Properties

Label 6010.2.a.c.1.4
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.23485\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.23485 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.23485 q^{6}\) \(-0.971978 q^{7}\) \(+1.00000 q^{8}\) \(+1.99454 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.23485 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.23485 q^{6}\) \(-0.971978 q^{7}\) \(+1.00000 q^{8}\) \(+1.99454 q^{9}\) \(+1.00000 q^{10}\) \(-2.26985 q^{11}\) \(-2.23485 q^{12}\) \(+4.74974 q^{13}\) \(-0.971978 q^{14}\) \(-2.23485 q^{15}\) \(+1.00000 q^{16}\) \(-5.16829 q^{17}\) \(+1.99454 q^{18}\) \(-2.10519 q^{19}\) \(+1.00000 q^{20}\) \(+2.17222 q^{21}\) \(-2.26985 q^{22}\) \(+3.32666 q^{23}\) \(-2.23485 q^{24}\) \(+1.00000 q^{25}\) \(+4.74974 q^{26}\) \(+2.24706 q^{27}\) \(-0.971978 q^{28}\) \(-7.06139 q^{29}\) \(-2.23485 q^{30}\) \(+5.27710 q^{31}\) \(+1.00000 q^{32}\) \(+5.07276 q^{33}\) \(-5.16829 q^{34}\) \(-0.971978 q^{35}\) \(+1.99454 q^{36}\) \(-6.88894 q^{37}\) \(-2.10519 q^{38}\) \(-10.6149 q^{39}\) \(+1.00000 q^{40}\) \(+11.4261 q^{41}\) \(+2.17222 q^{42}\) \(+5.15210 q^{43}\) \(-2.26985 q^{44}\) \(+1.99454 q^{45}\) \(+3.32666 q^{46}\) \(-2.01855 q^{47}\) \(-2.23485 q^{48}\) \(-6.05526 q^{49}\) \(+1.00000 q^{50}\) \(+11.5503 q^{51}\) \(+4.74974 q^{52}\) \(-9.34168 q^{53}\) \(+2.24706 q^{54}\) \(-2.26985 q^{55}\) \(-0.971978 q^{56}\) \(+4.70478 q^{57}\) \(-7.06139 q^{58}\) \(+8.51427 q^{59}\) \(-2.23485 q^{60}\) \(-3.05215 q^{61}\) \(+5.27710 q^{62}\) \(-1.93865 q^{63}\) \(+1.00000 q^{64}\) \(+4.74974 q^{65}\) \(+5.07276 q^{66}\) \(-4.20281 q^{67}\) \(-5.16829 q^{68}\) \(-7.43458 q^{69}\) \(-0.971978 q^{70}\) \(-3.81103 q^{71}\) \(+1.99454 q^{72}\) \(-13.6788 q^{73}\) \(-6.88894 q^{74}\) \(-2.23485 q^{75}\) \(-2.10519 q^{76}\) \(+2.20624 q^{77}\) \(-10.6149 q^{78}\) \(-14.8942 q^{79}\) \(+1.00000 q^{80}\) \(-11.0054 q^{81}\) \(+11.4261 q^{82}\) \(+11.4562 q^{83}\) \(+2.17222 q^{84}\) \(-5.16829 q^{85}\) \(+5.15210 q^{86}\) \(+15.7811 q^{87}\) \(-2.26985 q^{88}\) \(+2.24524 q^{89}\) \(+1.99454 q^{90}\) \(-4.61665 q^{91}\) \(+3.32666 q^{92}\) \(-11.7935 q^{93}\) \(-2.01855 q^{94}\) \(-2.10519 q^{95}\) \(-2.23485 q^{96}\) \(-8.88856 q^{97}\) \(-6.05526 q^{98}\) \(-4.52730 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.23485 −1.29029 −0.645144 0.764061i \(-0.723203\pi\)
−0.645144 + 0.764061i \(0.723203\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.23485 −0.912372
\(7\) −0.971978 −0.367373 −0.183687 0.982985i \(-0.558803\pi\)
−0.183687 + 0.982985i \(0.558803\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.99454 0.664845
\(10\) 1.00000 0.316228
\(11\) −2.26985 −0.684386 −0.342193 0.939630i \(-0.611170\pi\)
−0.342193 + 0.939630i \(0.611170\pi\)
\(12\) −2.23485 −0.645144
\(13\) 4.74974 1.31734 0.658671 0.752431i \(-0.271119\pi\)
0.658671 + 0.752431i \(0.271119\pi\)
\(14\) −0.971978 −0.259772
\(15\) −2.23485 −0.577035
\(16\) 1.00000 0.250000
\(17\) −5.16829 −1.25349 −0.626747 0.779223i \(-0.715614\pi\)
−0.626747 + 0.779223i \(0.715614\pi\)
\(18\) 1.99454 0.470117
\(19\) −2.10519 −0.482964 −0.241482 0.970405i \(-0.577634\pi\)
−0.241482 + 0.970405i \(0.577634\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.17222 0.474018
\(22\) −2.26985 −0.483934
\(23\) 3.32666 0.693658 0.346829 0.937928i \(-0.387258\pi\)
0.346829 + 0.937928i \(0.387258\pi\)
\(24\) −2.23485 −0.456186
\(25\) 1.00000 0.200000
\(26\) 4.74974 0.931501
\(27\) 2.24706 0.432446
\(28\) −0.971978 −0.183687
\(29\) −7.06139 −1.31127 −0.655633 0.755079i \(-0.727598\pi\)
−0.655633 + 0.755079i \(0.727598\pi\)
\(30\) −2.23485 −0.408025
\(31\) 5.27710 0.947794 0.473897 0.880580i \(-0.342847\pi\)
0.473897 + 0.880580i \(0.342847\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.07276 0.883055
\(34\) −5.16829 −0.886355
\(35\) −0.971978 −0.164294
\(36\) 1.99454 0.332423
\(37\) −6.88894 −1.13253 −0.566267 0.824222i \(-0.691613\pi\)
−0.566267 + 0.824222i \(0.691613\pi\)
\(38\) −2.10519 −0.341507
\(39\) −10.6149 −1.69975
\(40\) 1.00000 0.158114
\(41\) 11.4261 1.78446 0.892230 0.451582i \(-0.149140\pi\)
0.892230 + 0.451582i \(0.149140\pi\)
\(42\) 2.17222 0.335181
\(43\) 5.15210 0.785688 0.392844 0.919605i \(-0.371491\pi\)
0.392844 + 0.919605i \(0.371491\pi\)
\(44\) −2.26985 −0.342193
\(45\) 1.99454 0.297328
\(46\) 3.32666 0.490490
\(47\) −2.01855 −0.294436 −0.147218 0.989104i \(-0.547032\pi\)
−0.147218 + 0.989104i \(0.547032\pi\)
\(48\) −2.23485 −0.322572
\(49\) −6.05526 −0.865037
\(50\) 1.00000 0.141421
\(51\) 11.5503 1.61737
\(52\) 4.74974 0.658671
\(53\) −9.34168 −1.28318 −0.641589 0.767048i \(-0.721725\pi\)
−0.641589 + 0.767048i \(0.721725\pi\)
\(54\) 2.24706 0.305786
\(55\) −2.26985 −0.306067
\(56\) −0.971978 −0.129886
\(57\) 4.70478 0.623163
\(58\) −7.06139 −0.927206
\(59\) 8.51427 1.10846 0.554232 0.832362i \(-0.313012\pi\)
0.554232 + 0.832362i \(0.313012\pi\)
\(60\) −2.23485 −0.288517
\(61\) −3.05215 −0.390788 −0.195394 0.980725i \(-0.562599\pi\)
−0.195394 + 0.980725i \(0.562599\pi\)
\(62\) 5.27710 0.670192
\(63\) −1.93865 −0.244246
\(64\) 1.00000 0.125000
