Properties

Label 8042.2.a.a.1.1
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.09236 q^{3}\) \(+1.00000 q^{4}\) \(+1.36808 q^{5}\) \(-3.09236 q^{6}\) \(-2.10219 q^{7}\) \(+1.00000 q^{8}\) \(+6.56268 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.09236 q^{3}\) \(+1.00000 q^{4}\) \(+1.36808 q^{5}\) \(-3.09236 q^{6}\) \(-2.10219 q^{7}\) \(+1.00000 q^{8}\) \(+6.56268 q^{9}\) \(+1.36808 q^{10}\) \(+5.99202 q^{11}\) \(-3.09236 q^{12}\) \(-2.57624 q^{13}\) \(-2.10219 q^{14}\) \(-4.23058 q^{15}\) \(+1.00000 q^{16}\) \(+0.248087 q^{17}\) \(+6.56268 q^{18}\) \(+4.56321 q^{19}\) \(+1.36808 q^{20}\) \(+6.50073 q^{21}\) \(+5.99202 q^{22}\) \(-3.33361 q^{23}\) \(-3.09236 q^{24}\) \(-3.12837 q^{25}\) \(-2.57624 q^{26}\) \(-11.0171 q^{27}\) \(-2.10219 q^{28}\) \(-7.82796 q^{29}\) \(-4.23058 q^{30}\) \(-7.22741 q^{31}\) \(+1.00000 q^{32}\) \(-18.5295 q^{33}\) \(+0.248087 q^{34}\) \(-2.87596 q^{35}\) \(+6.56268 q^{36}\) \(+0.882506 q^{37}\) \(+4.56321 q^{38}\) \(+7.96665 q^{39}\) \(+1.36808 q^{40}\) \(+3.49989 q^{41}\) \(+6.50073 q^{42}\) \(-1.48430 q^{43}\) \(+5.99202 q^{44}\) \(+8.97824 q^{45}\) \(-3.33361 q^{46}\) \(+0.681955 q^{47}\) \(-3.09236 q^{48}\) \(-2.58079 q^{49}\) \(-3.12837 q^{50}\) \(-0.767174 q^{51}\) \(-2.57624 q^{52}\) \(-14.3164 q^{53}\) \(-11.0171 q^{54}\) \(+8.19753 q^{55}\) \(-2.10219 q^{56}\) \(-14.1111 q^{57}\) \(-7.82796 q^{58}\) \(+4.85974 q^{59}\) \(-4.23058 q^{60}\) \(+7.46200 q^{61}\) \(-7.22741 q^{62}\) \(-13.7960 q^{63}\) \(+1.00000 q^{64}\) \(-3.52449 q^{65}\) \(-18.5295 q^{66}\) \(-4.61731 q^{67}\) \(+0.248087 q^{68}\) \(+10.3087 q^{69}\) \(-2.87596 q^{70}\) \(+8.72880 q^{71}\) \(+6.56268 q^{72}\) \(+9.86687 q^{73}\) \(+0.882506 q^{74}\) \(+9.67404 q^{75}\) \(+4.56321 q^{76}\) \(-12.5964 q^{77}\) \(+7.96665 q^{78}\) \(-12.6367 q^{79}\) \(+1.36808 q^{80}\) \(+14.3807 q^{81}\) \(+3.49989 q^{82}\) \(-8.10500 q^{83}\) \(+6.50073 q^{84}\) \(+0.339402 q^{85}\) \(-1.48430 q^{86}\) \(+24.2068 q^{87}\) \(+5.99202 q^{88}\) \(+8.27053 q^{89}\) \(+8.97824 q^{90}\) \(+5.41574 q^{91}\) \(-3.33361 q^{92}\) \(+22.3497 q^{93}\) \(+0.681955 q^{94}\) \(+6.24282 q^{95}\) \(-3.09236 q^{96}\) \(-9.54244 q^{97}\) \(-2.58079 q^{98}\) \(+39.3237 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.09236 −1.78537 −0.892687 0.450677i \(-0.851183\pi\)
−0.892687 + 0.450677i \(0.851183\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.36808 0.611822 0.305911 0.952060i \(-0.401039\pi\)
0.305911 + 0.952060i \(0.401039\pi\)
\(6\) −3.09236 −1.26245
\(7\) −2.10219 −0.794553 −0.397277 0.917699i \(-0.630045\pi\)
−0.397277 + 0.917699i \(0.630045\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.56268 2.18756
\(10\) 1.36808 0.432623
\(11\) 5.99202 1.80666 0.903330 0.428946i \(-0.141115\pi\)
0.903330 + 0.428946i \(0.141115\pi\)
\(12\) −3.09236 −0.892687
\(13\) −2.57624 −0.714519 −0.357260 0.934005i \(-0.616289\pi\)
−0.357260 + 0.934005i \(0.616289\pi\)
\(14\) −2.10219 −0.561834
\(15\) −4.23058 −1.09233
\(16\) 1.00000 0.250000
\(17\) 0.248087 0.0601699 0.0300850 0.999547i \(-0.490422\pi\)
0.0300850 + 0.999547i \(0.490422\pi\)
\(18\) 6.56268 1.54684
\(19\) 4.56321 1.04687 0.523436 0.852065i \(-0.324650\pi\)
0.523436 + 0.852065i \(0.324650\pi\)
\(20\) 1.36808 0.305911
\(21\) 6.50073 1.41857
\(22\) 5.99202 1.27750
\(23\) −3.33361 −0.695105 −0.347553 0.937661i \(-0.612987\pi\)
−0.347553 + 0.937661i \(0.612987\pi\)
\(24\) −3.09236 −0.631225
\(25\) −3.12837 −0.625674
\(26\) −2.57624 −0.505241
\(27\) −11.0171 −2.12024
\(28\) −2.10219 −0.397277
\(29\) −7.82796 −1.45361 −0.726807 0.686841i \(-0.758997\pi\)
−0.726807 + 0.686841i \(0.758997\pi\)
\(30\) −4.23058 −0.772395
\(31\) −7.22741 −1.29808 −0.649041 0.760754i \(-0.724829\pi\)
−0.649041 + 0.760754i \(0.724829\pi\)
\(32\) 1.00000 0.176777
\(33\) −18.5295 −3.22556
\(34\) 0.248087 0.0425466
\(35\) −2.87596 −0.486125
\(36\) 6.56268 1.09378
\(37\) 0.882506 0.145083 0.0725416 0.997365i \(-0.476889\pi\)
0.0725416 + 0.997365i \(0.476889\pi\)
\(38\) 4.56321 0.740250
\(39\) 7.96665 1.27568
\(40\) 1.36808 0.216312
\(41\) 3.49989 0.546590 0.273295 0.961930i \(-0.411886\pi\)
0.273295 + 0.961930i \(0.411886\pi\)
\(42\) 6.50073 1.00308
\(43\) −1.48430 −0.226353 −0.113177 0.993575i \(-0.536103\pi\)
−0.113177 + 0.993575i \(0.536103\pi\)
\(44\) 5.99202 0.903330
\(45\) 8.97824 1.33840
\(46\) −3.33361 −0.491513
\(47\) 0.681955 0.0994734 0.0497367 0.998762i \(-0.484162\pi\)
0.0497367 + 0.998762i \(0.484162\pi\)
\(48\) −3.09236 −0.446343
\(49\) −2.58079 −0.368685
\(50\) −3.12837 −0.442418
\(51\) −0.767174 −0.107426
\(52\) −2.57624 −0.357260
\(53\) −14.3164 −1.96651 −0.983254 0.182239i \(-0.941665\pi\)
−0.983254 + 0.182239i \(0.941665\pi\)
\(54\) −11.0171 −1.49923
\(55\) 8.19753 1.10535
\(56\) −2.10219 −0.280917
\(57\) −14.1111 −1.86906
\(58\) −7.82796 −1.02786
\(59\) 4.85974 0.632685 0.316342 0.948645i \(-0.397545\pi\)
0.316342 + 0.948645i \(0.397545\pi\)
\(60\) −4.23058 −0.546165
\(61\) 7.46200 0.955411 0.477705 0.878520i \(-0.341469\pi\)
0.477705 + 0.878520i \(0.341469\pi\)
\(62\) −7.22741 −0.917882
\(63\) −13.7960 −1.73813
\(64\) 1.00000 0.125000
