Properties

Label 8042.2.a.a.1.18
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 1.18
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.59531 q^{3}\) \(+1.00000 q^{4}\) \(+2.52318 q^{5}\) \(-1.59531 q^{6}\) \(-1.75596 q^{7}\) \(+1.00000 q^{8}\) \(-0.454973 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.59531 q^{3}\) \(+1.00000 q^{4}\) \(+2.52318 q^{5}\) \(-1.59531 q^{6}\) \(-1.75596 q^{7}\) \(+1.00000 q^{8}\) \(-0.454973 q^{9}\) \(+2.52318 q^{10}\) \(+0.567436 q^{11}\) \(-1.59531 q^{12}\) \(-0.804323 q^{13}\) \(-1.75596 q^{14}\) \(-4.02526 q^{15}\) \(+1.00000 q^{16}\) \(+5.08505 q^{17}\) \(-0.454973 q^{18}\) \(+1.51333 q^{19}\) \(+2.52318 q^{20}\) \(+2.80130 q^{21}\) \(+0.567436 q^{22}\) \(-3.45744 q^{23}\) \(-1.59531 q^{24}\) \(+1.36643 q^{25}\) \(-0.804323 q^{26}\) \(+5.51177 q^{27}\) \(-1.75596 q^{28}\) \(-6.60941 q^{29}\) \(-4.02526 q^{30}\) \(-7.81110 q^{31}\) \(+1.00000 q^{32}\) \(-0.905239 q^{33}\) \(+5.08505 q^{34}\) \(-4.43059 q^{35}\) \(-0.454973 q^{36}\) \(-6.06802 q^{37}\) \(+1.51333 q^{38}\) \(+1.28315 q^{39}\) \(+2.52318 q^{40}\) \(-7.44313 q^{41}\) \(+2.80130 q^{42}\) \(+8.13872 q^{43}\) \(+0.567436 q^{44}\) \(-1.14798 q^{45}\) \(-3.45744 q^{46}\) \(+0.390686 q^{47}\) \(-1.59531 q^{48}\) \(-3.91661 q^{49}\) \(+1.36643 q^{50}\) \(-8.11225 q^{51}\) \(-0.804323 q^{52}\) \(-0.0978787 q^{53}\) \(+5.51177 q^{54}\) \(+1.43174 q^{55}\) \(-1.75596 q^{56}\) \(-2.41424 q^{57}\) \(-6.60941 q^{58}\) \(-5.89067 q^{59}\) \(-4.02526 q^{60}\) \(-3.77328 q^{61}\) \(-7.81110 q^{62}\) \(+0.798914 q^{63}\) \(+1.00000 q^{64}\) \(-2.02945 q^{65}\) \(-0.905239 q^{66}\) \(-2.77674 q^{67}\) \(+5.08505 q^{68}\) \(+5.51570 q^{69}\) \(-4.43059 q^{70}\) \(+2.79418 q^{71}\) \(-0.454973 q^{72}\) \(-0.0296022 q^{73}\) \(-6.06802 q^{74}\) \(-2.17988 q^{75}\) \(+1.51333 q^{76}\) \(-0.996394 q^{77}\) \(+1.28315 q^{78}\) \(+10.9999 q^{79}\) \(+2.52318 q^{80}\) \(-7.42808 q^{81}\) \(-7.44313 q^{82}\) \(+15.2509 q^{83}\) \(+2.80130 q^{84}\) \(+12.8305 q^{85}\) \(+8.13872 q^{86}\) \(+10.5441 q^{87}\) \(+0.567436 q^{88}\) \(+7.79244 q^{89}\) \(-1.14798 q^{90}\) \(+1.41236 q^{91}\) \(-3.45744 q^{92}\) \(+12.4612 q^{93}\) \(+0.390686 q^{94}\) \(+3.81841 q^{95}\) \(-1.59531 q^{96}\) \(-14.3668 q^{97}\) \(-3.91661 q^{98}\) \(-0.258168 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.59531 −0.921055 −0.460527 0.887645i \(-0.652340\pi\)
−0.460527 + 0.887645i \(0.652340\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.52318 1.12840 0.564200 0.825638i \(-0.309185\pi\)
0.564200 + 0.825638i \(0.309185\pi\)
\(6\) −1.59531 −0.651284
\(7\) −1.75596 −0.663690 −0.331845 0.943334i \(-0.607671\pi\)
−0.331845 + 0.943334i \(0.607671\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.454973 −0.151658
\(10\) 2.52318 0.797899
\(11\) 0.567436 0.171088 0.0855442 0.996334i \(-0.472737\pi\)
0.0855442 + 0.996334i \(0.472737\pi\)
\(12\) −1.59531 −0.460527
\(13\) −0.804323 −0.223079 −0.111540 0.993760i \(-0.535578\pi\)
−0.111540 + 0.993760i \(0.535578\pi\)
\(14\) −1.75596 −0.469299
\(15\) −4.02526 −1.03932
\(16\) 1.00000 0.250000
\(17\) 5.08505 1.23330 0.616652 0.787236i \(-0.288488\pi\)
0.616652 + 0.787236i \(0.288488\pi\)
\(18\) −0.454973 −0.107238
\(19\) 1.51333 0.347182 0.173591 0.984818i \(-0.444463\pi\)
0.173591 + 0.984818i \(0.444463\pi\)
\(20\) 2.52318 0.564200
\(21\) 2.80130 0.611295
\(22\) 0.567436 0.120978
\(23\) −3.45744 −0.720925 −0.360463 0.932774i \(-0.617381\pi\)
−0.360463 + 0.932774i \(0.617381\pi\)
\(24\) −1.59531 −0.325642
\(25\) 1.36643 0.273285
\(26\) −0.804323 −0.157741
\(27\) 5.51177 1.06074
\(28\) −1.75596 −0.331845
\(29\) −6.60941 −1.22734 −0.613668 0.789564i \(-0.710307\pi\)
−0.613668 + 0.789564i \(0.710307\pi\)
\(30\) −4.02526 −0.734909
\(31\) −7.81110 −1.40292 −0.701458 0.712711i \(-0.747467\pi\)
−0.701458 + 0.712711i \(0.747467\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.905239 −0.157582
\(34\) 5.08505 0.872078
\(35\) −4.43059 −0.748907
\(36\) −0.454973 −0.0758289
\(37\) −6.06802 −0.997576 −0.498788 0.866724i \(-0.666221\pi\)
−0.498788 + 0.866724i \(0.666221\pi\)
\(38\) 1.51333 0.245495
\(39\) 1.28315 0.205468
\(40\) 2.52318 0.398949
\(41\) −7.44313 −1.16242 −0.581211 0.813753i \(-0.697421\pi\)
−0.581211 + 0.813753i \(0.697421\pi\)
\(42\) 2.80130 0.432251
\(43\) 8.13872 1.24114 0.620572 0.784150i \(-0.286901\pi\)
0.620572 + 0.784150i \(0.286901\pi\)
\(44\) 0.567436 0.0855442
\(45\) −1.14798 −0.171130
\(46\) −3.45744 −0.509771
\(47\) 0.390686 0.0569874 0.0284937 0.999594i \(-0.490929\pi\)
0.0284937 + 0.999594i \(0.490929\pi\)
\(48\) −1.59531 −0.230264
\(49\) −3.91661 −0.559516
\(50\) 1.36643 0.193242
\(51\) −8.11225 −1.13594
\(52\) −0.804323 −0.111540
\(53\) −0.0978787 −0.0134447 −0.00672234 0.999977i \(-0.502140\pi\)
−0.00672234 + 0.999977i \(0.502140\pi\)
\(54\) 5.51177 0.750057
\(55\) 1.43174 0.193056
\(56\) −1.75596 −0.234650
\(57\) −2.41424 −0.319774
\(58\) −6.60941 −0.867858
\(59\) −5.89067 −0.766900 −0.383450 0.923562i \(-0.625264\pi\)
−0.383450 + 0.923562i \(0.625264\pi\)
\(60\) −4.02526 −0.519659
\(61\) −3.77328 −0.483119 −0.241559 0.970386i \(-0.577659\pi\)
−0.241559 + 0.970386i \(0.577659\pi\)
