Properties

Label 8042.2.a.a.1.17
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 1.17
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.67548 q^{3}\) \(+1.00000 q^{4}\) \(-3.27092 q^{5}\) \(-1.67548 q^{6}\) \(+1.23025 q^{7}\) \(+1.00000 q^{8}\) \(-0.192762 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.67548 q^{3}\) \(+1.00000 q^{4}\) \(-3.27092 q^{5}\) \(-1.67548 q^{6}\) \(+1.23025 q^{7}\) \(+1.00000 q^{8}\) \(-0.192762 q^{9}\) \(-3.27092 q^{10}\) \(+1.03060 q^{11}\) \(-1.67548 q^{12}\) \(-5.77159 q^{13}\) \(+1.23025 q^{14}\) \(+5.48037 q^{15}\) \(+1.00000 q^{16}\) \(-1.01519 q^{17}\) \(-0.192762 q^{18}\) \(+5.51119 q^{19}\) \(-3.27092 q^{20}\) \(-2.06125 q^{21}\) \(+1.03060 q^{22}\) \(-2.52383 q^{23}\) \(-1.67548 q^{24}\) \(+5.69895 q^{25}\) \(-5.77159 q^{26}\) \(+5.34941 q^{27}\) \(+1.23025 q^{28}\) \(+5.31836 q^{29}\) \(+5.48037 q^{30}\) \(+1.59392 q^{31}\) \(+1.00000 q^{32}\) \(-1.72674 q^{33}\) \(-1.01519 q^{34}\) \(-4.02404 q^{35}\) \(-0.192762 q^{36}\) \(-4.35474 q^{37}\) \(+5.51119 q^{38}\) \(+9.67019 q^{39}\) \(-3.27092 q^{40}\) \(+9.80940 q^{41}\) \(-2.06125 q^{42}\) \(+4.54208 q^{43}\) \(+1.03060 q^{44}\) \(+0.630511 q^{45}\) \(-2.52383 q^{46}\) \(-3.35414 q^{47}\) \(-1.67548 q^{48}\) \(-5.48649 q^{49}\) \(+5.69895 q^{50}\) \(+1.70093 q^{51}\) \(-5.77159 q^{52}\) \(+1.72285 q^{53}\) \(+5.34941 q^{54}\) \(-3.37100 q^{55}\) \(+1.23025 q^{56}\) \(-9.23390 q^{57}\) \(+5.31836 q^{58}\) \(+14.0138 q^{59}\) \(+5.48037 q^{60}\) \(-2.49991 q^{61}\) \(+1.59392 q^{62}\) \(-0.237145 q^{63}\) \(+1.00000 q^{64}\) \(+18.8784 q^{65}\) \(-1.72674 q^{66}\) \(-3.50881 q^{67}\) \(-1.01519 q^{68}\) \(+4.22863 q^{69}\) \(-4.02404 q^{70}\) \(-8.10150 q^{71}\) \(-0.192762 q^{72}\) \(+14.1753 q^{73}\) \(-4.35474 q^{74}\) \(-9.54848 q^{75}\) \(+5.51119 q^{76}\) \(+1.26789 q^{77}\) \(+9.67019 q^{78}\) \(-15.9550 q^{79}\) \(-3.27092 q^{80}\) \(-8.38456 q^{81}\) \(+9.80940 q^{82}\) \(-17.4681 q^{83}\) \(-2.06125 q^{84}\) \(+3.32061 q^{85}\) \(+4.54208 q^{86}\) \(-8.91082 q^{87}\) \(+1.03060 q^{88}\) \(+4.46238 q^{89}\) \(+0.630511 q^{90}\) \(-7.10047 q^{91}\) \(-2.52383 q^{92}\) \(-2.67058 q^{93}\) \(-3.35414 q^{94}\) \(-18.0267 q^{95}\) \(-1.67548 q^{96}\) \(-5.30079 q^{97}\) \(-5.48649 q^{98}\) \(-0.198660 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.67548 −0.967340 −0.483670 0.875251i \(-0.660696\pi\)
−0.483670 + 0.875251i \(0.660696\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.27092 −1.46280 −0.731401 0.681948i \(-0.761133\pi\)
−0.731401 + 0.681948i \(0.761133\pi\)
\(6\) −1.67548 −0.684012
\(7\) 1.23025 0.464989 0.232495 0.972598i \(-0.425311\pi\)
0.232495 + 0.972598i \(0.425311\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.192762 −0.0642541
\(10\) −3.27092 −1.03436
\(11\) 1.03060 0.310736 0.155368 0.987857i \(-0.450344\pi\)
0.155368 + 0.987857i \(0.450344\pi\)
\(12\) −1.67548 −0.483670
\(13\) −5.77159 −1.60075 −0.800375 0.599499i \(-0.795366\pi\)
