Properties

Label 8007.2.a.e.1.2
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.76060 q^{2}\) \(+1.00000 q^{3}\) \(+5.62090 q^{4}\) \(-0.677149 q^{5}\) \(-2.76060 q^{6}\) \(+3.14387 q^{7}\) \(-9.99585 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.76060 q^{2}\) \(+1.00000 q^{3}\) \(+5.62090 q^{4}\) \(-0.677149 q^{5}\) \(-2.76060 q^{6}\) \(+3.14387 q^{7}\) \(-9.99585 q^{8}\) \(+1.00000 q^{9}\) \(+1.86934 q^{10}\) \(-2.07367 q^{11}\) \(+5.62090 q^{12}\) \(+5.11851 q^{13}\) \(-8.67895 q^{14}\) \(-0.677149 q^{15}\) \(+16.3527 q^{16}\) \(-1.00000 q^{17}\) \(-2.76060 q^{18}\) \(+1.32055 q^{19}\) \(-3.80619 q^{20}\) \(+3.14387 q^{21}\) \(+5.72457 q^{22}\) \(+1.26188 q^{23}\) \(-9.99585 q^{24}\) \(-4.54147 q^{25}\) \(-14.1301 q^{26}\) \(+1.00000 q^{27}\) \(+17.6714 q^{28}\) \(+2.79382 q^{29}\) \(+1.86934 q^{30}\) \(-1.04665 q^{31}\) \(-25.1516 q^{32}\) \(-2.07367 q^{33}\) \(+2.76060 q^{34}\) \(-2.12887 q^{35}\) \(+5.62090 q^{36}\) \(+1.14118 q^{37}\) \(-3.64550 q^{38}\) \(+5.11851 q^{39}\) \(+6.76869 q^{40}\) \(-8.84359 q^{41}\) \(-8.67895 q^{42}\) \(-12.3593 q^{43}\) \(-11.6559 q^{44}\) \(-0.677149 q^{45}\) \(-3.48354 q^{46}\) \(+2.89101 q^{47}\) \(+16.3527 q^{48}\) \(+2.88389 q^{49}\) \(+12.5372 q^{50}\) \(-1.00000 q^{51}\) \(+28.7706 q^{52}\) \(-6.36246 q^{53}\) \(-2.76060 q^{54}\) \(+1.40418 q^{55}\) \(-31.4256 q^{56}\) \(+1.32055 q^{57}\) \(-7.71262 q^{58}\) \(-4.43671 q^{59}\) \(-3.80619 q^{60}\) \(-14.2855 q^{61}\) \(+2.88937 q^{62}\) \(+3.14387 q^{63}\) \(+36.7280 q^{64}\) \(-3.46599 q^{65}\) \(+5.72457 q^{66}\) \(-6.45138 q^{67}\) \(-5.62090 q^{68}\) \(+1.26188 q^{69}\) \(+5.87694 q^{70}\) \(-13.7214 q^{71}\) \(-9.99585 q^{72}\) \(-0.815601 q^{73}\) \(-3.15033 q^{74}\) \(-4.54147 q^{75}\) \(+7.42268 q^{76}\) \(-6.51934 q^{77}\) \(-14.1301 q^{78}\) \(-5.63591 q^{79}\) \(-11.0732 q^{80}\) \(+1.00000 q^{81}\) \(+24.4136 q^{82}\) \(+3.91819 q^{83}\) \(+17.6714 q^{84}\) \(+0.677149 q^{85}\) \(+34.1190 q^{86}\) \(+2.79382 q^{87}\) \(+20.7281 q^{88}\) \(+6.79853 q^{89}\) \(+1.86934 q^{90}\) \(+16.0919 q^{91}\) \(+7.09289 q^{92}\) \(-1.04665 q^{93}\) \(-7.98092 q^{94}\) \(-0.894209 q^{95}\) \(-25.1516 q^{96}\) \(-10.8745 q^{97}\) \(-7.96125 q^{98}\) \(-2.07367 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76060 −1.95204 −0.976019 0.217686i \(-0.930149\pi\)
−0.976019 + 0.217686i \(0.930149\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.62090 2.81045
\(5\) −0.677149 −0.302830 −0.151415 0.988470i \(-0.548383\pi\)
−0.151415 + 0.988470i \(0.548383\pi\)
\(6\) −2.76060 −1.12701
\(7\) 3.14387 1.18827 0.594135 0.804366i \(-0.297495\pi\)
0.594135 + 0.804366i \(0.297495\pi\)
\(8\) −9.99585 −3.53407
\(9\) 1.00000 0.333333
\(10\) 1.86934 0.591136
\(11\) −2.07367 −0.625235 −0.312617 0.949879i \(-0.601206\pi\)
−0.312617 + 0.949879i \(0.601206\pi\)
\(12\) 5.62090 1.62261
\(13\) 5.11851 1.41962 0.709809 0.704394i \(-0.248781\pi\)
0.709809 + 0.704394i \(0.248781\pi\)
\(14\) −8.67895 −2.31955
\(15\) −0.677149 −0.174839
\(16\) 16.3527 4.08818
\(17\) −1.00000 −0.242536
\(18\) −2.76060 −0.650679
\(19\) 1.32055 0.302955 0.151477 0.988461i \(-0.451597\pi\)
0.151477 + 0.988461i \(0.451597\pi\)
\(20\) −3.80619 −0.851090
\(21\) 3.14387 0.686048
\(22\) 5.72457 1.22048
\(23\) 1.26188 0.263120 0.131560 0.991308i \(-0.458001\pi\)
0.131560 + 0.991308i \(0.458001\pi\)
\(24\) −9.99585 −2.04040
\(25\) −4.54147 −0.908294
\(26\) −14.1301 −2.77115
\(27\) 1.00000 0.192450
\(28\) 17.6714 3.33957
\(29\) 2.79382 0.518800 0.259400 0.965770i \(-0.416475\pi\)
0.259400 + 0.965770i \(0.416475\pi\)
\(30\) 1.86934 0.341293
\(31\) −1.04665 −0.187983 −0.0939916 0.995573i \(-0.529963\pi\)
−0.0939916 + 0.995573i \(0.529963\pi\)
\(32\) −25.1516 −4.44622
\(33\) −2.07367 −0.360979
\(34\) 2.76060 0.473439
\(35\) −2.12887 −0.359844
\(36\) 5.62090 0.936817
\(37\) 1.14118 0.187608 0.0938042 0.995591i \(-0.470097\pi\)
0.0938042 + 0.995591i \(0.470097\pi\)
\(38\) −3.64550 −0.591379
\(39\) 5.11851 0.819617
\(40\) 6.76869 1.07022
\(41\) −8.84359 −1.38114 −0.690569 0.723267i \(-0.742640\pi\)
−0.690569 + 0.723267i \(0.742640\pi\)
\(42\) −8.67895 −1.33919
\(43\) −12.3593 −1.88477 −0.942385 0.334529i \(-0.891423\pi\)
−0.942385 + 0.334529i \(0.891423\pi\)
\(44\) −11.6559 −1.75719
\(45\) −0.677149 −0.100943
\(46\) −3.48354 −0.513620
\(47\) 2.89101 0.421698 0.210849 0.977519i \(-0.432377\pi\)
0.210849 + 0.977519i \(0.432377\pi\)
\(48\) 16.3527 2.36031
\(49\) 2.88389 0.411984
\(50\) 12.5372 1.77302
\(51\) −1.00000 −0.140028
\(52\) 28.7706 3.98977
\(53\) −6.36246 −0.873952 −0.436976 0.899473i \(-0.643950\pi\)
−0.436976 + 0.899473i \(0.643950\pi\)
\(54\) −2.76060 −0.375670
\(55\) 1.40418 0.189340
\(56\) −31.4256 −4.19942
\(57\) 1.32055 0.174911
\(58\) −7.71262 −1.01272
\(59\) −4.43671 −0.577610 −0.288805 0.957388i \(-0.593258\pi\)
−0.288805 + 0.957388i \(0.593258\pi\)
\(60\) −3.80619 −0.491377
\(61\) −14.2855 −1.82908 −0.914538 0.404499i \(-0.867446\pi\)
−0.914538 + 0.404499i \(0.867446\pi\)
\(62\) 2.88937 0.366950
\(63\) 3.14387 0.396090
\(64\) 36.7280 4.59100
\(65\) −3.46599 −0.429904
