Properties

Label 8047.2.a.a.1.2
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\)
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.61803 q^{2}\) \(-2.61803 q^{3}\) \(+0.618034 q^{4}\) \(-1.23607 q^{5}\) \(-4.23607 q^{6}\) \(-0.381966 q^{7}\) \(-2.23607 q^{8}\) \(+3.85410 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.61803 q^{2}\) \(-2.61803 q^{3}\) \(+0.618034 q^{4}\) \(-1.23607 q^{5}\) \(-4.23607 q^{6}\) \(-0.381966 q^{7}\) \(-2.23607 q^{8}\) \(+3.85410 q^{9}\) \(-2.00000 q^{10}\) \(+5.00000 q^{11}\) \(-1.61803 q^{12}\) \(-1.00000 q^{13}\) \(-0.618034 q^{14}\) \(+3.23607 q^{15}\) \(-4.85410 q^{16}\) \(-0.236068 q^{17}\) \(+6.23607 q^{18}\) \(-3.76393 q^{19}\) \(-0.763932 q^{20}\) \(+1.00000 q^{21}\) \(+8.09017 q^{22}\) \(-4.00000 q^{23}\) \(+5.85410 q^{24}\) \(-3.47214 q^{25}\) \(-1.61803 q^{26}\) \(-2.23607 q^{27}\) \(-0.236068 q^{28}\) \(+2.76393 q^{29}\) \(+5.23607 q^{30}\) \(-1.76393 q^{31}\) \(-3.38197 q^{32}\) \(-13.0902 q^{33}\) \(-0.381966 q^{34}\) \(+0.472136 q^{35}\) \(+2.38197 q^{36}\) \(+6.47214 q^{37}\) \(-6.09017 q^{38}\) \(+2.61803 q^{39}\) \(+2.76393 q^{40}\) \(-0.236068 q^{41}\) \(+1.61803 q^{42}\) \(-4.76393 q^{43}\) \(+3.09017 q^{44}\) \(-4.76393 q^{45}\) \(-6.47214 q^{46}\) \(+11.8541 q^{47}\) \(+12.7082 q^{48}\) \(-6.85410 q^{49}\) \(-5.61803 q^{50}\) \(+0.618034 q^{51}\) \(-0.618034 q^{52}\) \(-7.70820 q^{53}\) \(-3.61803 q^{54}\) \(-6.18034 q^{55}\) \(+0.854102 q^{56}\) \(+9.85410 q^{57}\) \(+4.47214 q^{58}\) \(-0.0901699 q^{59}\) \(+2.00000 q^{60}\) \(-5.94427 q^{61}\) \(-2.85410 q^{62}\) \(-1.47214 q^{63}\) \(+4.23607 q^{64}\) \(+1.23607 q^{65}\) \(-21.1803 q^{66}\) \(+6.70820 q^{67}\) \(-0.145898 q^{68}\) \(+10.4721 q^{69}\) \(+0.763932 q^{70}\) \(-13.1803 q^{71}\) \(-8.61803 q^{72}\) \(-13.4164 q^{73}\) \(+10.4721 q^{74}\) \(+9.09017 q^{75}\) \(-2.32624 q^{76}\) \(-1.90983 q^{77}\) \(+4.23607 q^{78}\) \(-0.527864 q^{79}\) \(+6.00000 q^{80}\) \(-5.70820 q^{81}\) \(-0.381966 q^{82}\) \(-6.23607 q^{83}\) \(+0.618034 q^{84}\) \(+0.291796 q^{85}\) \(-7.70820 q^{86}\) \(-7.23607 q^{87}\) \(-11.1803 q^{88}\) \(+6.85410 q^{89}\) \(-7.70820 q^{90}\) \(+0.381966 q^{91}\) \(-2.47214 q^{92}\) \(+4.61803 q^{93}\) \(+19.1803 q^{94}\) \(+4.65248 q^{95}\) \(+8.85410 q^{96}\) \(+15.0902 q^{97}\) \(-11.0902 q^{98}\) \(+19.2705 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 5q^{24} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut q^{26} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut q^{38} \) \(\mathstrut +\mathstrut 3q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 5q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 17q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut +\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut q^{62} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 7q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 11q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 12q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut +\mathstrut 14q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 10q^{87} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 7q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 22q^{95} \) \(\mathstrut +\mathstrut 11q^{96} \) \(\mathstrut +\mathstrut 19q^{97} \) \(\mathstrut -\mathstrut 11q^{98} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61803 1.14412 0.572061 0.820211i \(-0.306144\pi\)
0.572061 + 0.820211i \(0.306144\pi\)
\(3\) −2.61803 −1.51152 −0.755761 0.654847i \(-0.772733\pi\)
−0.755761 + 0.654847i \(0.772733\pi\)
\(4\) 0.618034 0.309017
\(5\) −1.23607 −0.552786 −0.276393 0.961045i \(-0.589139\pi\)
−0.276393 + 0.961045i \(0.589139\pi\)
\(6\) −4.23607 −1.72937
\(7\) −0.381966 −0.144370 −0.0721848 0.997391i \(-0.522997\pi\)
−0.0721848 + 0.997391i \(0.522997\pi\)
\(8\) −2.23607 −0.790569
\(9\) 3.85410 1.28470
\(10\) −2.00000 −0.632456
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) −1.61803 −0.467086
\(13\) −1.00000 −0.277350
\(14\) −0.618034 −0.165177
\(15\) 3.23607 0.835549
\(16\) −4.85410 −1.21353
\(17\) −0.236068 −0.0572549 −0.0286274 0.999590i \(-0.509114\pi\)
−0.0286274 + 0.999590i \(0.509114\pi\)
\(18\) 6.23607 1.46986
\(19\) −3.76393 −0.863505 −0.431753 0.901992i \(-0.642105\pi\)
−0.431753 + 0.901992i \(0.642105\pi\)
\(20\) −0.763932 −0.170820
\(21\) 1.00000 0.218218
\(22\) 8.09017 1.72483
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 5.85410 1.19496
\(25\) −3.47214 −0.694427
\(26\) −1.61803 −0.317323
\(27\) −2.23607 −0.430331
\(28\) −0.236068 −0.0446127
\(29\) 2.76393 0.513249 0.256625 0.966511i \(-0.417390\pi\)
0.256625 + 0.966511i \(0.417390\pi\)
\(30\) 5.23607 0.955971
\(31\) −1.76393 −0.316812 −0.158406 0.987374i \(-0.550635\pi\)
−0.158406 + 0.987374i \(0.550635\pi\)
\(32\) −3.38197 −0.597853
\(33\) −13.0902 −2.27871
\(34\) −0.381966 −0.0655066
\(35\) 0.472136 0.0798055
\(36\) 2.38197 0.396994
\(37\) 6.47214 1.06401 0.532006 0.846740i \(-0.321438\pi\)
0.532006 + 0.846740i \(0.321438\pi\)
\(38\) −6.09017 −0.987956
\(39\) 2.61803 0.419221
\(40\) 2.76393 0.437016
\(41\) −0.236068 −0.0368676 −0.0184338 0.999830i \(-0.505868\pi\)
−0.0184338 + 0.999830i \(0.505868\pi\)
\(42\) 1.61803 0.249668