\(62\) −7.81110 −0.992011
\(63\) 0.798914 0.100654
\(64\) 1.00000 0.125000
\(65\) −2.02945 −0.251722
\(66\) −0.905239 −0.111427
\(67\) −2.77674 −0.339233 −0.169617 0.985510i \(-0.554253\pi\)
−0.169617 + 0.985510i \(0.554253\pi\)
\(68\) 5.08505 0.616652
\(69\) 5.51570 0.664012
\(70\) −4.43059 −0.529557
\(71\) 2.79418 0.331608 0.165804 0.986159i \(-0.446978\pi\)
0.165804 + 0.986159i \(0.446978\pi\)
\(72\) −0.454973 −0.0536191
\(73\) −0.0296022 −0.00346468 −0.00173234 0.999998i \(-0.500551\pi\)
−0.00173234 + 0.999998i \(0.500551\pi\)
\(74\) −6.06802 −0.705393
\(75\) −2.17988 −0.251711
\(76\) 1.51333 0.173591
\(77\) −0.996394 −0.113550
\(78\) 1.28315 0.145288
\(79\) 10.9999 1.23758 0.618792 0.785555i \(-0.287622\pi\)
0.618792 + 0.785555i \(0.287622\pi\)
\(80\) 2.52318 0.282100
\(81\) −7.42808 −0.825342
\(82\) −7.44313 −0.821956
\(83\) 15.2509 1.67401 0.837003 0.547199i \(-0.184306\pi\)
0.837003 + 0.547199i \(0.184306\pi\)
\(84\) 2.80130 0.305647
\(85\) 12.8305 1.39166
\(86\) 8.13872 0.877621
\(87\) 10.5441 1.13044
\(88\) 0.567436 0.0604889
\(89\) 7.79244 0.825997 0.412999 0.910732i \(-0.364481\pi\)
0.412999 + 0.910732i \(0.364481\pi\)
\(90\) −1.14798 −0.121008
\(91\) 1.41236 0.148055
\(92\) −3.45744 −0.360463
\(93\) 12.4612 1.29216
\(94\) 0.390686 0.0402962
\(95\) 3.81841 0.391760
\(96\) −1.59531 −0.162821
\(97\) −14.3668 −1.45873 −0.729364 0.684126i \(-0.760184\pi\)
−0.729364 + 0.684126i \(0.760184\pi\)
\(98\) −3.91661 −0.395638
\(99\) −0.258168 −0.0259469
\(100\) 1.36643 0.136643
\(101\) −9.19530 −0.914966 −0.457483 0.889218i \(-0.651249\pi\)
−0.457483 + 0.889218i \(0.651249\pi\)
\(102\) −8.11225 −0.803232
\(103\) 4.30984 0.424661 0.212330 0.977198i \(-0.431895\pi\)
0.212330 + 0.977198i \(0.431895\pi\)
\(104\) −0.804323 −0.0788703
\(105\) 7.06819 0.689785
\(106\) −0.0978787 −0.00950682
\(107\) 1.97490 0.190921 0.0954605 0.995433i \(-0.469568\pi\)
0.0954605 + 0.995433i \(0.469568\pi\)
\(108\) 5.51177 0.530370
\(109\) 7.09215 0.679305 0.339652 0.940551i \(-0.389691\pi\)
0.339652 + 0.940551i \(0.389691\pi\)
\(110\) 1.43174 0.136511
\(111\) 9.68039 0.918822
\(112\) −1.75596 −0.165922
\(113\) −1.07604 −0.101226 −0.0506128 0.998718i \(-0.516117\pi\)
−0.0506128 + 0.998718i \(0.516117\pi\)
\(114\) −2.41424 −0.226114
\(115\) −8.72373 −0.813492
\(116\) −6.60941 −0.613668
\(117\) 0.365945 0.0338317
\(118\) −5.89067 −0.542281
\(119\) −8.92913 −0.818532
\(120\) −4.02526 −0.367454
\(121\) −10.6780 −0.970729
\(122\) −3.77328 −0.341617
\(123\) 11.8741 1.07065
\(124\) −7.81110 −0.701458
\(125\) −9.16815 −0.820025
\(126\) 0.798914 0.0711729
\(127\) −9.46065 −0.839497 −0.419748 0.907640i \(-0.637882\pi\)
−0.419748 + 0.907640i \(0.637882\pi\)
\(128\) 1.00000 0.0883883
\(129\) −12.9838 −1.14316
\(130\) −2.02945 −0.177994
\(131\) −13.3410 −1.16561 −0.582804 0.812613i \(-0.698044\pi\)
−0.582804 + 0.812613i \(0.698044\pi\)
\(132\) −0.905239 −0.0787909
\(133\) −2.65735 −0.230421
\(134\) −2.77674 −0.239874
\(135\) 13.9072 1.19694
\(136\) 5.08505 0.436039
\(137\) 0.778785 0.0665361 0.0332681 0.999446i \(-0.489408\pi\)
0.0332681 + 0.999446i \(0.489408\pi\)
\(138\) 5.51570 0.469527
\(139\) −21.5348 −1.82656 −0.913280 0.407333i \(-0.866459\pi\)
−0.913280 + 0.407333i \(0.866459\pi\)
\(140\) −4.43059 −0.374453
\(141\) −0.623267 −0.0524885
\(142\) 2.79418 0.234483
\(143\) −0.456402 −0.0381662
\(144\) −0.454973 −0.0379144
\(145\) −16.6767 −1.38493
\(146\) −0.0296022 −0.00244990
\(147\) 6.24823 0.515345
\(148\) −6.06802 −0.498788
\(149\) −0.971434 −0.0795830 −0.0397915 0.999208i \(-0.512669\pi\)
−0.0397915 + 0.999208i \(0.512669\pi\)
\(150\) −2.17988 −0.177986
\(151\) −6.55659 −0.533568 −0.266784 0.963756i \(-0.585961\pi\)
−0.266784 + 0.963756i \(0.585961\pi\)
\(152\) 1.51333 0.122747
\(153\) −2.31356 −0.187040
\(154\) −0.996394 −0.0802917
\(155\) −19.7088 −1.58305
\(156\) 1.28315 0.102734
\(157\) 15.4574 1.23364 0.616818 0.787106i \(-0.288421\pi\)
0.616818 + 0.787106i \(0.288421\pi\)
\(158\) 10.9999 0.875104
\(159\) 0.156147 0.0123833
\(160\) 2.52318 0.199475
\(161\) 6.07111 0.478471
\(162\) −7.42808 −0.583605
\(163\) −4.58599 −0.359203 −0.179601 0.983739i \(-0.557481\pi\)
−0.179601 + 0.983739i \(0.557481\pi\)
\(164\) −7.44313 −0.581211
\(165\) −2.28408 −0.177815
\(166\) 15.2509 1.18370
\(167\) 15.3669 1.18912 0.594562 0.804050i \(-0.297325\pi\)
0.594562 + 0.804050i \(0.297325\pi\)
\(168\) 2.80130 0.216125
\(169\) −12.3531 −0.950236
\(170\) 12.8305 0.984052
\(171\) −0.688525 −0.0526529
\(172\) 8.13872 0.620572
\(173\) −1.20405 −0.0915425 −0.0457712 0.998952i \(-0.514575\pi\)
−0.0457712 + 0.998952i \(0.514575\pi\)
\(174\) 10.5441 0.799345
\(175\) −2.39938 −0.181376
\(176\) 0.567436 0.0427721
\(177\) 9.39748 0.706357
\(178\) 7.79244 0.584068
\(179\) −16.3825 −1.22449 −0.612244 0.790669i \(-0.709733\pi\)
−0.612244 + 0.790669i \(0.709733\pi\)
\(180\) −1.14798 −0.0855652
\(181\) −3.77800 −0.280817 −0.140408 0.990094i \(-0.544842\pi\)
−0.140408 + 0.990094i \(0.544842\pi\)
\(182\) 1.41236 0.104691
\(183\) 6.01956 0.444979
\(184\) −3.45744 −0.254886
\(185\) −15.3107 −1.12566
\(186\) 12.4612 0.913696
\(187\) 2.88544 0.211004
\(188\) 0.390686 0.0284937
\(189\) −9.67843 −0.704002