\(66\) 5.72457 0.704645
\(67\) −6.45138 −0.788161 −0.394081 0.919076i \(-0.628937\pi\)
−0.394081 + 0.919076i \(0.628937\pi\)
\(68\) −5.62090 −0.681634
\(69\) 1.26188 0.151912
\(70\) 5.87694 0.702429
\(71\) −13.7214 −1.62843 −0.814217 0.580561i \(-0.802833\pi\)
−0.814217 + 0.580561i \(0.802833\pi\)
\(72\) −9.99585 −1.17802
\(73\) −0.815601 −0.0954589 −0.0477294 0.998860i \(-0.515199\pi\)
−0.0477294 + 0.998860i \(0.515199\pi\)
\(74\) −3.15033 −0.366219
\(75\) −4.54147 −0.524404
\(76\) 7.42268 0.851439
\(77\) −6.51934 −0.742947
\(78\) −14.1301 −1.59992
\(79\) −5.63591 −0.634090 −0.317045 0.948411i \(-0.602691\pi\)
−0.317045 + 0.948411i \(0.602691\pi\)
\(80\) −11.0732 −1.23803
\(81\) 1.00000 0.111111
\(82\) 24.4136 2.69603
\(83\) 3.91819 0.430078 0.215039 0.976605i \(-0.431012\pi\)
0.215039 + 0.976605i \(0.431012\pi\)
\(84\) 17.6714 1.92810
\(85\) 0.677149 0.0734471
\(86\) 34.1190 3.67914
\(87\) 2.79382 0.299529
\(88\) 20.7281 2.20962
\(89\) 6.79853 0.720643 0.360322 0.932828i \(-0.382667\pi\)
0.360322 + 0.932828i \(0.382667\pi\)
\(90\) 1.86934 0.197045
\(91\) 16.0919 1.68689
\(92\) 7.09289 0.739485
\(93\) −1.04665 −0.108532
\(94\) −7.98092 −0.823169
\(95\) −0.894209 −0.0917439
\(96\) −25.1516 −2.56703
\(97\) −10.8745 −1.10414 −0.552070 0.833797i \(-0.686162\pi\)
−0.552070 + 0.833797i \(0.686162\pi\)
\(98\) −7.96125 −0.804208
\(99\) −2.07367 −0.208412
\(100\) −25.5272 −2.55272
\(101\) −0.683072 −0.0679682 −0.0339841 0.999422i \(-0.510820\pi\)
−0.0339841 + 0.999422i \(0.510820\pi\)
\(102\) 2.76060 0.273340
\(103\) −10.4174 −1.02646 −0.513229 0.858252i \(-0.671551\pi\)
−0.513229 + 0.858252i \(0.671551\pi\)
\(104\) −51.1639 −5.01703
\(105\) −2.12887 −0.207756
\(106\) 17.5642 1.70599
\(107\) −4.74721 −0.458930 −0.229465 0.973317i \(-0.573698\pi\)
−0.229465 + 0.973317i \(0.573698\pi\)
\(108\) 5.62090 0.540872
\(109\) −5.05330 −0.484018 −0.242009 0.970274i \(-0.577806\pi\)
−0.242009 + 0.970274i \(0.577806\pi\)
\(110\) −3.87639 −0.369599
\(111\) 1.14118 0.108316
\(112\) 51.4108 4.85786
\(113\) 1.01792 0.0957581 0.0478790 0.998853i \(-0.484754\pi\)
0.0478790 + 0.998853i \(0.484754\pi\)
\(114\) −3.64550 −0.341433
\(115\) −0.854480 −0.0796806
\(116\) 15.7038 1.45806
\(117\) 5.11851 0.473206
\(118\) 12.2480 1.12752
\(119\) −3.14387 −0.288198
\(120\) 6.76869 0.617894
\(121\) −6.69990 −0.609081
\(122\) 39.4367 3.57043
\(123\) −8.84359 −0.797400
\(124\) −5.88310 −0.528318
\(125\) 6.46100 0.577889
\(126\) −8.67895 −0.773182
\(127\) 3.11216 0.276160 0.138080 0.990421i \(-0.455907\pi\)
0.138080 + 0.990421i \(0.455907\pi\)
\(128\) −51.0881 −4.51559
\(129\) −12.3593 −1.08817
\(130\) 9.56822 0.839188
\(131\) 4.19643 0.366644 0.183322 0.983053i \(-0.441315\pi\)
0.183322 + 0.983053i \(0.441315\pi\)
\(132\) −11.6559 −1.01452
\(133\) 4.15163 0.359992
\(134\) 17.8097 1.53852
\(135\) −0.677149 −0.0582797
\(136\) 9.99585 0.857137
\(137\) 13.4645 1.15035 0.575174 0.818031i \(-0.304934\pi\)
0.575174 + 0.818031i \(0.304934\pi\)
\(138\) −3.48354 −0.296538
\(139\) −4.51887 −0.383285 −0.191643 0.981465i \(-0.561381\pi\)
−0.191643 + 0.981465i \(0.561381\pi\)
\(140\) −11.9661 −1.01132
\(141\) 2.89101 0.243467
\(142\) 37.8793 3.17876
\(143\) −10.6141 −0.887595
\(144\) 16.3527 1.36273
\(145\) −1.89183 −0.157108
\(146\) 2.25155 0.186339
\(147\) 2.88389 0.237859
\(148\) 6.41444 0.527264
\(149\) −6.44984 −0.528391 −0.264196 0.964469i \(-0.585106\pi\)
−0.264196 + 0.964469i \(0.585106\pi\)
\(150\) 12.5372 1.02366
\(151\) 18.8081 1.53058 0.765291 0.643684i \(-0.222595\pi\)
0.765291 + 0.643684i \(0.222595\pi\)
\(152\) −13.2000 −1.07066
\(153\) −1.00000 −0.0808452
\(154\) 17.9973 1.45026
\(155\) 0.708736 0.0569270
\(156\) 28.7706 2.30349
\(157\) 1.00000 0.0798087
\(158\) 15.5585 1.23777
\(159\) −6.36246 −0.504576
\(160\) 17.0314 1.34645
\(161\) 3.96717 0.312657
\(162\) −2.76060 −0.216893
\(163\) −24.8104 −1.94330 −0.971651 0.236418i \(-0.924026\pi\)
−0.971651 + 0.236418i \(0.924026\pi\)
\(164\) −49.7090 −3.88162
\(165\) 1.40418 0.109316
\(166\) −10.8166 −0.839528
\(167\) 7.58853 0.587218 0.293609 0.955926i \(-0.405144\pi\)
0.293609 + 0.955926i \(0.405144\pi\)
\(168\) −31.4256 −2.42454
\(169\) 13.1991 1.01532
\(170\) −1.86934 −0.143372
\(171\) 1.32055 0.100985
\(172\) −69.4702 −5.29706
\(173\) −0.321536 −0.0244459 −0.0122230 0.999925i \(-0.503891\pi\)
−0.0122230 + 0.999925i \(0.503891\pi\)
\(174\) −7.71262 −0.584692
\(175\) −14.2778 −1.07930
\(176\) −33.9102 −2.55607
\(177\) −4.43671 −0.333483
\(178\) −18.7680 −1.40672
\(179\) 19.2910 1.44188 0.720940 0.692998i \(-0.243710\pi\)
0.720940 + 0.692998i \(0.243710\pi\)
\(180\) −3.80619 −0.283697
\(181\) −10.4593 −0.777436 −0.388718 0.921357i \(-0.627082\pi\)
−0.388718 + 0.921357i \(0.627082\pi\)
\(182\) −44.4233 −3.29287
\(183\) −14.2855 −1.05602
\(184\) −12.6135 −0.929883
\(185\) −0.772747 −0.0568135
\(186\) 2.88937 0.211859
\(187\) 2.07367 0.151642
\(188\) 16.2501 1.18516
\(189\) 3.14387 0.228683
\(190\) 2.46855 0.179087
\(191\) −17.6034 −1.27374 −0.636869 0.770972i \(-0.719771\pi\)
−0.636869 + 0.770972i \(0.719771\pi\)
\(192\) 36.7280 2.65062