\(43\) −4.76393 −0.726493 −0.363246 0.931693i \(-0.618332\pi\)
−0.363246 + 0.931693i \(0.618332\pi\)
\(44\) 3.09017 0.465861
\(45\) −4.76393 −0.710165
\(46\) −6.47214 −0.954264
\(47\) 11.8541 1.72910 0.864549 0.502548i \(-0.167604\pi\)
0.864549 + 0.502548i \(0.167604\pi\)
\(48\) 12.7082 1.83427
\(49\) −6.85410 −0.979157
\(50\) −5.61803 −0.794510
\(51\) 0.618034 0.0865421
\(52\) −0.618034 −0.0857059
\(53\) −7.70820 −1.05880 −0.529402 0.848371i \(-0.677584\pi\)
−0.529402 + 0.848371i \(0.677584\pi\)
\(54\) −3.61803 −0.492352
\(55\) −6.18034 −0.833357
\(56\) 0.854102 0.114134
\(57\) 9.85410 1.30521
\(58\) 4.47214 0.587220
\(59\) −0.0901699 −0.0117391 −0.00586956 0.999983i \(-0.501868\pi\)
−0.00586956 + 0.999983i \(0.501868\pi\)
\(60\) 2.00000 0.258199
\(61\) −5.94427 −0.761086 −0.380543 0.924763i \(-0.624263\pi\)
−0.380543 + 0.924763i \(0.624263\pi\)
\(62\) −2.85410 −0.362471
\(63\) −1.47214 −0.185472
\(64\) 4.23607 0.529508
\(65\) 1.23607 0.153315
\(66\) −21.1803 −2.60712
\(67\) 6.70820 0.819538 0.409769 0.912189i \(-0.365609\pi\)
0.409769 + 0.912189i \(0.365609\pi\)
\(68\) −0.145898 −0.0176927
\(69\) 10.4721 1.26070
\(70\) 0.763932 0.0913073
\(71\) −13.1803 −1.56422 −0.782109 0.623141i \(-0.785856\pi\)
−0.782109 + 0.623141i \(0.785856\pi\)
\(72\) −8.61803 −1.01565
\(73\) −13.4164 −1.57027 −0.785136 0.619324i \(-0.787407\pi\)
−0.785136 + 0.619324i \(0.787407\pi\)
\(74\) 10.4721 1.21736
\(75\) 9.09017 1.04964
\(76\) −2.32624 −0.266838
\(77\) −1.90983 −0.217645
\(78\) 4.23607 0.479640
\(79\) −0.527864 −0.0593893 −0.0296947 0.999559i \(-0.509453\pi\)
−0.0296947 + 0.999559i \(0.509453\pi\)
\(80\) 6.00000 0.670820
\(81\) −5.70820 −0.634245
\(82\) −0.381966 −0.0421811
\(83\) −6.23607 −0.684497 −0.342249 0.939609i \(-0.611189\pi\)
−0.342249 + 0.939609i \(0.611189\pi\)
\(84\) 0.618034 0.0674330
\(85\) 0.291796 0.0316497
\(86\) −7.70820 −0.831197
\(87\) −7.23607 −0.775788
\(88\) −11.1803 −1.19183
\(89\) 6.85410 0.726533 0.363267 0.931685i \(-0.381661\pi\)
0.363267 + 0.931685i \(0.381661\pi\)
\(90\) −7.70820 −0.812516
\(91\) 0.381966 0.0400409
\(92\) −2.47214 −0.257738
\(93\) 4.61803 0.478868
\(94\) 19.1803 1.97830
\(95\) 4.65248 0.477334
\(96\) 8.85410 0.903668
\(97\) 15.0902 1.53217 0.766087 0.642737i \(-0.222201\pi\)
0.766087 + 0.642737i \(0.222201\pi\)
\(98\) −11.0902 −1.12028
\(99\) 19.2705 1.93676
\(100\) −2.14590 −0.214590
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 1.00000 0.0990148
\(103\) 10.7984 1.06400 0.531998 0.846746i \(-0.321441\pi\)
0.531998 + 0.846746i \(0.321441\pi\)
\(104\) 2.23607 0.219265
\(105\) −1.23607 −0.120628
\(106\) −12.4721 −1.21140
\(107\) −11.0000 −1.06341 −0.531705 0.846930i \(-0.678449\pi\)
−0.531705 + 0.846930i \(0.678449\pi\)
\(108\) −1.38197 −0.132980
\(109\) −5.29180 −0.506862 −0.253431 0.967353i \(-0.581559\pi\)
−0.253431 + 0.967353i \(0.581559\pi\)
\(110\) −10.0000 −0.953463
\(111\) −16.9443 −1.60828
\(112\) 1.85410 0.175196
\(113\) −5.09017 −0.478843 −0.239421 0.970916i \(-0.576958\pi\)
−0.239421 + 0.970916i \(0.576958\pi\)
\(114\) 15.9443 1.49332
\(115\) 4.94427 0.461056
\(116\) 1.70820 0.158603
\(117\) −3.85410 −0.356312
\(118\) −0.145898 −0.0134310
\(119\) 0.0901699 0.00826587
\(120\) −7.23607 −0.660560
\(121\) 14.0000 1.27273
\(122\) −9.61803 −0.870776
\(123\) 0.618034 0.0557262
\(124\) −1.09017 −0.0979002
\(125\) 10.4721 0.936656
\(126\) −2.38197 −0.212202
\(127\) −4.79837 −0.425787 −0.212893 0.977075i \(-0.568289\pi\)
−0.212893 + 0.977075i \(0.568289\pi\)
\(128\) 13.6180 1.20368
\(129\) 12.4721 1.09811
\(130\) 2.00000 0.175412
\(131\) 10.4164 0.910086 0.455043 0.890470i \(-0.349624\pi\)
0.455043 + 0.890470i \(0.349624\pi\)
\(132\) −8.09017 −0.704159
\(133\) 1.43769 0.124664
\(134\) 10.8541 0.937652
\(135\) 2.76393 0.237881
\(136\) 0.527864 0.0452640
\(137\) 0.291796 0.0249298 0.0124649 0.999922i \(-0.496032\pi\)
0.0124649 + 0.999922i \(0.496032\pi\)
\(138\) 16.9443 1.44239
\(139\) −1.23607 −0.104842 −0.0524210 0.998625i \(-0.516694\pi\)
−0.0524210 + 0.998625i \(0.516694\pi\)
\(140\) 0.291796 0.0246613
\(141\) −31.0344 −2.61357
\(142\) −21.3262 −1.78966
\(143\) −5.00000 −0.418121
\(144\) −18.7082 −1.55902
\(145\) −3.41641 −0.283717
\(146\) −21.7082 −1.79658
\(147\) 17.9443 1.48002
\(148\) 4.00000 0.328798
\(149\) −14.3820 −1.17822 −0.589108 0.808054i \(-0.700521\pi\)
−0.589108 + 0.808054i \(0.700521\pi\)
\(150\) 14.7082 1.20092
\(151\) 20.9443 1.70442 0.852210 0.523199i \(-0.175262\pi\)
0.852210 + 0.523199i \(0.175262\pi\)
\(152\) 8.41641 0.682661
\(153\) −0.909830 −0.0735554
\(154\) −3.09017 −0.249013
\(155\) 2.18034 0.175129
\(156\) 1.61803 0.129546
\(157\) 16.9443 1.35230 0.676150 0.736764i \(-0.263647\pi\)
0.676150 + 0.736764i \(0.263647\pi\)
\(158\) −0.854102 −0.0679487
\(159\) 20.1803 1.60041
\(160\) 4.18034 0.330485
\(161\) 1.52786 0.120413
\(162\) −9.23607 −0.725654
\(163\) −12.7082 −0.995383 −0.497692 0.867354i \(-0.665819\pi\)
−0.497692 + 0.867354i \(0.665819\pi\)
\(164\) −0.145898 −0.0113927
\(165\) 16.1803 1.25964
\(166\) −10.0902 −0.783149
\(167\) 3.05573 0.236459 0.118230 0.992986i \(-0.462278\pi\)
0.118230 + 0.992986i \(0.462278\pi\)
\(168\) −2.23607 −0.172516
\(169\) 1.00000 0.0769231
\(170\) 0.472136 0.0362112