−0.800375 + 0.599499i \(0.795366\pi\)
\(14\) 1.23025 0.328797
\(15\) 5.48037 1.41503
\(16\) 1.00000 0.250000
\(17\) −1.01519 −0.246220 −0.123110 0.992393i \(-0.539287\pi\)
−0.123110 + 0.992393i \(0.539287\pi\)
\(18\) −0.192762 −0.0454345
\(19\) 5.51119 1.26435 0.632177 0.774824i \(-0.282162\pi\)
0.632177 + 0.774824i \(0.282162\pi\)
\(20\) −3.27092 −0.731401
\(21\) −2.06125 −0.449803
\(22\) 1.03060 0.219724
\(23\) −2.52383 −0.526255 −0.263128 0.964761i \(-0.584754\pi\)
−0.263128 + 0.964761i \(0.584754\pi\)
\(24\) −1.67548 −0.342006
\(25\) 5.69895 1.13979
\(26\) −5.77159 −1.13190
\(27\) 5.34941 1.02950
\(28\) 1.23025 0.232495
\(29\) 5.31836 0.987595 0.493798 0.869577i \(-0.335608\pi\)
0.493798 + 0.869577i \(0.335608\pi\)
\(30\) 5.48037 1.00057
\(31\) 1.59392 0.286276 0.143138 0.989703i \(-0.454281\pi\)
0.143138 + 0.989703i \(0.454281\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.72674 −0.300588
\(34\) −1.01519 −0.174104
\(35\) −4.02404 −0.680187
\(36\) −0.192762 −0.0321271
\(37\) −4.35474 −0.715914 −0.357957 0.933738i \(-0.616527\pi\)
−0.357957 + 0.933738i \(0.616527\pi\)
\(38\) 5.51119 0.894033
\(39\) 9.67019 1.54847
\(40\) −3.27092 −0.517179
\(41\) 9.80940 1.53197 0.765986 0.642858i \(-0.222251\pi\)
0.765986 + 0.642858i \(0.222251\pi\)
\(42\) −2.06125 −0.318058
\(43\) 4.54208 0.692661 0.346331 0.938113i \(-0.387428\pi\)
0.346331 + 0.938113i \(0.387428\pi\)
\(44\) 1.03060 0.155368
\(45\) 0.630511 0.0939911
\(46\) −2.52383 −0.372119
\(47\) −3.35414 −0.489252 −0.244626 0.969617i \(-0.578665\pi\)
−0.244626 + 0.969617i \(0.578665\pi\)
\(48\) −1.67548 −0.241835
\(49\) −5.48649 −0.783785
\(50\) 5.69895 0.805953
\(51\) 1.70093 0.238178
\(52\) −5.77159 −0.800375
\(53\) 1.72285 0.236652 0.118326 0.992975i \(-0.462247\pi\)
0.118326 + 0.992975i \(0.462247\pi\)
\(54\) 5.34941 0.727963
\(55\) −3.37100 −0.454546
\(56\) 1.23025 0.164399
\(57\) −9.23390 −1.22306
\(58\) 5.31836 0.698335
\(59\) 14.0138 1.82444 0.912220 0.409700i \(-0.134367\pi\)
0.912220 + 0.409700i \(0.134367\pi\)
\(60\) 5.48037 0.707513
\(61\) −2.49991 −0.320081 −0.160040 0.987110i \(-0.551162\pi\)
−0.160040 + 0.987110i \(0.551162\pi\)
\(62\) 1.59392 0.202428
\(63\) −0.237145 −0.0298775
\(64\) 1.00000 0.125000
\(65\) 18.8784 2.34158
\(66\) −1.72674 −0.212548
\(67\) −3.50881 −0.428669 −0.214335 0.976760i \(-0.568758\pi\)
−0.214335 + 0.976760i \(0.568758\pi\)
\(68\) −1.01519 −0.123110
\(69\) 4.22863 0.509067
\(70\) −4.02404 −0.480965
\(71\) −8.10150 −0.961472 −0.480736 0.876865i \(-0.659630\pi\)
−0.480736 + 0.876865i \(0.659630\pi\)
\(72\) −0.192762 −0.0227173
\(73\) 14.1753 1.65909 0.829545 0.558440i \(-0.188600\pi\)
0.829545 + 0.558440i \(0.188600\pi\)
\(74\) −4.35474 −0.506228
\(75\) −9.54848 −1.10256
\(76\) 5.51119 0.632177
\(77\) 1.26789 0.144489
\(78\) 9.67019 1.09493
\(79\) −15.9550 −1.79508 −0.897538 0.440938i \(-0.854646\pi\)
−0.897538 + 0.440938i \(0.854646\pi\)
\(80\) −3.27092 −0.365700
\(81\) −8.38456 −0.931617
\(82\) 9.80940 1.08327