\(65\) 4.74974 0.589133
\(66\) 5.07276 0.624414
\(67\) −4.20281 −0.513455 −0.256728 0.966484i \(-0.582644\pi\)
−0.256728 + 0.966484i \(0.582644\pi\)
\(68\) −5.16829 −0.626747
\(69\) −7.43458 −0.895019
\(70\) −0.971978 −0.116174
\(71\) −3.81103 −0.452286 −0.226143 0.974094i \(-0.572612\pi\)
−0.226143 + 0.974094i \(0.572612\pi\)
\(72\) 1.99454 0.235058
\(73\) −13.6788 −1.60098 −0.800491 0.599345i \(-0.795428\pi\)
−0.800491 + 0.599345i \(0.795428\pi\)
\(74\) −6.88894 −0.800823
\(75\) −2.23485 −0.258058
\(76\) −2.10519 −0.241482
\(77\) 2.20624 0.251425
\(78\) −10.6149 −1.20191
\(79\) −14.8942 −1.67573 −0.837864 0.545879i \(-0.816196\pi\)
−0.837864 + 0.545879i \(0.816196\pi\)
\(80\) 1.00000 0.111803
\(81\) −11.0054 −1.22283
\(82\) 11.4261 1.26180
\(83\) 11.4562 1.25748 0.628742 0.777614i \(-0.283570\pi\)
0.628742 + 0.777614i \(0.283570\pi\)
\(84\) 2.17222 0.237009
\(85\) −5.16829 −0.560580
\(86\) 5.15210 0.555565
\(87\) 15.7811 1.69191
\(88\) −2.26985 −0.241967
\(89\) 2.24524 0.237995 0.118997 0.992895i \(-0.462032\pi\)
0.118997 + 0.992895i \(0.462032\pi\)
\(90\) 1.99454 0.210243
\(91\) −4.61665 −0.483956
\(92\) 3.32666 0.346829
\(93\) −11.7935 −1.22293
\(94\) −2.01855 −0.208198
\(95\) −2.10519 −0.215988
\(96\) −2.23485 −0.228093
\(97\) −8.88856 −0.902497 −0.451248 0.892398i \(-0.649021\pi\)
−0.451248 + 0.892398i \(0.649021\pi\)
\(98\) −6.05526 −0.611673
\(99\) −4.52730 −0.455010
\(100\) 1.00000 0.100000
\(101\) −10.5587 −1.05063 −0.525314 0.850909i \(-0.676052\pi\)
−0.525314 + 0.850909i \(0.676052\pi\)
\(102\) 11.5503 1.14365
\(103\) 5.85412 0.576823 0.288412 0.957506i \(-0.406873\pi\)
0.288412 + 0.957506i \(0.406873\pi\)
\(104\) 4.74974 0.465751
\(105\) 2.17222 0.211987
\(106\) −9.34168 −0.907344
\(107\) −3.31588 −0.320558 −0.160279 0.987072i \(-0.551239\pi\)
−0.160279 + 0.987072i \(0.551239\pi\)
\(108\) 2.24706 0.216223
\(109\) 18.9440 1.81450 0.907252 0.420587i \(-0.138176\pi\)
0.907252 + 0.420587i \(0.138176\pi\)
\(110\) −2.26985 −0.216422
\(111\) 15.3957 1.46130
\(112\) −0.971978 −0.0918433
\(113\) 13.9917 1.31623 0.658113 0.752919i \(-0.271355\pi\)
0.658113 + 0.752919i \(0.271355\pi\)
\(114\) 4.70478 0.440643
\(115\) 3.32666 0.310213
\(116\) −7.06139 −0.655633
\(117\) 9.47353 0.875828
\(118\) 8.51427 0.783802
\(119\) 5.02347 0.460500
\(120\) −2.23485 −0.204013
\(121\) −5.84778 −0.531616
\(122\) −3.05215 −0.276329
\(123\) −25.5356 −2.30247
\(124\) 5.27710 0.473897
\(125\) 1.00000 0.0894427
\(126\) −1.93865 −0.172708
\(127\) 10.9412 0.970871 0.485435 0.874273i \(-0.338661\pi\)
0.485435 + 0.874273i \(0.338661\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.5142 −1.01376
\(130\) 4.74974 0.416580
\(131\) −10.7917 −0.942879 −0.471440 0.881898i \(-0.656265\pi\)
−0.471440 + 0.881898i \(0.656265\pi\)
\(132\) 5.07276 0.441528
\(133\) 2.04620 0.177428
\(134\) −4.20281 −0.363068
\(135\) 2.24706 0.193396
\(136\) −5.16829 −0.443177
\(137\) −9.17558 −0.783923 −0.391961 0.919982i \(-0.628203\pi\)
−0.391961 + 0.919982i \(0.628203\pi\)
\(138\) −7.43458 −0.632874
\(139\) 20.1877 1.71230 0.856149 0.516728i \(-0.172850\pi\)
0.856149 + 0.516728i \(0.172850\pi\)
\(140\) −0.971978 −0.0821471
\(141\) 4.51116 0.379908
\(142\) −3.81103 −0.319814
\(143\) −10.7812 −0.901570
\(144\) 1.99454 0.166211
\(145\) −7.06139 −0.586416
\(146\) −13.6788 −1.13207
\(147\) 13.5326 1.11615
\(148\) −6.88894 −0.566267
\(149\) −12.3242 −1.00964 −0.504820 0.863225i \(-0.668441\pi\)
−0.504820 + 0.863225i \(0.668441\pi\)
\(150\) −2.23485 −0.182474
\(151\) −3.50054 −0.284870 −0.142435 0.989804i \(-0.545493\pi\)
−0.142435 + 0.989804i \(0.545493\pi\)
\(152\) −2.10519 −0.170754
\(153\) −10.3083 −0.833380
\(154\) 2.20624 0.177784
\(155\) 5.27710 0.423866
\(156\) −10.6149 −0.849876
\(157\) −8.93461 −0.713059 −0.356530 0.934284i \(-0.616040\pi\)
−0.356530 + 0.934284i \(0.616040\pi\)
\(158\) −14.8942 −1.18492
\(159\) 20.8772 1.65567
\(160\) 1.00000 0.0790569
\(161\) −3.23345 −0.254831
\(162\) −11.0054 −0.864669
\(163\) 16.2048 1.26926 0.634629 0.772817i \(-0.281153\pi\)
0.634629 + 0.772817i \(0.281153\pi\)
\(164\) 11.4261 0.892230
\(165\) 5.07276 0.394914
\(166\) 11.4562 0.889176
\(167\) −17.0541 −1.31968 −0.659842 0.751404i \(-0.729377\pi\)
−0.659842 + 0.751404i \(0.729377\pi\)
\(168\) 2.17222 0.167591
\(169\) 9.56006 0.735389
\(170\) −5.16829 −0.396390
\(171\) −4.19888 −0.321096
\(172\) 5.15210 0.392844
\(173\) −19.1959 −1.45944 −0.729719 0.683747i \(-0.760349\pi\)
−0.729719 + 0.683747i \(0.760349\pi\)
\(174\) 15.7811 1.19636
\(175\) −0.971978 −0.0734746
\(176\) −2.26985 −0.171096
\(177\) −19.0281 −1.43024
\(178\) 2.24524 0.168288
\(179\) −4.48302 −0.335076 −0.167538 0.985866i \(-0.553582\pi\)
−0.167538 + 0.985866i \(0.553582\pi\)
\(180\) 1.99454 0.148664
\(181\) −2.13871 −0.158969 −0.0794847 0.996836i \(-0.525327\pi\)
−0.0794847 + 0.996836i \(0.525327\pi\)
\(182\) −4.61665 −0.342209
\(183\) 6.82109 0.504230
\(184\) 3.32666 0.245245
\(185\) −6.88894 −0.506485
\(186\) −11.7935 −0.864741
\(187\) 11.7312 0.857874
\(188\) −2.01855 −0.147218
\(189\) −2.18409 −0.158869
\(190\) −2.10519 −0.152727