\(171\) −14.5066 −1.10935
\(172\) −2.94427 −0.224499
\(173\) 16.7082 1.27030 0.635151 0.772388i \(-0.280938\pi\)
0.635151 + 0.772388i \(0.280938\pi\)
\(174\) −11.7082 −0.887597
\(175\) 1.32624 0.100254
\(176\) −24.2705 −1.82946
\(177\) 0.236068 0.0177440
\(178\) 11.0902 0.831243
\(179\) 9.29180 0.694501 0.347251 0.937772i \(-0.387115\pi\)
0.347251 + 0.937772i \(0.387115\pi\)
\(180\) −2.94427 −0.219453
\(181\) 13.7639 1.02307 0.511533 0.859264i \(-0.329078\pi\)
0.511533 + 0.859264i \(0.329078\pi\)
\(182\) 0.618034 0.0458117
\(183\) 15.5623 1.15040
\(184\) 8.94427 0.659380
\(185\) −8.00000 −0.588172
\(186\) 7.47214 0.547884
\(187\) −1.18034 −0.0863150
\(188\) 7.32624 0.534321
\(189\) 0.854102 0.0621268
\(190\) 7.52786 0.546129
\(191\) −22.7984 −1.64963 −0.824816 0.565401i \(-0.808721\pi\)
−0.824816 + 0.565401i \(0.808721\pi\)
\(192\) −11.0902 −0.800364
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 24.4164 1.75300
\(195\) −3.23607 −0.231740
\(196\) −4.23607 −0.302576
\(197\) −7.56231 −0.538792 −0.269396 0.963029i \(-0.586824\pi\)
−0.269396 + 0.963029i \(0.586824\pi\)
\(198\) 31.1803 2.21589
\(199\) −0.381966 −0.0270769 −0.0135384 0.999908i \(-0.504310\pi\)
−0.0135384 + 0.999908i \(0.504310\pi\)
\(200\) 7.76393 0.548993
\(201\) −17.5623 −1.23875
\(202\) −9.70820 −0.683067
\(203\) −1.05573 −0.0740976
\(204\) 0.381966 0.0267430
\(205\) 0.291796 0.0203799
\(206\) 17.4721 1.21734
\(207\) −15.4164 −1.07151
\(208\) 4.85410 0.336571
\(209\) −18.8197 −1.30178
\(210\) −2.00000 −0.138013
\(211\) 14.2705 0.982422 0.491211 0.871040i \(-0.336554\pi\)
0.491211 + 0.871040i \(0.336554\pi\)
\(212\) −4.76393 −0.327188
\(213\) 34.5066 2.36435
\(214\) −17.7984 −1.21667
\(215\) 5.88854 0.401595
\(216\) 5.00000 0.340207
\(217\) 0.673762 0.0457380
\(218\) −8.56231 −0.579913
\(219\) 35.1246 2.37350
\(220\) −3.81966 −0.257521
\(221\) 0.236068 0.0158797
\(222\) −27.4164 −1.84007
\(223\) 7.90983 0.529681 0.264841 0.964292i \(-0.414681\pi\)
0.264841 + 0.964292i \(0.414681\pi\)
\(224\) 1.29180 0.0863118
\(225\) −13.3820 −0.892131
\(226\) −8.23607 −0.547855
\(227\) 6.41641 0.425872 0.212936 0.977066i \(-0.431697\pi\)
0.212936 + 0.977066i \(0.431697\pi\)
\(228\) 6.09017 0.403331
\(229\) 17.4164 1.15091 0.575454 0.817834i \(-0.304825\pi\)
0.575454 + 0.817834i \(0.304825\pi\)
\(230\) 8.00000 0.527504
\(231\) 5.00000 0.328976
\(232\) −6.18034 −0.405759
\(233\) 15.5623 1.01952 0.509760 0.860316i \(-0.329734\pi\)
0.509760 + 0.860316i \(0.329734\pi\)
\(234\) −6.23607 −0.407665
\(235\) −14.6525 −0.955822
\(236\) −0.0557281 −0.00362759
\(237\) 1.38197 0.0897683
\(238\) 0.145898 0.00945716
\(239\) 2.29180 0.148244 0.0741220 0.997249i \(-0.476385\pi\)
0.0741220 + 0.997249i \(0.476385\pi\)
\(240\) −15.7082 −1.01396
\(241\) 24.8885 1.60321 0.801606 0.597853i \(-0.203979\pi\)
0.801606 + 0.597853i \(0.203979\pi\)
\(242\) 22.6525 1.45616
\(243\) 21.6525 1.38901
\(244\) −3.67376 −0.235189
\(245\) 8.47214 0.541265
\(246\) 1.00000 0.0637577
\(247\) 3.76393 0.239493
\(248\) 3.94427 0.250462
\(249\) 16.3262 1.03463
\(250\) 16.9443 1.07165
\(251\) 10.5279 0.664513 0.332256 0.943189i \(-0.392190\pi\)
0.332256 + 0.943189i \(0.392190\pi\)
\(252\) −0.909830 −0.0573139
\(253\) −20.0000 −1.25739
\(254\) −7.76393 −0.487152
\(255\) −0.763932 −0.0478393
\(256\) 13.5623 0.847644
\(257\) 23.1803 1.44595 0.722975 0.690874i \(-0.242774\pi\)
0.722975 + 0.690874i \(0.242774\pi\)
\(258\) 20.1803 1.25637
\(259\) −2.47214 −0.153611
\(260\) 0.763932 0.0473771
\(261\) 10.6525 0.659372
\(262\) 16.8541 1.04125
\(263\) 13.7639 0.848720 0.424360 0.905493i \(-0.360499\pi\)
0.424360 + 0.905493i \(0.360499\pi\)
\(264\) 29.2705 1.80148
\(265\) 9.52786 0.585292
\(266\) 2.32624 0.142631
\(267\) −17.9443 −1.09817
\(268\) 4.14590 0.253251
\(269\) 10.7639 0.656289 0.328144 0.944628i \(-0.393577\pi\)
0.328144 + 0.944628i \(0.393577\pi\)
\(270\) 4.47214 0.272166
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) 1.14590 0.0694803
\(273\) −1.00000 −0.0605228
\(274\) 0.472136 0.0285228
\(275\) −17.3607 −1.04689
\(276\) 6.47214 0.389577
\(277\) 7.03444 0.422659 0.211329 0.977415i \(-0.432221\pi\)
0.211329 + 0.977415i \(0.432221\pi\)
\(278\) −2.00000 −0.119952
\(279\) −6.79837 −0.407008
\(280\) −1.05573 −0.0630918
\(281\) 13.2918 0.792922 0.396461 0.918052i \(-0.370238\pi\)
0.396461 + 0.918052i \(0.370238\pi\)
\(282\) −50.2148 −2.99025
\(283\) 20.7082 1.23097 0.615487 0.788147i \(-0.288959\pi\)
0.615487 + 0.788147i \(0.288959\pi\)
\(284\) −8.14590 −0.483370
\(285\) −12.1803 −0.721501
\(286\) −8.09017 −0.478382
\(287\) 0.0901699 0.00532256
\(288\) −13.0344 −0.768062
\(289\) −16.9443 −0.996722
\(290\) −5.52786 −0.324607
\(291\) −39.5066 −2.31592
\(292\) −8.29180 −0.485241
\(293\) 19.7426 1.15338 0.576689 0.816964i \(-0.304345\pi\)
0.576689 + 0.816964i \(0.304345\pi\)
\(294\) 29.0344 1.69332
\(295\) 0.111456 0.00648923
\(296\) −14.4721 −0.841176
\(297\) −11.1803 −0.648749
\(298\) −23.2705 −1.34802
\(299\) 4.00000 0.231326
\(300\) 5.61803 0.324357
\(301\) 1.81966 0.104883
\(302\) 33.8885 1.95007
\(303\) 15.7082 0.902413
\(304\) 18.2705 1.04789
\(305\) 7.34752 0.420718
\(306\) −1.47214 −0.0841564
\(307\) 10.8541 0.619476 0.309738 0.950822i \(-0.399759\pi\)