\(193\) 1.13470 0.0816773 0.0408386 0.999166i \(-0.486997\pi\)
0.0408386 + 0.999166i \(0.486997\pi\)
\(194\) 30.0202 2.15532
\(195\) −3.46599 −0.248205
\(196\) 16.2100 1.15786
\(197\) −15.6748 −1.11678 −0.558392 0.829577i \(-0.688581\pi\)
−0.558392 + 0.829577i \(0.688581\pi\)
\(198\) 5.72457 0.406827
\(199\) −2.91334 −0.206521 −0.103261 0.994654i \(-0.532928\pi\)
−0.103261 + 0.994654i \(0.532928\pi\)
\(200\) 45.3959 3.20997
\(201\) −6.45138 −0.455045
\(202\) 1.88569 0.132676
\(203\) 8.78340 0.616474
\(204\) −5.62090 −0.393542
\(205\) 5.98843 0.418250
\(206\) 28.7583 2.00368
\(207\) 1.26188 0.0877066
\(208\) 83.7016 5.80366
\(209\) −2.73838 −0.189418
\(210\) 5.87694 0.405548
\(211\) 1.99437 0.137298 0.0686490 0.997641i \(-0.478131\pi\)
0.0686490 + 0.997641i \(0.478131\pi\)
\(212\) −35.7628 −2.45620
\(213\) −13.7214 −0.940176
\(214\) 13.1051 0.895849
\(215\) 8.36907 0.570766
\(216\) −9.99585 −0.680132
\(217\) −3.29051 −0.223375
\(218\) 13.9501 0.944822
\(219\) −0.815601 −0.0551132
\(220\) 7.89278 0.532131
\(221\) −5.11851 −0.344308
\(222\) −3.15033 −0.211436
\(223\) −2.95748 −0.198047 −0.0990237 0.995085i \(-0.531572\pi\)
−0.0990237 + 0.995085i \(0.531572\pi\)
\(224\) −79.0733 −5.28331
\(225\) −4.54147 −0.302765
\(226\) −2.81007 −0.186923
\(227\) −12.6127 −0.837132 −0.418566 0.908186i \(-0.637467\pi\)
−0.418566 + 0.908186i \(0.637467\pi\)
\(228\) 7.42268 0.491579
\(229\) 8.41701 0.556212 0.278106 0.960550i \(-0.410293\pi\)
0.278106 + 0.960550i \(0.410293\pi\)
\(230\) 2.35887 0.155540
\(231\) −6.51934 −0.428941
\(232\) −27.9266 −1.83347
\(233\) 6.72680 0.440688 0.220344 0.975422i \(-0.429282\pi\)
0.220344 + 0.975422i \(0.429282\pi\)
\(234\) −14.1301 −0.923716
\(235\) −1.95765 −0.127703
\(236\) −24.9383 −1.62334
\(237\) −5.63591 −0.366092
\(238\) 8.67895 0.562573
\(239\) 13.6784 0.884782 0.442391 0.896822i \(-0.354130\pi\)
0.442391 + 0.896822i \(0.354130\pi\)
\(240\) −11.0732 −0.714775
\(241\) −8.88981 −0.572643 −0.286322 0.958134i \(-0.592433\pi\)
−0.286322 + 0.958134i \(0.592433\pi\)
\(242\) 18.4957 1.18895
\(243\) 1.00000 0.0641500
\(244\) −80.2977 −5.14053
\(245\) −1.95282 −0.124761
\(246\) 24.4136 1.55655
\(247\) 6.75924 0.430080
\(248\) 10.4621 0.664346
\(249\) 3.91819 0.248305
\(250\) −17.8362 −1.12806
\(251\) 2.89315 0.182614 0.0913070 0.995823i \(-0.470896\pi\)
0.0913070 + 0.995823i \(0.470896\pi\)
\(252\) 17.6714 1.11319
\(253\) −2.61672 −0.164512
\(254\) −8.59144 −0.539075
\(255\) 0.677149 0.0424047
\(256\) 67.5777 4.22361
\(257\) 5.42647 0.338494 0.169247 0.985574i \(-0.445866\pi\)
0.169247 + 0.985574i \(0.445866\pi\)
\(258\) 34.1190 2.12415
\(259\) 3.58771 0.222929
\(260\) −19.4820 −1.20822
\(261\) 2.79382 0.172933
\(262\) −11.5847 −0.715702
\(263\) −19.4244 −1.19776 −0.598881 0.800838i \(-0.704388\pi\)
−0.598881 + 0.800838i \(0.704388\pi\)
\(264\) 20.7281 1.27573
\(265\) 4.30834 0.264659
\(266\) −11.4610 −0.702717
\(267\) 6.79853 0.416063
\(268\) −36.2626 −2.21509
\(269\) −13.0613 −0.796359 −0.398179 0.917308i \(-0.630358\pi\)
−0.398179 + 0.917308i \(0.630358\pi\)
\(270\) 1.86934 0.113764
\(271\) −22.4597 −1.36433 −0.682164 0.731199i \(-0.738961\pi\)
−0.682164 + 0.731199i \(0.738961\pi\)
\(272\) −16.3527 −0.991530
\(273\) 16.0919 0.973926
\(274\) −37.1700 −2.24552
\(275\) 9.41750 0.567897
\(276\) 7.09289 0.426942
\(277\) 18.1823 1.09247 0.546233 0.837633i \(-0.316061\pi\)
0.546233 + 0.837633i \(0.316061\pi\)
\(278\) 12.4748 0.748187
\(279\) −1.04665 −0.0626611
\(280\) 21.2798 1.27171
\(281\) −12.2995 −0.733726 −0.366863 0.930275i \(-0.619568\pi\)
−0.366863 + 0.930275i \(0.619568\pi\)
\(282\) −7.98092 −0.475257
\(283\) 13.4204 0.797758 0.398879 0.917004i \(-0.369399\pi\)
0.398879 + 0.917004i \(0.369399\pi\)
\(284\) −77.1268 −4.57663
\(285\) −0.894209 −0.0529683
\(286\) 29.3012 1.73262
\(287\) −27.8031 −1.64116
\(288\) −25.1516 −1.48207
\(289\) 1.00000 0.0588235
\(290\) 5.22260 0.306681
\(291\) −10.8745 −0.637476
\(292\) −4.58441 −0.268283
\(293\) 21.0032 1.22702 0.613509 0.789688i \(-0.289757\pi\)
0.613509 + 0.789688i \(0.289757\pi\)
\(294\) −7.96125 −0.464310
\(295\) 3.00431 0.174918
\(296\) −11.4070 −0.663021
\(297\) −2.07367 −0.120326
\(298\) 17.8054 1.03144
\(299\) 6.45893 0.373530
\(300\) −25.5272 −1.47381
\(301\) −38.8559 −2.23962
\(302\) −51.9216 −2.98775
\(303\) −0.683072 −0.0392414
\(304\) 21.5946 1.23853
\(305\) 9.67345 0.553900
\(306\) 2.76060 0.157813
\(307\) −2.31157 −0.131928 −0.0659642 0.997822i \(-0.521012\pi\)
−0.0659642 + 0.997822i \(0.521012\pi\)
\(308\) −36.6445 −2.08802
\(309\) −10.4174 −0.592626
\(310\) −1.95653 −0.111124
\(311\) 2.29825 0.130322 0.0651609 0.997875i \(-0.479244\pi\)
0.0651609 + 0.997875i \(0.479244\pi\)
\(312\) −51.1639 −2.89658
\(313\) 7.60296 0.429745 0.214872 0.976642i \(-0.431066\pi\)
0.214872 + 0.976642i \(0.431066\pi\)
\(314\) −2.76060 −0.155790
\(315\) −2.12887 −0.119948
\(316\) −31.6789 −1.78208
\(317\) −0.421117 −0.0236523 −0.0118262 0.999930i \(-0.503764\pi\)
−0.0118262 + 0.999930i \(0.503764\pi\)
\(318\) 17.5642 0.984952
\(319\) −5.79346 −0.324372
\(320\) −24.8704 −1.39030