\(191\) −23.9579 −1.73353 −0.866767 0.498713i \(-0.833806\pi\)
−0.866767 + 0.498713i \(0.833806\pi\)
\(192\) −2.23485 −0.161286
\(193\) 8.02182 0.577423 0.288712 0.957416i \(-0.406773\pi\)
0.288712 + 0.957416i \(0.406773\pi\)
\(194\) −8.88856 −0.638162
\(195\) −10.6149 −0.760152
\(196\) −6.05526 −0.432518
\(197\) −21.4228 −1.52631 −0.763155 0.646215i \(-0.776351\pi\)
−0.763155 + 0.646215i \(0.776351\pi\)
\(198\) −4.52730 −0.321741
\(199\) 0.485772 0.0344354 0.0172177 0.999852i \(-0.494519\pi\)
0.0172177 + 0.999852i \(0.494519\pi\)
\(200\) 1.00000 0.0707107
\(201\) 9.39264 0.662506
\(202\) −10.5587 −0.742906
\(203\) 6.86352 0.481724
\(204\) 11.5503 0.808685
\(205\) 11.4261 0.798034
\(206\) 5.85412 0.407876
\(207\) 6.63515 0.461175
\(208\) 4.74974 0.329335
\(209\) 4.77847 0.330534
\(210\) 2.17222 0.149898
\(211\) −20.6922 −1.42451 −0.712256 0.701920i \(-0.752326\pi\)
−0.712256 + 0.701920i \(0.752326\pi\)
\(212\) −9.34168 −0.641589
\(213\) 8.51706 0.583579
\(214\) −3.31588 −0.226669
\(215\) 5.15210 0.351370
\(216\) 2.24706 0.152893
\(217\) −5.12922 −0.348194
\(218\) 18.9440 1.28305
\(219\) 30.5700 2.06573
\(220\) −2.26985 −0.153033
\(221\) −24.5481 −1.65128
\(222\) 15.3957 1.03329
\(223\) 3.28186 0.219770 0.109885 0.993944i \(-0.464952\pi\)
0.109885 + 0.993944i \(0.464952\pi\)
\(224\) −0.971978 −0.0649430
\(225\) 1.99454 0.132969
\(226\) 13.9917 0.930712
\(227\) 20.8167 1.38166 0.690828 0.723020i \(-0.257246\pi\)
0.690828 + 0.723020i \(0.257246\pi\)
\(228\) 4.70478 0.311582
\(229\) −11.5039 −0.760201 −0.380101 0.924945i \(-0.624111\pi\)
−0.380101 + 0.924945i \(0.624111\pi\)
\(230\) 3.32666 0.219354
\(231\) −4.93062 −0.324411
\(232\) −7.06139 −0.463603
\(233\) −15.6360 −1.02435 −0.512175 0.858881i \(-0.671160\pi\)
−0.512175 + 0.858881i \(0.671160\pi\)
\(234\) 9.47353 0.619304
\(235\) −2.01855 −0.131676
\(236\) 8.51427 0.554232
\(237\) 33.2862 2.16217
\(238\) 5.02347 0.325623
\(239\) −24.3679 −1.57623 −0.788114 0.615529i \(-0.788942\pi\)
−0.788114 + 0.615529i \(0.788942\pi\)
\(240\) −2.23485 −0.144259
\(241\) 1.23492 0.0795480 0.0397740 0.999209i \(-0.487336\pi\)
0.0397740 + 0.999209i \(0.487336\pi\)
\(242\) −5.84778 −0.375910
\(243\) 17.8543 1.14535
\(244\) −3.05215 −0.195394
\(245\) −6.05526 −0.386856
\(246\) −25.5356 −1.62809
\(247\) −9.99912 −0.636229
\(248\) 5.27710 0.335096
\(249\) −25.6029 −1.62252
\(250\) 1.00000 0.0632456
\(251\) −2.98498 −0.188410 −0.0942050 0.995553i \(-0.530031\pi\)
−0.0942050 + 0.995553i \(0.530031\pi\)
\(252\) −1.93865 −0.122123
\(253\) −7.55103 −0.474729
\(254\) 10.9412 0.686509
\(255\) 11.5503 0.723310
\(256\) 1.00000 0.0625000
\(257\) 7.22097 0.450432 0.225216 0.974309i \(-0.427691\pi\)
0.225216 + 0.974309i \(0.427691\pi\)
\(258\) −11.5142 −0.716840
\(259\) 6.69590 0.416063
\(260\) 4.74974 0.294567
\(261\) −14.0842 −0.871790
\(262\) −10.7917 −0.666716
\(263\) 25.9333 1.59911 0.799557 0.600590i \(-0.205068\pi\)
0.799557 + 0.600590i \(0.205068\pi\)
\(264\) 5.07276 0.312207
\(265\) −9.34168 −0.573855
\(266\) 2.04620 0.125461
\(267\) −5.01776 −0.307082
\(268\) −4.20281 −0.256728
\(269\) −20.2849 −1.23679 −0.618395 0.785868i \(-0.712217\pi\)
−0.618395 + 0.785868i \(0.712217\pi\)
\(270\) 2.24706 0.136752
\(271\) −12.3933 −0.752841 −0.376421 0.926449i \(-0.622845\pi\)
−0.376421 + 0.926449i \(0.622845\pi\)
\(272\) −5.16829 −0.313374
\(273\) 10.3175 0.624443
\(274\) −9.17558 −0.554317
\(275\) −2.26985 −0.136877
\(276\) −7.43458 −0.447509
\(277\) −0.498628 −0.0299596 −0.0149798 0.999888i \(-0.504768\pi\)
−0.0149798 + 0.999888i \(0.504768\pi\)
\(278\) 20.1877 1.21078
\(279\) 10.5254 0.630137
\(280\) −0.971978 −0.0580868
\(281\) −26.5416 −1.58334 −0.791668 0.610951i \(-0.790787\pi\)
−0.791668 + 0.610951i \(0.790787\pi\)
\(282\) 4.51116 0.268636
\(283\) −22.7403 −1.35177 −0.675885 0.737007i \(-0.736238\pi\)
−0.675885 + 0.737007i \(0.736238\pi\)
\(284\) −3.81103 −0.226143
\(285\) 4.70478 0.278687
\(286\) −10.7812 −0.637506
\(287\) −11.1059 −0.655563
\(288\) 1.99454 0.117529
\(289\) 9.71123 0.571249
\(290\) −7.06139 −0.414659
\(291\) 19.8646 1.16448
\(292\) −13.6788 −0.800491
\(293\) −9.05231 −0.528842 −0.264421 0.964407i \(-0.585181\pi\)
−0.264421 + 0.964407i \(0.585181\pi\)
\(294\) 13.5326 0.789235
\(295\) 8.51427 0.495720
\(296\) −6.88894 −0.400411
\(297\) −5.10048 −0.295960
\(298\) −12.3242 −0.713923
\(299\) 15.8008 0.913784
\(300\) −2.23485 −0.129029
\(301\) −5.00773 −0.288641
\(302\) −3.50054 −0.201434
\(303\) 23.5970 1.35561
\(304\) −2.10519 −0.120741
\(305\) −3.05215 −0.174766
\(306\) −10.3083 −0.589289
\(307\) −15.4543 −0.882021 −0.441011 0.897502i \(-0.645380\pi\)
−0.441011 + 0.897502i \(0.645380\pi\)
\(308\) 2.20624 0.125712
\(309\) −13.0831 −0.744269
\(310\) 5.27710 0.299719
\(311\) −26.0874 −1.47928 −0.739640 0.673003i \(-0.765004\pi\)
−0.739640 + 0.673003i \(0.765004\pi\)
\(312\) −10.6149 −0.600953
\(313\) 9.66909 0.546529 0.273265 0.961939i \(-0.411896\pi\)
0.273265 + 0.961939i \(0.411896\pi\)
\(314\) −8.93461 −0.504209
\(315\) −1.93865 −0.109230
\(316\) −14.8942 −0.837864
\(317\) 22.1831 1.24593 0.622963 0.782251i \(-0.285929\pi\)