\(190\) 3.81841 0.277016
\(191\) 8.80926 0.637415 0.318708 0.947853i \(-0.396751\pi\)
0.318708 + 0.947853i \(0.396751\pi\)
\(192\) −1.59531 −0.115132
\(193\) −3.87984 −0.279277 −0.139639 0.990203i \(-0.544594\pi\)
−0.139639 + 0.990203i \(0.544594\pi\)
\(194\) −14.3668 −1.03148
\(195\) 3.23761 0.231850
\(196\) −3.91661 −0.279758
\(197\) −27.5906 −1.96575 −0.982875 0.184272i \(-0.941007\pi\)
−0.982875 + 0.184272i \(0.941007\pi\)
\(198\) −0.258168 −0.0183472
\(199\) −10.6045 −0.751734 −0.375867 0.926674i \(-0.622655\pi\)
−0.375867 + 0.926674i \(0.622655\pi\)
\(200\) 1.36643 0.0966208
\(201\) 4.42978 0.312452
\(202\) −9.19530 −0.646979
\(203\) 11.6058 0.814571
\(204\) −8.11225 −0.567971
\(205\) −18.7803 −1.31168
\(206\) 4.30984 0.300280
\(207\) 1.57304 0.109334
\(208\) −0.804323 −0.0557698
\(209\) 0.858719 0.0593988
\(210\) 7.06819 0.487751
\(211\) 25.2722 1.73981 0.869905 0.493219i \(-0.164180\pi\)
0.869905 + 0.493219i \(0.164180\pi\)
\(212\) −0.0978787 −0.00672234
\(213\) −4.45760 −0.305430
\(214\) 1.97490 0.135002
\(215\) 20.5354 1.40051
\(216\) 5.51177 0.375028
\(217\) 13.7160 0.931100
\(218\) 7.09215 0.480341
\(219\) 0.0472249 0.00319116
\(220\) 1.43174 0.0965280
\(221\) −4.09002 −0.275124
\(222\) 9.68039 0.649705
\(223\) −1.40610 −0.0941596 −0.0470798 0.998891i \(-0.514992\pi\)
−0.0470798 + 0.998891i \(0.514992\pi\)
\(224\) −1.75596 −0.117325
\(225\) −0.621687 −0.0414458
\(226\) −1.07604 −0.0715772
\(227\) 17.3271 1.15004 0.575021 0.818139i \(-0.304994\pi\)
0.575021 + 0.818139i \(0.304994\pi\)
\(228\) −2.41424 −0.159887
\(229\) −14.2781 −0.943520 −0.471760 0.881727i \(-0.656381\pi\)
−0.471760 + 0.881727i \(0.656381\pi\)
\(230\) −8.72373 −0.575225
\(231\) 1.58956 0.104585
\(232\) −6.60941 −0.433929
\(233\) −2.31363 −0.151571 −0.0757854 0.997124i \(-0.524146\pi\)
−0.0757854 + 0.997124i \(0.524146\pi\)
\(234\) 0.365945 0.0239226
\(235\) 0.985770 0.0643045
\(236\) −5.89067 −0.383450
\(237\) −17.5483 −1.13988
\(238\) −8.92913 −0.578789
\(239\) 7.31592 0.473227 0.236614 0.971604i \(-0.423962\pi\)
0.236614 + 0.971604i \(0.423962\pi\)
\(240\) −4.02526 −0.259829
\(241\) 21.0925 1.35868 0.679342 0.733822i \(-0.262265\pi\)
0.679342 + 0.733822i \(0.262265\pi\)
\(242\) −10.6780 −0.686409
\(243\) −4.68518 −0.300555
\(244\) −3.77328 −0.241559
\(245\) −9.88231 −0.631357
\(246\) 11.8741 0.757067
\(247\) −1.21721 −0.0774491
\(248\) −7.81110 −0.496005
\(249\) −24.3300 −1.54185
\(250\) −9.16815 −0.579845
\(251\) −19.5196 −1.23207 −0.616033 0.787720i \(-0.711261\pi\)
−0.616033 + 0.787720i \(0.711261\pi\)
\(252\) 0.798914 0.0503268
\(253\) −1.96187 −0.123342
\(254\) −9.46065 −0.593614
\(255\) −20.4686 −1.28180
\(256\) 1.00000 0.0625000
\(257\) −28.3700 −1.76967 −0.884835 0.465905i \(-0.845729\pi\)
−0.884835 + 0.465905i \(0.845729\pi\)
\(258\) −12.9838 −0.808337
\(259\) 10.6552 0.662081
\(260\) −2.02945 −0.125861
\(261\) 3.00710 0.186135
\(262\) −13.3410 −0.824209
\(263\) −8.74935 −0.539508 −0.269754 0.962929i \(-0.586942\pi\)
−0.269754 + 0.962929i \(0.586942\pi\)
\(264\) −0.905239 −0.0557136
\(265\) −0.246965 −0.0151710
\(266\) −2.65735 −0.162932
\(267\) −12.4314 −0.760789
\(268\) −2.77674 −0.169617
\(269\) −13.9896 −0.852964 −0.426482 0.904496i \(-0.640247\pi\)
−0.426482 + 0.904496i \(0.640247\pi\)
\(270\) 13.9072 0.846363
\(271\) 6.82598 0.414649 0.207324 0.978272i \(-0.433524\pi\)
0.207324 + 0.978272i \(0.433524\pi\)
\(272\) 5.08505 0.308326
\(273\) −2.25315 −0.136367
\(274\) 0.778785 0.0470481
\(275\) 0.775359 0.0467559
\(276\) 5.51570 0.332006
\(277\) −3.41024 −0.204902 −0.102451 0.994738i \(-0.532668\pi\)
−0.102451 + 0.994738i \(0.532668\pi\)
\(278\) −21.5348 −1.29157
\(279\) 3.55384 0.212763
\(280\) −4.43059 −0.264779
\(281\) 26.4075 1.57534 0.787671 0.616096i \(-0.211287\pi\)
0.787671 + 0.616096i \(0.211287\pi\)
\(282\) −0.623267 −0.0371150
\(283\) 7.34816 0.436803 0.218401 0.975859i \(-0.429916\pi\)
0.218401 + 0.975859i \(0.429916\pi\)
\(284\) 2.79418 0.165804
\(285\) −6.09156 −0.360833
\(286\) −0.456402 −0.0269876
\(287\) 13.0698 0.771487
\(288\) −0.454973 −0.0268096
\(289\) 8.85769 0.521041
\(290\) −16.6767 −0.979290
\(291\) 22.9196 1.34357
\(292\) −0.0296022 −0.00173234
\(293\) −23.5159 −1.37381 −0.686907 0.726745i \(-0.741032\pi\)
−0.686907 + 0.726745i \(0.741032\pi\)
\(294\) 6.24823 0.364404
\(295\) −14.8632 −0.865370
\(296\) −6.06802 −0.352696
\(297\) 3.12758 0.181480
\(298\) −0.971434 −0.0562737
\(299\) 2.78089 0.160823
\(300\) −2.17988 −0.125855
\(301\) −14.2913 −0.823734
\(302\) −6.55659 −0.377290
\(303\) 14.6694 0.842734
\(304\) 1.51333 0.0867955
\(305\) −9.52065 −0.545151
\(306\) −2.31356 −0.132257
\(307\) −3.19291 −0.182229 −0.0911144 0.995840i \(-0.529043\pi\)
−0.0911144 + 0.995840i \(0.529043\pi\)
\(308\) −0.996394 −0.0567748
\(309\) −6.87554 −0.391136
\(310\) −19.7088 −1.11938
\(311\) 16.3953 0.929693 0.464847 0.885391i \(-0.346109\pi\)
0.464847 + 0.885391i \(0.346109\pi\)
\(312\) 1.28315 0.0726439
\(313\) 19.6926 1.11309 0.556546 0.830817i \(-0.312126\pi\)
0.556546 + 0.830817i \(0.312126\pi\)
\(314\) 15.4574 0.872313
\(315\) 2.01580 0.113578
\(316\) 10.9999 0.618792
\(317\) 14.6377 0.822136 0.411068 0.911605i \(-0.365156\pi\)
