\) −13.1748 −0.674965
\(382\) 11.4265 0.584628
\(383\) −9.33025 −0.476754 −0.238377 0.971173i \(-0.576615\pi\)
−0.238377 + 0.971173i \(0.576615\pi\)
\(384\) 4.10377 0.209420
\(385\) −28.7168 −1.46355
\(386\) 56.8758 2.89490
\(387\) −5.35037 −0.271975
\(388\) 19.7156 1.00091
\(389\) 17.3548 0.879921 0.439961 0.898017i \(-0.354992\pi\)
0.439961 + 0.898017i \(0.354992\pi\)
\(390\) −131.830 −6.67548
\(391\) 0.458072 0.0231657
\(392\) 4.06199 0.205161
\(393\) −51.6617 −2.60599
\(394\) 2.50575 0.126238
\(395\) −1.35753 −0.0683050
\(396\) 77.9086 3.91505
\(397\) −33.2702 −1.66979 −0.834893 0.550412i \(-0.814471\pi\)
−0.834893 + 0.550412i \(0.814471\pi\)
\(398\) −11.9797 −0.600486
\(399\) −7.16761 −0.358829
\(400\) 71.5290 3.57645
\(401\) −12.0296 −0.600729 −0.300365 0.953824i \(-0.597108\pi\)
−0.300365 + 0.953824i \(0.597108\pi\)
\(402\) −3.67789 −0.183437
\(403\) −38.9916 −1.94231
\(404\) −69.8826 −3.47679
\(405\) −2.39616 −0.119066
\(406\) 49.6815 2.46565
\(407\) −5.14603 −0.255079
\(408\) 68.9959 3.41580
\(409\) 22.2804 1.10169 0.550847 0.834607i \(-0.314305\pi\)
0.550847 + 0.834607i \(0.314305\pi\)
\(410\) 5.02327 0.248082
\(411\) 52.1140 2.57059
\(412\) 53.1086 2.61647
\(413\) −19.6782 −0.968300
\(414\) −1.82257 −0.0895746
\(415\) 7.62832 0.374460
\(416\) −56.0986 −2.75046
\(417\) −9.09574 −0.445420
\(418\) −8.47108 −0.414334
\(419\) −20.8185 −1.01705 −0.508525 0.861048i \(-0.669809\pi\)
−0.508525 + 0.861048i \(0.669809\pi\)
\(420\) 121.791 5.94281
\(421\) −31.1740 −1.51933 −0.759664 0.650316i \(-0.774636\pi\)
−0.759664 + 0.650316i \(0.774636\pi\)
\(422\) −2.61964 −0.127522
\(423\) −14.4820 −0.704138
\(424\) −107.409 −5.21623
\(425\) 23.5249 1.14113
\(426\) −109.619 −5.31106
\(427\) 26.3869 1.27695
\(428\) 24.8060 1.19904
\(429\) −46.5682 −2.24833
\(430\) −9.88506 −0.476700
\(431\) −14.7514 −0.710548 −0.355274 0.934762i \(-0.615612\pi\)
−0.355274 + 0.934762i \(0.615612\pi\)
\(432\) −54.6878 −2.63117
\(433\) −3.88447 −0.186676 −0.0933379 0.995634i \(-0.529754\pi\)
−0.0933379 + 0.995634i \(0.529754\pi\)
\(434\) 50.8387 2.44034
\(435\) −73.5510 −3.52650
\(436\) −86.0654 −4.12179
\(437\) 0.140416 0.00671700
\(438\) −34.8567 −1.66552
\(439\) 5.96184 0.284543 0.142271 0.989828i \(-0.454559\pi\)
0.142271 + 0.989828i \(0.454559\pi\)
\(440\) 84.7359 4.03963
\(441\) −2.68395 −0.127807
\(442\) −43.6352 −2.07552
\(443\) −10.9439 −0.519959 −0.259980 0.965614i \(-0.583716\pi\)
−0.259980 + 0.965614i \(0.583716\pi\)
\(444\) 21.8249 1.03576
\(445\) 14.7543 0.699419
\(446\) 39.6780 1.87881
\(447\) −29.8571 −1.41219
\(448\) 22.7283 1.07381
\(449\) 20.0939 0.948292 0.474146 0.880446i \(-0.342757\pi\)
0.474146 + 0.880446i \(0.342757\pi\)
\(450\) −93.6008 −4.41239
\(451\) 1.77444 0.0835551
\(452\) −54.7291 −2.57424
\(453\) −25.6444 −1.20488
\(454\) 6.50903 0.305484
\(455\) −45.3438 −2.12575
\(456\) 21.1498 0.990429