0.309738 + 0.950822i \(0.399759\pi\)
\(308\) −1.18034 −0.0672561
\(309\) −28.2705 −1.60825
\(310\) 3.52786 0.200369
\(311\) −24.7082 −1.40107 −0.700537 0.713616i \(-0.747056\pi\)
−0.700537 + 0.713616i \(0.747056\pi\)
\(312\) −5.85410 −0.331423
\(313\) 18.0000 1.01742 0.508710 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 27.4164 1.54720
\(315\) 1.81966 0.102526
\(316\) −0.326238 −0.0183523
\(317\) −20.8885 −1.17322 −0.586609 0.809870i \(-0.699537\pi\)
−0.586609 + 0.809870i \(0.699537\pi\)
\(318\) 32.6525 1.83106
\(319\) 13.8197 0.773752
\(320\) −5.23607 −0.292705
\(321\) 28.7984 1.60737
\(322\) 2.47214 0.137767
\(323\) 0.888544 0.0494399
\(324\) −3.52786 −0.195992
\(325\) 3.47214 0.192599
\(326\) −20.5623 −1.13884
\(327\) 13.8541 0.766134
\(328\) 0.527864 0.0291464
\(329\) −4.52786 −0.249629
\(330\) 26.1803 1.44118
\(331\) 22.0344 1.21112 0.605561 0.795799i \(-0.292949\pi\)
0.605561 + 0.795799i \(0.292949\pi\)
\(332\) −3.85410 −0.211521
\(333\) 24.9443 1.36694
\(334\) 4.94427 0.270539
\(335\) −8.29180 −0.453029
\(336\) −4.85410 −0.264813
\(337\) 24.3262 1.32513 0.662567 0.749002i \(-0.269467\pi\)
0.662567 + 0.749002i \(0.269467\pi\)
\(338\) 1.61803 0.0880094
\(339\) 13.3262 0.723782
\(340\) 0.180340 0.00978030
\(341\) −8.81966 −0.477611
\(342\) −23.4721 −1.26923
\(343\) 5.29180 0.285730
\(344\) 10.6525 0.574343
\(345\) −12.9443 −0.696896
\(346\) 27.0344 1.45338
\(347\) −0.763932 −0.0410100 −0.0205050 0.999790i \(-0.506527\pi\)
−0.0205050 + 0.999790i \(0.506527\pi\)
\(348\) −4.47214 −0.239732
\(349\) −11.4721 −0.614089 −0.307045 0.951695i \(-0.599340\pi\)
−0.307045 + 0.951695i \(0.599340\pi\)
\(350\) 2.14590 0.114703
\(351\) 2.23607 0.119352
\(352\) −16.9098 −0.901297
\(353\) −19.6525 −1.04600 −0.522998 0.852334i \(-0.675186\pi\)
−0.522998 + 0.852334i \(0.675186\pi\)
\(354\) 0.381966 0.0203013
\(355\) 16.2918 0.864679
\(356\) 4.23607 0.224511
\(357\) −0.236068 −0.0124940
\(358\) 15.0344 0.794595
\(359\) 3.47214 0.183252 0.0916262 0.995793i \(-0.470794\pi\)
0.0916262 + 0.995793i \(0.470794\pi\)
\(360\) 10.6525 0.561435
\(361\) −4.83282 −0.254359
\(362\) 22.2705 1.17051
\(363\) −36.6525 −1.92376
\(364\) 0.236068 0.0123733
\(365\) 16.5836 0.868025
\(366\) 25.1803 1.31620
\(367\) 21.5623 1.12554 0.562772 0.826612i \(-0.309735\pi\)
0.562772 + 0.826612i \(0.309735\pi\)
\(368\) 19.4164 1.01215
\(369\) −0.909830 −0.0473639
\(370\) −12.9443 −0.672941
\(371\) 2.94427 0.152859
\(372\) 2.85410 0.147978
\(373\) −1.85410 −0.0960018 −0.0480009 0.998847i \(-0.515285\pi\)
−0.0480009 + 0.998847i \(0.515285\pi\)
\(374\) −1.90983 −0.0987550
\(375\) −27.4164 −1.41578
\(376\) −26.5066 −1.36697
\(377\) −2.76393 −0.142350
\(378\) 1.38197 0.0710807
\(379\) −27.1246 −1.39330 −0.696649 0.717412i \(-0.745326\pi\)
−0.696649 + 0.717412i \(0.745326\pi\)
\(380\) 2.87539 0.147504
\(381\) 12.5623 0.643586
\(382\) −36.8885 −1.88738
\(383\) −25.7082 −1.31363 −0.656814 0.754053i \(-0.728096\pi\)
−0.656814 + 0.754053i \(0.728096\pi\)
\(384\) −35.6525 −1.81938
\(385\) 2.36068 0.120311
\(386\) 9.70820 0.494135
\(387\) −18.3607 −0.933326
\(388\) 9.32624 0.473468
\(389\) 25.4164 1.28866 0.644332 0.764746i \(-0.277136\pi\)
0.644332 + 0.764746i \(0.277136\pi\)
\(390\) −5.23607 −0.265139
\(391\) 0.944272 0.0477539
\(392\) 15.3262 0.774092
\(393\) −27.2705 −1.37562
\(394\) −12.2361 −0.616444
\(395\) 0.652476 0.0328296
\(396\) 11.9098 0.598491
\(397\) −25.9443 −1.30211 −0.651053 0.759032i \(-0.725672\pi\)
−0.651053 + 0.759032i \(0.725672\pi\)
\(398\) −0.618034 −0.0309792
\(399\) −3.76393 −0.188432
\(400\) 16.8541 0.842705
\(401\) 15.4721 0.772642 0.386321 0.922364i \(-0.373746\pi\)
0.386321 + 0.922364i \(0.373746\pi\)
\(402\) −28.4164 −1.41728
\(403\) 1.76393 0.0878677
\(404\) −3.70820 −0.184490
\(405\) 7.05573 0.350602
\(406\) −1.70820 −0.0847767
\(407\) 32.3607 1.60406
\(408\) −1.38197 −0.0684175
\(409\) 4.27051 0.211163 0.105582 0.994411i \(-0.466330\pi\)
0.105582 + 0.994411i \(0.466330\pi\)
\(410\) 0.472136 0.0233171
\(411\) −0.763932 −0.0376820
\(412\) 6.67376 0.328793
\(413\) 0.0344419 0.00169477
\(414\) −24.9443 −1.22594
\(415\) 7.70820 0.378381
\(416\) 3.38197 0.165815
\(417\) 3.23607 0.158471
\(418\) −30.4508 −1.48940
\(419\) 15.6525 0.764673 0.382337 0.924023i \(-0.375119\pi\)
0.382337 + 0.924023i \(0.375119\pi\)
\(420\) −0.763932 −0.0372761
\(421\) 26.4721 1.29017 0.645086 0.764110i \(-0.276821\pi\)
0.645086 + 0.764110i \(0.276821\pi\)
\(422\) 23.0902 1.12401
\(423\) 45.6869 2.22137
\(424\) 17.2361 0.837057
\(425\) 0.819660 0.0397594
\(426\) 55.8328 2.70511
\(427\) 2.27051 0.109878
\(428\) −6.79837 −0.328612
\(429\) 13.0902 0.631999
\(430\) 9.52786 0.459474
\(431\) 26.4164 1.27243 0.636217 0.771510i \(-0.280498\pi\)
0.636217 + 0.771510i \(0.280498\pi\)
\(432\) 10.8541 0.522218
\(433\) 5.43769 0.261319 0.130659 0.991427i \(-0.458291\pi\)
0.130659 + 0.991427i \(0.458291\pi\)
\(434\) 1.09017 0.0523298
\(435\) 8.94427 0.428845
\(436\) −3.27051 −0.156629
\(437\) 15.0557 0.720213
\(438\) 56.8328 2.71558
\(439\) 23.0557 1.10039 0.550195 0.835036i \(-0.314553\pi\)
0.550195 + 0.835036i \(0.314553\pi\)
\(440\) 13.8197 0.658826
\(441\) −26.4164 −1.25792
\(442\) 0.381966 0.0181683