0.622963 + 0.782251i \(0.285929\pi\)
\(318\) 20.8772 1.17074
\(319\) 16.0283 0.897412
\(320\) 1.00000 0.0559017
\(321\) 7.41048 0.413613
\(322\) −3.23345 −0.180193
\(323\) 10.8802 0.605393
\(324\) −11.0054 −0.611413
\(325\) 4.74974 0.263468
\(326\) 16.2048 0.897501
\(327\) −42.3369 −2.34123
\(328\) 11.4261 0.630902
\(329\) 1.96199 0.108168
\(330\) 5.07276 0.279247
\(331\) −3.43067 −0.188567 −0.0942833 0.995545i \(-0.530056\pi\)
−0.0942833 + 0.995545i \(0.530056\pi\)
\(332\) 11.4562 0.628742
\(333\) −13.7402 −0.752960
\(334\) −17.0541 −0.933158
\(335\) −4.20281 −0.229624
\(336\) 2.17222 0.118504
\(337\) 19.2095 1.04641 0.523204 0.852208i \(-0.324737\pi\)
0.523204 + 0.852208i \(0.324737\pi\)
\(338\) 9.56006 0.519999
\(339\) −31.2692 −1.69831
\(340\) −5.16829 −0.280290
\(341\) −11.9782 −0.648657
\(342\) −4.19888 −0.227049
\(343\) 12.6894 0.685165
\(344\) 5.15210 0.277783
\(345\) −7.43458 −0.400264
\(346\) −19.1959 −1.03198
\(347\) 28.0513 1.50587 0.752937 0.658093i \(-0.228637\pi\)
0.752937 + 0.658093i \(0.228637\pi\)
\(348\) 15.7811 0.845957
\(349\) −18.7428 −1.00328 −0.501640 0.865076i \(-0.667270\pi\)
−0.501640 + 0.865076i \(0.667270\pi\)
\(350\) −0.971978 −0.0519544
\(351\) 10.6729 0.569680
\(352\) −2.26985 −0.120983
\(353\) −2.39277 −0.127354 −0.0636772 0.997971i \(-0.520283\pi\)
−0.0636772 + 0.997971i \(0.520283\pi\)
\(354\) −19.0281 −1.01133
\(355\) −3.81103 −0.202268
\(356\) 2.24524 0.118997
\(357\) −11.2267 −0.594178
\(358\) −4.48302 −0.236935
\(359\) −24.3064 −1.28284 −0.641421 0.767189i \(-0.721655\pi\)
−0.641421 + 0.767189i \(0.721655\pi\)
\(360\) 1.99454 0.105121
\(361\) −14.5682 −0.766746
\(362\) −2.13871 −0.112408
\(363\) 13.0689 0.685939
\(364\) −4.61665 −0.241978
\(365\) −13.6788 −0.715981
\(366\) 6.82109 0.356544
\(367\) 0.508134 0.0265244 0.0132622 0.999912i \(-0.495778\pi\)
0.0132622 + 0.999912i \(0.495778\pi\)
\(368\) 3.32666 0.173414
\(369\) 22.7898 1.18639
\(370\) −6.88894 −0.358139
\(371\) 9.07991 0.471405
\(372\) −11.7935 −0.611464
\(373\) −20.4909 −1.06098 −0.530490 0.847691i \(-0.677992\pi\)
−0.530490 + 0.847691i \(0.677992\pi\)
\(374\) 11.7312 0.606608
\(375\) −2.23485 −0.115407
\(376\) −2.01855 −0.104099
\(377\) −33.5398 −1.72739
\(378\) −2.18409 −0.112338
\(379\) 21.5832 1.10865 0.554326 0.832299i \(-0.312976\pi\)
0.554326 + 0.832299i \(0.312976\pi\)
\(380\) −2.10519 −0.107994
\(381\) −24.4518 −1.25270
\(382\) −23.9579 −1.22579
\(383\) −30.7891 −1.57325 −0.786625 0.617431i \(-0.788174\pi\)
−0.786625 + 0.617431i \(0.788174\pi\)
\(384\) −2.23485 −0.114046
\(385\) 2.20624 0.112441
\(386\) 8.02182 0.408300
\(387\) 10.2761 0.522361
\(388\) −8.88856 −0.451248
\(389\) 11.3147 0.573680 0.286840 0.957979i \(-0.407395\pi\)
0.286840 + 0.957979i \(0.407395\pi\)
\(390\) −10.6149 −0.537509
\(391\) −17.1932 −0.869496
\(392\) −6.05526 −0.305837
\(393\) 24.1179 1.21659
\(394\) −21.4228 −1.07926
\(395\) −14.8942 −0.749408
\(396\) −4.52730 −0.227505
\(397\) −25.7552 −1.29261 −0.646307 0.763077i \(-0.723688\pi\)
−0.646307 + 0.763077i \(0.723688\pi\)
\(398\) 0.485772 0.0243495
\(399\) −4.57294 −0.228934
\(400\) 1.00000 0.0500000
\(401\) 36.4590 1.82068 0.910338 0.413866i \(-0.135822\pi\)
0.910338 + 0.413866i \(0.135822\pi\)
\(402\) 9.39264 0.468462
\(403\) 25.0648 1.24857
\(404\) −10.5587 −0.525314
\(405\) −11.0054 −0.546864
\(406\) 6.86352 0.340631
\(407\) 15.6369 0.775090
\(408\) 11.5503 0.571827
\(409\) −15.2347 −0.753307 −0.376654 0.926354i \(-0.622925\pi\)
−0.376654 + 0.926354i \(0.622925\pi\)
\(410\) 11.4261 0.564296
\(411\) 20.5060 1.01149
\(412\) 5.85412 0.288412
\(413\) −8.27568 −0.407220
\(414\) 6.63515 0.326100
\(415\) 11.4562 0.562364
\(416\) 4.74974 0.232875
\(417\) −45.1164 −2.20936
\(418\) 4.77847 0.233723
\(419\) −4.27469 −0.208832 −0.104416 0.994534i \(-0.533297\pi\)
−0.104416 + 0.994534i \(0.533297\pi\)
\(420\) 2.17222 0.105994
\(421\) 28.7923 1.40325 0.701625 0.712546i \(-0.252458\pi\)
0.701625 + 0.712546i \(0.252458\pi\)
\(422\) −20.6922 −1.00728
\(423\) −4.02608 −0.195755
\(424\) −9.34168 −0.453672
\(425\) −5.16829 −0.250699
\(426\) 8.51706 0.412653
\(427\) 2.96663 0.143565
\(428\) −3.31588 −0.160279
\(429\) 24.0943 1.16329
\(430\) 5.15210 0.248456
\(431\) 17.5168 0.843755 0.421878 0.906653i \(-0.361371\pi\)
0.421878 + 0.906653i \(0.361371\pi\)
\(432\) 2.24706 0.108112
\(433\) 10.8362 0.520755 0.260377 0.965507i \(-0.416153\pi\)
0.260377 + 0.965507i \(0.416153\pi\)
\(434\) −5.12922 −0.246210
\(435\) 15.7811 0.756647
\(436\) 18.9440 0.907252
\(437\) −7.00327 −0.335012
\(438\) 30.5700 1.46069
\(439\) −23.8707 −1.13929 −0.569643 0.821893i \(-0.692918\pi\)
−0.569643 + 0.821893i \(0.692918\pi\)
\(440\) −2.26985 −0.108211
\(441\) −12.0774 −0.575116
\(442\) −24.5481 −1.16763
\(443\) −27.9217 −1.32660 −0.663299 0.748355i \(-0.730844\pi\)
−0.663299 + 0.748355i \(0.730844\pi\)
\(444\) 15.3957 0.730648
\(445\) 2.24524 0.106434
\(446\) 3.28186 0.155401
\(447\) 27.5427 1.30273
\(448\) −0.971978 −0.0459217
\(449\) 32.8472 1.55015 0.775077 0.631867i \(-0.217711\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(450\) 1.99454 0.0940233
\(451\) −25.9356 −1.22126