\(457\) −18.7847 −0.878713 −0.439356 0.898313i \(-0.644793\pi\)
−0.439356 + 0.898313i \(0.644793\pi\)
\(458\) −33.2128 −1.55193
\(459\) −17.9861 −0.839518
\(460\) −2.38593 −0.111245
\(461\) 5.34488 0.248936 0.124468 0.992224i \(-0.460278\pi\)
0.124468 + 0.992224i \(0.460278\pi\)
\(462\) 60.7174 2.82483
\(463\) 4.73731 0.220161 0.110081 0.993923i \(-0.464889\pi\)
0.110081 + 0.993923i \(0.464889\pi\)
\(464\) −74.0227 −3.43642
\(465\) −75.2641 −3.49029
\(466\) 45.0804 2.08831
\(467\) 33.3733 1.54433 0.772165 0.635422i \(-0.219174\pi\)
0.772165 + 0.635422i \(0.219174\pi\)
\(468\) 123.017 5.68648
\(469\) −1.26503 −0.0584138
\(470\) −26.7561 −1.23417
\(471\) −61.9339 −2.85376
\(472\) 58.0653 2.67267
\(473\) −3.49184 −0.160555
\(474\) 2.87030 0.131837
\(475\) 7.21126 0.330875
\(476\) 40.3124 1.84772
\(477\) 70.9702 3.24950
\(478\) −11.1045 −0.507908
\(479\) 27.7874 1.26964 0.634818 0.772661i \(-0.281075\pi\)
0.634818 + 0.772661i \(0.281075\pi\)
\(480\) −108.285 −4.94252
\(481\) −8.12556 −0.370494
\(482\) 28.5455 1.30021
\(483\) −1.00645 −0.0457949
\(484\) −2.64195 −0.120089
\(485\) −14.1687 −0.643367
\(486\) −38.2630 −1.73565
\(487\) −12.6010 −0.571007 −0.285504 0.958378i \(-0.592161\pi\)
−0.285504 + 0.958378i \(0.592161\pi\)
\(488\) −77.8609 −3.52460
\(489\) 24.0061 1.08559
\(490\) −4.95872 −0.224012
\(491\) −28.6359 −1.29232 −0.646159 0.763202i \(-0.723626\pi\)
−0.646159 + 0.763202i \(0.723626\pi\)
\(492\) −7.52560 −0.339280
\(493\) −24.3451 −1.09645
\(494\) −13.3758 −0.601806
\(495\) −55.9891 −2.51652
\(496\) −75.7468 −3.40113
\(497\) −37.7041 −1.69126
\(498\) −16.1289 −0.722755
\(499\) 0.0697231 0.00312123 0.00156062 0.999999i \(-0.499503\pi\)
0.00156062 + 0.999999i \(0.499503\pi\)
\(500\) −37.5734 −1.68034
\(501\) 62.7262 2.80240
\(502\) −50.7879 −2.26677
\(503\) −42.0619 −1.87545 −0.937723 0.347383i \(-0.887070\pi\)
−0.937723 + 0.347383i \(0.887070\pi\)
\(504\) −94.4229 −4.20593
\(505\) 50.2212 2.23482
\(506\) −1.18947 −0.0528786
\(507\) −36.8655 −1.63725
\(508\) 22.7138 1.00776
\(509\) −28.0786 −1.24456 −0.622281 0.782794i \(-0.713794\pi\)
−0.622281 + 0.782794i \(0.713794\pi\)
\(510\) −84.2276 −3.72966
\(511\) −11.9892 −0.530370
\(512\) 39.7824 1.75815
\(513\) −5.51340 −0.243422
\(514\) 47.9713 2.11593
\(515\) −38.1666 −1.68182
\(516\) 14.8093 0.651942
\(517\) −9.45144 −0.415674
\(518\) 10.5944 0.465492
\(519\) −33.9683 −1.49104
\(520\) 133.798 5.86742
\(521\) −3.66228 −0.160447 −0.0802237 0.996777i \(-0.525563\pi\)
−0.0802237 + 0.996777i \(0.525563\pi\)
\(522\) 96.8640 4.23962
\(523\) 6.91382 0.302320 0.151160 0.988509i \(-0.451699\pi\)
0.151160 + 0.988509i \(0.451699\pi\)
\(524\) 89.0667 3.89089
\(525\) −51.6875 −2.25583
\(526\) −11.3904 −0.496644
\(527\) −24.9121 −1.08519
\(528\) −90.4655 −3.93700
\(529\) −22.9803 −0.999143
\(530\) 131.121 5.69552
\(531\) −38.3665 −1.66497
\(532\) 12.3572 0.535754