\(443\) −15.1459 −0.719603 −0.359802 0.933029i \(-0.617156\pi\)
−0.359802 + 0.933029i \(0.617156\pi\)
\(444\) −10.4721 −0.496986
\(445\) −8.47214 −0.401618
\(446\) 12.7984 0.606021
\(447\) 37.6525 1.78090
\(448\) −1.61803 −0.0764449
\(449\) −6.12461 −0.289038 −0.144519 0.989502i \(-0.546164\pi\)
−0.144519 + 0.989502i \(0.546164\pi\)
\(450\) −21.6525 −1.02071
\(451\) −1.18034 −0.0555800
\(452\) −3.14590 −0.147971
\(453\) −54.8328 −2.57627
\(454\) 10.3820 0.487250
\(455\) −0.472136 −0.0221341
\(456\) −22.0344 −1.03186
\(457\) 3.76393 0.176069 0.0880347 0.996117i \(-0.471941\pi\)
0.0880347 + 0.996117i \(0.471941\pi\)
\(458\) 28.1803 1.31678
\(459\) 0.527864 0.0246386
\(460\) 3.05573 0.142474
\(461\) −0.0901699 −0.00419963 −0.00209982 0.999998i \(-0.500668\pi\)
−0.00209982 + 0.999998i \(0.500668\pi\)
\(462\) 8.09017 0.376389
\(463\) −34.1246 −1.58591 −0.792953 0.609283i \(-0.791457\pi\)
−0.792953 + 0.609283i \(0.791457\pi\)
\(464\) −13.4164 −0.622841
\(465\) −5.70820 −0.264712
\(466\) 25.1803 1.16646
\(467\) 21.7082 1.00454 0.502268 0.864712i \(-0.332499\pi\)
0.502268 + 0.864712i \(0.332499\pi\)
\(468\) −2.38197 −0.110106
\(469\) −2.56231 −0.118316
\(470\) −23.7082 −1.09358
\(471\) −44.3607 −2.04403
\(472\) 0.201626 0.00928059
\(473\) −23.8197 −1.09523
\(474\) 2.23607 0.102706
\(475\) 13.0689 0.599642
\(476\) 0.0557281 0.00255429
\(477\) −29.7082 −1.36025
\(478\) 3.70820 0.169609
\(479\) −25.3607 −1.15876 −0.579380 0.815058i \(-0.696705\pi\)
−0.579380 + 0.815058i \(0.696705\pi\)
\(480\) −10.9443 −0.499535
\(481\) −6.47214 −0.295104
\(482\) 40.2705 1.83427
\(483\) −4.00000 −0.182006
\(484\) 8.65248 0.393294
\(485\) −18.6525 −0.846965
\(486\) 35.0344 1.58919
\(487\) −16.6869 −0.756156 −0.378078 0.925774i \(-0.623415\pi\)
−0.378078 + 0.925774i \(0.623415\pi\)
\(488\) 13.2918 0.601691
\(489\) 33.2705 1.50454
\(490\) 13.7082 0.619274
\(491\) 7.23607 0.326559 0.163280 0.986580i \(-0.447793\pi\)
0.163280 + 0.986580i \(0.447793\pi\)
\(492\) 0.381966 0.0172204
\(493\) −0.652476 −0.0293860
\(494\) 6.09017 0.274010
\(495\) −23.8197 −1.07061
\(496\) 8.56231 0.384459
\(497\) 5.03444 0.225826
\(498\) 26.4164 1.18375
\(499\) −26.9787 −1.20773 −0.603867 0.797085i \(-0.706374\pi\)
−0.603867 + 0.797085i \(0.706374\pi\)
\(500\) 6.47214 0.289443
\(501\) −8.00000 −0.357414
\(502\) 17.0344 0.760284
\(503\) −34.5410 −1.54011 −0.770054 0.637979i \(-0.779771\pi\)
−0.770054 + 0.637979i \(0.779771\pi\)
\(504\) 3.29180 0.146628
\(505\) 7.41641 0.330026
\(506\) −32.3607 −1.43861
\(507\) −2.61803 −0.116271
\(508\) −2.96556 −0.131575
\(509\) 1.85410 0.0821816 0.0410908 0.999155i \(-0.486917\pi\)
0.0410908 + 0.999155i \(0.486917\pi\)
\(510\) −1.23607 −0.0547340
\(511\) 5.12461 0.226699
\(512\) −5.29180 −0.233867
\(513\) 8.41641 0.371593
\(514\) 37.5066 1.65434
\(515\) −13.3475 −0.588162
\(516\) 7.70820 0.339335
\(517\) 59.2705 2.60671
\(518\) −4.00000 −0.175750
\(519\) −43.7426 −1.92009
\(520\) −2.76393 −0.121206
\(521\) −38.2148 −1.67422 −0.837110 0.547035i \(-0.815757\pi\)
−0.837110 + 0.547035i \(0.815757\pi\)
\(522\) 17.2361 0.754402
\(523\) 42.6525 1.86506 0.932531 0.361089i \(-0.117595\pi\)
0.932531 + 0.361089i \(0.117595\pi\)
\(524\) 6.43769 0.281232
\(525\) −3.47214 −0.151536
\(526\) 22.2705 0.971040
\(527\) 0.416408 0.0181390
\(528\) 63.5410 2.76527
\(529\) −7.00000 −0.304348
\(530\) 15.4164 0.669646
\(531\) −0.347524 −0.0150813
\(532\) 0.888544 0.0385233
\(533\) 0.236068 0.0102252
\(534\) −29.0344 −1.25644
\(535\) 13.5967 0.587839
\(536\) −15.0000 −0.647901
\(537\) −24.3262 −1.04975
\(538\) 17.4164 0.750875
\(539\) −34.2705 −1.47614
\(540\) 1.70820 0.0735094
\(541\) −5.94427 −0.255564 −0.127782 0.991802i \(-0.540786\pi\)
−0.127782 + 0.991802i \(0.540786\pi\)
\(542\) −21.0344 −0.903507
\(543\) −36.0344 −1.54639
\(544\) 0.798374 0.0342300
\(545\) 6.54102 0.280186
\(546\) −1.61803 −0.0692455
\(547\) 36.1803 1.54696 0.773480 0.633821i \(-0.218514\pi\)
0.773480 + 0.633821i \(0.218514\pi\)
\(548\) 0.180340 0.00770374
\(549\) −22.9098 −0.977768
\(550\) −28.0902 −1.19777
\(551\) −10.4033 −0.443193
\(552\) −23.4164 −0.996669
\(553\) 0.201626 0.00857401
\(554\) 11.3820 0.483573
\(555\) 20.9443 0.889035
\(556\) −0.763932 −0.0323979
\(557\) −11.6180 −0.492272 −0.246136 0.969235i \(-0.579161\pi\)
−0.246136 + 0.969235i \(0.579161\pi\)
\(558\) −11.0000 −0.465667
\(559\) 4.76393 0.201493
\(560\) −2.29180 −0.0968461
\(561\) 3.09017 0.130467
\(562\) 21.5066 0.907200
\(563\) −2.09017 −0.0880902 −0.0440451 0.999030i \(-0.514025\pi\)
−0.0440451 + 0.999030i \(0.514025\pi\)
\(564\) −19.1803 −0.807638
\(565\) 6.29180 0.264698
\(566\) 33.5066 1.40839
\(567\) 2.18034 0.0915657
\(568\) 29.4721 1.23662
\(569\) 29.0902 1.21952 0.609762 0.792585i \(-0.291265\pi\)
0.609762 + 0.792585i \(0.291265\pi\)
\(570\) −19.7082 −0.825486
\(571\) −38.7771 −1.62277 −0.811385 0.584512i \(-0.801286\pi\)
−0.811385 + 0.584512i \(0.801286\pi\)
\(572\) −3.09017 −0.129206
\(573\) 59.6869 2.49346
\(574\) 0.145898 0.00608967
\(575\) 13.8885 0.579192
\(576\) 16.3262 0.680260
\(577\) 17.1246 0.712907 0.356453 0.934313i \(-0.383986\pi\)
0.356453 + 0.934313i \(0.383986\pi\)
\(578\) −27.4164 −1.14037
\(579\) −15.7082 −0.652811