\(83\) −17.4681 −1.91738 −0.958689 0.284457i \(-0.908187\pi\)
−0.958689 + 0.284457i \(0.908187\pi\)
\(84\) −2.06125 −0.224901
\(85\) 3.32061 0.360171
\(86\) 4.54208 0.489785
\(87\) −8.91082 −0.955340
\(88\) 1.03060 0.109862
\(89\) 4.46238 0.473011 0.236505 0.971630i \(-0.423998\pi\)
0.236505 + 0.971630i \(0.423998\pi\)
\(90\) 0.630511 0.0664617
\(91\) −7.10047 −0.744332
\(92\) −2.52383 −0.263128
\(93\) −2.67058 −0.276926
\(94\) −3.35414 −0.345954
\(95\) −18.0267 −1.84950
\(96\) −1.67548 −0.171003
\(97\) −5.30079 −0.538213 −0.269107 0.963110i \(-0.586728\pi\)
−0.269107 + 0.963110i \(0.586728\pi\)
\(98\) −5.48649 −0.554220
\(99\) −0.198660 −0.0199661
\(100\) 5.69895 0.569895
\(101\) 4.01787 0.399793 0.199897 0.979817i \(-0.435939\pi\)
0.199897 + 0.979817i \(0.435939\pi\)
\(102\) 1.70093 0.168417
\(103\) 4.67937 0.461072 0.230536 0.973064i \(-0.425952\pi\)
0.230536 + 0.973064i \(0.425952\pi\)
\(104\) −5.77159 −0.565951
\(105\) 6.74221 0.657972
\(106\) 1.72285 0.167338
\(107\) −14.0413 −1.35742 −0.678712 0.734404i \(-0.737462\pi\)
−0.678712 + 0.734404i \(0.737462\pi\)
\(108\) 5.34941 0.514748
\(109\) 8.69881 0.833195 0.416598 0.909091i \(-0.363222\pi\)
0.416598 + 0.909091i \(0.363222\pi\)
\(110\) −3.37100 −0.321412
\(111\) 7.29628 0.692532
\(112\) 1.23025 0.116247
\(113\) 5.08862 0.478697 0.239348 0.970934i \(-0.423066\pi\)
0.239348 + 0.970934i \(0.423066\pi\)
\(114\) −9.23390 −0.864834
\(115\) 8.25526 0.769807
\(116\) 5.31836 0.493798
\(117\) 1.11255 0.102855
\(118\) 14.0138 1.29007
\(119\) −1.24893 −0.114490
\(120\) 5.48037 0.500287
\(121\) −9.93787 −0.903443
\(122\) −2.49991 −0.226331
\(123\) −16.4355 −1.48194
\(124\) 1.59392 0.143138
\(125\) −2.28620 −0.204484
\(126\) −0.237145 −0.0211266
\(127\) 7.81182 0.693187 0.346593 0.938016i \(-0.387338\pi\)
0.346593 + 0.938016i \(0.387338\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.61018 −0.670039
\(130\) 18.8784 1.65575
\(131\) 5.85723 0.511748 0.255874 0.966710i \(-0.417637\pi\)
0.255874 + 0.966710i \(0.417637\pi\)
\(132\) −1.72674 −0.150294
\(133\) 6.78012 0.587911
\(134\) −3.50881 −0.303115
\(135\) −17.4975 −1.50595
\(136\) −1.01519 −0.0870519
\(137\) −4.58587 −0.391798 −0.195899 0.980624i \(-0.562762\pi\)
−0.195899 + 0.980624i \(0.562762\pi\)
\(138\) 4.22863 0.359965
\(139\) −9.70172 −0.822890 −0.411445 0.911435i \(-0.634976\pi\)
−0.411445 + 0.911435i \(0.634976\pi\)
\(140\) −4.02404 −0.340094
\(141\) 5.61981 0.473273
\(142\) −8.10150 −0.679863
\(143\) −5.94817 −0.497411
\(144\) −0.192762 −0.0160635
\(145\) −17.3960 −1.44466
\(146\) 14.1753 1.17315
\(147\) 9.19252 0.758186
\(148\) −4.35474 −0.357957
\(149\) −6.58321 −0.539318 −0.269659 0.962956i \(-0.586911\pi\)
−0.269659 + 0.962956i \(0.586911\pi\)
\(150\) −9.54848 −0.779630
\(151\) 21.8645 1.77931 0.889653 0.456636i \(-0.150946\pi\)
0.889653 + 0.456636i \(0.150946\pi\)
\(152\) 5.51119 0.447017
\(153\) 0.195691 0.0158207
\(154\) 1.26789 0.102169
\(155\) −5.21358 −0.418765
\(156\) 9.67019 0.774235