\(533\) 2.80183 0.121361
\(534\) −31.1956 −1.34997
\(535\) −17.8269 −0.770724
\(536\) 3.73279 0.161232
\(537\) 25.2213 1.08838
\(538\) 12.1762 0.524954
\(539\) −1.75164 −0.0754484
\(540\) 93.6830 4.03148
\(541\) 5.08815 0.218757 0.109378 0.994000i \(-0.465114\pi\)
0.109378 + 0.994000i \(0.465114\pi\)
\(542\) −56.5681 −2.42981
\(543\) 52.3016 2.24448
\(544\) −35.8419 −1.53671
\(545\) 61.8511 2.64941
\(546\) 95.8725 4.10297
\(547\) −40.9404 −1.75049 −0.875243 0.483683i \(-0.839299\pi\)
−0.875243 + 0.483683i \(0.839299\pi\)
\(548\) −89.8465 −3.83805
\(549\) 51.4465 2.19568
\(550\) −61.0871 −2.60476
\(551\) −7.46266 −0.317920
\(552\) 2.96976 0.126402
\(553\) 0.987257 0.0419824
\(554\) 36.4165 1.54719
\(555\) −15.6845 −0.665769
\(556\) 15.6814 0.665039
\(557\) 12.2491 0.519012 0.259506 0.965741i \(-0.416440\pi\)
0.259506 + 0.965741i \(0.416440\pi\)
\(558\) 99.1201 4.19609
\(559\) −5.51360 −0.233200
\(560\) −88.0869 −3.72235
\(561\) −29.7529 −1.25617
\(562\) −52.5083 −2.21493
\(563\) 37.2561 1.57016 0.785079 0.619396i \(-0.212623\pi\)
0.785079 + 0.619396i \(0.212623\pi\)
\(564\) 40.0846 1.68787
\(565\) 39.3312 1.65467
\(566\) 4.87301 0.204828
\(567\) 1.74259 0.0731820
\(568\) 111.255 4.66816
\(569\) 16.2595 0.681635 0.340817 0.940129i \(-0.389296\pi\)
0.340817 + 0.940129i \(0.389296\pi\)
\(570\) −25.8189 −1.08143
\(571\) −1.39643 −0.0584389 −0.0292195 0.999573i \(-0.509302\pi\)
−0.0292195 + 0.999573i \(0.509302\pi\)
\(572\) 80.2853 3.35690
\(573\) 12.3022 0.513934
\(574\) −3.65314 −0.152479
\(575\) 1.01258 0.0422273
\(576\) 44.3133 1.84639
\(577\) −33.4098 −1.39087 −0.695434 0.718590i \(-0.744788\pi\)
−0.695434 + 0.718590i \(0.744788\pi\)
\(578\) 16.6549 0.692754
\(579\) 61.2351 2.54484
\(580\) 126.805 5.26528
\(581\) −5.54764 −0.230155
\(582\) 29.9575 1.24178
\(583\) 46.3176 1.91828
\(584\) 35.3769 1.46391
\(585\) −88.4067 −3.65517
\(586\) −84.6092 −3.49517
\(587\) −15.5792 −0.643023 −0.321512 0.946906i \(-0.604191\pi\)
−0.321512 + 0.946906i \(0.604191\pi\)
\(588\) 7.42889 0.306362
\(589\) −7.63648 −0.314656
\(590\) −70.8839 −2.91824
\(591\) 2.69781 0.110973
\(592\) −15.7851 −0.648763
\(593\) 44.1209 1.81183 0.905913 0.423463i \(-0.139186\pi\)
0.905913 + 0.423463i \(0.139186\pi\)
\(594\) 46.7044 1.91630
\(595\) −28.9706 −1.18768
\(596\) 51.4748 2.10849
\(597\) −12.8979 −0.527874
\(598\) −1.87818 −0.0768043
\(599\) −6.58108 −0.268895 −0.134448 0.990921i \(-0.542926\pi\)
−0.134448 + 0.990921i \(0.542926\pi\)
\(600\) 152.516 6.22646
\(601\) 38.6449 1.57636 0.788179 0.615447i \(-0.211024\pi\)
0.788179 + 0.615447i \(0.211024\pi\)
\(602\) 7.18884 0.292995
\(603\) −2.46643 −0.100441
\(604\) 44.2119 1.79896
\(605\) 1.89864 0.0771908
\(606\) −106.185 −4.31348
\(607\) −16.0203 −0.650243 −0.325121 0.945672i \(-0.605405\pi\)
−0.325121 + 0.945672i \(0.605405\pi\)
\(608\) −10.9869 −0.445576
\(609\) 53.4894 2.16750