\(321\) −4.74721 −0.264963
\(322\) −10.9518 −0.610318
\(323\) −1.32055 −0.0734773
\(324\) 5.62090 0.312272
\(325\) −23.2455 −1.28943
\(326\) 68.4916 3.79340
\(327\) −5.05330 −0.279448
\(328\) 88.3993 4.88103
\(329\) 9.08895 0.501090
\(330\) −3.87639 −0.213388
\(331\) −6.39080 −0.351270 −0.175635 0.984455i \(-0.556198\pi\)
−0.175635 + 0.984455i \(0.556198\pi\)
\(332\) 22.0238 1.20871
\(333\) 1.14118 0.0625361
\(334\) −20.9489 −1.14627
\(335\) 4.36854 0.238679
\(336\) 51.4108 2.80469
\(337\) −22.7087 −1.23702 −0.618510 0.785777i \(-0.712263\pi\)
−0.618510 + 0.785777i \(0.712263\pi\)
\(338\) −36.4375 −1.98194
\(339\) 1.01792 0.0552859
\(340\) 3.80619 0.206420
\(341\) 2.17040 0.117534
\(342\) −3.64550 −0.197126
\(343\) −12.9405 −0.698721
\(344\) 123.541 6.66091
\(345\) −0.854480 −0.0460036
\(346\) 0.887631 0.0477194
\(347\) 21.7522 1.16772 0.583861 0.811854i \(-0.301541\pi\)
0.583861 + 0.811854i \(0.301541\pi\)
\(348\) 15.7038 0.841812
\(349\) 12.0038 0.642551 0.321275 0.946986i \(-0.395888\pi\)
0.321275 + 0.946986i \(0.395888\pi\)
\(350\) 39.4152 2.10683
\(351\) 5.11851 0.273206
\(352\) 52.1561 2.77993
\(353\) −1.00882 −0.0536939 −0.0268470 0.999640i \(-0.508547\pi\)
−0.0268470 + 0.999640i \(0.508547\pi\)
\(354\) 12.2480 0.650972
\(355\) 9.29145 0.493139
\(356\) 38.2139 2.02533
\(357\) −3.14387 −0.166391
\(358\) −53.2548 −2.81460
\(359\) 26.7983 1.41436 0.707180 0.707033i \(-0.249967\pi\)
0.707180 + 0.707033i \(0.249967\pi\)
\(360\) 6.76869 0.356741
\(361\) −17.2562 −0.908218
\(362\) 28.8740 1.51758
\(363\) −6.69990 −0.351653
\(364\) 90.4510 4.74092
\(365\) 0.552284 0.0289078
\(366\) 39.4367 2.06139
\(367\) 26.8416 1.40112 0.700560 0.713594i \(-0.252934\pi\)
0.700560 + 0.713594i \(0.252934\pi\)
\(368\) 20.6352 1.07568
\(369\) −8.84359 −0.460379
\(370\) 2.13324 0.110902
\(371\) −20.0027 −1.03849
\(372\) −5.88310 −0.305024
\(373\) −0.452858 −0.0234481 −0.0117241 0.999931i \(-0.503732\pi\)
−0.0117241 + 0.999931i \(0.503732\pi\)
\(374\) −5.72457 −0.296010
\(375\) 6.46100 0.333645
\(376\) −28.8981 −1.49031
\(377\) 14.3002 0.736498
\(378\) −8.67895 −0.446397
\(379\) 25.2634 1.29770 0.648848 0.760918i \(-0.275251\pi\)
0.648848 + 0.760918i \(0.275251\pi\)
\(380\) −5.02626 −0.257842
\(381\) 3.11216 0.159441
\(382\) 48.5959 2.48638
\(383\) 21.4661 1.09687 0.548434 0.836194i \(-0.315224\pi\)
0.548434 + 0.836194i \(0.315224\pi\)
\(384\) −51.0881 −2.60708
\(385\) 4.41456 0.224987
\(386\) −3.13244 −0.159437
\(387\) −12.3593 −0.628257
\(388\) −61.1246 −3.10313
\(389\) 2.06444 0.104671 0.0523356 0.998630i \(-0.483333\pi\)
0.0523356 + 0.998630i \(0.483333\pi\)
\(390\) 9.56822 0.484505
\(391\) −1.26188 −0.0638159
\(392\) −28.8269 −1.45598
\(393\) 4.19643 0.211682
\(394\) 43.2718 2.18000
\(395\) 3.81636 0.192022
\(396\) −11.6559 −0.585731
\(397\) −12.0212 −0.603326 −0.301663 0.953415i \(-0.597542\pi\)
−0.301663 + 0.953415i \(0.597542\pi\)
\(398\) 8.04257 0.403138
\(399\) 4.15163 0.207841
\(400\) −74.2654 −3.71327
\(401\) −32.9380 −1.64484 −0.822422 0.568878i \(-0.807378\pi\)
−0.822422 + 0.568878i \(0.807378\pi\)
\(402\) 17.8097 0.888265
\(403\) −5.35727 −0.266865
\(404\) −3.83948 −0.191021
\(405\) −0.677149 −0.0336478
\(406\) −24.2474 −1.20338
\(407\) −2.36642 −0.117299
\(408\) 9.99585 0.494869
\(409\) 17.8596 0.883100 0.441550 0.897237i \(-0.354429\pi\)
0.441550 + 0.897237i \(0.354429\pi\)
\(410\) −16.5317 −0.816440
\(411\) 13.4645 0.664154
\(412\) −58.5552 −2.88481
\(413\) −13.9484 −0.686356
\(414\) −3.48354 −0.171207
\(415\) −2.65320 −0.130241
\(416\) −128.739 −6.31194
\(417\) −4.51887 −0.221290
\(418\) 7.55957 0.369751
\(419\) −8.79922 −0.429870 −0.214935 0.976628i \(-0.568954\pi\)
−0.214935 + 0.976628i \(0.568954\pi\)
\(420\) −11.9661 −0.583888
\(421\) 36.8792 1.79738 0.898691 0.438583i \(-0.144519\pi\)
0.898691 + 0.438583i \(0.144519\pi\)
\(422\) −5.50565 −0.268011
\(423\) 2.89101 0.140566
\(424\) 63.5983 3.08860
\(425\) 4.54147 0.220294
\(426\) 37.8793 1.83526
\(427\) −44.9118 −2.17344
\(428\) −26.6836 −1.28980
\(429\) −10.6141 −0.512453
\(430\) −23.1036 −1.11416
\(431\) −10.5544 −0.508388 −0.254194 0.967153i \(-0.581810\pi\)
−0.254194 + 0.967153i \(0.581810\pi\)
\(432\) 16.3527 0.786771
\(433\) 12.1603 0.584385 0.292193 0.956359i \(-0.405615\pi\)
0.292193 + 0.956359i \(0.405615\pi\)
\(434\) 9.08379 0.436036
\(435\) −1.89183 −0.0907065
\(436\) −28.4041 −1.36031
\(437\) 1.66637 0.0797133
\(438\) 2.25155 0.107583
\(439\) 39.3094 1.87614 0.938068 0.346453i \(-0.112614\pi\)
0.938068 + 0.346453i \(0.112614\pi\)
\(440\) −14.0360 −0.669141
\(441\) 2.88389 0.137328
\(442\) 14.1301 0.672102
\(443\) 7.46622 0.354731 0.177365 0.984145i \(-0.443243\pi\)
0.177365 + 0.984145i \(0.443243\pi\)
\(444\) 6.41444 0.304416
\(445\) −4.60362 −0.218233
\(446\) 8.16441 0.386596
\(447\) −6.44984 −0.305067
\(448\) 115.468 5.45535
\(449\) 36.1899 1.70791 0.853954 0.520348i \(-0.174198\pi\)
0.853954 + 0.520348i \(0.174198\pi\)
\(450\) 12.5372 0.591008
\(451\) 18.3387 0.863535
\(452\) 5.72164 0.269123
\(453\) 18.8081 0.883682
\(454\) 34.8185 1.63411
\(455\) −10.8966 −0.510841