\(65\) −3.52449 −0.437159
\(66\) −18.5295 −2.28082
\(67\) −4.61731 −0.564094 −0.282047 0.959401i \(-0.591013\pi\)
−0.282047 + 0.959401i \(0.591013\pi\)
\(68\) 0.248087 0.0300850
\(69\) 10.3087 1.24102
\(70\) −2.87596 −0.343742
\(71\) 8.72880 1.03592 0.517959 0.855405i \(-0.326692\pi\)
0.517959 + 0.855405i \(0.326692\pi\)
\(72\) 6.56268 0.773419
\(73\) 9.86687 1.15483 0.577415 0.816451i \(-0.304062\pi\)
0.577415 + 0.816451i \(0.304062\pi\)
\(74\) 0.882506 0.102589
\(75\) 9.67404 1.11706
\(76\) 4.56321 0.523436
\(77\) −12.5964 −1.43549
\(78\) 7.96665 0.902045
\(79\) −12.6367 −1.42174 −0.710870 0.703324i \(-0.751698\pi\)
−0.710870 + 0.703324i \(0.751698\pi\)
\(80\) 1.36808 0.152955
\(81\) 14.3807 1.59786
\(82\) 3.49989 0.386498
\(83\) −8.10500 −0.889640 −0.444820 0.895620i \(-0.646732\pi\)
−0.444820 + 0.895620i \(0.646732\pi\)
\(84\) 6.50073 0.709287
\(85\) 0.339402 0.0368133
\(86\) −1.48430 −0.160056
\(87\) 24.2068 2.59525
\(88\) 5.99202 0.638751
\(89\) 8.27053 0.876675 0.438337 0.898811i \(-0.355568\pi\)
0.438337 + 0.898811i \(0.355568\pi\)
\(90\) 8.97824 0.946390
\(91\) 5.41574 0.567724
\(92\) −3.33361 −0.347553
\(93\) 22.3497 2.31756
\(94\) 0.681955 0.0703383
\(95\) 6.24282 0.640499
\(96\) −3.09236 −0.315612
\(97\) −9.54244 −0.968888 −0.484444 0.874822i \(-0.660978\pi\)
−0.484444 + 0.874822i \(0.660978\pi\)
\(98\) −2.58079 −0.260700
\(99\) 39.3237 3.95218
\(100\) −3.12837 −0.312837
\(101\) 1.23076 0.122465 0.0612327 0.998124i \(-0.480497\pi\)
0.0612327 + 0.998124i \(0.480497\pi\)
\(102\) −0.767174 −0.0759615
\(103\) −5.37778 −0.529888 −0.264944 0.964264i \(-0.585354\pi\)
−0.264944 + 0.964264i \(0.585354\pi\)
\(104\) −2.57624 −0.252621
\(105\) 8.89349 0.867915
\(106\) −14.3164 −1.39053
\(107\) 8.26019 0.798543 0.399271 0.916833i \(-0.369263\pi\)
0.399271 + 0.916833i \(0.369263\pi\)
\(108\) −11.0171 −1.06012
\(109\) −15.7223 −1.50592 −0.752960 0.658066i \(-0.771375\pi\)
−0.752960 + 0.658066i \(0.771375\pi\)
\(110\) 8.19753 0.781604
\(111\) −2.72903 −0.259028
\(112\) −2.10219 −0.198638
\(113\) 2.25758 0.212375 0.106187 0.994346i \(-0.466136\pi\)
0.106187 + 0.994346i \(0.466136\pi\)
\(114\) −14.1111 −1.32162
\(115\) −4.56063 −0.425281
\(116\) −7.82796 −0.726807
\(117\) −16.9070 −1.56305
\(118\) 4.85974 0.447376
\(119\) −0.521526 −0.0478082
\(120\) −4.23058 −0.386197
\(121\) 24.9042 2.26402
\(122\) 7.46200 0.675577
\(123\) −10.8229 −0.975868
\(124\) −7.22741 −0.649041
\(125\) −11.1202 −0.994623
\(126\) −13.7960 −1.22905
\(127\) 2.84754 0.252678 0.126339 0.991987i \(-0.459677\pi\)
0.126339 + 0.991987i \(0.459677\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.58998 0.404125
\(130\) −3.52449 −0.309118
\(131\) 11.9236 1.04177 0.520885 0.853627i \(-0.325602\pi\)
0.520885 + 0.853627i \(0.325602\pi\)
\(132\) −18.5295 −1.61278
\(133\) −9.59274 −0.831796
\(134\) −4.61731 −0.398875
\(135\) −15.0722 −1.29721
\(136\) 0.248087 0.0212733
\(137\) −2.54852 −0.217735 −0.108867 0.994056i \(-0.534722\pi\)
−0.108867 + 0.994056i \(0.534722\pi\)
\(138\) 10.3087 0.877535
\(139\) 6.71861 0.569865 0.284933 0.958548i \(-0.408029\pi\)
0.284933 + 0.958548i \(0.408029\pi\)
\(140\) −2.87596 −0.243063
\(141\) −2.10885 −0.177597
\(142\) 8.72880 0.732505
\(143\) −15.4368 −1.29089
\(144\) 6.56268 0.546890
\(145\) −10.7092 −0.889354
\(146\) 9.86687 0.816588
\(147\) 7.98074 0.658240
\(148\) 0.882506 0.0725416
\(149\) 0.229505 0.0188017 0.00940087 0.999956i \(-0.497008\pi\)
0.00940087 + 0.999956i \(0.497008\pi\)
\(150\) 9.67404 0.789882
\(151\) 16.0131 1.30312 0.651562 0.758595i \(-0.274114\pi\)
0.651562 + 0.758595i \(0.274114\pi\)
\(152\) 4.56321 0.370125
\(153\) 1.62812 0.131625
\(154\) −12.5964 −1.01504
\(155\) −9.88764 −0.794195
\(156\) 7.96665 0.637842
\(157\) −15.6839 −1.25171 −0.625856 0.779938i \(-0.715250\pi\)
−0.625856 + 0.779938i \(0.715250\pi\)
\(158\) −12.6367 −1.00532
\(159\) 44.2714 3.51095
\(160\) 1.36808 0.108156
\(161\) 7.00788 0.552298
\(162\) 14.3807 1.12986
\(163\) −9.45836 −0.740836 −0.370418 0.928865i \(-0.620786\pi\)
−0.370418 + 0.928865i \(0.620786\pi\)
\(164\) 3.49989 0.273295
\(165\) −25.3497 −1.97347
\(166\) −8.10500 −0.629070
\(167\) 7.09820 0.549275 0.274637 0.961548i \(-0.411442\pi\)
0.274637 + 0.961548i \(0.411442\pi\)
\(168\) 6.50073 0.501542
\(169\) −6.36301 −0.489462
\(170\) 0.339402 0.0260309
\(171\) 29.9469 2.29010
\(172\) −1.48430 −0.113177
\(173\) −10.4870 −0.797310 −0.398655 0.917101i \(-0.630523\pi\)
−0.398655 + 0.917101i \(0.630523\pi\)
\(174\) 24.2068 1.83512
\(175\) 6.57643 0.497131
\(176\) 5.99202 0.451665
\(177\) −15.0281 −1.12958
\(178\) 8.27053 0.619903
\(179\) −15.3884 −1.15018 −0.575091 0.818089i \(-0.695033\pi\)
−0.575091 + 0.818089i \(0.695033\pi\)
\(180\) 8.97824 0.669199
\(181\) 12.5150 0.930229 0.465115 0.885250i \(-0.346013\pi\)
0.465115 + 0.885250i \(0.346013\pi\)
\(182\) 5.41574 0.401441
\(183\) −23.0752 −1.70577
\(184\) −3.33361 −0.245757
\(185\) 1.20734 0.0887650
\(186\) 22.3497 1.63876
\(187\) 1.48654 0.108707
\(188\) 0.681955 0.0497367
\(189\) 23.1600 1.68464
\(190\) 6.24282 0.452901
\(191\) 7.68452 0.556032 0.278016 0.960576i \(-0.410323\pi\)