\(452\) 13.9917 0.658113
\(453\) 7.82317 0.367565
\(454\) 20.8167 0.976978
\(455\) −4.61665 −0.216432
\(456\) 4.70478 0.220322
\(457\) 21.6199 1.01133 0.505667 0.862729i \(-0.331246\pi\)
0.505667 + 0.862729i \(0.331246\pi\)
\(458\) −11.5039 −0.537543
\(459\) −11.6134 −0.542069
\(460\) 3.32666 0.155107
\(461\) 4.00324 0.186449 0.0932247 0.995645i \(-0.470283\pi\)
0.0932247 + 0.995645i \(0.470283\pi\)
\(462\) −4.93062 −0.229393
\(463\) 8.14567 0.378561 0.189281 0.981923i \(-0.439384\pi\)
0.189281 + 0.981923i \(0.439384\pi\)
\(464\) −7.06139 −0.327817
\(465\) −11.7935 −0.546910
\(466\) −15.6360 −0.724324
\(467\) 12.1779 0.563528 0.281764 0.959484i \(-0.409081\pi\)
0.281764 + 0.959484i \(0.409081\pi\)
\(468\) 9.47353 0.437914
\(469\) 4.08504 0.188630
\(470\) −2.01855 −0.0931090
\(471\) 19.9675 0.920052
\(472\) 8.51427 0.391901
\(473\) −11.6945 −0.537714
\(474\) 33.2862 1.52889
\(475\) −2.10519 −0.0965928
\(476\) 5.02347 0.230250
\(477\) −18.6323 −0.853115
\(478\) −24.3679 −1.11456
\(479\) −28.2514 −1.29084 −0.645420 0.763828i \(-0.723318\pi\)
−0.645420 + 0.763828i \(0.723318\pi\)
\(480\) −2.23485 −0.102006
\(481\) −32.7207 −1.49193
\(482\) 1.23492 0.0562489
\(483\) 7.22625 0.328806
\(484\) −5.84778 −0.265808
\(485\) −8.88856 −0.403609
\(486\) 17.8543 0.809886
\(487\) 41.3590 1.87416 0.937078 0.349119i \(-0.113519\pi\)
0.937078 + 0.349119i \(0.113519\pi\)
\(488\) −3.05215 −0.138164
\(489\) −36.2152 −1.63771
\(490\) −6.05526 −0.273549
\(491\) −18.1492 −0.819061 −0.409530 0.912296i \(-0.634307\pi\)
−0.409530 + 0.912296i \(0.634307\pi\)
\(492\) −25.5356 −1.15123
\(493\) 36.4953 1.64367
\(494\) −9.99912 −0.449882
\(495\) −4.52730 −0.203487
\(496\) 5.27710 0.236949
\(497\) 3.70424 0.166158
\(498\) −25.6029 −1.14729
\(499\) −18.0488 −0.807973 −0.403987 0.914765i \(-0.632376\pi\)
−0.403987 + 0.914765i \(0.632376\pi\)
\(500\) 1.00000 0.0447214
\(501\) 38.1132 1.70277
\(502\) −2.98498 −0.133226
\(503\) 39.2573 1.75040 0.875199 0.483764i \(-0.160731\pi\)
0.875199 + 0.483764i \(0.160731\pi\)
\(504\) −1.93865 −0.0863541
\(505\) −10.5587 −0.469855
\(506\) −7.55103 −0.335684
\(507\) −21.3653 −0.948865
\(508\) 10.9412 0.485435
\(509\) −36.6908 −1.62629 −0.813145 0.582061i \(-0.802247\pi\)
−0.813145 + 0.582061i \(0.802247\pi\)
\(510\) 11.5503 0.511457
\(511\) 13.2955 0.588158
\(512\) 1.00000 0.0441942
\(513\) −4.73049 −0.208856
\(514\) 7.22097 0.318503
\(515\) 5.85412 0.257963
\(516\) −11.5142 −0.506882
\(517\) 4.58182 0.201508
\(518\) 6.69590 0.294201
\(519\) 42.8999 1.88310
\(520\) 4.74974 0.208290
\(521\) −35.2070 −1.54245 −0.771224 0.636564i \(-0.780355\pi\)
−0.771224 + 0.636564i \(0.780355\pi\)
\(522\) −14.0842 −0.616448
\(523\) −5.54557 −0.242491 −0.121245 0.992623i \(-0.538689\pi\)
−0.121245 + 0.992623i \(0.538689\pi\)
\(524\) −10.7917 −0.471440
\(525\) 2.17222 0.0948035
\(526\) 25.9333 1.13074
\(527\) −27.2736 −1.18806
\(528\) 5.07276 0.220764
\(529\) −11.9333 −0.518839
\(530\) −9.34168 −0.405777
\(531\) 16.9820 0.736957
\(532\) 2.04620 0.0887141
\(533\) 54.2711 2.35074
\(534\) −5.01776 −0.217140
\(535\) −3.31588 −0.143358
\(536\) −4.20281 −0.181534
\(537\) 10.0189 0.432345
\(538\) −20.2849 −0.874542
\(539\) 13.7445 0.592019
\(540\) 2.24706 0.0966980
\(541\) −20.4403 −0.878798 −0.439399 0.898292i \(-0.644809\pi\)
−0.439399 + 0.898292i \(0.644809\pi\)
\(542\) −12.3933 −0.532339
\(543\) 4.77970 0.205116
\(544\) −5.16829 −0.221589
\(545\) 18.9440 0.811471
\(546\) 10.3175 0.441548
\(547\) −18.5405 −0.792735 −0.396367 0.918092i \(-0.629729\pi\)
−0.396367 + 0.918092i \(0.629729\pi\)
\(548\) −9.17558 −0.391961
\(549\) −6.08763 −0.259814
\(550\) −2.26985 −0.0967867
\(551\) 14.8656 0.633295
\(552\) −7.43458 −0.316437
\(553\) 14.4768 0.615617
\(554\) −0.498628 −0.0211847
\(555\) 15.3957 0.653512
\(556\) 20.1877 0.856149
\(557\) −7.03593 −0.298122 −0.149061 0.988828i \(-0.547625\pi\)
−0.149061 + 0.988828i \(0.547625\pi\)
\(558\) 10.5254 0.445574
\(559\) 24.4712 1.03502
\(560\) −0.971978 −0.0410736
\(561\) −26.2175 −1.10690
\(562\) −26.5416 −1.11959
\(563\) −4.69898 −0.198039 −0.0990193 0.995086i \(-0.531571\pi\)
−0.0990193 + 0.995086i \(0.531571\pi\)
\(564\) 4.51116 0.189954
\(565\) 13.9917 0.588634
\(566\) −22.7403 −0.955845
\(567\) 10.6970 0.449234
\(568\) −3.81103 −0.159907
\(569\) 21.3855 0.896528 0.448264 0.893901i \(-0.352042\pi\)
0.448264 + 0.893901i \(0.352042\pi\)
\(570\) 4.70478 0.197062
\(571\) −12.3691 −0.517629 −0.258814 0.965927i \(-0.583332\pi\)
−0.258814 + 0.965927i \(0.583332\pi\)
\(572\) −10.7812 −0.450785
\(573\) 53.5423 2.23676
\(574\) −11.1059 −0.463553
\(575\) 3.32666 0.138732
\(576\) 1.99454 0.0831057
\(577\) 6.83425 0.284513 0.142257 0.989830i \(-0.454564\pi\)
0.142257 + 0.989830i \(0.454564\pi\)
\(578\) 9.71123 0.403934
\(579\) −17.9275 −0.745043
\(580\) −7.06139 −0.293208
\(581\) −11.1352 −0.461966
\(582\) 19.8646 0.823413
\(583\) 21.2042 0.878189
\(584\) −13.6788 −0.566033
\(585\) 9.47353 0.391682
\(586\) −9.05231 −0.373948
\(587\) 29.0110 1.19741 0.598706 0.800969i \(-0.295682\pi\)
0.598706 + 0.800969i \(0.295682\pi\)
\(588\) 13.5326 0.558074
\(589\) −11.1093 −0.457751