\(456\) −13.2000 −0.618147
\(457\) 4.00965 0.187563 0.0937817 0.995593i \(-0.470104\pi\)
0.0937817 + 0.995593i \(0.470104\pi\)
\(458\) −23.2360 −1.08575
\(459\) −1.00000 −0.0466760
\(460\) −4.80295 −0.223938
\(461\) −14.0063 −0.652340 −0.326170 0.945311i \(-0.605758\pi\)
−0.326170 + 0.945311i \(0.605758\pi\)
\(462\) 17.9973 0.837309
\(463\) −40.8451 −1.89823 −0.949117 0.314924i \(-0.898021\pi\)
−0.949117 + 0.314924i \(0.898021\pi\)
\(464\) 45.6866 2.12095
\(465\) 0.708736 0.0328668
\(466\) −18.5700 −0.860239
\(467\) 19.8667 0.919322 0.459661 0.888095i \(-0.347971\pi\)
0.459661 + 0.888095i \(0.347971\pi\)
\(468\) 28.7706 1.32992
\(469\) −20.2823 −0.936548
\(470\) 5.40428 0.249281
\(471\) 1.00000 0.0460776
\(472\) 44.3487 2.04131
\(473\) 25.6290 1.17842
\(474\) 15.5585 0.714625
\(475\) −5.99723 −0.275172
\(476\) −17.6714 −0.809965
\(477\) −6.36246 −0.291317
\(478\) −37.7606 −1.72713
\(479\) −20.1498 −0.920669 −0.460334 0.887746i \(-0.652270\pi\)
−0.460334 + 0.887746i \(0.652270\pi\)
\(480\) 17.0314 0.777373
\(481\) 5.84112 0.266332
\(482\) 24.5412 1.11782
\(483\) 3.96717 0.180513
\(484\) −37.6595 −1.71179
\(485\) 7.36368 0.334367
\(486\) −2.76060 −0.125223
\(487\) 17.5488 0.795211 0.397606 0.917556i \(-0.369841\pi\)
0.397606 + 0.917556i \(0.369841\pi\)
\(488\) 142.796 6.46408
\(489\) −24.8104 −1.12197
\(490\) 5.39096 0.243539
\(491\) 18.4100 0.830833 0.415416 0.909631i \(-0.363636\pi\)
0.415416 + 0.909631i \(0.363636\pi\)
\(492\) −49.7090 −2.24105
\(493\) −2.79382 −0.125827
\(494\) −18.6595 −0.839533
\(495\) 1.40418 0.0631134
\(496\) −17.1155 −0.768510
\(497\) −43.1383 −1.93502
\(498\) −10.8166 −0.484702
\(499\) 37.7091 1.68809 0.844045 0.536273i \(-0.180168\pi\)
0.844045 + 0.536273i \(0.180168\pi\)
\(500\) 36.3166 1.62413
\(501\) 7.58853 0.339030
\(502\) −7.98682 −0.356469
\(503\) −22.1498 −0.987613 −0.493806 0.869572i \(-0.664395\pi\)
−0.493806 + 0.869572i \(0.664395\pi\)
\(504\) −31.4256 −1.39981
\(505\) 0.462541 0.0205828
\(506\) 7.22370 0.321133
\(507\) 13.1991 0.586194
\(508\) 17.4932 0.776134
\(509\) 27.7313 1.22917 0.614585 0.788851i \(-0.289323\pi\)
0.614585 + 0.788851i \(0.289323\pi\)
\(510\) −1.86934 −0.0827756
\(511\) −2.56414 −0.113431
\(512\) −84.3786 −3.72904
\(513\) 1.32055 0.0583037
\(514\) −14.9803 −0.660753
\(515\) 7.05414 0.310842
\(516\) −69.4702 −3.05826
\(517\) −5.99500 −0.263660
\(518\) −9.90421 −0.435166
\(519\) −0.321536 −0.0141139
\(520\) 34.6456 1.51931
\(521\) 21.2034 0.928938 0.464469 0.885589i \(-0.346245\pi\)
0.464469 + 0.885589i \(0.346245\pi\)
\(522\) −7.71262 −0.337572
\(523\) −27.4540 −1.20048 −0.600240 0.799820i \(-0.704928\pi\)
−0.600240 + 0.799820i \(0.704928\pi\)
\(524\) 23.5877 1.03043
\(525\) −14.2778 −0.623133
\(526\) 53.6231 2.33808
\(527\) 1.04665 0.0455926
\(528\) −33.9102 −1.47575
\(529\) −21.4077 −0.930768
\(530\) −11.8936 −0.516624
\(531\) −4.43671 −0.192537
\(532\) 23.3359 1.01174
\(533\) −45.2660 −1.96069
\(534\) −18.7680 −0.812172
\(535\) 3.21457 0.138978
\(536\) 64.4870 2.78541
\(537\) 19.2910 0.832470
\(538\) 36.0569 1.55452
\(539\) −5.98023 −0.257587
\(540\) −3.80619 −0.163792
\(541\) 18.8676 0.811182 0.405591 0.914055i \(-0.367066\pi\)
0.405591 + 0.914055i \(0.367066\pi\)
\(542\) 62.0021 2.66322
\(543\) −10.4593 −0.448853
\(544\) 25.1516 1.07837
\(545\) 3.42184 0.146575
\(546\) −44.4233 −1.90114
\(547\) 24.8923 1.06432 0.532159 0.846645i \(-0.321381\pi\)
0.532159 + 0.846645i \(0.321381\pi\)
\(548\) 75.6825 3.23300
\(549\) −14.2855 −0.609692
\(550\) −25.9979 −1.10856
\(551\) 3.68938 0.157173
\(552\) −12.6135 −0.536868
\(553\) −17.7186 −0.753470
\(554\) −50.1939 −2.13254
\(555\) −0.772747 −0.0328013
\(556\) −25.4001 −1.07720
\(557\) −24.7797 −1.04995 −0.524974 0.851118i \(-0.675925\pi\)
−0.524974 + 0.851118i \(0.675925\pi\)
\(558\) 2.88937 0.122317
\(559\) −63.2610 −2.67566
\(560\) −34.8128 −1.47111
\(561\) 2.07367 0.0875504
\(562\) 33.9539 1.43226
\(563\) −42.4418 −1.78871 −0.894354 0.447360i \(-0.852364\pi\)
−0.894354 + 0.447360i \(0.852364\pi\)
\(564\) 16.2501 0.684253
\(565\) −0.689285 −0.0289984
\(566\) −37.0482 −1.55725
\(567\) 3.14387 0.132030
\(568\) 137.157 5.75499
\(569\) −18.6400 −0.781431 −0.390715 0.920512i \(-0.627772\pi\)
−0.390715 + 0.920512i \(0.627772\pi\)
\(570\) 2.46855 0.103396
\(571\) 20.0120 0.837474 0.418737 0.908108i \(-0.362473\pi\)
0.418737 + 0.908108i \(0.362473\pi\)
\(572\) −59.6608 −2.49454
\(573\) −17.6034 −0.735393
\(574\) 76.7531 3.20361
\(575\) −5.73078 −0.238990
\(576\) 36.7280 1.53033
\(577\) −16.1352 −0.671718 −0.335859 0.941912i \(-0.609027\pi\)
−0.335859 + 0.941912i \(0.609027\pi\)
\(578\) −2.76060 −0.114826
\(579\) 1.13470 0.0471564
\(580\) −10.6338 −0.441545
\(581\) 12.3183 0.511048
\(582\) 30.0202 1.24438
\(583\) 13.1936 0.546425
\(584\) 8.15263 0.337358
\(585\) −3.46599 −0.143301
\(586\) −57.9813 −2.39519
\(587\) 23.8858 0.985871 0.492935 0.870066i \(-0.335924\pi\)
0.492935 + 0.870066i \(0.335924\pi\)
\(588\) 16.2100 0.668491
\(589\) −1.38215 −0.0569504
\(590\) −8.29370 −0.341446
\(591\) −15.6748 −0.644776
\(592\) 18.6614 0.766977