0.411068 + 0.911605i \(0.365156\pi\)
\(318\) 0.156147 0.00875631
\(319\) −3.75042 −0.209983
\(320\) 2.52318 0.141050
\(321\) −3.15059 −0.175849
\(322\) 6.07111 0.338330
\(323\) 7.69536 0.428181
\(324\) −7.42808 −0.412671
\(325\) −1.09905 −0.0609642
\(326\) −4.58599 −0.253995
\(327\) −11.3142 −0.625677
\(328\) −7.44313 −0.410978
\(329\) −0.686028 −0.0378219
\(330\) −2.28408 −0.125734
\(331\) 2.56201 0.140821 0.0704105 0.997518i \(-0.477569\pi\)
0.0704105 + 0.997518i \(0.477569\pi\)
\(332\) 15.2509 0.837003
\(333\) 2.76078 0.151290
\(334\) 15.3669 0.840838
\(335\) −7.00622 −0.382790
\(336\) 2.80130 0.152824
\(337\) −6.73137 −0.366681 −0.183341 0.983049i \(-0.558691\pi\)
−0.183341 + 0.983049i \(0.558691\pi\)
\(338\) −12.3531 −0.671918
\(339\) 1.71662 0.0932343
\(340\) 12.8305 0.695830
\(341\) −4.43230 −0.240022
\(342\) −0.688525 −0.0372312
\(343\) 19.1691 1.03503
\(344\) 8.13872 0.438810
\(345\) 13.9171 0.749270
\(346\) −1.20405 −0.0647303
\(347\) −23.3312 −1.25249 −0.626243 0.779628i \(-0.715408\pi\)
−0.626243 + 0.779628i \(0.715408\pi\)
\(348\) 10.5441 0.565222
\(349\) 5.26790 0.281984 0.140992 0.990011i \(-0.454971\pi\)
0.140992 + 0.990011i \(0.454971\pi\)
\(350\) −2.39938 −0.128253
\(351\) −4.43324 −0.236629
\(352\) 0.567436 0.0302444
\(353\) −4.57867 −0.243698 −0.121849 0.992549i \(-0.538882\pi\)
−0.121849 + 0.992549i \(0.538882\pi\)
\(354\) 9.39748 0.499470
\(355\) 7.05022 0.374187
\(356\) 7.79244 0.412999
\(357\) 14.2448 0.753913
\(358\) −16.3825 −0.865843
\(359\) 1.48423 0.0783346 0.0391673 0.999233i \(-0.487529\pi\)
0.0391673 + 0.999233i \(0.487529\pi\)
\(360\) −1.14798 −0.0605038
\(361\) −16.7098 −0.879465
\(362\) −3.77800 −0.198568
\(363\) 17.0348 0.894095
\(364\) 1.41236 0.0740276
\(365\) −0.0746917 −0.00390954
\(366\) 6.01956 0.314648
\(367\) 5.56617 0.290552 0.145276 0.989391i \(-0.453593\pi\)
0.145276 + 0.989391i \(0.453593\pi\)
\(368\) −3.45744 −0.180231
\(369\) 3.38642 0.176290
\(370\) −15.3107 −0.795965
\(371\) 0.171871 0.00892309
\(372\) 12.4612 0.646081
\(373\) −4.97219 −0.257450 −0.128725 0.991680i \(-0.541089\pi\)
−0.128725 + 0.991680i \(0.541089\pi\)
\(374\) 2.88544 0.149202
\(375\) 14.6261 0.755288
\(376\) 0.390686 0.0201481
\(377\) 5.31610 0.273793
\(378\) −9.67843 −0.497805
\(379\) 31.7453 1.63065 0.815323 0.579006i \(-0.196559\pi\)
0.815323 + 0.579006i \(0.196559\pi\)
\(380\) 3.81841 0.195880
\(381\) 15.0927 0.773223
\(382\) 8.80926 0.450721
\(383\) −13.1805 −0.673490 −0.336745 0.941596i \(-0.609326\pi\)
−0.336745 + 0.941596i \(0.609326\pi\)
\(384\) −1.59531 −0.0814105
\(385\) −2.51408 −0.128129
\(386\) −3.87984 −0.197479
\(387\) −3.70290 −0.188229
\(388\) −14.3668 −0.729364
\(389\) −29.9685 −1.51946 −0.759731 0.650238i \(-0.774669\pi\)
−0.759731 + 0.650238i \(0.774669\pi\)
\(390\) 3.23761 0.163943
\(391\) −17.5812 −0.889121
\(392\) −3.91661 −0.197819
\(393\) 21.2831 1.07359
\(394\) −27.5906 −1.39000
\(395\) 27.7547 1.39649
\(396\) −0.258168 −0.0129734
\(397\) −32.2937 −1.62077 −0.810386 0.585896i \(-0.800743\pi\)
−0.810386 + 0.585896i \(0.800743\pi\)
\(398\) −10.6045 −0.531556
\(399\) 4.23930 0.212231
\(400\) 1.36643 0.0683213
\(401\) −10.9849 −0.548557 −0.274279 0.961650i \(-0.588439\pi\)
−0.274279 + 0.961650i \(0.588439\pi\)
\(402\) 4.42978 0.220937
\(403\) 6.28265 0.312961
\(404\) −9.19530 −0.457483
\(405\) −18.7424 −0.931316
\(406\) 11.6058 0.575988
\(407\) −3.44321 −0.170674
\(408\) −8.11225 −0.401616
\(409\) 0.863408 0.0426928 0.0213464 0.999772i \(-0.493205\pi\)
0.0213464 + 0.999772i \(0.493205\pi\)
\(410\) −18.7803 −0.927495
\(411\) −1.24241 −0.0612834
\(412\) 4.30984 0.212330
\(413\) 10.3438 0.508984
\(414\) 1.57304 0.0773107
\(415\) 38.4808 1.88895
\(416\) −0.804323 −0.0394352
\(417\) 34.3548 1.68236
\(418\) 0.858719 0.0420013
\(419\) 10.1254 0.494658 0.247329 0.968932i \(-0.420447\pi\)
0.247329 + 0.968932i \(0.420447\pi\)
\(420\) 7.06819 0.344892
\(421\) 15.1397 0.737865 0.368933 0.929456i \(-0.379723\pi\)
0.368933 + 0.929456i \(0.379723\pi\)
\(422\) 25.2722 1.23023
\(423\) −0.177752 −0.00864258
\(424\) −0.0978787 −0.00475341
\(425\) 6.94833 0.337044
\(426\) −4.45760 −0.215971
\(427\) 6.62572 0.320641
\(428\) 1.97490 0.0954605
\(429\) 0.728104 0.0351532
\(430\) 20.5354 0.990307
\(431\) −15.3926 −0.741434 −0.370717 0.928746i \(-0.620888\pi\)
−0.370717 + 0.928746i \(0.620888\pi\)
\(432\) 5.51177 0.265185
\(433\) −28.6449 −1.37659 −0.688293 0.725433i \(-0.741640\pi\)
−0.688293 + 0.725433i \(0.741640\pi\)
\(434\) 13.7160 0.658387
\(435\) 26.6046 1.27559
\(436\) 7.09215 0.339652
\(437\) −5.23225 −0.250292
\(438\) 0.0472249 0.00225649
\(439\) −14.0733 −0.671684 −0.335842 0.941918i \(-0.609021\pi\)
−0.335842 + 0.941918i \(0.609021\pi\)
\(440\) 1.43174 0.0682556
\(441\) 1.78195 0.0848549
\(442\) −4.09002 −0.194542
\(443\) −37.5776 −1.78537 −0.892684 0.450684i \(-0.851180\pi\)
−0.892684 + 0.450684i \(0.851180\pi\)
\(444\) 9.68039 0.459411
\(445\) 19.6617 0.932055
\(446\) −1.40610 −0.0665809
\(447\) 1.54974 0.0733003
\(448\) −1.75596 −0.0829612
\(449\) 25.2836 1.19321 0.596604 0.802536i \(-0.296516\pi\)
0.596604 + 0.802536i \(0.296516\pi\)
\(450\) −0.621687 −0.0293066
\(451\) −4.22350 −0.198877