\(590\) 8.51427 0.350527
\(591\) 47.8766 1.96938
\(592\) −6.88894 −0.283134
\(593\) −25.3143 −1.03953 −0.519767 0.854308i \(-0.673981\pi\)
−0.519767 + 0.854308i \(0.673981\pi\)
\(594\) −5.10048 −0.209275
\(595\) 5.02347 0.205942
\(596\) −12.3242 −0.504820
\(597\) −1.08562 −0.0444317
\(598\) 15.8008 0.646143
\(599\) 21.0656 0.860719 0.430359 0.902658i \(-0.358387\pi\)
0.430359 + 0.902658i \(0.358387\pi\)
\(600\) −2.23485 −0.0912372
\(601\) −1.00000 −0.0407909
\(602\) −5.00773 −0.204100
\(603\) −8.38266 −0.341368
\(604\) −3.50054 −0.142435
\(605\) −5.84778 −0.237746
\(606\) 23.5970 0.958563
\(607\) 38.1811 1.54972 0.774861 0.632132i \(-0.217820\pi\)
0.774861 + 0.632132i \(0.217820\pi\)
\(608\) −2.10519 −0.0853768
\(609\) −15.3389 −0.621564
\(610\) −3.05215 −0.123578
\(611\) −9.58762 −0.387873
\(612\) −10.3083 −0.416690
\(613\) 13.1729 0.532050 0.266025 0.963966i \(-0.414290\pi\)
0.266025 + 0.963966i \(0.414290\pi\)
\(614\) −15.4543 −0.623683
\(615\) −25.5356 −1.02969
\(616\) 2.20624 0.0888921
\(617\) −35.6371 −1.43470 −0.717348 0.696715i \(-0.754644\pi\)
−0.717348 + 0.696715i \(0.754644\pi\)
\(618\) −13.0831 −0.526277
\(619\) 20.2223 0.812804 0.406402 0.913694i \(-0.366783\pi\)
0.406402 + 0.913694i \(0.366783\pi\)
\(620\) 5.27710 0.211933
\(621\) 7.47521 0.299970
\(622\) −26.0874 −1.04601
\(623\) −2.18232 −0.0874328
\(624\) −10.6149 −0.424938
\(625\) 1.00000 0.0400000
\(626\) 9.66909 0.386455
\(627\) −10.6791 −0.426484
\(628\) −8.93461 −0.356530
\(629\) 35.6040 1.41963
\(630\) −1.93865 −0.0772375
\(631\) −38.0512 −1.51479 −0.757397 0.652954i \(-0.773529\pi\)
−0.757397 + 0.652954i \(0.773529\pi\)
\(632\) −14.8942 −0.592459
\(633\) 46.2439 1.83803
\(634\) 22.1831 0.881003
\(635\) 10.9412 0.434187
\(636\) 20.8772 0.827835
\(637\) −28.7609 −1.13955
\(638\) 16.0283 0.634566
\(639\) −7.60123 −0.300700
\(640\) 1.00000 0.0395285
\(641\) 38.2182 1.50953 0.754764 0.655997i \(-0.227751\pi\)
0.754764 + 0.655997i \(0.227751\pi\)
\(642\) 7.41048 0.292468
\(643\) 30.5939 1.20650 0.603252 0.797550i \(-0.293871\pi\)
0.603252 + 0.797550i \(0.293871\pi\)
\(644\) −3.23345 −0.127416
\(645\) −11.5142 −0.453369
\(646\) 10.8802 0.428078
\(647\) −42.3448 −1.66474 −0.832372 0.554217i \(-0.813018\pi\)
−0.832372 + 0.554217i \(0.813018\pi\)
\(648\) −11.0054 −0.432334
\(649\) −19.3261 −0.758616
\(650\) 4.74974 0.186300
\(651\) 11.4630 0.449271
\(652\) 16.2048 0.634629
\(653\) 28.5492 1.11722 0.558608 0.829432i \(-0.311336\pi\)
0.558608 + 0.829432i \(0.311336\pi\)
\(654\) −42.3369 −1.65550
\(655\) −10.7917 −0.421668
\(656\) 11.4261 0.446115
\(657\) −27.2828 −1.06441
\(658\) 1.96199 0.0764864
\(659\) 46.7842 1.82245 0.911227 0.411904i \(-0.135136\pi\)
0.911227 + 0.411904i \(0.135136\pi\)
\(660\) 5.07276 0.197457
\(661\) 17.4629 0.679230 0.339615 0.940565i \(-0.389703\pi\)
0.339615 + 0.940565i \(0.389703\pi\)
\(662\) −3.43067 −0.133337
\(663\) 54.8611 2.13063
\(664\) 11.4562 0.444588
\(665\) 2.04620 0.0793483
\(666\) −13.7402 −0.532423
\(667\) −23.4909 −0.909570
\(668\) −17.0541 −0.659842
\(669\) −7.33445 −0.283566
\(670\) −4.20281 −0.162369
\(671\) 6.92793 0.267450
\(672\) 2.17222 0.0837953
\(673\) 36.7696 1.41736 0.708682 0.705528i \(-0.249290\pi\)
0.708682 + 0.705528i \(0.249290\pi\)
\(674\) 19.2095 0.739922
\(675\) 2.24706 0.0864893
\(676\) 9.56006 0.367695
\(677\) 3.22116 0.123799 0.0618996 0.998082i \(-0.480284\pi\)
0.0618996 + 0.998082i \(0.480284\pi\)
\(678\) −31.2692 −1.20089
\(679\) 8.63949 0.331553
\(680\) −5.16829 −0.198195
\(681\) −46.5222 −1.78273
\(682\) −11.9782 −0.458670
\(683\) −8.36421 −0.320047 −0.160024 0.987113i \(-0.551157\pi\)
−0.160024 + 0.987113i \(0.551157\pi\)
\(684\) −4.19888 −0.160548
\(685\) −9.17558 −0.350581
\(686\) 12.6894 0.484485
\(687\) 25.7095 0.980879
\(688\) 5.15210 0.196422
\(689\) −44.3706 −1.69038
\(690\) −7.43458 −0.283030
\(691\) −32.9538 −1.25362 −0.626811 0.779171i \(-0.715640\pi\)
−0.626811 + 0.779171i \(0.715640\pi\)
\(692\) −19.1959 −0.729719
\(693\) 4.40043 0.167159
\(694\) 28.0513 1.06481
\(695\) 20.1877 0.765763
\(696\) 15.7811 0.598182
\(697\) −59.0535 −2.23681
\(698\) −18.7428 −0.709426
\(699\) 34.9441 1.32171
\(700\) −0.971978 −0.0367373
\(701\) −4.58362 −0.173121 −0.0865605 0.996247i \(-0.527588\pi\)
−0.0865605 + 0.996247i \(0.527588\pi\)
\(702\) 10.6729 0.402824
\(703\) 14.5025 0.546974
\(704\) −2.26985 −0.0855482
\(705\) 4.51116 0.169900
\(706\) −2.39277 −0.0900531
\(707\) 10.2628 0.385972
\(708\) −19.0281 −0.715119
\(709\) −12.1221 −0.455255 −0.227628 0.973748i \(-0.573097\pi\)
−0.227628 + 0.973748i \(0.573097\pi\)
\(710\) −3.81103 −0.143025
\(711\) −29.7070 −1.11410
\(712\) 2.24524 0.0841438
\(713\) 17.5551 0.657445
\(714\) −11.2267 −0.420148
\(715\) −10.7812 −0.403194
\(716\) −4.48302 −0.167538
\(717\) 54.4585 2.03379
\(718\) −24.3064 −0.907107
\(719\) −5.44915 −0.203219 −0.101610 0.994824i \(-0.532399\pi\)
−0.101610 + 0.994824i \(0.532399\pi\)
\(720\) 1.99454 0.0743320
\(721\) −5.69007 −0.211909
\(722\) −14.5682 −0.542171
\(723\) −2.75985 −0.102640
\(724\) −2.13871 −0.0794847
\(725\) −7.06139 −0.262253
\(726\) 13.0689 0.485032