\(593\) −9.10968 −0.374090 −0.187045 0.982351i \(-0.559891\pi\)
−0.187045 + 0.982351i \(0.559891\pi\)
\(594\) 5.72457 0.234882
\(595\) 2.12887 0.0872750
\(596\) −36.2539 −1.48502
\(597\) −2.91334 −0.119235
\(598\) −17.8305 −0.729144
\(599\) −19.0805 −0.779606 −0.389803 0.920898i \(-0.627457\pi\)
−0.389803 + 0.920898i \(0.627457\pi\)
\(600\) 45.3959 1.85328
\(601\) 3.40864 0.139041 0.0695207 0.997581i \(-0.477853\pi\)
0.0695207 + 0.997581i \(0.477853\pi\)
\(602\) 107.265 4.37181
\(603\) −6.45138 −0.262720
\(604\) 105.719 4.30163
\(605\) 4.53683 0.184448
\(606\) 1.88569 0.0766008
\(607\) 8.80303 0.357304 0.178652 0.983912i \(-0.442826\pi\)
0.178652 + 0.983912i \(0.442826\pi\)
\(608\) −33.2139 −1.34700
\(609\) 8.78340 0.355921
\(610\) −26.7045 −1.08123
\(611\) 14.7977 0.598650
\(612\) −5.62090 −0.227211
\(613\) 23.2586 0.939405 0.469703 0.882825i \(-0.344361\pi\)
0.469703 + 0.882825i \(0.344361\pi\)
\(614\) 6.38132 0.257529
\(615\) 5.98843 0.241477
\(616\) 65.1663 2.62563
\(617\) 2.03154 0.0817866 0.0408933 0.999164i \(-0.486980\pi\)
0.0408933 + 0.999164i \(0.486980\pi\)
\(618\) 28.7583 1.15683
\(619\) 31.1951 1.25384 0.626919 0.779084i \(-0.284316\pi\)
0.626919 + 0.779084i \(0.284316\pi\)
\(620\) 3.98373 0.159991
\(621\) 1.26188 0.0506374
\(622\) −6.34455 −0.254393
\(623\) 21.3737 0.856318
\(624\) 83.7016 3.35075
\(625\) 18.3323 0.733291
\(626\) −20.9887 −0.838878
\(627\) −2.73838 −0.109360
\(628\) 5.62090 0.224298
\(629\) −1.14118 −0.0455017
\(630\) 5.87694 0.234143
\(631\) 20.2642 0.806705 0.403352 0.915045i \(-0.367845\pi\)
0.403352 + 0.915045i \(0.367845\pi\)
\(632\) 56.3358 2.24092
\(633\) 1.99437 0.0792691
\(634\) 1.16254 0.0461702
\(635\) −2.10740 −0.0836296
\(636\) −35.7628 −1.41809
\(637\) 14.7612 0.584860
\(638\) 15.9934 0.633186
\(639\) −13.7214 −0.542811
\(640\) 34.5943 1.36746
\(641\) 47.7941 1.88775 0.943876 0.330299i \(-0.107150\pi\)
0.943876 + 0.330299i \(0.107150\pi\)
\(642\) 13.1051 0.517219
\(643\) −29.9901 −1.18269 −0.591346 0.806418i \(-0.701403\pi\)
−0.591346 + 0.806418i \(0.701403\pi\)
\(644\) 22.2991 0.878707
\(645\) 8.36907 0.329532
\(646\) 3.64550 0.143430
\(647\) −41.6952 −1.63921 −0.819604 0.572930i \(-0.805807\pi\)
−0.819604 + 0.572930i \(0.805807\pi\)
\(648\) −9.99585 −0.392674
\(649\) 9.20026 0.361142
\(650\) 64.1716 2.51702
\(651\) −3.29051 −0.128965
\(652\) −139.457 −5.46156
\(653\) 19.4940 0.762858 0.381429 0.924398i \(-0.375432\pi\)
0.381429 + 0.924398i \(0.375432\pi\)
\(654\) 13.9501 0.545493
\(655\) −2.84161 −0.111031
\(656\) −144.617 −5.64634
\(657\) −0.815601 −0.0318196
\(658\) −25.0909 −0.978147
\(659\) 13.5672 0.528504 0.264252 0.964454i \(-0.414875\pi\)
0.264252 + 0.964454i \(0.414875\pi\)
\(660\) 7.89278 0.307226
\(661\) 5.59687 0.217693 0.108847 0.994059i \(-0.465284\pi\)
0.108847 + 0.994059i \(0.465284\pi\)
\(662\) 17.6424 0.685692
\(663\) −5.11851 −0.198786
\(664\) −39.1657 −1.51992
\(665\) −2.81127 −0.109016
\(666\) −3.15033 −0.122073
\(667\) 3.52546 0.136506
\(668\) 42.6544 1.65035
\(669\) −2.95748 −0.114343
\(670\) −12.0598 −0.465911
\(671\) 29.6235 1.14360
\(672\) −79.0733 −3.05032
\(673\) 19.1066 0.736504 0.368252 0.929726i \(-0.379956\pi\)
0.368252 + 0.929726i \(0.379956\pi\)
\(674\) 62.6895 2.41471
\(675\) −4.54147 −0.174801
\(676\) 74.1910 2.85350
\(677\) −45.8575 −1.76245 −0.881223 0.472701i \(-0.843279\pi\)
−0.881223 + 0.472701i \(0.843279\pi\)
\(678\) −2.81007 −0.107920
\(679\) −34.1880 −1.31202
\(680\) −6.76869 −0.259567
\(681\) −12.6127 −0.483318
\(682\) −5.99160 −0.229430
\(683\) −19.8726 −0.760402 −0.380201 0.924904i \(-0.624145\pi\)
−0.380201 + 0.924904i \(0.624145\pi\)
\(684\) 7.42268 0.283813
\(685\) −9.11746 −0.348360
\(686\) 35.7235 1.36393
\(687\) 8.41701 0.321129
\(688\) −202.108 −7.70529
\(689\) −32.5663 −1.24068
\(690\) 2.35887 0.0898008
\(691\) 21.1493 0.804557 0.402278 0.915517i \(-0.368218\pi\)
0.402278 + 0.915517i \(0.368218\pi\)
\(692\) −1.80732 −0.0687041
\(693\) −6.51934 −0.247649
\(694\) −60.0492 −2.27944
\(695\) 3.05995 0.116070
\(696\) −27.9266 −1.05856
\(697\) 8.84359 0.334975
\(698\) −33.1378 −1.25428
\(699\) 6.72680 0.254431
\(700\) −80.2539 −3.03331
\(701\) −43.5604 −1.64525 −0.822626 0.568583i \(-0.807492\pi\)
−0.822626 + 0.568583i \(0.807492\pi\)
\(702\) −14.1301 −0.533308
\(703\) 1.50698 0.0568368
\(704\) −76.1618 −2.87046
\(705\) −1.95765 −0.0737292
\(706\) 2.78494 0.104813
\(707\) −2.14748 −0.0807645
\(708\) −24.9383 −0.937238
\(709\) −16.9167 −0.635322 −0.317661 0.948204i \(-0.602897\pi\)
−0.317661 + 0.948204i \(0.602897\pi\)
\(710\) −25.6500 −0.962626
\(711\) −5.63591 −0.211363
\(712\) −67.9572 −2.54680
\(713\) −1.32074 −0.0494621
\(714\) 8.67895 0.324801
\(715\) 7.18732 0.268791
\(716\) 108.433 4.05233
\(717\) 13.6784 0.510829
\(718\) −73.9794 −2.76089
\(719\) −28.2602 −1.05393 −0.526964 0.849888i \(-0.676670\pi\)
−0.526964 + 0.849888i \(0.676670\pi\)
\(720\) −11.0732 −0.412675
\(721\) −32.7509 −1.21971
\(722\) 47.6373 1.77288
\(723\) −8.88981 −0.330616
\(724\) −58.7909 −2.18495
\(725\) −12.6881 −0.471223
\(726\) 18.4957 0.686441
\(727\) 36.1396 1.34034 0.670171 0.742206i \(-0.266221\pi\)