\(610\) 95.0497 3.84845
\(611\) −14.9238 −0.603752
\(612\) 78.5970 3.17710
\(613\) −1.19280 −0.0481765 −0.0240883 0.999710i \(-0.507668\pi\)
−0.0240883 + 0.999710i \(0.507668\pi\)
\(614\) 42.8333 1.72861
\(615\) 5.40829 0.218083
\(616\) −61.6236 −2.48289
\(617\) 38.5792 1.55314 0.776570 0.630031i \(-0.216958\pi\)
0.776570 + 0.630031i \(0.216958\pi\)
\(618\) 80.6975 3.24613
\(619\) 1.00325 0.0403242 0.0201621 0.999797i \(-0.493582\pi\)
0.0201621 + 0.999797i \(0.493582\pi\)
\(620\) 129.758 5.21121
\(621\) −0.774169 −0.0310663
\(622\) 68.1163 2.73122
\(623\) −10.7299 −0.429885
\(624\) −142.845 −5.71836
\(625\) −9.05406 −0.362162
\(626\) −14.0864 −0.563005
\(627\) −9.12035 −0.364232
\(628\) 106.776 4.26084
\(629\) −5.19150 −0.206999
\(630\) 115.268 4.59238
\(631\) 24.5959 0.979146 0.489573 0.871962i \(-0.337153\pi\)
0.489573 + 0.871962i \(0.337153\pi\)
\(632\) −2.91314 −0.115878
\(633\) −2.82043 −0.112102
\(634\) −81.3228 −3.22974
\(635\) −16.3233 −0.647772
\(636\) −196.438 −7.78928
\(637\) −2.76583 −0.109586
\(638\) 63.2168 2.50278
\(639\) −73.5116 −2.90808
\(640\) 5.08451 0.200983
\(641\) 6.50912 0.257095 0.128547 0.991703i \(-0.458969\pi\)
0.128547 + 0.991703i \(0.458969\pi\)
\(642\) 37.6923 1.48760
\(643\) −16.5049 −0.650890 −0.325445 0.945561i \(-0.605514\pi\)
−0.325445 + 0.945561i \(0.605514\pi\)
\(644\) 1.73515 0.0683746
\(645\) −10.6427 −0.419056
\(646\) −8.54593 −0.336235
\(647\) −6.52260 −0.256430 −0.128215 0.991746i \(-0.540925\pi\)
−0.128215 + 0.991746i \(0.540925\pi\)
\(648\) −5.14194 −0.201994
\(649\) −25.0393 −0.982879
\(650\) −96.4563 −3.78333
\(651\) 54.7353 2.14525
\(652\) −41.3874 −1.62085
\(653\) 4.85288 0.189908 0.0949539 0.995482i \(-0.469730\pi\)
0.0949539 + 0.995482i \(0.469730\pi\)
\(654\) −130.775 −5.11370
\(655\) −64.0079 −2.50100
\(656\) 5.44297 0.212512
\(657\) −23.3753 −0.911955
\(658\) 19.4582 0.758560
\(659\) 34.6302 1.34900 0.674500 0.738275i \(-0.264359\pi\)
0.674500 + 0.738275i \(0.264359\pi\)
\(660\) 154.972 6.03228
\(661\) −9.97032 −0.387801 −0.193900 0.981021i \(-0.562114\pi\)
−0.193900 + 0.981021i \(0.562114\pi\)
\(662\) 62.4038 2.42539
\(663\) −46.9797 −1.82454
\(664\) 16.3697 0.635266
\(665\) −8.88055 −0.344373
\(666\) 20.6559 0.800400
\(667\) −1.04788 −0.0405739
\(668\) −108.142 −4.18415
\(669\) 42.7192 1.65162
\(670\) −4.55685 −0.176046
\(671\) 33.5757 1.29618
\(672\) 78.7496 3.03783
\(673\) 38.2539 1.47458 0.737290 0.675576i \(-0.236105\pi\)
0.737290 + 0.675576i \(0.236105\pi\)
\(674\) −75.1091 −2.89310
\(675\) −39.7585 −1.53031
\(676\) 63.5575 2.44452
\(677\) −11.2916 −0.433973 −0.216987 0.976175i \(-0.569623\pi\)
−0.216987 + 0.976175i \(0.569623\pi\)
\(678\) −83.1598 −3.19373
\(679\) 10.3041 0.395434
\(680\) 85.4847 3.27819
\(681\) 7.00792 0.268544
\(682\) 64.6892 2.47708
\(683\) 9.43449 0.361001 0.180500 0.983575i \(-0.442228\pi\)
0.180500 + 0.983575i \(0.442228\pi\)