0.278016 + 0.960576i \(0.410323\pi\)
\(192\) −3.09236 −0.223172
\(193\) −9.27752 −0.667811 −0.333905 0.942607i \(-0.608367\pi\)
−0.333905 + 0.942607i \(0.608367\pi\)
\(194\) −9.54244 −0.685108
\(195\) 10.8990 0.780492
\(196\) −2.58079 −0.184342
\(197\) 9.06369 0.645761 0.322881 0.946440i \(-0.395349\pi\)
0.322881 + 0.946440i \(0.395349\pi\)
\(198\) 39.3237 2.79461
\(199\) −3.54355 −0.251196 −0.125598 0.992081i \(-0.540085\pi\)
−0.125598 + 0.992081i \(0.540085\pi\)
\(200\) −3.12837 −0.221209
\(201\) 14.2784 1.00712
\(202\) 1.23076 0.0865961
\(203\) 16.4559 1.15497
\(204\) −0.767174 −0.0537129
\(205\) 4.78811 0.334416
\(206\) −5.37778 −0.374688
\(207\) −21.8774 −1.52058
\(208\) −2.57624 −0.178630
\(209\) 27.3428 1.89134
\(210\) 8.89349 0.613709
\(211\) 11.1019 0.764286 0.382143 0.924103i \(-0.375186\pi\)
0.382143 + 0.924103i \(0.375186\pi\)
\(212\) −14.3164 −0.983254
\(213\) −26.9926 −1.84950
\(214\) 8.26019 0.564655
\(215\) −2.03063 −0.138488
\(216\) −11.0171 −0.749617
\(217\) 15.1934 1.03139
\(218\) −15.7223 −1.06485
\(219\) −30.5119 −2.06180
\(220\) 8.19753 0.552677
\(221\) −0.639131 −0.0429926
\(222\) −2.72903 −0.183160
\(223\) 5.88417 0.394033 0.197017 0.980400i \(-0.436875\pi\)
0.197017 + 0.980400i \(0.436875\pi\)
\(224\) −2.10219 −0.140459
\(225\) −20.5305 −1.36870
\(226\) 2.25758 0.150172
\(227\) −26.4098 −1.75288 −0.876441 0.481509i \(-0.840089\pi\)
−0.876441 + 0.481509i \(0.840089\pi\)
\(228\) −14.1111 −0.934529
\(229\) −12.5836 −0.831547 −0.415774 0.909468i \(-0.636489\pi\)
−0.415774 + 0.909468i \(0.636489\pi\)
\(230\) −4.56063 −0.300719
\(231\) 38.9525 2.56288
\(232\) −7.82796 −0.513930
\(233\) −16.5173 −1.08208 −0.541042 0.840996i \(-0.681970\pi\)
−0.541042 + 0.840996i \(0.681970\pi\)
\(234\) −16.9070 −1.10525
\(235\) 0.932966 0.0608600
\(236\) 4.85974 0.316342
\(237\) 39.0772 2.53834
\(238\) −0.521526 −0.0338055
\(239\) −20.5683 −1.33045 −0.665225 0.746643i \(-0.731665\pi\)
−0.665225 + 0.746643i \(0.731665\pi\)
\(240\) −4.23058 −0.273083
\(241\) −7.95649 −0.512523 −0.256261 0.966608i \(-0.582491\pi\)
−0.256261 + 0.966608i \(0.582491\pi\)
\(242\) 24.9042 1.60091
\(243\) −11.4191 −0.732536
\(244\) 7.46200 0.477705
\(245\) −3.53072 −0.225569
\(246\) −10.8229 −0.690043
\(247\) −11.7559 −0.748010
\(248\) −7.22741 −0.458941
\(249\) 25.0636 1.58834
\(250\) −11.1202 −0.703305
\(251\) −25.3474 −1.59991 −0.799957 0.600057i \(-0.795145\pi\)
−0.799957 + 0.600057i \(0.795145\pi\)
\(252\) −13.7960 −0.869067
\(253\) −19.9750 −1.25582
\(254\) 2.84754 0.178671
\(255\) −1.04955 −0.0657255
\(256\) 1.00000 0.0625000
\(257\) −26.2281 −1.63606 −0.818031 0.575174i \(-0.804935\pi\)
−0.818031 + 0.575174i \(0.804935\pi\)
\(258\) 4.58998 0.285760
\(259\) −1.85520 −0.115276
\(260\) −3.52449 −0.218579
\(261\) −51.3724 −3.17987
\(262\) 11.9236 0.736642
\(263\) 31.8182 1.96199 0.980997 0.194025i \(-0.0621543\pi\)
0.980997 + 0.194025i \(0.0621543\pi\)
\(264\) −18.5295 −1.14041
\(265\) −19.5859 −1.20315
\(266\) −9.59274 −0.588169
\(267\) −25.5754 −1.56519
\(268\) −4.61731 −0.282047
\(269\) −32.2727 −1.96770 −0.983852 0.178986i \(-0.942718\pi\)
−0.983852 + 0.178986i \(0.942718\pi\)
\(270\) −15.0722 −0.917265
\(271\) −7.56067 −0.459278 −0.229639 0.973276i \(-0.573755\pi\)
−0.229639 + 0.973276i \(0.573755\pi\)
\(272\) 0.248087 0.0150425
\(273\) −16.7474 −1.01360
\(274\) −2.54852 −0.153962
\(275\) −18.7452 −1.13038
\(276\) 10.3087 0.620511
\(277\) −2.99103 −0.179713 −0.0898567 0.995955i \(-0.528641\pi\)
−0.0898567 + 0.995955i \(0.528641\pi\)
\(278\) 6.71861 0.402956
\(279\) −47.4312 −2.83963
\(280\) −2.87596 −0.171871
\(281\) −16.1628 −0.964193 −0.482097 0.876118i \(-0.660125\pi\)
−0.482097 + 0.876118i \(0.660125\pi\)
\(282\) −2.10885 −0.125580
\(283\) 16.2054 0.963308 0.481654 0.876361i \(-0.340036\pi\)
0.481654 + 0.876361i \(0.340036\pi\)
\(284\) 8.72880 0.517959
\(285\) −19.3050 −1.14353
\(286\) −15.4368 −0.912800
\(287\) −7.35743 −0.434295
\(288\) 6.56268 0.386710
\(289\) −16.9385 −0.996380
\(290\) −10.7092 −0.628868
\(291\) 29.5087 1.72983
\(292\) 9.86687 0.577415
\(293\) 4.28849 0.250536 0.125268 0.992123i \(-0.460021\pi\)
0.125268 + 0.992123i \(0.460021\pi\)
\(294\) 7.98074 0.465446
\(295\) 6.64850 0.387090
\(296\) 0.882506 0.0512946
\(297\) −66.0145 −3.83055
\(298\) 0.229505 0.0132948
\(299\) 8.58816 0.496666
\(300\) 9.67404 0.558531
\(301\) 3.12028 0.179850
\(302\) 16.0131 0.921448
\(303\) −3.80596 −0.218646
\(304\) 4.56321 0.261718
\(305\) 10.2086 0.584541
\(306\) 1.62812 0.0930732
\(307\) 4.34903 0.248212 0.124106 0.992269i \(-0.460394\pi\)
0.124106 + 0.992269i \(0.460394\pi\)
\(308\) −12.5964 −0.717744
\(309\) 16.6300 0.946049
\(310\) −9.88764 −0.561580
\(311\) −8.43326 −0.478206 −0.239103 0.970994i \(-0.576853\pi\)
−0.239103 + 0.970994i \(0.576853\pi\)
\(312\) 7.96665 0.451022
\(313\) −21.6656 −1.22461 −0.612307 0.790620i \(-0.709758\pi\)
−0.612307 + 0.790620i \(0.709758\pi\)
\(314\) −15.6839 −0.885095
\(315\) −18.8740 −1.06343
\(316\) −12.6367 −0.710870
\(317\) −27.3935 −1.53857 −0.769286 0.638905i \(-0.779388\pi\)
−0.769286 + 0.638905i \(0.779388\pi\)