\(452\) −1.07604 −0.0506128
\(453\) 10.4598 0.491445
\(454\) 17.3271 0.813202
\(455\) 3.56363 0.167065
\(456\) −2.41424 −0.113057
\(457\) 3.10932 0.145448 0.0727240 0.997352i \(-0.476831\pi\)
0.0727240 + 0.997352i \(0.476831\pi\)
\(458\) −14.2781 −0.667170
\(459\) 28.0276 1.30822
\(460\) −8.72373 −0.406746
\(461\) −30.2967 −1.41106 −0.705529 0.708681i \(-0.749291\pi\)
−0.705529 + 0.708681i \(0.749291\pi\)
\(462\) 1.58956 0.0739531
\(463\) −30.6325 −1.42361 −0.711807 0.702375i \(-0.752123\pi\)
−0.711807 + 0.702375i \(0.752123\pi\)
\(464\) −6.60941 −0.306834
\(465\) 31.4417 1.45807
\(466\) −2.31363 −0.107177
\(467\) −8.25943 −0.382201 −0.191100 0.981571i \(-0.561206\pi\)
−0.191100 + 0.981571i \(0.561206\pi\)
\(468\) 0.365945 0.0169158
\(469\) 4.87584 0.225146
\(470\) 0.985770 0.0454702
\(471\) −24.6594 −1.13625
\(472\) −5.89067 −0.271140
\(473\) 4.61820 0.212345
\(474\) −17.5483 −0.806019
\(475\) 2.06785 0.0948797
\(476\) −8.92913 −0.409266
\(477\) 0.0445322 0.00203899
\(478\) 7.31592 0.334622
\(479\) 2.56371 0.117139 0.0585694 0.998283i \(-0.481346\pi\)
0.0585694 + 0.998283i \(0.481346\pi\)
\(480\) −4.02526 −0.183727
\(481\) 4.88064 0.222538
\(482\) 21.0925 0.960735
\(483\) −9.68533 −0.440698
\(484\) −10.6780 −0.485364
\(485\) −36.2500 −1.64603
\(486\) −4.68518 −0.212524
\(487\) −0.185623 −0.00841138 −0.00420569 0.999991i \(-0.501339\pi\)
−0.00420569 + 0.999991i \(0.501339\pi\)
\(488\) −3.77328 −0.170808
\(489\) 7.31610 0.330845
\(490\) −9.88231 −0.446437
\(491\) 2.45074 0.110600 0.0553002 0.998470i \(-0.482388\pi\)
0.0553002 + 0.998470i \(0.482388\pi\)
\(492\) 11.8741 0.535327
\(493\) −33.6092 −1.51368
\(494\) −1.21721 −0.0547647
\(495\) −0.651404 −0.0292784
\(496\) −7.81110 −0.350729
\(497\) −4.90647 −0.220085
\(498\) −24.3300 −1.09025
\(499\) 23.6939 1.06068 0.530342 0.847784i \(-0.322063\pi\)
0.530342 + 0.847784i \(0.322063\pi\)
\(500\) −9.16815 −0.410012
\(501\) −24.5150 −1.09525
\(502\) −19.5196 −0.871202
\(503\) −33.2403 −1.48211 −0.741056 0.671443i \(-0.765675\pi\)
−0.741056 + 0.671443i \(0.765675\pi\)
\(504\) 0.798914 0.0355864
\(505\) −23.2014 −1.03245
\(506\) −1.96187 −0.0872159
\(507\) 19.7070 0.875219
\(508\) −9.46065 −0.419748
\(509\) 3.07485 0.136290 0.0681452 0.997675i \(-0.478292\pi\)
0.0681452 + 0.997675i \(0.478292\pi\)
\(510\) −20.4686 −0.906366
\(511\) 0.0519803 0.00229947
\(512\) 1.00000 0.0441942
\(513\) 8.34113 0.368270
\(514\) −28.3700 −1.25135
\(515\) 10.8745 0.479187
\(516\) −12.9838 −0.571581
\(517\) 0.221689 0.00974988
\(518\) 10.6552 0.468162
\(519\) 1.92084 0.0843157
\(520\) −2.02945 −0.0889972
\(521\) −23.3857 −1.02455 −0.512274 0.858822i \(-0.671197\pi\)
−0.512274 + 0.858822i \(0.671197\pi\)
\(522\) 3.00710 0.131617
\(523\) −15.8681 −0.693862 −0.346931 0.937891i \(-0.612776\pi\)
−0.346931 + 0.937891i \(0.612776\pi\)
\(524\) −13.3410 −0.582804
\(525\) 3.82777 0.167058
\(526\) −8.74935 −0.381490
\(527\) −39.7198 −1.73022
\(528\) −0.905239 −0.0393955
\(529\) −11.0461 −0.480267
\(530\) −0.246965 −0.0107275
\(531\) 2.68010 0.116306
\(532\) −2.65735 −0.115211
\(533\) 5.98668 0.259312
\(534\) −12.4314 −0.537959
\(535\) 4.98303 0.215435
\(536\) −2.77674 −0.119937
\(537\) 26.1353 1.12782
\(538\) −13.9896 −0.603137
\(539\) −2.22243 −0.0957267
\(540\) 13.9072 0.598469
\(541\) −2.93630 −0.126241 −0.0631207 0.998006i \(-0.520105\pi\)
−0.0631207 + 0.998006i \(0.520105\pi\)
\(542\) 6.82598 0.293201
\(543\) 6.02710 0.258648
\(544\) 5.08505 0.218020
\(545\) 17.8948 0.766527
\(546\) −2.25315 −0.0964260
\(547\) 31.3660 1.34112 0.670558 0.741858i \(-0.266055\pi\)
0.670558 + 0.741858i \(0.266055\pi\)
\(548\) 0.778785 0.0332681
\(549\) 1.71674 0.0732687
\(550\) 0.775359 0.0330614
\(551\) −10.0022 −0.426109
\(552\) 5.51570 0.234764
\(553\) −19.3153 −0.821372
\(554\) −3.41024 −0.144887
\(555\) 24.4253 1.03680
\(556\) −21.5348 −0.913280
\(557\) 37.1507 1.57413 0.787064 0.616872i \(-0.211600\pi\)
0.787064 + 0.616872i \(0.211600\pi\)
\(558\) 3.55384 0.150446
\(559\) −6.54616 −0.276873
\(560\) −4.43059 −0.187227
\(561\) −4.60318 −0.194346
\(562\) 26.4075 1.11394
\(563\) −17.8471 −0.752166 −0.376083 0.926586i \(-0.622729\pi\)
−0.376083 + 0.926586i \(0.622729\pi\)
\(564\) −0.623267 −0.0262443
\(565\) −2.71505 −0.114223
\(566\) 7.34816 0.308866
\(567\) 13.0434 0.547771
\(568\) 2.79418 0.117241
\(569\) −40.2938 −1.68921 −0.844603 0.535394i \(-0.820163\pi\)
−0.844603 + 0.535394i \(0.820163\pi\)
\(570\) −6.09156 −0.255147
\(571\) 22.7850 0.953522 0.476761 0.879033i \(-0.341811\pi\)
0.476761 + 0.879033i \(0.341811\pi\)
\(572\) −0.456402 −0.0190831
\(573\) −14.0535 −0.587095
\(574\) 13.0698 0.545524
\(575\) −4.72433 −0.197018
\(576\) −0.454973 −0.0189572
\(577\) 40.0111 1.66568 0.832841 0.553512i \(-0.186713\pi\)
0.832841 + 0.553512i \(0.186713\pi\)
\(578\) 8.85769 0.368431
\(579\) 6.18956 0.257229
\(580\) −16.6767 −0.692463
\(581\) −26.7800 −1.11102
\(582\) 22.9196 0.950046
\(583\) −0.0555399 −0.00230023
\(584\) −0.0296022 −0.00122495
\(585\) 0.923345 0.0381756
\(586\) −23.5159 −0.971433
\(587\) −36.7041 −1.51494 −0.757471 0.652869i \(-0.773565\pi\)
−0.757471 + 0.652869i \(0.773565\pi\)
\(588\) 6.24823 0.257672