\(727\) 31.6468 1.17371 0.586857 0.809690i \(-0.300365\pi\)
0.586857 + 0.809690i \(0.300365\pi\)
\(728\) −4.61665 −0.171104
\(729\) −6.88525 −0.255009
\(730\) −13.6788 −0.506275
\(731\) −26.6276 −0.984856
\(732\) 6.82109 0.252115
\(733\) −31.2485 −1.15419 −0.577094 0.816677i \(-0.695814\pi\)
−0.577094 + 0.816677i \(0.695814\pi\)
\(734\) 0.508134 0.0187556
\(735\) 13.5326 0.499156
\(736\) 3.32666 0.122622
\(737\) 9.53976 0.351401
\(738\) 22.7898 0.838904
\(739\) −26.4086 −0.971457 −0.485729 0.874110i \(-0.661446\pi\)
−0.485729 + 0.874110i \(0.661446\pi\)
\(740\) −6.88894 −0.253242
\(741\) 22.3465 0.820919
\(742\) 9.07991 0.333334
\(743\) −6.88970 −0.252758 −0.126379 0.991982i \(-0.540336\pi\)
−0.126379 + 0.991982i \(0.540336\pi\)
\(744\) −11.7935 −0.432370
\(745\) −12.3242 −0.451524
\(746\) −20.4909 −0.750226
\(747\) 22.8499 0.836032
\(748\) 11.7312 0.428937
\(749\) 3.22296 0.117765
\(750\) −2.23485 −0.0816050
\(751\) −31.6083 −1.15340 −0.576702 0.816955i \(-0.695661\pi\)
−0.576702 + 0.816955i \(0.695661\pi\)
\(752\) −2.01855 −0.0736091
\(753\) 6.67096 0.243103
\(754\) −33.5398 −1.22145
\(755\) −3.50054 −0.127398
\(756\) −2.18409 −0.0794346
\(757\) −35.2565 −1.28142 −0.640709 0.767784i \(-0.721360\pi\)
−0.640709 + 0.767784i \(0.721360\pi\)
\(758\) 21.5832 0.783936
\(759\) 16.8754 0.612538
\(760\) −2.10519 −0.0763633
\(761\) −10.1589 −0.368259 −0.184129 0.982902i \(-0.558947\pi\)
−0.184129 + 0.982902i \(0.558947\pi\)
\(762\) −24.4518 −0.885795
\(763\) −18.4131 −0.666600
\(764\) −23.9579 −0.866767
\(765\) −10.3083 −0.372699
\(766\) −30.7891 −1.11246
\(767\) 40.4406 1.46023
\(768\) −2.23485 −0.0806431
\(769\) 39.7266 1.43258 0.716289 0.697804i \(-0.245839\pi\)
0.716289 + 0.697804i \(0.245839\pi\)
\(770\) 2.20624 0.0795075
\(771\) −16.1378 −0.581187
\(772\) 8.02182 0.288712
\(773\) 33.8580 1.21779 0.608893 0.793252i \(-0.291614\pi\)
0.608893 + 0.793252i \(0.291614\pi\)
\(774\) 10.2761 0.369365
\(775\) 5.27710 0.189559
\(776\) −8.88856 −0.319081
\(777\) −14.9643 −0.536841
\(778\) 11.3147 0.405653
\(779\) −24.0542 −0.861830
\(780\) −10.6149 −0.380076
\(781\) 8.65046 0.309538
\(782\) −17.1932 −0.614827
\(783\) −15.8673 −0.567053
\(784\) −6.05526 −0.216259
\(785\) −8.93461 −0.318890
\(786\) 24.1179 0.860257
\(787\) 44.0259 1.56935 0.784677 0.619905i \(-0.212829\pi\)
0.784677 + 0.619905i \(0.212829\pi\)
\(788\) −21.4228 −0.763155
\(789\) −57.9569 −2.06332
\(790\) −14.8942 −0.529912
\(791\) −13.5996 −0.483546
\(792\) −4.52730 −0.160870
\(793\) −14.4969 −0.514802
\(794\) −25.7552 −0.914017
\(795\) 20.8772 0.740439
\(796\) 0.485772 0.0172177
\(797\) 28.6875 1.01616 0.508081 0.861309i \(-0.330355\pi\)
0.508081 + 0.861309i \(0.330355\pi\)
\(798\) −4.57294 −0.161880
\(799\) 10.4325 0.369074
\(800\) 1.00000 0.0353553
\(801\) 4.47820 0.158230
\(802\) 36.4590 1.28741
\(803\) 31.0488 1.09569
\(804\) 9.39264 0.331253
\(805\) −3.23345 −0.113964
\(806\) 25.0648 0.882872
\(807\) 45.3335 1.59582
\(808\) −10.5587 −0.371453
\(809\) 13.3210 0.468343 0.234172 0.972195i \(-0.424762\pi\)
0.234172 + 0.972195i \(0.424762\pi\)
\(810\) −11.0054 −0.386692
\(811\) −12.2378 −0.429729 −0.214864 0.976644i \(-0.568931\pi\)
−0.214864 + 0.976644i \(0.568931\pi\)
\(812\) 6.86352 0.240862
\(813\) 27.6972 0.971382
\(814\) 15.6369 0.548072
\(815\) 16.2048 0.567629
\(816\) 11.5503 0.404343
\(817\) −10.8462 −0.379459
\(818\) −15.2347 −0.532669
\(819\) −9.20807 −0.321756
\(820\) 11.4261 0.399017
\(821\) 30.5918 1.06766 0.533831 0.845591i \(-0.320752\pi\)
0.533831 + 0.845591i \(0.320752\pi\)
\(822\) 20.5060 0.715229
\(823\) 22.8423 0.796232 0.398116 0.917335i \(-0.369664\pi\)
0.398116 + 0.917335i \(0.369664\pi\)
\(824\) 5.85412 0.203938
\(825\) 5.07276 0.176611
\(826\) −8.27568 −0.287948
\(827\) 6.71335 0.233446 0.116723 0.993165i \(-0.462761\pi\)
0.116723 + 0.993165i \(0.462761\pi\)
\(828\) 6.63515 0.230587
\(829\) 0.256997 0.00892587 0.00446293 0.999990i \(-0.498579\pi\)
0.00446293 + 0.999990i \(0.498579\pi\)
\(830\) 11.4562 0.397651
\(831\) 1.11436 0.0386566
\(832\) 4.74974 0.164668
\(833\) 31.2953 1.08432
\(834\) −45.1164 −1.56225
\(835\) −17.0541 −0.590181
\(836\) 4.77847 0.165267
\(837\) 11.8579 0.409870
\(838\) −4.27469 −0.147667
\(839\) 6.09546 0.210439 0.105219 0.994449i \(-0.466446\pi\)
0.105219 + 0.994449i \(0.466446\pi\)
\(840\) 2.17222 0.0749488
\(841\) 20.8632 0.719421
\(842\) 28.7923 0.992248
\(843\) 59.3163 2.04296
\(844\) −20.6922 −0.712256
\(845\) 9.56006 0.328876
\(846\) −4.02608 −0.138419
\(847\) 5.68392 0.195302
\(848\) −9.34168 −0.320795
\(849\) 50.8210 1.74417
\(850\) −5.16829 −0.177271
\(851\) −22.9172 −0.785591
\(852\) 8.51706 0.291790
\(853\) 46.8459 1.60397 0.801986 0.597342i \(-0.203777\pi\)
0.801986 + 0.597342i \(0.203777\pi\)
\(854\) 2.96663 0.101516
\(855\) −4.19888 −0.143599
\(856\) −3.31588 −0.113334
\(857\) −21.3035 −0.727715 −0.363857 0.931455i \(-0.618540\pi\)
−0.363857 + 0.931455i \(0.618540\pi\)
\(858\) 24.0943 0.822567
\(859\) 19.3737 0.661023 0.330511 0.943802i \(-0.392779\pi\)
0.330511 + 0.943802i \(0.392779\pi\)
\(860\) 5.15210 0.175685
\(861\) 24.8200 0.845865