\(318\) 44.2714 2.48262
\(319\) −46.9052 −2.62619
\(320\) 1.36808 0.0764777
\(321\) −25.5435 −1.42570
\(322\) 7.00788 0.390534
\(323\) 1.13207 0.0629902
\(324\) 14.3807 0.798929
\(325\) 8.05942 0.447056
\(326\) −9.45836 −0.523850
\(327\) 48.6189 2.68863
\(328\) 3.49989 0.193249
\(329\) −1.43360 −0.0790369
\(330\) −25.3497 −1.39546
\(331\) 21.1062 1.16010 0.580050 0.814581i \(-0.303033\pi\)
0.580050 + 0.814581i \(0.303033\pi\)
\(332\) −8.10500 −0.444820
\(333\) 5.79161 0.317378
\(334\) 7.09820 0.388396
\(335\) −6.31683 −0.345125
\(336\) 6.50073 0.354644
\(337\) 14.7214 0.801924 0.400962 0.916095i \(-0.368676\pi\)
0.400962 + 0.916095i \(0.368676\pi\)
\(338\) −6.36301 −0.346102
\(339\) −6.98123 −0.379168
\(340\) 0.339402 0.0184066
\(341\) −43.3068 −2.34519
\(342\) 29.9469 1.61934
\(343\) 20.1407 1.08749
\(344\) −1.48430 −0.0800279
\(345\) 14.1031 0.759285
\(346\) −10.4870 −0.563784
\(347\) −10.2337 −0.549373 −0.274687 0.961534i \(-0.588574\pi\)
−0.274687 + 0.961534i \(0.588574\pi\)
\(348\) 24.2068 1.29762
\(349\) 24.1958 1.29517 0.647585 0.761993i \(-0.275779\pi\)
0.647585 + 0.761993i \(0.275779\pi\)
\(350\) 6.57643 0.351525
\(351\) 28.3826 1.51495
\(352\) 5.99202 0.319375
\(353\) 22.2544 1.18448 0.592241 0.805761i \(-0.298243\pi\)
0.592241 + 0.805761i \(0.298243\pi\)
\(354\) −15.0281 −0.798733
\(355\) 11.9417 0.633798
\(356\) 8.27053 0.438337
\(357\) 1.61275 0.0853556
\(358\) −15.3884 −0.813302
\(359\) 2.15262 0.113611 0.0568055 0.998385i \(-0.481909\pi\)
0.0568055 + 0.998385i \(0.481909\pi\)
\(360\) 8.97824 0.473195
\(361\) 1.82289 0.0959414
\(362\) 12.5150 0.657771
\(363\) −77.0129 −4.04213
\(364\) 5.41574 0.283862
\(365\) 13.4986 0.706550
\(366\) −23.0752 −1.20616
\(367\) 2.92078 0.152464 0.0762318 0.997090i \(-0.475711\pi\)
0.0762318 + 0.997090i \(0.475711\pi\)
\(368\) −3.33361 −0.173776
\(369\) 22.9686 1.19570
\(370\) 1.20734 0.0627664
\(371\) 30.0958 1.56250
\(372\) 22.3497 1.15878
\(373\) 27.6528 1.43181 0.715905 0.698198i \(-0.246014\pi\)
0.715905 + 0.698198i \(0.246014\pi\)
\(374\) 1.48654 0.0768672
\(375\) 34.3877 1.77577
\(376\) 0.681955 0.0351692
\(377\) 20.1667 1.03864
\(378\) 23.1600 1.19122
\(379\) −18.4122 −0.945773 −0.472887 0.881123i \(-0.656788\pi\)
−0.472887 + 0.881123i \(0.656788\pi\)
\(380\) 6.24282 0.320250
\(381\) −8.80562 −0.451125
\(382\) 7.68452 0.393174
\(383\) 14.0045 0.715599 0.357799 0.933798i \(-0.383527\pi\)
0.357799 + 0.933798i \(0.383527\pi\)
\(384\) −3.09236 −0.157806
\(385\) −17.2328 −0.878263
\(386\) −9.27752 −0.472213
\(387\) −9.74096 −0.495161
\(388\) −9.54244 −0.484444
\(389\) −10.4227 −0.528451 −0.264225 0.964461i \(-0.585116\pi\)
−0.264225 + 0.964461i \(0.585116\pi\)
\(390\) 10.8990 0.551891
\(391\) −0.827025 −0.0418244
\(392\) −2.58079 −0.130350
\(393\) −36.8720 −1.85995
\(394\) 9.06369 0.456622
\(395\) −17.2880 −0.869851
\(396\) 39.3237 1.97609
\(397\) 6.26976 0.314670 0.157335 0.987545i \(-0.449710\pi\)
0.157335 + 0.987545i \(0.449710\pi\)
\(398\) −3.54355 −0.177622
\(399\) 29.6642 1.48507
\(400\) −3.12837 −0.156418
\(401\) −24.2227 −1.20962 −0.604811 0.796369i \(-0.706751\pi\)
−0.604811 + 0.796369i \(0.706751\pi\)
\(402\) 14.2784 0.712141
\(403\) 18.6195 0.927504
\(404\) 1.23076 0.0612327
\(405\) 19.6739 0.977605
\(406\) 16.4559 0.816690
\(407\) 5.28799 0.262116
\(408\) −0.767174 −0.0379808
\(409\) 3.27243 0.161811 0.0809056 0.996722i \(-0.474219\pi\)
0.0809056 + 0.996722i \(0.474219\pi\)
\(410\) 4.78811 0.236468
\(411\) 7.88093 0.388738
\(412\) −5.37778 −0.264944
\(413\) −10.2161 −0.502702
\(414\) −21.8774 −1.07522
\(415\) −11.0883 −0.544301
\(416\) −2.57624 −0.126310
\(417\) −20.7764 −1.01742
\(418\) 27.3428 1.33738
\(419\) 28.7923 1.40659 0.703297 0.710896i \(-0.251710\pi\)
0.703297 + 0.710896i \(0.251710\pi\)
\(420\) 8.89349 0.433958
\(421\) −5.08828 −0.247988 −0.123994 0.992283i \(-0.539570\pi\)
−0.123994 + 0.992283i \(0.539570\pi\)
\(422\) 11.1019 0.540432
\(423\) 4.47545 0.217604
\(424\) −14.3164 −0.695266
\(425\) −0.776108 −0.0376468
\(426\) −26.9926 −1.30780
\(427\) −15.6865 −0.759125
\(428\) 8.26019 0.399271
\(429\) 47.7363 2.30473
\(430\) −2.03063 −0.0979257
\(431\) 18.1842 0.875904 0.437952 0.898998i \(-0.355704\pi\)
0.437952 + 0.898998i \(0.355704\pi\)
\(432\) −11.0171 −0.530060
\(433\) 20.9723 1.00787 0.503933 0.863743i \(-0.331886\pi\)
0.503933 + 0.863743i \(0.331886\pi\)
\(434\) 15.1934 0.729306
\(435\) 33.1168 1.58783
\(436\) −15.7223 −0.752960
\(437\) −15.2119 −0.727686
\(438\) −30.5119 −1.45791
\(439\) 15.1799 0.724499 0.362250 0.932081i \(-0.382009\pi\)
0.362250 + 0.932081i \(0.382009\pi\)
\(440\) 8.19753 0.390802
\(441\) −16.9369 −0.806520
\(442\) −0.639131 −0.0304004
\(443\) −20.6263 −0.979987 −0.489993 0.871726i \(-0.663001\pi\)
−0.489993 + 0.871726i \(0.663001\pi\)
\(444\) −2.72903 −0.129514
\(445\) 11.3147 0.536369
\(446\) 5.88417 0.278624
\(447\) −0.709710 −0.0335681
\(448\) −2.10219 −0.0993192
\(449\) −27.8874 −1.31609 −0.658045 0.752979i \(-0.728616\pi\)
−0.658045 + 0.752979i \(0.728616\pi\)
\(450\) −20.5305 −0.967816
\(451\) 20.9714 0.987503
\(452\) 2.25758 0.106187
\(453\) −49.5181 −2.32656