\(589\) −11.8208 −0.487067
\(590\) −14.8632 −0.611909
\(591\) 44.0157 1.81056
\(592\) −6.06802 −0.249394
\(593\) 33.1841 1.36271 0.681354 0.731954i \(-0.261392\pi\)
0.681354 + 0.731954i \(0.261392\pi\)
\(594\) 3.12758 0.128326
\(595\) −22.5298 −0.923631
\(596\) −0.971434 −0.0397915
\(597\) 16.9175 0.692388
\(598\) 2.78089 0.113719
\(599\) 14.0006 0.572050 0.286025 0.958222i \(-0.407666\pi\)
0.286025 + 0.958222i \(0.407666\pi\)
\(600\) −2.17988 −0.0889931
\(601\) 22.5328 0.919134 0.459567 0.888143i \(-0.348005\pi\)
0.459567 + 0.888143i \(0.348005\pi\)
\(602\) −14.2913 −0.582468
\(603\) 1.26334 0.0514473
\(604\) −6.55659 −0.266784
\(605\) −26.9425 −1.09537
\(606\) 14.6694 0.595903
\(607\) 12.2100 0.495587 0.247794 0.968813i \(-0.420295\pi\)
0.247794 + 0.968813i \(0.420295\pi\)
\(608\) 1.51333 0.0613737
\(609\) −18.5150 −0.750264
\(610\) −9.52065 −0.385480
\(611\) −0.314238 −0.0127127
\(612\) −2.31356 −0.0935201
\(613\) −31.2474 −1.26207 −0.631036 0.775754i \(-0.717370\pi\)
−0.631036 + 0.775754i \(0.717370\pi\)
\(614\) −3.19291 −0.128855
\(615\) 29.9605 1.20813
\(616\) −0.996394 −0.0401458
\(617\) 24.2178 0.974973 0.487486 0.873131i \(-0.337914\pi\)
0.487486 + 0.873131i \(0.337914\pi\)
\(618\) −6.87554 −0.276575
\(619\) 23.2082 0.932814 0.466407 0.884570i \(-0.345548\pi\)
0.466407 + 0.884570i \(0.345548\pi\)
\(620\) −19.7088 −0.791524
\(621\) −19.0566 −0.764714
\(622\) 16.3953 0.657392
\(623\) −13.6832 −0.548206
\(624\) 1.28315 0.0513670
\(625\) −29.9650 −1.19860
\(626\) 19.6926 0.787075
\(627\) −1.36993 −0.0547096
\(628\) 15.4574 0.616818
\(629\) −30.8561 −1.23032
\(630\) 2.01580 0.0803114
\(631\) −6.98747 −0.278167 −0.139083 0.990281i \(-0.544416\pi\)
−0.139083 + 0.990281i \(0.544416\pi\)
\(632\) 10.9999 0.437552
\(633\) −40.3171 −1.60246
\(634\) 14.6377 0.581338
\(635\) −23.8709 −0.947288
\(636\) 0.156147 0.00619164
\(637\) 3.15022 0.124816
\(638\) −3.75042 −0.148480
\(639\) −1.27128 −0.0502910
\(640\) 2.52318 0.0997374
\(641\) −7.54540 −0.298025 −0.149013 0.988835i \(-0.547609\pi\)
−0.149013 + 0.988835i \(0.547609\pi\)
\(642\) −3.15059 −0.124344
\(643\) 16.3074 0.643102 0.321551 0.946892i \(-0.395796\pi\)
0.321551 + 0.946892i \(0.395796\pi\)
\(644\) 6.07111 0.239235
\(645\) −32.7605 −1.28994
\(646\) 7.69536 0.302770
\(647\) −0.219016 −0.00861040 −0.00430520 0.999991i \(-0.501370\pi\)
−0.00430520 + 0.999991i \(0.501370\pi\)
\(648\) −7.42808 −0.291803
\(649\) −3.34258 −0.131208
\(650\) −1.09905 −0.0431082
\(651\) −21.8813 −0.857595
\(652\) −4.58599 −0.179601
\(653\) −10.0239 −0.392266 −0.196133 0.980577i \(-0.562838\pi\)
−0.196133 + 0.980577i \(0.562838\pi\)
\(654\) −11.3142 −0.442421
\(655\) −33.6617 −1.31527
\(656\) −7.44313 −0.290605
\(657\) 0.0134682 0.000525445 0
\(658\) −0.686028 −0.0267442
\(659\) −20.6979 −0.806275 −0.403138 0.915139i \(-0.632080\pi\)
−0.403138 + 0.915139i \(0.632080\pi\)
\(660\) −2.28408 −0.0889076
\(661\) −15.9330 −0.619723 −0.309861 0.950782i \(-0.600283\pi\)
−0.309861 + 0.950782i \(0.600283\pi\)
\(662\) 2.56201 0.0995755
\(663\) 6.52486 0.253405
\(664\) 15.2509 0.591850
\(665\) −6.70496 −0.260007
\(666\) 2.76078 0.106978
\(667\) 22.8516 0.884818
\(668\) 15.3669 0.594562
\(669\) 2.24318 0.0867262
\(670\) −7.00622 −0.270674
\(671\) −2.14109 −0.0826560
\(672\) 2.80130 0.108063
\(673\) −17.3756 −0.669781 −0.334890 0.942257i \(-0.608699\pi\)
−0.334890 + 0.942257i \(0.608699\pi\)
\(674\) −6.73137 −0.259283
\(675\) 7.53142 0.289884
\(676\) −12.3531 −0.475118
\(677\) 42.7772 1.64406 0.822030 0.569444i \(-0.192841\pi\)
0.822030 + 0.569444i \(0.192841\pi\)
\(678\) 1.71662 0.0659266
\(679\) 25.2275 0.968143
\(680\) 12.8305 0.492026
\(681\) −27.6422 −1.05925
\(682\) −4.43230 −0.169722
\(683\) 44.0039 1.68376 0.841882 0.539662i \(-0.181448\pi\)
0.841882 + 0.539662i \(0.181448\pi\)
\(684\) −0.688525 −0.0263264
\(685\) 1.96501 0.0750793
\(686\) 19.1691 0.731880
\(687\) 22.7780 0.869034
\(688\) 8.13872 0.310286
\(689\) 0.0787261 0.00299923
\(690\) 13.9171 0.529814
\(691\) 40.1056 1.52569 0.762845 0.646581i \(-0.223802\pi\)
0.762845 + 0.646581i \(0.223802\pi\)
\(692\) −1.20405 −0.0457712
\(693\) 0.453332 0.0172207
\(694\) −23.3312 −0.885641
\(695\) −54.3362 −2.06109
\(696\) 10.5441 0.399672
\(697\) −37.8487 −1.43362
\(698\) 5.26790 0.199393
\(699\) 3.69096 0.139605
\(700\) −2.39938 −0.0906882
\(701\) 34.0934 1.28769 0.643845 0.765156i \(-0.277338\pi\)
0.643845 + 0.765156i \(0.277338\pi\)
\(702\) −4.43324 −0.167322
\(703\) −9.18292 −0.346340
\(704\) 0.567436 0.0213860
\(705\) −1.57261 −0.0592280
\(706\) −4.57867 −0.172320
\(707\) 16.1466 0.607254
\(708\) 9.39748 0.353179
\(709\) −25.4063 −0.954154 −0.477077 0.878862i \(-0.658304\pi\)
−0.477077 + 0.878862i \(0.658304\pi\)
\(710\) 7.05022 0.264590
\(711\) −5.00465 −0.187689
\(712\) 7.79244 0.292034
\(713\) 27.0064 1.01140
\(714\) 14.2448 0.533097
\(715\) −1.15158 −0.0430667
\(716\) −16.3825 −0.612244
\(717\) −11.6712 −0.435868
\(718\) 1.48423 0.0553909
\(719\) −29.0124 −1.08198 −0.540990 0.841029i \(-0.681950\pi\)
−0.540990 + 0.841029i \(0.681950\pi\)
\(720\) −1.14798 −0.0427826
\(721\) −7.56789 −0.281843
\(722\) −16.7098 −0.621875
\(723\) −33.6491 −1.25142