\(862\) 17.5168 0.596625
\(863\) −53.0306 −1.80518 −0.902591 0.430498i \(-0.858338\pi\)
−0.902591 + 0.430498i \(0.858338\pi\)
\(864\) 2.24706 0.0764464
\(865\) −19.1959 −0.652680
\(866\) 10.8362 0.368229
\(867\) −21.7031 −0.737076
\(868\) −5.12922 −0.174097
\(869\) 33.8076 1.14684
\(870\) 15.7811 0.535030
\(871\) −19.9623 −0.676396
\(872\) 18.9440 0.641524
\(873\) −17.7286 −0.600021
\(874\) −7.00327 −0.236889
\(875\) −0.971978 −0.0328589
\(876\) 30.5700 1.03286
\(877\) 52.1085 1.75958 0.879789 0.475364i \(-0.157683\pi\)
0.879789 + 0.475364i \(0.157683\pi\)
\(878\) −23.8707 −0.805596
\(879\) 20.2305 0.682358
\(880\) −2.26985 −0.0765166
\(881\) 28.5352 0.961376 0.480688 0.876892i \(-0.340387\pi\)
0.480688 + 0.876892i \(0.340387\pi\)
\(882\) −12.0774 −0.406668
\(883\) 15.2947 0.514707 0.257354 0.966317i \(-0.417150\pi\)
0.257354 + 0.966317i \(0.417150\pi\)
\(884\) −24.5481 −0.825640
\(885\) −19.0281 −0.639622
\(886\) −27.9217 −0.938046
\(887\) −3.30869 −0.111095 −0.0555475 0.998456i \(-0.517690\pi\)
−0.0555475 + 0.998456i \(0.517690\pi\)
\(888\) 15.3957 0.516646
\(889\) −10.6346 −0.356672
\(890\) 2.24524 0.0752605
\(891\) 24.9807 0.836884
\(892\) 3.28186 0.109885
\(893\) 4.24945 0.142202
\(894\) 27.5427 0.921166
\(895\) −4.48302 −0.149851
\(896\) −0.971978 −0.0324715
\(897\) −35.3124 −1.17905
\(898\) 32.8472 1.09612
\(899\) −37.2636 −1.24281
\(900\) 1.99454 0.0664845
\(901\) 48.2805 1.60846
\(902\) −25.9356 −0.863560
\(903\) 11.1915 0.372430
\(904\) 13.9917 0.465356
\(905\) −2.13871 −0.0710933
\(906\) 7.82317 0.259908
\(907\) −47.9859 −1.59334 −0.796672 0.604412i \(-0.793408\pi\)
−0.796672 + 0.604412i \(0.793408\pi\)
\(908\) 20.8167 0.690828
\(909\) −21.0597 −0.698505
\(910\) −4.61665 −0.153040
\(911\) −40.8483 −1.35336 −0.676682 0.736275i \(-0.736583\pi\)
−0.676682 + 0.736275i \(0.736583\pi\)
\(912\) 4.70478 0.155791
\(913\) −26.0039 −0.860604
\(914\) 21.6199 0.715121
\(915\) 6.82109 0.225498
\(916\) −11.5039 −0.380101
\(917\) 10.4893 0.346389
\(918\) −11.6134 −0.383301
\(919\) 22.7650 0.750949 0.375474 0.926833i \(-0.377480\pi\)
0.375474 + 0.926833i \(0.377480\pi\)
\(920\) 3.32666 0.109677
\(921\) 34.5379 1.13806
\(922\) 4.00324 0.131840
\(923\) −18.1014 −0.595815
\(924\) −4.93062 −0.162205
\(925\) −6.88894 −0.226507
\(926\) 8.14567 0.267683
\(927\) 11.6762 0.383498
\(928\) −7.06139 −0.231801
\(929\) −8.25807 −0.270938 −0.135469 0.990782i \(-0.543254\pi\)
−0.135469 + 0.990782i \(0.543254\pi\)
\(930\) −11.7935 −0.386724
\(931\) 12.7475 0.417782
\(932\) −15.6360 −0.512175
\(933\) 58.3013 1.90870
\(934\) 12.1779 0.398474
\(935\) 11.7312 0.383653
\(936\) 9.47353 0.309652
\(937\) −27.7469 −0.906453 −0.453227 0.891395i \(-0.649727\pi\)
−0.453227 + 0.891395i \(0.649727\pi\)
\(938\) 4.08504 0.133381
\(939\) −21.6089 −0.705181
\(940\) −2.01855 −0.0658380
\(941\) 6.47070 0.210939 0.105469 0.994423i \(-0.466365\pi\)
0.105469 + 0.994423i \(0.466365\pi\)
\(942\) 19.9675 0.650575
\(943\) 38.0109 1.23780
\(944\) 8.51427 0.277116
\(945\) −2.18409 −0.0710485
\(946\) −11.6945 −0.380221
\(947\) 18.3903 0.597604 0.298802 0.954315i \(-0.403413\pi\)
0.298802 + 0.954315i \(0.403413\pi\)
\(948\) 33.2862 1.08109
\(949\) −64.9708 −2.10904
\(950\) −2.10519 −0.0683015
\(951\) −49.5758 −1.60761
\(952\) 5.02347 0.162811
\(953\) 26.8309 0.869137 0.434568 0.900639i \(-0.356901\pi\)
0.434568 + 0.900639i \(0.356901\pi\)
\(954\) −18.6323 −0.603244
\(955\) −23.9579 −0.775260
\(956\) −24.3679 −0.788114
\(957\) −35.8208 −1.15792
\(958\) −28.2514 −0.912762
\(959\) 8.91846 0.287992
\(960\) −2.23485 −0.0721293
\(961\) −3.15227 −0.101686
\(962\) −32.7207 −1.05496
\(963\) −6.61364 −0.213122
\(964\) 1.23492 0.0397740
\(965\) 8.02182 0.258231
\(966\) 7.22625 0.232501
\(967\) −45.4897 −1.46285 −0.731425 0.681921i \(-0.761145\pi\)
−0.731425 + 0.681921i \(0.761145\pi\)
\(968\) −5.84778 −0.187955
\(969\) −24.3157 −0.781132
\(970\) −8.88856 −0.285395
\(971\) −53.3021 −1.71055 −0.855273 0.518177i \(-0.826611\pi\)
−0.855273 + 0.518177i \(0.826611\pi\)
\(972\) 17.8543 0.572676
\(973\) −19.6220 −0.629053
\(974\) 41.3590 1.32523
\(975\) −10.6149 −0.339950
\(976\) −3.05215 −0.0976970
\(977\) −5.36889 −0.171766 −0.0858829 0.996305i \(-0.527371\pi\)
−0.0858829 + 0.996305i \(0.527371\pi\)
\(978\) −36.2152 −1.15804
\(979\) −5.09635 −0.162880
\(980\) −6.05526 −0.193428
\(981\) 37.7844 1.20636
\(982\) −18.1492 −0.579164
\(983\) −38.4174 −1.22532 −0.612662 0.790345i \(-0.709901\pi\)
−0.612662 + 0.790345i \(0.709901\pi\)
\(984\) −25.5356 −0.814045
\(985\) −21.4228 −0.682587
\(986\) 36.4953 1.16225
\(987\) −4.38475 −0.139568
\(988\) −9.99912 −0.318114
\(989\) 17.1393 0.544999
\(990\) −4.52730 −0.143887
\(991\) 38.7074 1.22958 0.614790 0.788691i \(-0.289241\pi\)
0.614790 + 0.788691i \(0.289241\pi\)
\(992\) 5.27710 0.167548
\(993\) 7.66701 0.243305
\(994\) 3.70424 0.117491
\(995\) 0.485772 0.0154000
\(996\) −25.6029 −0.811259
\(997\) 41.9316 1.32799 0.663993 0.747739i \(-0.268860\pi\)
0.663993 + 0.747739i \(0.268860\pi\)
\(998\) −18.0488 −0.571323
\(999\) −15.4798 −0.489760
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 \(a_p\))