\(454\) −26.4098 −1.23948
\(455\) 7.40914 0.347346
\(456\) −14.1111 −0.660812
\(457\) 12.6366 0.591116 0.295558 0.955325i \(-0.404494\pi\)
0.295558 + 0.955325i \(0.404494\pi\)
\(458\) −12.5836 −0.587993
\(459\) −2.73320 −0.127575
\(460\) −4.56063 −0.212640
\(461\) 3.60201 0.167763 0.0838813 0.996476i \(-0.473268\pi\)
0.0838813 + 0.996476i \(0.473268\pi\)
\(462\) 38.9525 1.81223
\(463\) 10.6340 0.494204 0.247102 0.968989i \(-0.420522\pi\)
0.247102 + 0.968989i \(0.420522\pi\)
\(464\) −7.82796 −0.363404
\(465\) 30.5761 1.41793
\(466\) −16.5173 −0.765148
\(467\) −21.5758 −0.998410 −0.499205 0.866484i \(-0.666375\pi\)
−0.499205 + 0.866484i \(0.666375\pi\)
\(468\) −16.9070 −0.781527
\(469\) 9.70647 0.448203
\(470\) 0.932966 0.0430345
\(471\) 48.5003 2.23478
\(472\) 4.85974 0.223688
\(473\) −8.89393 −0.408943
\(474\) 39.0772 1.79487
\(475\) −14.2754 −0.655001
\(476\) −0.521526 −0.0239041
\(477\) −93.9539 −4.30185
\(478\) −20.5683 −0.940771
\(479\) 8.95356 0.409099 0.204549 0.978856i \(-0.434427\pi\)
0.204549 + 0.978856i \(0.434427\pi\)
\(480\) −4.23058 −0.193099
\(481\) −2.27354 −0.103665
\(482\) −7.95649 −0.362408
\(483\) −21.6709 −0.986059
\(484\) 24.9042 1.13201
\(485\) −13.0548 −0.592787
\(486\) −11.4191 −0.517981
\(487\) −24.7815 −1.12296 −0.561479 0.827491i \(-0.689767\pi\)
−0.561479 + 0.827491i \(0.689767\pi\)
\(488\) 7.46200 0.337789
\(489\) 29.2486 1.32267
\(490\) −3.53072 −0.159502
\(491\) 40.2848 1.81803 0.909015 0.416764i \(-0.136836\pi\)
0.909015 + 0.416764i \(0.136836\pi\)
\(492\) −10.8229 −0.487934
\(493\) −1.94201 −0.0874639
\(494\) −11.7559 −0.528923
\(495\) 53.7978 2.41803
\(496\) −7.22741 −0.324520
\(497\) −18.3496 −0.823093
\(498\) 25.0636 1.12313
\(499\) −30.8820 −1.38247 −0.691234 0.722631i \(-0.742933\pi\)
−0.691234 + 0.722631i \(0.742933\pi\)
\(500\) −11.1202 −0.497312
\(501\) −21.9502 −0.980661
\(502\) −25.3474 −1.13131
\(503\) 42.2660 1.88455 0.942273 0.334846i \(-0.108684\pi\)
0.942273 + 0.334846i \(0.108684\pi\)
\(504\) −13.7960 −0.614523
\(505\) 1.68377 0.0749270
\(506\) −19.9750 −0.887998
\(507\) 19.6767 0.873873
\(508\) 2.84754 0.126339
\(509\) −18.9976 −0.842055 −0.421028 0.907048i \(-0.638331\pi\)
−0.421028 + 0.907048i \(0.638331\pi\)
\(510\) −1.04955 −0.0464749
\(511\) −20.7420 −0.917574
\(512\) 1.00000 0.0441942
\(513\) −50.2733 −2.21962
\(514\) −26.2281 −1.15687
\(515\) −7.35721 −0.324197
\(516\) 4.58998 0.202062
\(517\) 4.08629 0.179715
\(518\) −1.85520 −0.0815126
\(519\) 32.4295 1.42350
\(520\) −3.52449 −0.154559
\(521\) −5.64189 −0.247176 −0.123588 0.992334i \(-0.539440\pi\)
−0.123588 + 0.992334i \(0.539440\pi\)
\(522\) −51.3724 −2.24851
\(523\) −1.70483 −0.0745471 −0.0372736 0.999305i \(-0.511867\pi\)
−0.0372736 + 0.999305i \(0.511867\pi\)
\(524\) 11.9236 0.520885
\(525\) −20.3367 −0.887565
\(526\) 31.8182 1.38734
\(527\) −1.79303 −0.0781055
\(528\) −18.5295 −0.806391
\(529\) −11.8871 −0.516829
\(530\) −19.5859 −0.850758
\(531\) 31.8929 1.38404
\(532\) −9.59274 −0.415898
\(533\) −9.01653 −0.390549
\(534\) −25.5754 −1.10676
\(535\) 11.3006 0.488566
\(536\) −4.61731 −0.199437
\(537\) 47.5864 2.05351
\(538\) −32.2727 −1.39138
\(539\) −15.4642 −0.666088
\(540\) −15.0722 −0.648604
\(541\) −7.76184 −0.333707 −0.166854 0.985982i \(-0.553361\pi\)
−0.166854 + 0.985982i \(0.553361\pi\)
\(542\) −7.56067 −0.324759
\(543\) −38.7007 −1.66081
\(544\) 0.248087 0.0106366
\(545\) −21.5093 −0.921356
\(546\) −16.7474 −0.716723
\(547\) 32.8392 1.40410 0.702050 0.712127i \(-0.252268\pi\)
0.702050 + 0.712127i \(0.252268\pi\)
\(548\) −2.54852 −0.108867
\(549\) 48.9707 2.09002
\(550\) −18.7452 −0.799300
\(551\) −35.7206 −1.52175
\(552\) 10.3087 0.438768
\(553\) 26.5647 1.12965
\(554\) −2.99103 −0.127077
\(555\) −3.73351 −0.158479
\(556\) 6.71861 0.284933
\(557\) −43.0435 −1.82381 −0.911906 0.410400i \(-0.865389\pi\)
−0.911906 + 0.410400i \(0.865389\pi\)
\(558\) −47.4312 −2.00792
\(559\) 3.82390 0.161734
\(560\) −2.87596 −0.121531
\(561\) −4.59692 −0.194082
\(562\) −16.1628 −0.681788
\(563\) −34.8590 −1.46913 −0.734565 0.678538i \(-0.762614\pi\)
−0.734565 + 0.678538i \(0.762614\pi\)
\(564\) −2.10885 −0.0887986
\(565\) 3.08853 0.129936
\(566\) 16.2054 0.681162
\(567\) −30.2310 −1.26958
\(568\) 8.72880 0.366252
\(569\) −10.8582 −0.455199 −0.227599 0.973755i \(-0.573088\pi\)
−0.227599 + 0.973755i \(0.573088\pi\)
\(570\) −19.3050 −0.808598
\(571\) −27.9029 −1.16770 −0.583850 0.811862i \(-0.698454\pi\)
−0.583850 + 0.811862i \(0.698454\pi\)
\(572\) −15.4368 −0.645447
\(573\) −23.7633 −0.992725
\(574\) −7.35743 −0.307093
\(575\) 10.4288 0.434909
\(576\) 6.56268 0.273445
\(577\) −37.9808 −1.58116 −0.790581 0.612357i \(-0.790221\pi\)
−0.790581 + 0.612357i \(0.790221\pi\)
\(578\) −16.9385 −0.704547
\(579\) 28.6894 1.19229
\(580\) −10.7092 −0.444677
\(581\) 17.0383 0.706866
\(582\) 29.5087 1.22317
\(583\) −85.7841 −3.55281
\(584\) 9.86687 0.408294
\(585\) −23.1301 −0.956311
\(586\) 4.28849 0.177156
\(587\) 42.7518 1.76456 0.882278 0.470728i \(-0.156009\pi\)
0.882278 + 0.470728i \(0.156009\pi\)
\(588\) 7.98074 0.329120
\(589\) −32.9802 −1.35893
\(590\) 6.64850 0.273714