\(684\) 24.0929 0.921214
\(685\) 64.5683 2.46703
\(686\) 50.2077 1.91694
\(687\) −35.7585 −1.36427
\(688\) −10.7110 −0.408352
\(689\) 73.1353 2.78623
\(690\) −3.62538 −0.138016
\(691\) 44.7149 1.70104 0.850518 0.525946i \(-0.176289\pi\)
0.850518 + 0.525946i \(0.176289\pi\)
\(692\) 58.5626 2.22622
\(693\) 40.7177 1.54674
\(694\) 40.4656 1.53605
\(695\) −11.2695 −0.427475
\(696\) −157.834 −5.98266
\(697\) 1.79012 0.0678056
\(698\) 74.6097 2.82402
\(699\) 48.5357 1.83579
\(700\) 89.1112 3.36809
\(701\) −14.7181 −0.555896 −0.277948 0.960596i \(-0.589654\pi\)
−0.277948 + 0.960596i \(0.589654\pi\)
\(702\) 73.7461 2.78337
\(703\) −1.59139 −0.0600202
\(704\) 28.9204 1.08998
\(705\) −28.8069 −1.08493
\(706\) −68.5281 −2.57909
\(707\) −36.5230 −1.37359
\(708\) 106.195 3.99103
\(709\) −12.4198 −0.466434 −0.233217 0.972425i \(-0.574925\pi\)
−0.233217 + 0.972425i \(0.574925\pi\)
\(710\) −135.816 −5.09709
\(711\) 1.92485 0.0721876
\(712\) 31.6612 1.18655
\(713\) −1.07228 −0.0401573
\(714\) 61.2539 2.29237
\(715\) −57.6972 −2.15775
\(716\) −43.4824 −1.62501
\(717\) −11.9556 −0.446491
\(718\) 27.3101 1.01920
\(719\) 39.8503 1.48616 0.743082 0.669200i \(-0.233363\pi\)
0.743082 + 0.669200i \(0.233363\pi\)
\(720\) −171.743 −6.40047
\(721\) 27.7564 1.03370
\(722\) −2.61964 −0.0974930
\(723\) 30.7334 1.14299
\(724\) −90.1699 −3.35114
\(725\) −53.8152 −1.99864
\(726\) −4.01439 −0.148988
\(727\) −2.18563 −0.0810604 −0.0405302 0.999178i \(-0.512905\pi\)
−0.0405302 + 0.999178i \(0.512905\pi\)
\(728\) −97.3035 −3.60631
\(729\) −43.2529 −1.60196
\(730\) −43.1868 −1.59842
\(731\) −3.52269 −0.130291
\(732\) −142.398 −5.26320
\(733\) 14.0231 0.517953 0.258977 0.965884i \(-0.416615\pi\)
0.258977 + 0.965884i \(0.416615\pi\)
\(734\) 81.3376 3.00223
\(735\) −5.33879 −0.196924
\(736\) −1.54273 −0.0568658
\(737\) −1.60968 −0.0592933
\(738\) −7.12251 −0.262183
\(739\) −11.5138 −0.423542 −0.211771 0.977319i \(-0.567923\pi\)
−0.211771 + 0.977319i \(0.567923\pi\)
\(740\) 27.0406 0.994034
\(741\) −14.4010 −0.529034
\(742\) −95.3566 −3.50065
\(743\) −9.91626 −0.363792 −0.181896 0.983318i \(-0.558223\pi\)
−0.181896 + 0.983318i \(0.558223\pi\)
\(744\) −161.510 −5.92123
\(745\) −36.9925 −1.35530
\(746\) −51.0116 −1.86767
\(747\) −10.8162 −0.395745
\(748\) 51.2951 1.87553
\(749\) 12.9645 0.473712
\(750\) −57.0921 −2.08471
\(751\) −44.2693 −1.61541 −0.807705 0.589587i \(-0.799290\pi\)
−0.807705 + 0.589587i \(0.799290\pi\)
\(752\) −28.9916 −1.05722
\(753\) −54.6806 −1.99267
\(754\) 99.8190 3.63520
\(755\) −31.7730 −1.15634
\(756\) −68.1303 −2.47788
\(757\) −44.0438 −1.60080 −0.800399 0.599468i \(-0.795379\pi\)
−0.800399 + 0.599468i \(0.795379\pi\)
\(758\) −18.3233 −0.665532
\(759\) −1.28064 −0.0464844
\(760\) 26.2042 0.950526
\(761\) −5.44608 −0.197420 −0.0987102 0.995116i \(-0.531472\pi\)
−0.0987102 + 0.995116i \(0.531472\pi\)
\(762\) 34.5132 1.25028