\(580\) −2.11146 −0.0876734
\(581\) 2.38197 0.0988206
\(582\) −63.9230 −2.64969
\(583\) −38.5410 −1.59621
\(584\) 30.0000 1.24141
\(585\) 4.76393 0.196964
\(586\) 31.9443 1.31961
\(587\) −12.2016 −0.503615 −0.251808 0.967777i \(-0.581025\pi\)
−0.251808 + 0.967777i \(0.581025\pi\)
\(588\) 11.0902 0.457351
\(589\) 6.63932 0.273568
\(590\) 0.180340 0.00742448
\(591\) 19.7984 0.814396
\(592\) −31.4164 −1.29121
\(593\) −8.03444 −0.329935 −0.164967 0.986299i \(-0.552752\pi\)
−0.164967 + 0.986299i \(0.552752\pi\)
\(594\) −18.0902 −0.742249
\(595\) −0.111456 −0.00456926
\(596\) −8.88854 −0.364089
\(597\) 1.00000 0.0409273
\(598\) 6.47214 0.264665
\(599\) 38.1246 1.55773 0.778865 0.627192i \(-0.215796\pi\)
0.778865 + 0.627192i \(0.215796\pi\)
\(600\) −20.3262 −0.829815
\(601\) 4.72949 0.192920 0.0964600 0.995337i \(-0.469248\pi\)
0.0964600 + 0.995337i \(0.469248\pi\)
\(602\) 2.94427 0.120000
\(603\) 25.8541 1.05286
\(604\) 12.9443 0.526695
\(605\) −17.3050 −0.703546
\(606\) 25.4164 1.03247
\(607\) −25.3607 −1.02936 −0.514679 0.857383i \(-0.672089\pi\)
−0.514679 + 0.857383i \(0.672089\pi\)
\(608\) 12.7295 0.516249
\(609\) 2.76393 0.112000
\(610\) 11.8885 0.481353
\(611\) −11.8541 −0.479566
\(612\) −0.562306 −0.0227299
\(613\) −17.0344 −0.688015 −0.344007 0.938967i \(-0.611785\pi\)
−0.344007 + 0.938967i \(0.611785\pi\)
\(614\) 17.5623 0.708757
\(615\) −0.763932 −0.0308047
\(616\) 4.27051 0.172064
\(617\) 7.34752 0.295800 0.147900 0.989002i \(-0.452749\pi\)
0.147900 + 0.989002i \(0.452749\pi\)
\(618\) −45.7426 −1.84004
\(619\) 1.00000 0.0401934
\(620\) 1.34752 0.0541179
\(621\) 8.94427 0.358921
\(622\) −39.9787 −1.60300
\(623\) −2.61803 −0.104889
\(624\) −12.7082 −0.508735
\(625\) 4.41641 0.176656
\(626\) 29.1246 1.16405
\(627\) 49.2705 1.96767
\(628\) 10.4721 0.417884
\(629\) −1.52786 −0.0609199
\(630\) 2.94427 0.117303
\(631\) 21.2148 0.844547 0.422274 0.906468i \(-0.361232\pi\)
0.422274 + 0.906468i \(0.361232\pi\)
\(632\) 1.18034 0.0469514
\(633\) −37.3607 −1.48495
\(634\) −33.7984 −1.34230
\(635\) 5.93112 0.235369
\(636\) 12.4721 0.494552
\(637\) 6.85410 0.271569
\(638\) 22.3607 0.885268
\(639\) −50.7984 −2.00955
\(640\) −16.8328 −0.665375
\(641\) 24.0000 0.947943 0.473972 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) 46.5967 1.83903
\(643\) −14.4164 −0.568528 −0.284264 0.958746i \(-0.591749\pi\)
−0.284264 + 0.958746i \(0.591749\pi\)
\(644\) 0.944272 0.0372095
\(645\) −15.4164 −0.607020
\(646\) 1.43769 0.0565653
\(647\) −45.1246 −1.77403 −0.887016 0.461739i \(-0.847226\pi\)
−0.887016 + 0.461739i \(0.847226\pi\)
\(648\) 12.7639 0.501415
\(649\) −0.450850 −0.0176974
\(650\) 5.61803 0.220357
\(651\) −1.76393 −0.0691339
\(652\) −7.85410 −0.307590
\(653\) 1.00000 0.0391330 0.0195665 0.999809i \(-0.493771\pi\)
0.0195665 + 0.999809i \(0.493771\pi\)
\(654\) 22.4164 0.876551
\(655\) −12.8754 −0.503083
\(656\) 1.14590 0.0447398
\(657\) −51.7082 −2.01733
\(658\) −7.32624 −0.285606
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 10.0000 0.389249
\(661\) −7.29180 −0.283618 −0.141809 0.989894i \(-0.545292\pi\)
−0.141809 + 0.989894i \(0.545292\pi\)
\(662\) 35.6525 1.38567
\(663\) −0.618034 −0.0240025
\(664\) 13.9443 0.541143
\(665\) −1.77709 −0.0689125
\(666\) 40.3607 1.56394
\(667\) −11.0557 −0.428080
\(668\) 1.88854 0.0730700
\(669\) −20.7082 −0.800625
\(670\) −13.4164 −0.518321
\(671\) −29.7214 −1.14738
\(672\) −3.38197 −0.130462
\(673\) −6.43769 −0.248155 −0.124077 0.992273i \(-0.539597\pi\)
−0.124077 + 0.992273i \(0.539597\pi\)
\(674\) 39.3607 1.51612
\(675\) 7.76393 0.298834
\(676\) 0.618034 0.0237705
\(677\) −24.7082 −0.949613 −0.474807 0.880090i \(-0.657482\pi\)
−0.474807 + 0.880090i \(0.657482\pi\)
\(678\) 21.5623 0.828095
\(679\) −5.76393 −0.221199
\(680\) −0.652476 −0.0250213
\(681\) −16.7984 −0.643715
\(682\) −14.2705 −0.546446
\(683\) −9.43769 −0.361123 −0.180562 0.983564i \(-0.557792\pi\)
−0.180562 + 0.983564i \(0.557792\pi\)
\(684\) −8.96556 −0.342807
\(685\) −0.360680 −0.0137809
\(686\) 8.56231 0.326910
\(687\) −45.5967 −1.73962
\(688\) 23.1246 0.881618
\(689\) 7.70820 0.293659
\(690\) −20.9443 −0.797335
\(691\) −17.8328 −0.678392 −0.339196 0.940716i \(-0.610155\pi\)
−0.339196 + 0.940716i \(0.610155\pi\)
\(692\) 10.3262 0.392545
\(693\) −7.36068 −0.279609
\(694\) −1.23607 −0.0469205
\(695\) 1.52786 0.0579552
\(696\) 16.1803 0.613314
\(697\) 0.0557281 0.00211085
\(698\) −18.5623 −0.702594
\(699\) −40.7426 −1.54103
\(700\) 0.819660 0.0309802
\(701\) 25.7639 0.973090 0.486545 0.873655i \(-0.338257\pi\)
0.486545 + 0.873655i \(0.338257\pi\)
\(702\) 3.61803 0.136554
\(703\) −24.3607 −0.918780
\(704\) 21.1803 0.798264
\(705\) 38.3607 1.44475
\(706\) −31.7984 −1.19675
\(707\) 2.29180 0.0861919
\(708\) 0.145898 0.00548318
\(709\) −6.87539 −0.258211 −0.129105 0.991631i \(-0.541211\pi\)
−0.129105 + 0.991631i \(0.541211\pi\)
\(710\) 26.3607 0.989299
\(711\) −2.03444 −0.0762975
\(712\) −15.3262 −0.574375
\(713\) 7.05573 0.264239
\(714\) −0.381966 −0.0142947
\(715\) 6.18034 0.231132
\(716\) 5.74265 0.214613
\(717\) −6.00000 −0.224074
\(718\) 5.61803 0.209663
\(719\) 45.7082 1.70463 0.852314 0.523030i \(-0.175198\pi\)
0.852314 + 0.523030i \(0.175198\pi\)
\(720\) 23.1246 0.861803