\(591\) −28.0282 −1.15292
\(592\) 0.882506 0.0362708
\(593\) −10.7785 −0.442621 −0.221311 0.975203i \(-0.571033\pi\)
−0.221311 + 0.975203i \(0.571033\pi\)
\(594\) −66.0145 −2.70861
\(595\) −0.713487 −0.0292501
\(596\) 0.229505 0.00940087
\(597\) 10.9579 0.448478
\(598\) 8.58816 0.351196
\(599\) −47.2491 −1.93055 −0.965273 0.261242i \(-0.915868\pi\)
−0.965273 + 0.261242i \(0.915868\pi\)
\(600\) 9.67404 0.394941
\(601\) 31.3870 1.28030 0.640151 0.768249i \(-0.278872\pi\)
0.640151 + 0.768249i \(0.278872\pi\)
\(602\) 3.12028 0.127173
\(603\) −30.3019 −1.23399
\(604\) 16.0131 0.651562
\(605\) 34.0709 1.38518
\(606\) −3.80596 −0.154606
\(607\) −41.1417 −1.66989 −0.834946 0.550332i \(-0.814501\pi\)
−0.834946 + 0.550332i \(0.814501\pi\)
\(608\) 4.56321 0.185063
\(609\) −50.8874 −2.06206
\(610\) 10.2086 0.413333
\(611\) −1.75688 −0.0710757
\(612\) 1.62812 0.0658127
\(613\) 0.386544 0.0156124 0.00780619 0.999970i \(-0.497515\pi\)
0.00780619 + 0.999970i \(0.497515\pi\)
\(614\) 4.34903 0.175512
\(615\) −14.8065 −0.597057
\(616\) −12.5964 −0.507522
\(617\) −20.9657 −0.844047 −0.422023 0.906585i \(-0.638680\pi\)
−0.422023 + 0.906585i \(0.638680\pi\)
\(618\) 16.6300 0.668957
\(619\) 19.0616 0.766150 0.383075 0.923717i \(-0.374865\pi\)
0.383075 + 0.923717i \(0.374865\pi\)
\(620\) −9.88764 −0.397097
\(621\) 36.7266 1.47379
\(622\) −8.43326 −0.338143
\(623\) −17.3862 −0.696565
\(624\) 7.96665 0.318921
\(625\) 0.428541 0.0171416
\(626\) −21.6656 −0.865933
\(627\) −84.5538 −3.37675
\(628\) −15.6839 −0.625856
\(629\) 0.218938 0.00872964
\(630\) −18.8740 −0.751957
\(631\) 17.3131 0.689223 0.344611 0.938745i \(-0.388011\pi\)
0.344611 + 0.938745i \(0.388011\pi\)
\(632\) −12.6367 −0.502661
\(633\) −34.3310 −1.36454
\(634\) −27.3935 −1.08793
\(635\) 3.89565 0.154594
\(636\) 44.2714 1.75548
\(637\) 6.64873 0.263432
\(638\) −46.9052 −1.85700
\(639\) 57.2843 2.26613
\(640\) 1.36808 0.0540779
\(641\) −19.1137 −0.754945 −0.377472 0.926021i \(-0.623207\pi\)
−0.377472 + 0.926021i \(0.623207\pi\)
\(642\) −25.5435 −1.00812
\(643\) 33.9579 1.33917 0.669584 0.742737i \(-0.266473\pi\)
0.669584 + 0.742737i \(0.266473\pi\)
\(644\) 7.00788 0.276149
\(645\) 6.27944 0.247253
\(646\) 1.13207 0.0445408
\(647\) −21.4306 −0.842525 −0.421262 0.906939i \(-0.638413\pi\)
−0.421262 + 0.906939i \(0.638413\pi\)
\(648\) 14.3807 0.564928
\(649\) 29.1197 1.14305
\(650\) 8.05942 0.316116
\(651\) −46.9834 −1.84143
\(652\) −9.45836 −0.370418
\(653\) 2.87892 0.112661 0.0563303 0.998412i \(-0.482060\pi\)
0.0563303 + 0.998412i \(0.482060\pi\)
\(654\) 48.6189 1.90115
\(655\) 16.3124 0.637377
\(656\) 3.49989 0.136648
\(657\) 64.7531 2.52626
\(658\) −1.43360 −0.0558876
\(659\) 23.5376 0.916895 0.458447 0.888722i \(-0.348406\pi\)
0.458447 + 0.888722i \(0.348406\pi\)
\(660\) −25.3497 −0.986736
\(661\) −35.8626 −1.39489 −0.697447 0.716636i \(-0.745681\pi\)
−0.697447 + 0.716636i \(0.745681\pi\)
\(662\) 21.1062 0.820314
\(663\) 1.97642 0.0767578
\(664\) −8.10500 −0.314535
\(665\) −13.1236 −0.508911
\(666\) 5.79161 0.224420
\(667\) 26.0953 1.01042
\(668\) 7.09820 0.274637
\(669\) −18.1960 −0.703497
\(670\) −6.31683 −0.244040
\(671\) 44.7124 1.72610
\(672\) 6.50073 0.250771
\(673\) 24.9358 0.961204 0.480602 0.876939i \(-0.340418\pi\)
0.480602 + 0.876939i \(0.340418\pi\)
\(674\) 14.7214 0.567046
\(675\) 34.4655 1.32658
\(676\) −6.36301 −0.244731
\(677\) −0.296017 −0.0113768 −0.00568842 0.999984i \(-0.501811\pi\)
−0.00568842 + 0.999984i \(0.501811\pi\)
\(678\) −6.98123 −0.268113
\(679\) 20.0600 0.769834
\(680\) 0.339402 0.0130155
\(681\) 81.6687 3.12955
\(682\) −43.3068 −1.65830
\(683\) −44.6867 −1.70989 −0.854945 0.518719i \(-0.826409\pi\)
−0.854945 + 0.518719i \(0.826409\pi\)
\(684\) 29.9469 1.14505
\(685\) −3.48657 −0.133215
\(686\) 20.1407 0.768974
\(687\) 38.9130 1.48462
\(688\) −1.48430 −0.0565883
\(689\) 36.8824 1.40511
\(690\) 14.1031 0.536895
\(691\) −31.9717 −1.21626 −0.608130 0.793838i \(-0.708080\pi\)
−0.608130 + 0.793838i \(0.708080\pi\)
\(692\) −10.4870 −0.398655
\(693\) −82.6659 −3.14022
\(694\) −10.2337 −0.388466
\(695\) 9.19157 0.348656
\(696\) 24.2068 0.917558
\(697\) 0.868276 0.0328883
\(698\) 24.1958 0.915823
\(699\) 51.0774 1.93192
\(700\) 6.57643 0.248566
\(701\) −14.8299 −0.560117 −0.280058 0.959983i \(-0.590354\pi\)
−0.280058 + 0.959983i \(0.590354\pi\)
\(702\) 28.3826 1.07123
\(703\) 4.02706 0.151883
\(704\) 5.99202 0.225833
\(705\) −2.88507 −0.108658
\(706\) 22.2544 0.837556
\(707\) −2.58730 −0.0973053
\(708\) −15.0281 −0.564789
\(709\) −12.5701 −0.472080 −0.236040 0.971743i \(-0.575850\pi\)
−0.236040 + 0.971743i \(0.575850\pi\)
\(710\) 11.9417 0.448163
\(711\) −82.9306 −3.11014
\(712\) 8.27053 0.309951
\(713\) 24.0933 0.902303
\(714\) 1.61275 0.0603555
\(715\) −21.1188 −0.789797
\(716\) −15.3884 −0.575091
\(717\) 63.6045 2.37535
\(718\) 2.15262 0.0803351
\(719\) −8.29338 −0.309291 −0.154646 0.987970i \(-0.549424\pi\)
−0.154646 + 0.987970i \(0.549424\pi\)
\(720\) 8.97824 0.334599
\(721\) 11.3051 0.421025
\(722\) 1.82289 0.0678408
\(723\) 24.6043 0.915045
\(724\) 12.5150 0.465115
\(725\) 24.4887 0.909489
\(726\) −77.0129 −2.85822