\(724\) −3.77800 −0.140408
\(725\) −9.03126 −0.335413
\(726\) 17.0348 0.632220
\(727\) −19.1273 −0.709394 −0.354697 0.934981i \(-0.615416\pi\)
−0.354697 + 0.934981i \(0.615416\pi\)
\(728\) 1.41236 0.0523454
\(729\) 29.7586 1.10217
\(730\) −0.0746917 −0.00276446
\(731\) 41.3858 1.53071
\(732\) 6.01956 0.222489
\(733\) 51.7685 1.91211 0.956056 0.293183i \(-0.0947145\pi\)
0.956056 + 0.293183i \(0.0947145\pi\)
\(734\) 5.56617 0.205451
\(735\) 15.7654 0.581515
\(736\) −3.45744 −0.127443
\(737\) −1.57562 −0.0580388
\(738\) 3.38642 0.124656
\(739\) 3.86051 0.142011 0.0710055 0.997476i \(-0.477379\pi\)
0.0710055 + 0.997476i \(0.477379\pi\)
\(740\) −15.3107 −0.562832
\(741\) 1.94183 0.0713348
\(742\) 0.171871 0.00630958
\(743\) 4.73400 0.173674 0.0868369 0.996223i \(-0.472324\pi\)
0.0868369 + 0.996223i \(0.472324\pi\)
\(744\) 12.4612 0.456848
\(745\) −2.45110 −0.0898014
\(746\) −4.97219 −0.182045
\(747\) −6.93876 −0.253876
\(748\) 2.88544 0.105502
\(749\) −3.46785 −0.126712
\(750\) 14.6261 0.534069
\(751\) 32.0930 1.17109 0.585545 0.810640i \(-0.300881\pi\)
0.585545 + 0.810640i \(0.300881\pi\)
\(752\) 0.390686 0.0142468
\(753\) 31.1399 1.13480
\(754\) 5.31610 0.193601
\(755\) −16.5434 −0.602078
\(756\) −9.67843 −0.352001
\(757\) 16.4083 0.596371 0.298186 0.954508i \(-0.403619\pi\)
0.298186 + 0.954508i \(0.403619\pi\)
\(758\) 31.7453 1.15304
\(759\) 3.12980 0.113605
\(760\) 3.81841 0.138508
\(761\) −36.0755 −1.30774 −0.653869 0.756608i \(-0.726855\pi\)
−0.653869 + 0.756608i \(0.726855\pi\)
\(762\) 15.0927 0.546751
\(763\) −12.4535 −0.450848
\(764\) 8.80926 0.318708
\(765\) −5.83752 −0.211056
\(766\) −13.1805 −0.476229
\(767\) 4.73800 0.171079
\(768\) −1.59531 −0.0575659
\(769\) 29.3025 1.05668 0.528338 0.849034i \(-0.322815\pi\)
0.528338 + 0.849034i \(0.322815\pi\)
\(770\) −2.51408 −0.0906011
\(771\) 45.2590 1.62996
\(772\) −3.87984 −0.139639
\(773\) 8.29702 0.298423 0.149212 0.988805i \(-0.452326\pi\)
0.149212 + 0.988805i \(0.452326\pi\)
\(774\) −3.70290 −0.133098
\(775\) −10.6733 −0.383396
\(776\) −14.3668 −0.515738
\(777\) −16.9984 −0.609813
\(778\) −29.9685 −1.07442
\(779\) −11.2639 −0.403572
\(780\) 3.23761 0.115925
\(781\) 1.58552 0.0567344
\(782\) −17.5812 −0.628703
\(783\) −36.4295 −1.30189
\(784\) −3.91661 −0.139879
\(785\) 39.0018 1.39203
\(786\) 21.2831 0.759142
\(787\) 13.1369 0.468282 0.234141 0.972203i \(-0.424772\pi\)
0.234141 + 0.972203i \(0.424772\pi\)
\(788\) −27.5906 −0.982875
\(789\) 13.9580 0.496916
\(790\) 27.7547 0.987467
\(791\) 1.88948 0.0671823
\(792\) −0.258168 −0.00917361
\(793\) 3.03493 0.107774
\(794\) −32.2937 −1.14606
\(795\) 0.393987 0.0139733
\(796\) −10.6045 −0.375867
\(797\) −49.4952 −1.75321 −0.876604 0.481212i \(-0.840197\pi\)
−0.876604 + 0.481212i \(0.840197\pi\)
\(798\) 4.23930 0.150070
\(799\) 1.98666 0.0702828
\(800\) 1.36643 0.0483104
\(801\) −3.54535 −0.125269
\(802\) −10.9849 −0.387889
\(803\) −0.0167974 −0.000592766 0
\(804\) 4.42978 0.156226
\(805\) 15.3185 0.539906
\(806\) 6.28265 0.221297
\(807\) 22.3179 0.785627
\(808\) −9.19530 −0.323489
\(809\) 50.6723 1.78154 0.890772 0.454450i \(-0.150164\pi\)
0.890772 + 0.454450i \(0.150164\pi\)
\(810\) −18.7424 −0.658540
\(811\) −16.6077 −0.583176 −0.291588 0.956544i \(-0.594184\pi\)
−0.291588 + 0.956544i \(0.594184\pi\)
\(812\) 11.6058 0.407285
\(813\) −10.8896 −0.381914
\(814\) −3.44321 −0.120684
\(815\) −11.5713 −0.405324
\(816\) −8.11225 −0.283985
\(817\) 12.3166 0.430903
\(818\) 0.863408 0.0301883
\(819\) −0.642585 −0.0224537
\(820\) −18.7803 −0.655838
\(821\) 18.1437 0.633219 0.316610 0.948556i \(-0.397455\pi\)
0.316610 + 0.948556i \(0.397455\pi\)
\(822\) −1.24241 −0.0433339
\(823\) −44.7089 −1.55845 −0.779227 0.626742i \(-0.784388\pi\)
−0.779227 + 0.626742i \(0.784388\pi\)
\(824\) 4.30984 0.150140
\(825\) −1.23694 −0.0430648
\(826\) 10.3438 0.359906
\(827\) 4.91716 0.170987 0.0854933 0.996339i \(-0.472753\pi\)
0.0854933 + 0.996339i \(0.472753\pi\)
\(828\) 1.57304 0.0546669
\(829\) 14.5908 0.506759 0.253379 0.967367i \(-0.418458\pi\)
0.253379 + 0.967367i \(0.418458\pi\)
\(830\) 38.4808 1.33569
\(831\) 5.44041 0.188726
\(832\) −0.804323 −0.0278849
\(833\) −19.9162 −0.690054
\(834\) 34.3548 1.18961
\(835\) 38.7733 1.34181
\(836\) 0.858719 0.0296994
\(837\) −43.0530 −1.48813
\(838\) 10.1254 0.349776
\(839\) −22.6055 −0.780428 −0.390214 0.920724i \(-0.627599\pi\)
−0.390214 + 0.920724i \(0.627599\pi\)
\(840\) 7.06819 0.243876
\(841\) 14.6843 0.506355
\(842\) 15.1397 0.521749
\(843\) −42.1283 −1.45098
\(844\) 25.2722 0.869905
\(845\) −31.1690 −1.07225
\(846\) −0.177752 −0.00611123
\(847\) 18.7501 0.644263
\(848\) −0.0978787 −0.00336117
\(849\) −11.7226 −0.402320
\(850\) 6.94833 0.238326
\(851\) 20.9798 0.719178
\(852\) −4.45760 −0.152715
\(853\) 23.9858 0.821258 0.410629 0.911803i \(-0.365309\pi\)
0.410629 + 0.911803i \(0.365309\pi\)
\(854\) 6.62572 0.226727
\(855\) −1.73727 −0.0594134
\(856\) 1.97490 0.0675008
\(857\) 38.3542 1.31015 0.655077 0.755562i \(-0.272636\pi\)
0.655077 + 0.755562i \(0.272636\pi\)
\(858\) 0.728104 0.0248571
\(859\) −47.7816 −1.63029 −0.815144 0.579259i \(-0.803342\pi\)
−0.815144 + 0.579259i \(0.803342\pi\)
\(860\) 20.5354 0.700253