\(763\) −44.9807 −1.62841
\(764\) −21.2095 −0.767334
\(765\) −56.4839 −2.04218
\(766\) 24.4419 0.883122
\(767\) −39.5370 −1.42760
\(768\) 39.6985 1.43250
\(769\) 0.447380 0.0161330 0.00806648 0.999967i \(-0.497432\pi\)
0.00806648 + 0.999967i \(0.497432\pi\)
\(770\) 75.2278 2.71102
\(771\) 51.6482 1.86006
\(772\) −105.572 −3.79960
\(773\) 44.1238 1.58702 0.793511 0.608556i \(-0.208251\pi\)
0.793511 + 0.608556i \(0.208251\pi\)
\(774\) 14.0161 0.503797
\(775\) −55.0686 −1.97812
\(776\) −30.4047 −1.09146
\(777\) 11.4064 0.409203
\(778\) −45.4632 −1.62994
\(779\) 0.548737 0.0196606
\(780\) 244.700 8.76168
\(781\) −47.9762 −1.71672
\(782\) −1.19998 −0.0429114
\(783\) 41.1446 1.47039
\(784\) −5.37303 −0.191894
\(785\) −76.7351 −2.73879
\(786\) 135.335 4.82724
\(787\) 21.7535 0.775427 0.387713 0.921780i \(-0.373265\pi\)
0.387713 + 0.921780i \(0.373265\pi\)
\(788\) −4.65113 −0.165690
\(789\) −12.2634 −0.436588
\(790\) 3.55625 0.126526
\(791\) −28.6033 −1.01702
\(792\) −120.147 −4.26925
\(793\) 53.0159 1.88265
\(794\) 87.1561 3.09306
\(795\) 141.171 5.00680
\(796\) 22.2364 0.788148
\(797\) −36.7946 −1.30333 −0.651666 0.758506i \(-0.725930\pi\)
−0.651666 + 0.758506i \(0.725930\pi\)
\(798\) 18.7766 0.664683
\(799\) −9.53496 −0.337323
\(800\) −79.2291 −2.80117
\(801\) −20.9201 −0.739176
\(802\) 31.5132 1.11277
\(803\) −15.2555 −0.538355
\(804\) 6.82683 0.240764
\(805\) −1.24697 −0.0439499
\(806\) 102.144 3.59787
\(807\) 13.1095 0.461476
\(808\) 107.770 3.79134
\(809\) 14.1327 0.496878 0.248439 0.968648i \(-0.420082\pi\)
0.248439 + 0.968648i \(0.420082\pi\)
\(810\) 6.27709 0.220554
\(811\) −28.7826 −1.01070 −0.505348 0.862916i \(-0.668636\pi\)
−0.505348 + 0.862916i \(0.668636\pi\)
\(812\) −92.2178 −3.23621
\(813\) −60.9038 −2.13599
\(814\) 13.4807 0.472500
\(815\) 29.7431 1.04186
\(816\) −91.2649 −3.19491
\(817\) −1.07983 −0.0377786
\(818\) −58.3666 −2.04074
\(819\) 64.2931 2.24658
\(820\) −9.32409 −0.325611
\(821\) 43.5511 1.51994 0.759972 0.649956i \(-0.225212\pi\)
0.759972 + 0.649956i \(0.225212\pi\)
\(822\) −136.520 −4.76168
\(823\) 55.1594 1.92274 0.961368 0.275267i \(-0.0887663\pi\)
0.961368 + 0.275267i \(0.0887663\pi\)
\(824\) −81.9020 −2.85319
\(825\) −65.7692 −2.28979
\(826\) 51.5498 1.79365
\(827\) 13.1756 0.458160 0.229080 0.973408i \(-0.426428\pi\)
0.229080 + 0.973408i \(0.426428\pi\)
\(828\) 3.38302 0.117568
\(829\) 20.5821 0.714846 0.357423 0.933943i \(-0.383655\pi\)
0.357423 + 0.933943i \(0.383655\pi\)
\(830\) −19.9835 −0.693637
\(831\) 39.2077 1.36010
\(832\) 45.6652 1.58316
\(833\) −1.76712 −0.0612269
\(834\) 23.8276 0.825082
\(835\) 77.7167 2.68950
\(836\) 15.7238 0.543820
\(837\) 42.1029 1.45529
\(838\) 54.5369 1.88395
\(839\) −22.6837 −0.783128 −0.391564 0.920151i \(-0.628066\pi\)
−0.391564 + 0.920151i \(0.628066\pi\)
\(840\) −187.822 −6.48046
\(841\) 26.6913 0.920389
\(842\) 81.6647 2.81435