\(727\) −10.0388 −0.372320 −0.186160 0.982519i \(-0.559604\pi\)
−0.186160 + 0.982519i \(0.559604\pi\)
\(728\) 5.41574 0.200721
\(729\) −7.83020 −0.290007
\(730\) 13.4986 0.499606
\(731\) −0.368235 −0.0136197
\(732\) −23.0752 −0.852883
\(733\) 46.1604 1.70497 0.852487 0.522749i \(-0.175093\pi\)
0.852487 + 0.522749i \(0.175093\pi\)
\(734\) 2.92078 0.107808
\(735\) 10.9183 0.402726
\(736\) −3.33361 −0.122878
\(737\) −27.6670 −1.01913
\(738\) 22.9686 0.845487
\(739\) −27.2521 −1.00249 −0.501243 0.865307i \(-0.667124\pi\)
−0.501243 + 0.865307i \(0.667124\pi\)
\(740\) 1.20734 0.0443825
\(741\) 36.3535 1.33548
\(742\) 30.0958 1.10485
\(743\) −15.0504 −0.552145 −0.276072 0.961137i \(-0.589033\pi\)
−0.276072 + 0.961137i \(0.589033\pi\)
\(744\) 22.3497 0.819381
\(745\) 0.313980 0.0115033
\(746\) 27.6528 1.01244
\(747\) −53.1905 −1.94614
\(748\) 1.48654 0.0543533
\(749\) −17.3645 −0.634485
\(750\) 34.3877 1.25566
\(751\) −40.6259 −1.48246 −0.741231 0.671250i \(-0.765758\pi\)
−0.741231 + 0.671250i \(0.765758\pi\)
\(752\) 0.681955 0.0248684
\(753\) 78.3833 2.85645
\(754\) 20.1667 0.734427
\(755\) 21.9071 0.797280
\(756\) 23.1600 0.842321
\(757\) 7.67309 0.278883 0.139442 0.990230i \(-0.455469\pi\)
0.139442 + 0.990230i \(0.455469\pi\)
\(758\) −18.4122 −0.668763
\(759\) 61.7699 2.24211
\(760\) 6.24282 0.226451
\(761\) −39.6990 −1.43909 −0.719544 0.694447i \(-0.755649\pi\)
−0.719544 + 0.694447i \(0.755649\pi\)
\(762\) −8.80562 −0.318994
\(763\) 33.0512 1.19653
\(764\) 7.68452 0.278016
\(765\) 2.22739 0.0805313
\(766\) 14.0045 0.506005
\(767\) −12.5198 −0.452065
\(768\) −3.09236 −0.111586
\(769\) 6.99626 0.252292 0.126146 0.992012i \(-0.459739\pi\)
0.126146 + 0.992012i \(0.459739\pi\)
\(770\) −17.2328 −0.621026
\(771\) 81.1066 2.92098
\(772\) −9.27752 −0.333905
\(773\) 4.14296 0.149012 0.0745060 0.997221i \(-0.476262\pi\)
0.0745060 + 0.997221i \(0.476262\pi\)
\(774\) −9.74096 −0.350132
\(775\) 22.6100 0.812175
\(776\) −9.54244 −0.342554
\(777\) 5.73693 0.205811
\(778\) −10.4227 −0.373671
\(779\) 15.9707 0.572210
\(780\) 10.8990 0.390246
\(781\) 52.3031 1.87155
\(782\) −0.827025 −0.0295743
\(783\) 86.2412 3.08201
\(784\) −2.58079 −0.0921712
\(785\) −21.4568 −0.765825
\(786\) −36.8720 −1.31518
\(787\) 19.6426 0.700184 0.350092 0.936715i \(-0.386150\pi\)
0.350092 + 0.936715i \(0.386150\pi\)
\(788\) 9.06369 0.322881
\(789\) −98.3932 −3.50289
\(790\) −17.2880 −0.615078
\(791\) −4.74585 −0.168743
\(792\) 39.3237 1.39731
\(793\) −19.2239 −0.682659
\(794\) 6.26976 0.222505
\(795\) 60.5667 2.14808
\(796\) −3.54355 −0.125598
\(797\) −2.52181 −0.0893270 −0.0446635 0.999002i \(-0.514222\pi\)
−0.0446635 + 0.999002i \(0.514222\pi\)
\(798\) 29.6642 1.05010
\(799\) 0.169184 0.00598531
\(800\) −3.12837 −0.110605
\(801\) 54.2769 1.91778
\(802\) −24.2227 −0.855332
\(803\) 59.1224 2.08639
\(804\) 14.2784 0.503560
\(805\) 9.58731 0.337908
\(806\) 18.6195 0.655844
\(807\) 99.7988 3.51309
\(808\) 1.23076 0.0432980
\(809\) −15.9519 −0.560840 −0.280420 0.959877i \(-0.590474\pi\)
−0.280420 + 0.959877i \(0.590474\pi\)
\(810\) 19.6739 0.691271
\(811\) 18.2700 0.641547 0.320773 0.947156i \(-0.396057\pi\)
0.320773 + 0.947156i \(0.396057\pi\)
\(812\) 16.4559 0.577487
\(813\) 23.3803 0.819983
\(814\) 5.28799 0.185344
\(815\) −12.9398 −0.453260
\(816\) −0.767174 −0.0268565
\(817\) −6.77316 −0.236963
\(818\) 3.27243 0.114418
\(819\) 35.5418 1.24193
\(820\) 4.78811 0.167208
\(821\) −18.3530 −0.640524 −0.320262 0.947329i \(-0.603771\pi\)
−0.320262 + 0.947329i \(0.603771\pi\)
\(822\) 7.88093 0.274879
\(823\) 33.8367 1.17947 0.589737 0.807595i \(-0.299231\pi\)
0.589737 + 0.807595i \(0.299231\pi\)
\(824\) −5.37778 −0.187344
\(825\) 57.9670 2.01815
\(826\) −10.2161 −0.355464
\(827\) −27.1835 −0.945264 −0.472632 0.881260i \(-0.656696\pi\)
−0.472632 + 0.881260i \(0.656696\pi\)
\(828\) −21.8774 −0.760292
\(829\) 33.5296 1.16453 0.582265 0.812999i \(-0.302167\pi\)
0.582265 + 0.812999i \(0.302167\pi\)
\(830\) −11.0883 −0.384879
\(831\) 9.24932 0.320856
\(832\) −2.57624 −0.0893149
\(833\) −0.640261 −0.0221837
\(834\) −20.7764 −0.719427
\(835\) 9.71087 0.336059
\(836\) 27.3428 0.945671
\(837\) 79.6250 2.75224
\(838\) 28.7923 0.994613
\(839\) −42.7615 −1.47629 −0.738145 0.674642i \(-0.764298\pi\)
−0.738145 + 0.674642i \(0.764298\pi\)
\(840\) 8.89349 0.306854
\(841\) 32.2769 1.11300
\(842\) −5.08828 −0.175354
\(843\) 49.9812 1.72145
\(844\) 11.1019 0.382143
\(845\) −8.70507 −0.299464
\(846\) 4.47545 0.153869
\(847\) −52.3535 −1.79889
\(848\) −14.3164 −0.491627
\(849\) −50.1128 −1.71987
\(850\) −0.776108 −0.0266203
\(851\) −2.94193 −0.100848
\(852\) −26.9926 −0.924751
\(853\) −27.6935 −0.948207 −0.474103 0.880469i \(-0.657228\pi\)
−0.474103 + 0.880469i \(0.657228\pi\)
\(854\) −15.6865 −0.536782
\(855\) 40.9696 1.40113
\(856\) 8.26019 0.282327
\(857\) 5.76561 0.196950 0.0984748 0.995140i \(-0.468604\pi\)
0.0984748 + 0.995140i \(0.468604\pi\)
\(858\) 47.7363 1.62969
\(859\) 16.0286 0.546889 0.273445 0.961888i \(-0.411837\pi\)
0.273445 + 0.961888i \(0.411837\pi\)
\(860\) −2.03063 −0.0692439
\(861\) 22.7518 0.775379
\(862\) 18.1842 0.619357