\(721\) −4.12461 −0.153609
\(722\) −7.81966 −0.291018
\(723\) −65.1591 −2.42329
\(724\) 8.50658 0.316144
\(725\) −9.59675 −0.356414
\(726\) −59.3050 −2.20101
\(727\) 21.8197 0.809246 0.404623 0.914483i \(-0.367403\pi\)
0.404623 + 0.914483i \(0.367403\pi\)
\(728\) −0.854102 −0.0316551
\(729\) −39.5623 −1.46527
\(730\) 26.8328 0.993127
\(731\) 1.12461 0.0415953
\(732\) 9.61803 0.355493
\(733\) 47.4164 1.75136 0.875682 0.482887i \(-0.160412\pi\)
0.875682 + 0.482887i \(0.160412\pi\)
\(734\) 34.8885 1.28776
\(735\) −22.1803 −0.818134
\(736\) 13.5279 0.498644
\(737\) 33.5410 1.23550
\(738\) −1.47214 −0.0541901
\(739\) −4.18034 −0.153776 −0.0768881 0.997040i \(-0.524498\pi\)
−0.0768881 + 0.997040i \(0.524498\pi\)
\(740\) −4.94427 −0.181755
\(741\) −9.85410 −0.361999
\(742\) 4.76393 0.174889
\(743\) −4.14590 −0.152098 −0.0760491 0.997104i \(-0.524231\pi\)
−0.0760491 + 0.997104i \(0.524231\pi\)
\(744\) −10.3262 −0.378578
\(745\) 17.7771 0.651302
\(746\) −3.00000 −0.109838
\(747\) −24.0344 −0.879374
\(748\) −0.729490 −0.0266728
\(749\) 4.20163 0.153524
\(750\) −44.3607 −1.61982
\(751\) −7.21478 −0.263271 −0.131636 0.991298i \(-0.542023\pi\)
−0.131636 + 0.991298i \(0.542023\pi\)
\(752\) −57.5410 −2.09831
\(753\) −27.5623 −1.00443
\(754\) −4.47214 −0.162866
\(755\) −25.8885 −0.942181
\(756\) 0.527864 0.0191982
\(757\) −23.6180 −0.858412 −0.429206 0.903207i \(-0.641207\pi\)
−0.429206 + 0.903207i \(0.641207\pi\)
\(758\) −43.8885 −1.59410
\(759\) 52.3607 1.90057
\(760\) −10.4033 −0.377366
\(761\) −24.0902 −0.873268 −0.436634 0.899639i \(-0.643830\pi\)
−0.436634 + 0.899639i \(0.643830\pi\)
\(762\) 20.3262 0.736342
\(763\) 2.02129 0.0731755
\(764\) −14.0902 −0.509764
\(765\) 1.12461 0.0406604
\(766\) −41.5967 −1.50295
\(767\) 0.0901699 0.00325585
\(768\) −35.5066 −1.28123
\(769\) −50.9787 −1.83834 −0.919170 0.393862i \(-0.871139\pi\)
−0.919170 + 0.393862i \(0.871139\pi\)
\(770\) 3.81966 0.137651
\(771\) −60.6869 −2.18559
\(772\) 3.70820 0.133461
\(773\) 12.7426 0.458321 0.229161 0.973389i \(-0.426402\pi\)
0.229161 + 0.973389i \(0.426402\pi\)
\(774\) −29.7082 −1.06784
\(775\) 6.12461 0.220003
\(776\) −33.7426 −1.21129
\(777\) 6.47214 0.232187
\(778\) 41.1246 1.47439
\(779\) 0.888544 0.0318354
\(780\) −2.00000 −0.0716115
\(781\) −65.9017 −2.35815
\(782\) 1.52786 0.0546363
\(783\) −6.18034 −0.220867
\(784\) 33.2705 1.18823
\(785\) −20.9443 −0.747533
\(786\) −44.1246 −1.57387
\(787\) 43.0000 1.53278 0.766392 0.642373i \(-0.222050\pi\)
0.766392 + 0.642373i \(0.222050\pi\)
\(788\) −4.67376 −0.166496
\(789\) −36.0344 −1.28286
\(790\) 1.05573 0.0375611
\(791\) 1.94427 0.0691304
\(792\) −43.0902 −1.53114
\(793\) 5.94427 0.211087
\(794\) −41.9787 −1.48977
\(795\) −24.9443 −0.884682
\(796\) −0.236068 −0.00836721
\(797\) 8.83282 0.312874 0.156437 0.987688i \(-0.449999\pi\)
0.156437 + 0.987688i \(0.449999\pi\)
\(798\) −6.09017 −0.215590
\(799\) −2.79837 −0.0989994
\(800\) 11.7426 0.415165
\(801\) 26.4164 0.933378
\(802\) 25.0344 0.883997
\(803\) −67.0820 −2.36727
\(804\) −10.8541 −0.382795
\(805\) −1.88854 −0.0665624
\(806\) 2.85410 0.100531
\(807\) −28.1803 −0.991995
\(808\) 13.4164 0.471988
\(809\) −3.74265 −0.131584 −0.0657922 0.997833i \(-0.520957\pi\)
−0.0657922 + 0.997833i \(0.520957\pi\)
\(810\) 11.4164 0.401132
\(811\) −20.0557 −0.704252 −0.352126 0.935953i \(-0.614541\pi\)
−0.352126 + 0.935953i \(0.614541\pi\)
\(812\) −0.652476 −0.0228974
\(813\) 34.0344 1.19364
\(814\) 52.3607 1.83524
\(815\) 15.7082 0.550234
\(816\) −3.00000 −0.105021
\(817\) 17.9311 0.627330
\(818\) 6.90983 0.241597
\(819\) 1.47214 0.0514406
\(820\) 0.180340 0.00629774
\(821\) 12.2361 0.427042 0.213521 0.976939i \(-0.431507\pi\)
0.213521 + 0.976939i \(0.431507\pi\)
\(822\) −1.23607 −0.0431128
\(823\) 26.2361 0.914532 0.457266 0.889330i \(-0.348829\pi\)
0.457266 + 0.889330i \(0.348829\pi\)
\(824\) −24.1459 −0.841162
\(825\) 45.4508 1.58240
\(826\) 0.0557281 0.00193903
\(827\) −53.9574 −1.87628 −0.938142 0.346251i \(-0.887454\pi\)
−0.938142 + 0.346251i \(0.887454\pi\)
\(828\) −9.52786 −0.331116
\(829\) −5.20163 −0.180660 −0.0903300 0.995912i \(-0.528792\pi\)
−0.0903300 + 0.995912i \(0.528792\pi\)
\(830\) 12.4721 0.432914
\(831\) −18.4164 −0.638858
\(832\) −4.23607 −0.146859
\(833\) 1.61803 0.0560616
\(834\) 5.23607 0.181310
\(835\) −3.77709 −0.130712
\(836\) −11.6312 −0.402273
\(837\) 3.94427 0.136334
\(838\) 25.3262 0.874880
\(839\) −17.0344 −0.588094 −0.294047 0.955791i \(-0.595002\pi\)
−0.294047 + 0.955791i \(0.595002\pi\)
\(840\) 2.76393 0.0953647
\(841\) −21.3607 −0.736575
\(842\) 42.8328 1.47612
\(843\) −34.7984 −1.19852
\(844\) 8.81966 0.303585
\(845\) −1.23607 −0.0425220
\(846\) 73.9230 2.54152
\(847\) −5.34752 −0.183743
\(848\) 37.4164 1.28488
\(849\) −54.2148 −1.86065
\(850\) 1.32624 0.0454896
\(851\) −25.8885 −0.887448
\(852\) 21.3262 0.730625
\(853\) 25.4721 0.872149 0.436075 0.899910i \(-0.356368\pi\)
0.436075 + 0.899910i \(0.356368\pi\)
\(854\) 3.67376 0.125714
\(855\) 17.9311 0.613231
\(856\) 24.5967 0.840700
\(857\) −27.9230 −0.953831 −0.476916 0.878949i \(-0.658245\pi\)
−0.476916 + 0.878949i \(0.658245\pi\)
\(858\) 21.1803 0.723085
\(859\) −50.4508 −1.72136 −0.860680 0.509146i \(-0.829961\pi\)