\(843\) −56.5328 −1.94709
\(844\) 4.86252 0.167375
\(845\) −45.6757 −1.57129
\(846\) 37.9376 1.30432
\(847\) −1.38077 −0.0474440
\(848\) 142.076 4.87891
\(849\) 5.24651 0.180060
\(850\) −61.6269 −2.11379
\(851\) −0.223456 −0.00765997
\(852\) 203.472 6.97085
\(853\) 24.1198 0.825846 0.412923 0.910766i \(-0.364508\pi\)
0.412923 + 0.910766i \(0.364508\pi\)
\(854\) −69.1242 −2.36538
\(855\) −17.3144 −0.592139
\(856\) −38.2548 −1.30752
\(857\) 55.2831 1.88843 0.944217 0.329324i \(-0.106821\pi\)
0.944217 + 0.329324i \(0.106821\pi\)
\(858\) 121.992 4.16474
\(859\) −2.41234 −0.0823081 −0.0411540 0.999153i \(-0.513103\pi\)
−0.0411540 + 0.999153i \(0.513103\pi\)
\(860\) 18.3484 0.625676
\(861\) −3.93314 −0.134041
\(862\) 38.6433 1.31619
\(863\) −19.5846 −0.666669 −0.333334 0.942809i \(-0.608174\pi\)
−0.333334 + 0.942809i \(0.608174\pi\)
\(864\) 60.5749 2.06080
\(865\) −42.0861 −1.43097
\(866\) 10.1759 0.345792
\(867\) 17.9315 0.608985
\(868\) −94.3657 −3.20298
\(869\) 1.25622 0.0426145
\(870\) 192.677 6.53237
\(871\) −2.54168 −0.0861215
\(872\) 132.727 4.49469
\(873\) 20.0898 0.679938
\(874\) −0.367839 −0.0124424
\(875\) −19.6372 −0.663858
\(876\) 64.7002 2.18602
\(877\) 34.4715 1.16402 0.582010 0.813182i \(-0.302266\pi\)
0.582010 + 0.813182i \(0.302266\pi\)
\(878\) −15.6179 −0.527078
\(879\) −91.0942 −3.07253
\(880\) −112.085 −3.77839
\(881\) −45.2599 −1.52485 −0.762423 0.647079i \(-0.775990\pi\)
−0.762423 + 0.647079i \(0.775990\pi\)
\(882\) 7.03099 0.236746
\(883\) −47.2362 −1.58962 −0.794812 0.606856i \(-0.792431\pi\)
−0.794812 + 0.606856i \(0.792431\pi\)
\(884\) 80.9948 2.72415
\(885\) −76.3169 −2.56536
\(886\) 28.6690 0.963155
\(887\) −32.0304 −1.07547 −0.537737 0.843112i \(-0.680721\pi\)
−0.537737 + 0.843112i \(0.680721\pi\)
\(888\) −33.6574 −1.12947
\(889\) 11.8710 0.398142
\(890\) −38.6509 −1.29558
\(891\) 2.21734 0.0742838
\(892\) −73.6495 −2.46597
\(893\) −2.92282 −0.0978083
\(894\) 78.2150 2.61590
\(895\) 31.2487 1.04453
\(896\) −3.69767 −0.123530
\(897\) −2.02213 −0.0675170
\(898\) −52.6389 −1.75658
\(899\) 56.9884 1.90067
\(900\) 173.740 5.79133
\(901\) 46.7269 1.55670
\(902\) −4.64840 −0.154775
\(903\) 7.73983 0.257566
\(904\) 84.4009 2.80713
\(905\) 64.8008 2.15405
\(906\) 67.1792 2.23188
\(907\) −33.6567 −1.11755 −0.558776 0.829318i \(-0.688729\pi\)
−0.558776 + 0.829318i \(0.688729\pi\)
\(908\) −12.0819 −0.400952
\(909\) −71.2089 −2.36185
\(910\) 118.784 3.93767
\(911\) −56.6691 −1.87753 −0.938765 0.344558i \(-0.888029\pi\)
−0.938765 + 0.344558i \(0.888029\pi\)
\(912\) −27.9760 −0.926379
\(913\) −7.05904 −0.233620
\(914\) 49.2093 1.62770
\(915\) 102.335 3.38309
\(916\) 61.6490 2.03694
\(917\) 46.5493 1.53719
\(918\) 47.1171 1.55510
\(919\) −35.5443 −1.17250 −0.586249 0.810131i \(-0.699396\pi\)
−0.586249 + 0.810131i \(0.699396\pi\)
\(920\) 3.67949 0.121309
\(921\) 46.1163 1.51958