\(863\) 4.15194 0.141334 0.0706668 0.997500i \(-0.477487\pi\)
0.0706668 + 0.997500i \(0.477487\pi\)
\(864\) −11.0171 −0.374809
\(865\) −14.3470 −0.487812
\(866\) 20.9723 0.712669
\(867\) 52.3798 1.77891
\(868\) 15.1934 0.515697
\(869\) −75.7193 −2.56860
\(870\) 33.1168 1.12276
\(871\) 11.8953 0.403056
\(872\) −15.7223 −0.532423
\(873\) −62.6240 −2.11950
\(874\) −15.2119 −0.514552
\(875\) 23.3768 0.790281
\(876\) −30.5119 −1.03090
\(877\) −11.5177 −0.388925 −0.194463 0.980910i \(-0.562296\pi\)
−0.194463 + 0.980910i \(0.562296\pi\)
\(878\) 15.1799 0.512298
\(879\) −13.2616 −0.447301
\(880\) 8.19753 0.276339
\(881\) 33.6704 1.13438 0.567192 0.823586i \(-0.308030\pi\)
0.567192 + 0.823586i \(0.308030\pi\)
\(882\) −16.9369 −0.570296
\(883\) 3.86850 0.130185 0.0650927 0.997879i \(-0.479266\pi\)
0.0650927 + 0.997879i \(0.479266\pi\)
\(884\) −0.639131 −0.0214963
\(885\) −20.5595 −0.691101
\(886\) −20.6263 −0.692955
\(887\) −21.5826 −0.724673 −0.362336 0.932047i \(-0.618021\pi\)
−0.362336 + 0.932047i \(0.618021\pi\)
\(888\) −2.72903 −0.0915801
\(889\) −5.98607 −0.200766
\(890\) 11.3147 0.379270
\(891\) 86.1695 2.88679
\(892\) 5.88417 0.197017
\(893\) 3.11191 0.104136
\(894\) −0.709710 −0.0237363
\(895\) −21.0525 −0.703707
\(896\) −2.10219 −0.0702293
\(897\) −26.5577 −0.886735
\(898\) −27.8874 −0.930616
\(899\) 56.5758 1.88691
\(900\) −20.5305 −0.684350
\(901\) −3.55171 −0.118325
\(902\) 20.9714 0.698270
\(903\) −9.64901 −0.321099
\(904\) 2.25758 0.0750858
\(905\) 17.1214 0.569135
\(906\) −49.5181 −1.64513
\(907\) −23.2352 −0.771512 −0.385756 0.922601i \(-0.626059\pi\)
−0.385756 + 0.922601i \(0.626059\pi\)
\(908\) −26.4098 −0.876441
\(909\) 8.07709 0.267900
\(910\) 7.40914 0.245611
\(911\) −29.8677 −0.989561 −0.494780 0.869018i \(-0.664751\pi\)
−0.494780 + 0.869018i \(0.664751\pi\)
\(912\) −14.1111 −0.467265
\(913\) −48.5653 −1.60728
\(914\) 12.6366 0.417982
\(915\) −31.5686 −1.04362
\(916\) −12.5836 −0.415774
\(917\) −25.0657 −0.827741
\(918\) −2.73320 −0.0902089
\(919\) −52.7357 −1.73959 −0.869795 0.493413i \(-0.835749\pi\)
−0.869795 + 0.493413i \(0.835749\pi\)
\(920\) −4.56063 −0.150359
\(921\) −13.4487 −0.443151
\(922\) 3.60201 0.118626
\(923\) −22.4875 −0.740184
\(924\) 38.9525 1.28144
\(925\) −2.76081 −0.0907747
\(926\) 10.6340 0.349455
\(927\) −35.2926 −1.15916
\(928\) −7.82796 −0.256965
\(929\) 23.9287 0.785075 0.392538 0.919736i \(-0.371597\pi\)
0.392538 + 0.919736i \(0.371597\pi\)
\(930\) 30.5761 1.00263
\(931\) −11.7767 −0.385966
\(932\) −16.5173 −0.541042
\(933\) 26.0787 0.853777
\(934\) −21.5758 −0.705983
\(935\) 2.03370 0.0665091
\(936\) −16.9070 −0.552623
\(937\) 31.7703 1.03789 0.518945 0.854808i \(-0.326325\pi\)
0.518945 + 0.854808i \(0.326325\pi\)
\(938\) 9.70647 0.316927
\(939\) 66.9979 2.18639
\(940\) 0.932966 0.0304300
\(941\) −15.5503 −0.506925 −0.253463 0.967345i \(-0.581570\pi\)
−0.253463 + 0.967345i \(0.581570\pi\)
\(942\) 48.5003 1.58022
\(943\) −11.6672 −0.379938
\(944\) 4.85974 0.158171
\(945\) 31.6846 1.03070
\(946\) −8.89393 −0.289167
\(947\) −12.8134 −0.416381 −0.208190 0.978088i \(-0.566757\pi\)
−0.208190 + 0.978088i \(0.566757\pi\)
\(948\) 39.0772 1.26917
\(949\) −25.4194 −0.825148
\(950\) −14.2754 −0.463155
\(951\) 84.7105 2.74693
\(952\) −0.521526 −0.0169028
\(953\) −6.07738 −0.196866 −0.0984328 0.995144i \(-0.531383\pi\)
−0.0984328 + 0.995144i \(0.531383\pi\)
\(954\) −93.9539 −3.04187
\(955\) 10.5130 0.340193
\(956\) −20.5683 −0.665225
\(957\) 145.048 4.68873
\(958\) 8.95356 0.289276
\(959\) 5.35747 0.173002
\(960\) −4.23058 −0.136541
\(961\) 21.2355 0.685015
\(962\) −2.27354 −0.0733020
\(963\) 54.2090 1.74686
\(964\) −7.95649 −0.256261
\(965\) −12.6924 −0.408581
\(966\) −21.6709 −0.697249
\(967\) −31.2998 −1.00653 −0.503266 0.864131i \(-0.667868\pi\)
−0.503266 + 0.864131i \(0.667868\pi\)
\(968\) 24.9042 0.800453
\(969\) −3.50078 −0.112461
\(970\) −13.0548 −0.419164
\(971\) −14.9618 −0.480146 −0.240073 0.970755i \(-0.577171\pi\)
−0.240073 + 0.970755i \(0.577171\pi\)
\(972\) −11.4191 −0.366268
\(973\) −14.1238 −0.452789
\(974\) −24.7815 −0.794051
\(975\) −24.9226 −0.798162
\(976\) 7.46200 0.238853
\(977\) −29.4155 −0.941086 −0.470543 0.882377i \(-0.655942\pi\)
−0.470543 + 0.882377i \(0.655942\pi\)
\(978\) 29.2486 0.935268
\(979\) 49.5572 1.58385
\(980\) −3.53072 −0.112785
\(981\) −103.180 −3.29429
\(982\) 40.2848 1.28554
\(983\) 46.8690 1.49489 0.747445 0.664324i \(-0.231280\pi\)
0.747445 + 0.664324i \(0.231280\pi\)
\(984\) −10.8229 −0.345021
\(985\) 12.3998 0.395091
\(986\) −1.94201 −0.0618463
\(987\) 4.43321 0.141110
\(988\) −11.7559 −0.374005
\(989\) 4.94806 0.157339
\(990\) 53.7978 1.70981
\(991\) 15.4237 0.489950 0.244975 0.969529i \(-0.421220\pi\)
0.244975 + 0.969529i \(0.421220\pi\)
\(992\) −7.22741 −0.229471
\(993\) −65.2678 −2.07121
\(994\) −18.3496 −0.582014
\(995\) −4.84784 −0.153687
\(996\) 25.0636 0.794170
\(997\) 26.1900 0.829445 0.414722 0.909948i \(-0.363879\pi\)
0.414722 + 0.909948i \(0.363879\pi\)
\(998\) −30.8820 −0.977553
\(999\) −9.72264 −0.307611
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 \(a_p\))