0.670171 + 0.742206i \(0.266221\pi\)
\(728\) −160.852 −5.96158
\(729\) 1.00000 0.0370370
\(730\) −1.52463 −0.0564292
\(731\) 12.3593 0.457124
\(732\) −80.2977 −2.96789
\(733\) −5.29296 −0.195500 −0.0977500 0.995211i \(-0.531165\pi\)
−0.0977500 + 0.995211i \(0.531165\pi\)
\(734\) −74.0988 −2.73504
\(735\) −1.95282 −0.0720309
\(736\) −31.7383 −1.16989
\(737\) 13.3780 0.492786
\(738\) 24.4136 0.898677
\(739\) 13.0956 0.481730 0.240865 0.970559i \(-0.422569\pi\)
0.240865 + 0.970559i \(0.422569\pi\)
\(740\) −4.34354 −0.159672
\(741\) 6.75924 0.248307
\(742\) 55.2195 2.02717
\(743\) 5.27872 0.193658 0.0968288 0.995301i \(-0.469130\pi\)
0.0968288 + 0.995301i \(0.469130\pi\)
\(744\) 10.4621 0.383560
\(745\) 4.36750 0.160013
\(746\) 1.25016 0.0457716
\(747\) 3.91819 0.143359
\(748\) 11.6559 0.426182
\(749\) −14.9246 −0.545333
\(750\) −17.8362 −0.651287
\(751\) 8.96559 0.327159 0.163579 0.986530i \(-0.447696\pi\)
0.163579 + 0.986530i \(0.447696\pi\)
\(752\) 47.2760 1.72398
\(753\) 2.89315 0.105432
\(754\) −39.4771 −1.43767
\(755\) −12.7359 −0.463507
\(756\) 17.6714 0.642701
\(757\) −10.0218 −0.364249 −0.182125 0.983275i \(-0.558297\pi\)
−0.182125 + 0.983275i \(0.558297\pi\)
\(758\) −69.7422 −2.53315
\(759\) −2.61672 −0.0949808
\(760\) 8.93838 0.324229
\(761\) 52.6570 1.90881 0.954407 0.298510i \(-0.0964895\pi\)
0.954407 + 0.298510i \(0.0964895\pi\)
\(762\) −8.59144 −0.311235
\(763\) −15.8869 −0.575144
\(764\) −98.9470 −3.57978
\(765\) 0.677149 0.0244824
\(766\) −59.2594 −2.14113
\(767\) −22.7093 −0.819986
\(768\) 67.5777 2.43850
\(769\) 46.5962 1.68030 0.840150 0.542353i \(-0.182467\pi\)
0.840150 + 0.542353i \(0.182467\pi\)
\(770\) −12.1868 −0.439183
\(771\) 5.42647 0.195430
\(772\) 6.37802 0.229550
\(773\) −20.4378 −0.735097 −0.367548 0.930004i \(-0.619803\pi\)
−0.367548 + 0.930004i \(0.619803\pi\)
\(774\) 34.1190 1.22638
\(775\) 4.75331 0.170744
\(776\) 108.700 3.90211
\(777\) 3.58771 0.128708
\(778\) −5.69909 −0.204322
\(779\) −11.6784 −0.418422
\(780\) −19.4820 −0.697568
\(781\) 28.4537 1.01815
\(782\) 3.48354 0.124571
\(783\) 2.79382 0.0998431
\(784\) 47.1594 1.68427
\(785\) −0.677149 −0.0241685
\(786\) −11.5847 −0.413211
\(787\) 42.8208 1.52640 0.763199 0.646163i \(-0.223628\pi\)
0.763199 + 0.646163i \(0.223628\pi\)
\(788\) −88.1066 −3.13867
\(789\) −19.4244 −0.691528
\(790\) −10.5354 −0.374834
\(791\) 3.20021 0.113786
\(792\) 20.7281 0.736541
\(793\) −73.1207 −2.59659
\(794\) 33.1856 1.17771
\(795\) 4.30834 0.152801
\(796\) −16.3756 −0.580418
\(797\) 11.1258 0.394095 0.197048 0.980394i \(-0.436865\pi\)
0.197048 + 0.980394i \(0.436865\pi\)
\(798\) −11.4610 −0.405714
\(799\) −2.89101 −0.102277
\(800\) 114.225 4.03847
\(801\) 6.79853 0.240214
\(802\) 90.9285 3.21080
\(803\) 1.69129 0.0596842
\(804\) −36.2626 −1.27888
\(805\) −2.68637 −0.0946820
\(806\) 14.7893 0.520930
\(807\) −13.0613 −0.459778
\(808\) 6.82788 0.240204
\(809\) −18.4187 −0.647566 −0.323783 0.946131i \(-0.604955\pi\)
−0.323783 + 0.946131i \(0.604955\pi\)
\(810\) 1.86934 0.0656818
\(811\) 28.6276 1.00525 0.502626 0.864504i \(-0.332367\pi\)
0.502626 + 0.864504i \(0.332367\pi\)
\(812\) 49.3706 1.73257
\(813\) −22.4597 −0.787695
\(814\) 6.53274 0.228973
\(815\) 16.8004 0.588491
\(816\) −16.3527 −0.572460
\(817\) −16.3210 −0.571000
\(818\) −49.3031 −1.72384
\(819\) 16.0919 0.562296
\(820\) 33.6604 1.17547
\(821\) 48.7037 1.69977 0.849885 0.526968i \(-0.176671\pi\)
0.849885 + 0.526968i \(0.176671\pi\)
\(822\) −37.1700 −1.29645
\(823\) −50.6702 −1.76625 −0.883126 0.469136i \(-0.844565\pi\)
−0.883126 + 0.469136i \(0.844565\pi\)
\(824\) 104.131 3.62757
\(825\) 9.41750 0.327875
\(826\) 38.5059 1.33979
\(827\) −20.2177 −0.703038 −0.351519 0.936181i \(-0.614335\pi\)
−0.351519 + 0.936181i \(0.614335\pi\)
\(828\) 7.09289 0.246495
\(829\) −1.11565 −0.0387481 −0.0193740 0.999812i \(-0.506167\pi\)
−0.0193740 + 0.999812i \(0.506167\pi\)
\(830\) 7.32443 0.254235
\(831\) 18.1823 0.630736
\(832\) 187.993 6.51748
\(833\) −2.88389 −0.0999208
\(834\) 12.4748 0.431966
\(835\) −5.13857 −0.177827
\(836\) −15.3922 −0.532349
\(837\) −1.04665 −0.0361774
\(838\) 24.2911 0.839122
\(839\) −46.7403 −1.61366 −0.806828 0.590787i \(-0.798817\pi\)
−0.806828 + 0.590787i \(0.798817\pi\)
\(840\) 21.2798 0.734224
\(841\) −21.1946 −0.730847
\(842\) −101.809 −3.50856
\(843\) −12.2995 −0.423617
\(844\) 11.2102 0.385869
\(845\) −8.93778 −0.307469
\(846\) −7.98092 −0.274390
\(847\) −21.0636 −0.723753
\(848\) −104.044 −3.57287
\(849\) 13.4204 0.460586
\(850\) −12.5372 −0.430021
\(851\) 1.44003 0.0493634
\(852\) −77.1268 −2.64232
\(853\) −33.0862 −1.13285 −0.566424 0.824114i \(-0.691674\pi\)
−0.566424 + 0.824114i \(0.691674\pi\)
\(854\) 123.984 4.24263
\(855\) −0.894209 −0.0305813
\(856\) 47.4524 1.62189
\(857\) 37.8379 1.29252 0.646259 0.763118i \(-0.276333\pi\)
0.646259 + 0.763118i \(0.276333\pi\)
\(858\) 29.3012 1.00033
\(859\) −39.3519 −1.34267 −0.671335 0.741154i \(-0.734279\pi\)
−0.671335 + 0.741154i \(0.734279\pi\)
\(860\) 47.0417 1.60411
\(861\) −27.8031 −0.947526
\(862\) 29.1365 0.992393