\(922\) −14.0017 −0.461120
\(923\) −75.7543 −2.49348
\(924\) −112.702 −3.70763
\(925\) −11.4759 −0.377325
\(926\) −12.4100 −0.407819
\(927\) 54.1166 1.77742
\(928\) 81.9912 2.69149
\(929\) 14.3698 0.471457 0.235729 0.971819i \(-0.424252\pi\)
0.235729 + 0.971819i \(0.424252\pi\)
\(930\) 197.165 6.46530
\(931\) −0.541686 −0.0177530
\(932\) −83.6773 −2.74094
\(933\) 73.3372 2.40095
\(934\) −87.4260 −2.86066
\(935\) −36.8633 −1.20556
\(936\) −189.712 −6.20094
\(937\) 9.49677 0.310246 0.155123 0.987895i \(-0.450423\pi\)
0.155123 + 0.987895i \(0.450423\pi\)
\(938\) 3.31394 0.108204
\(939\) −15.1660 −0.494925
\(940\) 49.6642 1.61987
\(941\) −28.5965 −0.932219 −0.466109 0.884727i \(-0.654345\pi\)
−0.466109 + 0.884727i \(0.654345\pi\)
\(942\) 162.245 5.28622
\(943\) 0.0770515 0.00250914
\(944\) −76.8063 −2.49983
\(945\) 48.9620 1.59273
\(946\) 9.14736 0.297406
\(947\) 50.6715 1.64660 0.823302 0.567604i \(-0.192129\pi\)
0.823302 + 0.567604i \(0.192129\pi\)
\(948\) −5.32779 −0.173039
\(949\) −24.0884 −0.781941
\(950\) −18.8909 −0.612902
\(951\) −87.5559 −2.83919
\(952\) −62.1681 −2.01488
\(953\) −6.59431 −0.213611 −0.106805 0.994280i \(-0.534062\pi\)
−0.106805 + 0.994280i \(0.534062\pi\)
\(954\) −185.916 −6.01927
\(955\) 15.2423 0.493228
\(956\) 20.6119 0.666638
\(957\) 68.0621 2.20013
\(958\) −72.7929 −2.35183
\(959\) −46.9569 −1.51632
\(960\) 88.1459 2.84490
\(961\) 27.3158 0.881154
\(962\) 21.2860 0.686290
\(963\) 25.2768 0.814534
\(964\) −52.9855 −1.70655
\(965\) 75.8692 2.44232
\(966\) 2.63653 0.0848290
\(967\) 47.3508 1.52270 0.761350 0.648341i \(-0.224537\pi\)
0.761350 + 0.648341i \(0.224537\pi\)
\(968\) 4.07431 0.130953
\(969\) −9.20094 −0.295577
\(970\) 37.1169 1.19175
\(971\) 43.5047 1.39613 0.698066 0.716033i \(-0.254044\pi\)
0.698066 + 0.716033i \(0.254044\pi\)
\(972\) 71.0230 2.27806
\(973\) 8.19564 0.262740
\(974\) 33.0102 1.05771
\(975\) −103.849 −3.32584
\(976\) 102.991 3.29667
\(977\) −56.9925 −1.82335 −0.911676 0.410910i \(-0.865211\pi\)
−0.911676 + 0.410910i \(0.865211\pi\)
\(978\) −62.8873 −2.01091
\(979\) −13.6532 −0.436357
\(980\) 9.20427 0.294020
\(981\) −87.6989 −2.80001
\(982\) 75.0157 2.39385
\(983\) −40.8934 −1.30430 −0.652149 0.758091i \(-0.726132\pi\)
−0.652149 + 0.758091i \(0.726132\pi\)
\(984\) 11.6057 0.369975
\(985\) 3.34254 0.106502
\(986\) 63.7754 2.03102
\(987\) 20.9496 0.666833
\(988\) 24.8279 0.789880
\(989\) −0.151626 −0.00482142
\(990\) 146.671 4.66153
\(991\) −27.7482 −0.881451 −0.440726 0.897642i \(-0.645279\pi\)
−0.440726 + 0.897642i \(0.645279\pi\)
\(992\) 83.9009 2.66386
\(993\) 67.1868 2.13211
\(994\) 98.7713 3.13283
\(995\) −15.9802 −0.506607
\(996\) 29.9382 0.948628
\(997\) 50.9146 1.61248 0.806241 0.591587i \(-0.201498\pi\)
0.806241 + 0.591587i \(0.201498\pi\)
\(998\) −0.182650 −0.00578167
\(999\) 8.77393 0.277595
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 \(a_p\))