\(861\) −20.8505 −0.710582
\(862\) −15.3926 −0.524273
\(863\) 25.9928 0.884807 0.442403 0.896816i \(-0.354126\pi\)
0.442403 + 0.896816i \(0.354126\pi\)
\(864\) 5.51177 0.187514
\(865\) −3.03804 −0.103296
\(866\) −28.6449 −0.973393
\(867\) −14.1308 −0.479907
\(868\) 13.7160 0.465550
\(869\) 6.24173 0.211736
\(870\) 26.6046 0.901980
\(871\) 2.23340 0.0756758
\(872\) 7.09215 0.240171
\(873\) 6.53651 0.221227
\(874\) −5.23225 −0.176983
\(875\) 16.0989 0.544242
\(876\) 0.0472249 0.00159558
\(877\) 7.05799 0.238331 0.119166 0.992874i \(-0.461978\pi\)
0.119166 + 0.992874i \(0.461978\pi\)
\(878\) −14.0733 −0.474952
\(879\) 37.5153 1.26536
\(880\) 1.43174 0.0482640
\(881\) −11.3977 −0.383999 −0.192000 0.981395i \(-0.561497\pi\)
−0.192000 + 0.981395i \(0.561497\pi\)
\(882\) 1.78195 0.0600015
\(883\) −8.56646 −0.288284 −0.144142 0.989557i \(-0.546042\pi\)
−0.144142 + 0.989557i \(0.546042\pi\)
\(884\) −4.09002 −0.137562
\(885\) 23.7115 0.797053
\(886\) −37.5776 −1.26245
\(887\) −15.9017 −0.533928 −0.266964 0.963706i \(-0.586021\pi\)
−0.266964 + 0.963706i \(0.586021\pi\)
\(888\) 9.68039 0.324853
\(889\) 16.6125 0.557165
\(890\) 19.6617 0.659062
\(891\) −4.21496 −0.141206
\(892\) −1.40610 −0.0470798
\(893\) 0.591237 0.0197850
\(894\) 1.54974 0.0518311
\(895\) −41.3360 −1.38171
\(896\) −1.75596 −0.0586624
\(897\) −4.43640 −0.148127
\(898\) 25.2836 0.843726
\(899\) 51.6268 1.72185
\(900\) −0.621687 −0.0207229
\(901\) −0.497718 −0.0165814
\(902\) −4.22350 −0.140627
\(903\) 22.7990 0.758704
\(904\) −1.07604 −0.0357886
\(905\) −9.53258 −0.316874
\(906\) 10.4598 0.347504
\(907\) −26.6818 −0.885956 −0.442978 0.896532i \(-0.646078\pi\)
−0.442978 + 0.896532i \(0.646078\pi\)
\(908\) 17.3271 0.575021
\(909\) 4.18361 0.138762
\(910\) 3.56363 0.118133
\(911\) 52.2869 1.73234 0.866172 0.499746i \(-0.166573\pi\)
0.866172 + 0.499746i \(0.166573\pi\)
\(912\) −2.41424 −0.0799435
\(913\) 8.65392 0.286403
\(914\) 3.10932 0.102847
\(915\) 15.1884 0.502114
\(916\) −14.2781 −0.471760
\(917\) 23.4262 0.773602
\(918\) 28.0276 0.925048
\(919\) 20.2470 0.667886 0.333943 0.942593i \(-0.391621\pi\)
0.333943 + 0.942593i \(0.391621\pi\)
\(920\) −8.72373 −0.287613
\(921\) 5.09369 0.167843
\(922\) −30.2967 −0.997769
\(923\) −2.24742 −0.0739749
\(924\) 1.58956 0.0522927
\(925\) −8.29149 −0.272623
\(926\) −30.6325 −1.00665
\(927\) −1.96086 −0.0644031
\(928\) −6.60941 −0.216965
\(929\) 21.5852 0.708188 0.354094 0.935210i \(-0.384789\pi\)
0.354094 + 0.935210i \(0.384789\pi\)
\(930\) 31.4417 1.03101
\(931\) −5.92713 −0.194254
\(932\) −2.31363 −0.0757854
\(933\) −26.1557 −0.856298
\(934\) −8.25943 −0.270257
\(935\) 7.28047 0.238097
\(936\) 0.365945 0.0119613
\(937\) 26.7059 0.872444 0.436222 0.899839i \(-0.356316\pi\)
0.436222 + 0.899839i \(0.356316\pi\)
\(938\) 4.87584 0.159202
\(939\) −31.4159 −1.02522
\(940\) 0.985770 0.0321523
\(941\) 2.96519 0.0966625 0.0483313 0.998831i \(-0.484610\pi\)
0.0483313 + 0.998831i \(0.484610\pi\)
\(942\) −24.6594 −0.803448
\(943\) 25.7341 0.838019
\(944\) −5.89067 −0.191725
\(945\) −24.4204 −0.794396
\(946\) 4.61820 0.150151
\(947\) 52.3832 1.70223 0.851113 0.524983i \(-0.175928\pi\)
0.851113 + 0.524983i \(0.175928\pi\)
\(948\) −17.5483 −0.569941
\(949\) 0.0238098 0.000772897 0
\(950\) 2.06785 0.0670901
\(951\) −23.3518 −0.757233
\(952\) −8.92913 −0.289395
\(953\) 19.3951 0.628267 0.314134 0.949379i \(-0.398286\pi\)
0.314134 + 0.949379i \(0.398286\pi\)
\(954\) 0.0445322 0.00144178
\(955\) 22.2273 0.719259
\(956\) 7.31592 0.236614
\(957\) 5.98309 0.193406
\(958\) 2.56371 0.0828296
\(959\) −1.36751 −0.0441593
\(960\) −4.02526 −0.129915
\(961\) 30.0133 0.968171
\(962\) 4.88064 0.157358
\(963\) −0.898528 −0.0289547
\(964\) 21.0925 0.679342
\(965\) −9.78953 −0.315136
\(966\) −9.68533 −0.311620
\(967\) −6.75666 −0.217280 −0.108640 0.994081i \(-0.534650\pi\)
−0.108640 + 0.994081i \(0.534650\pi\)
\(968\) −10.6780 −0.343204
\(969\) −12.2765 −0.394379
\(970\) −36.2500 −1.16392
\(971\) −36.5801 −1.17391 −0.586956 0.809619i \(-0.699674\pi\)
−0.586956 + 0.809619i \(0.699674\pi\)
\(972\) −4.68518 −0.150277
\(973\) 37.8142 1.21227
\(974\) −0.185623 −0.00594774
\(975\) 1.75332 0.0561513
\(976\) −3.77328 −0.120780
\(977\) 33.1882 1.06179 0.530893 0.847439i \(-0.321857\pi\)
0.530893 + 0.847439i \(0.321857\pi\)
\(978\) 7.31610 0.233943
\(979\) 4.42171 0.141319
\(980\) −9.88231 −0.315679
\(981\) −3.22674 −0.103022
\(982\) 2.45074 0.0782062
\(983\) −12.3856 −0.395040 −0.197520 0.980299i \(-0.563289\pi\)
−0.197520 + 0.980299i \(0.563289\pi\)
\(984\) 11.8741 0.378533
\(985\) −69.6160 −2.21815
\(986\) −33.6092 −1.07033
\(987\) 1.09443 0.0348361
\(988\) −1.21721 −0.0387245
\(989\) −28.1391 −0.894772
\(990\) −0.651404 −0.0207030
\(991\) −42.2842 −1.34320 −0.671601 0.740913i \(-0.734393\pi\)
−0.671601 + 0.740913i \(0.734393\pi\)
\(992\) −7.81110 −0.248003
\(993\) −4.08722 −0.129704
\(994\) −4.90647 −0.155624
\(995\) −26.7571 −0.848256
\(996\) −24.3300 −0.770925
\(997\) 10.0661 0.318796 0.159398 0.987214i \(-0.449045\pi\)
0.159398 + 0.987214i \(0.449045\pi\)
\(998\) 23.6939 0.750017
\(999\) −33.4455 −1.05817
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 \(a_p\))