\(863\) 28.8886 0.983379 0.491690 0.870771i \(-0.336379\pi\)
0.491690 + 0.870771i \(0.336379\pi\)
\(864\) −25.1516 −0.855675
\(865\) 0.217728 0.00740297
\(866\) −33.5696 −1.14074
\(867\) 1.00000 0.0339618
\(868\) −18.4957 −0.627784
\(869\) 11.6870 0.396455
\(870\) 5.22260 0.177063
\(871\) −33.0214 −1.11889
\(872\) 50.5121 1.71055
\(873\) −10.8745 −0.368047
\(874\) −4.60018 −0.155603
\(875\) 20.3125 0.686688
\(876\) −4.58441 −0.154893
\(877\) −24.2504 −0.818876 −0.409438 0.912338i \(-0.634275\pi\)
−0.409438 + 0.912338i \(0.634275\pi\)
\(878\) −108.517 −3.66229
\(879\) 21.0032 0.708419
\(880\) 22.9622 0.774057
\(881\) −33.3623 −1.12400 −0.562002 0.827136i \(-0.689969\pi\)
−0.562002 + 0.827136i \(0.689969\pi\)
\(882\) −7.96125 −0.268069
\(883\) 25.2569 0.849962 0.424981 0.905202i \(-0.360281\pi\)
0.424981 + 0.905202i \(0.360281\pi\)
\(884\) −28.7706 −0.967661
\(885\) 3.00431 0.100989
\(886\) −20.6112 −0.692448
\(887\) −12.6760 −0.425619 −0.212809 0.977094i \(-0.568261\pi\)
−0.212809 + 0.977094i \(0.568261\pi\)
\(888\) −11.4070 −0.382795
\(889\) 9.78423 0.328152
\(890\) 12.7087 0.425998
\(891\) −2.07367 −0.0694705
\(892\) −16.6237 −0.556602
\(893\) 3.81772 0.127755
\(894\) 17.8054 0.595502
\(895\) −13.0629 −0.436645
\(896\) −160.614 −5.36574
\(897\) 6.45893 0.215657
\(898\) −99.9059 −3.33390
\(899\) −2.92414 −0.0975257
\(900\) −25.5272 −0.850905
\(901\) 6.36246 0.211964
\(902\) −50.6257 −1.68565
\(903\) −38.8559 −1.29304
\(904\) −10.1750 −0.338416
\(905\) 7.08253 0.235431
\(906\) −51.9216 −1.72498
\(907\) −44.8810 −1.49025 −0.745124 0.666925i \(-0.767610\pi\)
−0.745124 + 0.666925i \(0.767610\pi\)
\(908\) −70.8946 −2.35272
\(909\) −0.683072 −0.0226561
\(910\) 30.0812 0.997181
\(911\) −47.8158 −1.58421 −0.792104 0.610386i \(-0.791014\pi\)
−0.792104 + 0.610386i \(0.791014\pi\)
\(912\) 21.5946 0.715068
\(913\) −8.12504 −0.268900
\(914\) −11.0690 −0.366131
\(915\) 9.67345 0.319794
\(916\) 47.3112 1.56321
\(917\) 13.1930 0.435671
\(918\) 2.76060 0.0911133
\(919\) −16.5303 −0.545285 −0.272642 0.962115i \(-0.587898\pi\)
−0.272642 + 0.962115i \(0.587898\pi\)
\(920\) 8.54125 0.281597
\(921\) −2.31157 −0.0761689
\(922\) 38.6659 1.27339
\(923\) −70.2332 −2.31175
\(924\) −36.6445 −1.20552
\(925\) −5.18262 −0.170403
\(926\) 112.757 3.70542
\(927\) −10.4174 −0.342152
\(928\) −70.2692 −2.30670
\(929\) −34.1173 −1.11935 −0.559676 0.828712i \(-0.689074\pi\)
−0.559676 + 0.828712i \(0.689074\pi\)
\(930\) −1.95653 −0.0641573
\(931\) 3.80831 0.124812
\(932\) 37.8107 1.23853
\(933\) 2.29825 0.0752414
\(934\) −54.8440 −1.79455
\(935\) −1.40418 −0.0459217
\(936\) −51.1639 −1.67234
\(937\) −38.1875 −1.24753 −0.623766 0.781611i \(-0.714398\pi\)
−0.623766 + 0.781611i \(0.714398\pi\)
\(938\) 55.9912 1.82818
\(939\) 7.60296 0.248113
\(940\) −11.0037 −0.358902
\(941\) −3.24152 −0.105671 −0.0528353 0.998603i \(-0.516826\pi\)
−0.0528353 + 0.998603i \(0.516826\pi\)
\(942\) −2.76060 −0.0899451
\(943\) −11.1595 −0.363404
\(944\) −72.5523 −2.36138
\(945\) −2.12887 −0.0692520
\(946\) −70.7515 −2.30033
\(947\) −19.4148 −0.630898 −0.315449 0.948943i \(-0.602155\pi\)
−0.315449 + 0.948943i \(0.602155\pi\)
\(948\) −31.6789 −1.02888
\(949\) −4.17466 −0.135515
\(950\) 16.5559 0.537146
\(951\) −0.421117 −0.0136557
\(952\) 31.4256 1.01851
\(953\) 22.8141 0.739023 0.369511 0.929226i \(-0.379525\pi\)
0.369511 + 0.929226i \(0.379525\pi\)
\(954\) 17.5642 0.568662
\(955\) 11.9201 0.385726
\(956\) 76.8850 2.48664
\(957\) −5.79346 −0.187276
\(958\) 55.6256 1.79718
\(959\) 42.3305 1.36692
\(960\) −24.8704 −0.802687
\(961\) −29.9045 −0.964662
\(962\) −16.1250 −0.519891
\(963\) −4.74721 −0.152977
\(964\) −49.9688 −1.60939
\(965\) −0.768359 −0.0247344
\(966\) −10.9518 −0.352367
\(967\) 2.41482 0.0776553 0.0388277 0.999246i \(-0.487638\pi\)
0.0388277 + 0.999246i \(0.487638\pi\)
\(968\) 66.9712 2.15254
\(969\) −1.32055 −0.0424221
\(970\) −20.3282 −0.652698
\(971\) −36.1202 −1.15915 −0.579576 0.814918i \(-0.696782\pi\)
−0.579576 + 0.814918i \(0.696782\pi\)
\(972\) 5.62090 0.180291
\(973\) −14.2067 −0.455446
\(974\) −48.4451 −1.55228
\(975\) −23.2455 −0.744453
\(976\) −233.608 −7.47760
\(977\) −23.1685 −0.741226 −0.370613 0.928787i \(-0.620852\pi\)
−0.370613 + 0.928787i \(0.620852\pi\)
\(978\) 68.4916 2.19012
\(979\) −14.0979 −0.450571
\(980\) −10.9766 −0.350635
\(981\) −5.05330 −0.161339
\(982\) −50.8227 −1.62182
\(983\) −37.6772 −1.20171 −0.600857 0.799356i \(-0.705174\pi\)
−0.600857 + 0.799356i \(0.705174\pi\)
\(984\) 88.3993 2.81807
\(985\) 10.6142 0.338196
\(986\) 7.71262 0.245620
\(987\) 9.08895 0.289305
\(988\) 37.9930 1.20872
\(989\) −15.5959 −0.495920
\(990\) −3.87639 −0.123200
\(991\) −13.8694 −0.440575 −0.220287 0.975435i \(-0.570700\pi\)
−0.220287 + 0.975435i \(0.570700\pi\)
\(992\) 26.3248 0.835815
\(993\) −6.39080 −0.202806
\(994\) 119.087 3.77723
\(995\) 1.97277 0.0625409
\(996\) 22.0238 0.697850
\(997\) 4.02316 0.127415 0.0637074 0.997969i \(-0.479708\pi\)
0.0637074 + 0.997969i \(0.479708\pi\)
\(998\) −104.100 −3.29521
\(999\) 1.14118 0.0361052
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 \(a_p\))