−0.860680 + 0.509146i \(0.829961\pi\)
\(860\) 3.63932 0.124100
\(861\) −0.236068 −0.00804518
\(862\) 42.7426 1.45582
\(863\) 46.2148 1.57317 0.786585 0.617482i \(-0.211847\pi\)
0.786585 + 0.617482i \(0.211847\pi\)
\(864\) 7.56231 0.257275
\(865\) −20.6525 −0.702205
\(866\) 8.79837 0.298981
\(867\) 44.3607 1.50657
\(868\) 0.416408 0.0141338
\(869\) −2.63932 −0.0895328
\(870\) 14.4721 0.490651
\(871\) −6.70820 −0.227299
\(872\) 11.8328 0.400710
\(873\) 58.1591 1.96839
\(874\) 24.3607 0.824012
\(875\) −4.00000 −0.135225
\(876\) 21.7082 0.733452
\(877\) 35.8328 1.20999 0.604994 0.796230i \(-0.293175\pi\)
0.604994 + 0.796230i \(0.293175\pi\)
\(878\) 37.3050 1.25898
\(879\) −51.6869 −1.74336
\(880\) 30.0000 1.01130
\(881\) 21.2148 0.714744 0.357372 0.933962i \(-0.383673\pi\)
0.357372 + 0.933962i \(0.383673\pi\)
\(882\) −42.7426 −1.43922
\(883\) −44.2148 −1.48795 −0.743973 0.668210i \(-0.767061\pi\)
−0.743973 + 0.668210i \(0.767061\pi\)
\(884\) 0.145898 0.00490708
\(885\) −0.291796 −0.00980862
\(886\) −24.5066 −0.823315
\(887\) 19.3262 0.648912 0.324456 0.945901i \(-0.394819\pi\)
0.324456 + 0.945901i \(0.394819\pi\)
\(888\) 37.8885 1.27146
\(889\) 1.83282 0.0614707
\(890\) −13.7082 −0.459500
\(891\) −28.5410 −0.956160
\(892\) 4.88854 0.163681
\(893\) −44.6180 −1.49309
\(894\) 60.9230 2.03757
\(895\) −11.4853 −0.383911
\(896\) −5.20163 −0.173774
\(897\) −10.4721 −0.349654
\(898\) −9.90983 −0.330695
\(899\) −4.87539 −0.162603
\(900\) −8.27051 −0.275684
\(901\) 1.81966 0.0606217
\(902\) −1.90983 −0.0635904
\(903\) −4.76393 −0.158534
\(904\) 11.3820 0.378559
\(905\) −17.0132 −0.565536
\(906\) −88.7214 −2.94757
\(907\) 23.9230 0.794350 0.397175 0.917743i \(-0.369991\pi\)
0.397175 + 0.917743i \(0.369991\pi\)
\(908\) 3.96556 0.131602
\(909\) −23.1246 −0.766995
\(910\) −0.763932 −0.0253241
\(911\) 28.4377 0.942183 0.471091 0.882084i \(-0.343860\pi\)
0.471091 + 0.882084i \(0.343860\pi\)
\(912\) −47.8328 −1.58390
\(913\) −31.1803 −1.03192
\(914\) 6.09017 0.201445
\(915\) −19.2361 −0.635925
\(916\) 10.7639 0.355650
\(917\) −3.97871 −0.131389
\(918\) 0.854102 0.0281896
\(919\) −4.41641 −0.145684 −0.0728419 0.997343i \(-0.523207\pi\)
−0.0728419 + 0.997343i \(0.523207\pi\)
\(920\) −11.0557 −0.364497
\(921\) −28.4164 −0.936352
\(922\) −0.145898 −0.00480490
\(923\) 13.1803 0.433836
\(924\) 3.09017 0.101659
\(925\) −22.4721 −0.738879
\(926\) −55.2148 −1.81447
\(927\) 41.6180 1.36692
\(928\) −9.34752 −0.306848
\(929\) −15.3607 −0.503968 −0.251984 0.967731i \(-0.581083\pi\)
−0.251984 + 0.967731i \(0.581083\pi\)
\(930\) −9.23607 −0.302863
\(931\) 25.7984 0.845508
\(932\) 9.61803 0.315049
\(933\) 64.6869 2.11775
\(934\) 35.1246 1.14931
\(935\) 1.45898 0.0477138
\(936\) 8.61803 0.281689
\(937\) 44.6525 1.45873 0.729366 0.684123i \(-0.239815\pi\)
0.729366 + 0.684123i \(0.239815\pi\)
\(938\) −4.14590 −0.135368
\(939\) −47.1246 −1.53785
\(940\) −9.05573 −0.295365
\(941\) 2.72949 0.0889788 0.0444894 0.999010i \(-0.485834\pi\)
0.0444894 + 0.999010i \(0.485834\pi\)
\(942\) −71.7771 −2.33862
\(943\) 0.944272 0.0307497
\(944\) 0.437694 0.0142457
\(945\) −1.05573 −0.0343428
\(946\) −38.5410 −1.25308
\(947\) 41.5410 1.34990 0.674951 0.737863i \(-0.264165\pi\)
0.674951 + 0.737863i \(0.264165\pi\)
\(948\) 0.854102 0.0277399
\(949\) 13.4164 0.435515
\(950\) 21.1459 0.686064
\(951\) 54.6869 1.77334
\(952\) −0.201626 −0.00653474
\(953\) 44.7771 1.45047 0.725236 0.688500i \(-0.241731\pi\)
0.725236 + 0.688500i \(0.241731\pi\)
\(954\) −48.0689 −1.55629
\(955\) 28.1803 0.911894
\(956\) 1.41641 0.0458099
\(957\) −36.1803 −1.16954
\(958\) −41.0344 −1.32576
\(959\) −0.111456 −0.00359911
\(960\) 13.7082 0.442430
\(961\) −27.8885 −0.899630
\(962\) −10.4721 −0.337635
\(963\) −42.3951 −1.36616
\(964\) 15.3820 0.495420
\(965\) −7.41641 −0.238743
\(966\) −6.47214 −0.208238
\(967\) 57.3951 1.84570 0.922851 0.385156i \(-0.125852\pi\)
0.922851 + 0.385156i \(0.125852\pi\)
\(968\) −31.3050 −1.00618
\(969\) −2.32624 −0.0747295
\(970\) −30.1803 −0.969032
\(971\) 22.1246 0.710013 0.355006 0.934864i \(-0.384479\pi\)
0.355006 + 0.934864i \(0.384479\pi\)
\(972\) 13.3820 0.429227
\(973\) 0.472136 0.0151360
\(974\) −27.0000 −0.865136
\(975\) −9.09017 −0.291118
\(976\) 28.8541 0.923597
\(977\) 48.3262 1.54609 0.773047 0.634349i \(-0.218732\pi\)
0.773047 + 0.634349i \(0.218732\pi\)
\(978\) 53.8328 1.72138
\(979\) 34.2705 1.09529
\(980\) 5.23607 0.167260
\(981\) −20.3951 −0.651166
\(982\) 11.7082 0.373624
\(983\) 16.7771 0.535106 0.267553 0.963543i \(-0.413785\pi\)
0.267553 + 0.963543i \(0.413785\pi\)
\(984\) −1.38197 −0.0440555
\(985\) 9.34752 0.297837
\(986\) −1.05573 −0.0336212
\(987\) 11.8541 0.377320
\(988\) 2.32624 0.0740075
\(989\) 19.0557 0.605937
\(990\) −38.5410 −1.22491
\(991\) −13.3050 −0.422646 −0.211323 0.977416i \(-0.567777\pi\)
−0.211323 + 0.977416i \(0.567777\pi\)
\(992\) 5.96556 0.189407
\(993\) −57.6869 −1.83064
\(994\) 8.14590 0.258372
\(995\) 0.472136 0.0149677
\(996\) 10.0902 0.319719
\(997\) 32.4508 1.02773 0.513864 0.857871i \(-0.328213\pi\)
0.513864 + 0.857871i \(0.328213\pi\)
\(998\) −43.6525 −1.38179
\(999\) −14.4721 −0.457878
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 \(a_p\))