\(157\) −2.72442 −0.217432 −0.108716 0.994073i \(-0.534674\pi\)
−0.108716 + 0.994073i \(0.534674\pi\)
\(158\) −15.9550 −1.26931
\(159\) −2.88660 −0.228923
\(160\) −3.27092 −0.258589
\(161\) −3.10493 −0.244703
\(162\) −8.38456 −0.658753
\(163\) −1.91800 −0.150229 −0.0751147 0.997175i \(-0.523932\pi\)
−0.0751147 + 0.997175i \(0.523932\pi\)
\(164\) 9.80940 0.765986
\(165\) 5.64805 0.439700
\(166\) −17.4681 −1.35579
\(167\) −12.2075 −0.944644 −0.472322 0.881426i \(-0.656584\pi\)
−0.472322 + 0.881426i \(0.656584\pi\)
\(168\) −2.06125 −0.159029
\(169\) 20.3112 1.56240
\(170\) 3.32061 0.254679
\(171\) −1.06235 −0.0812400
\(172\) 4.54208 0.346331
\(173\) 5.60069 0.425812 0.212906 0.977073i \(-0.431707\pi\)
0.212906 + 0.977073i \(0.431707\pi\)
\(174\) −8.91082 −0.675528
\(175\) 7.01111 0.529990
\(176\) 1.03060 0.0776841
\(177\) −23.4798 −1.76485
\(178\) 4.46238 0.334469
\(179\) −18.0700 −1.35062 −0.675309 0.737535i \(-0.735990\pi\)
−0.675309 + 0.737535i \(0.735990\pi\)
\(180\) 0.630511 0.0469955
\(181\) 8.65449 0.643284 0.321642 0.946861i \(-0.395765\pi\)
0.321642 + 0.946861i \(0.395765\pi\)
\(182\) −7.10047 −0.526322
\(183\) 4.18855 0.309627
\(184\) −2.52383 −0.186059
\(185\) 14.2440 1.04724
\(186\) −2.67058 −0.195816
\(187\) −1.04625 −0.0765095
\(188\) −3.35414 −0.244626
\(189\) 6.58110 0.478704
\(190\) −18.0267 −1.30779
\(191\) −18.3055 −1.32454 −0.662269 0.749266i \(-0.730407\pi\)
−0.662269 + 0.749266i \(0.730407\pi\)
\(192\) −1.67548 −0.120917
\(193\) 5.78081 0.416112 0.208056 0.978117i \(-0.433286\pi\)
0.208056 + 0.978117i \(0.433286\pi\)
\(194\) −5.30079 −0.380574
\(195\) −31.6305 −2.26510
\(196\) −5.48649 −0.391892
\(197\) 0.432448 0.0308106 0.0154053 0.999881i \(-0.495096\pi\)
0.0154053 + 0.999881i \(0.495096\pi\)
\(198\) −0.198660 −0.0141182
\(199\) −6.98443 −0.495113 −0.247557 0.968873i \(-0.579628\pi\)
−0.247557 + 0.968873i \(0.579628\pi\)
\(200\) 5.69895 0.402976
\(201\) 5.87894 0.414669
\(202\) 4.01787 0.282696
\(203\) 6.54290 0.459221
\(204\) 1.70093 0.119089
\(205\) −32.0858 −2.24097
\(206\) 4.67937 0.326027
\(207\) 0.486500 0.0338141
\(208\) −5.77159 −0.400188
\(209\) 5.67981 0.392881
\(210\) 6.74221 0.465256
\(211\) −6.16999 −0.424759 −0.212380 0.977187i \(-0.568121\pi\)
−0.212380 + 0.977187i \(0.568121\pi\)
\(212\) 1.72285 0.118326
\(213\) 13.5739 0.930070
\(214\) −14.0413 −0.959844
\(215\) −14.8568 −1.01323
\(216\) 5.34941 0.363982
\(217\) 1.96091 0.133115
\(218\) 8.69881 0.589158
\(219\) −23.7504 −1.60490
\(220\) −3.37100 −0.227273
\(221\) 5.85926 0.394137
\(222\) 7.29628 0.489694
\(223\) −21.9244 −1.46817 −0.734083 0.679059i \(-0.762388\pi\)
−0.734083 + 0.679059i \(0.762388\pi\)
\(224\) 1.23025 0.0821993
\(225\) −1.09854 −0.0732362
\(226\) 5.08862 0.338490
\(227\) 11.0850 0.735739 0.367870 0.929877i \(-0.380087\pi\)
0.367870 + 0.929877i \(0.380087\pi\)
\(228\) −9.23390 −0.611530
\(229\) −10.7911 −0.713097 −0.356549 0.934277i \(-0.616047\pi\)
−0.356549 + 0.934277i \(0.616047\pi\)
\(230\) 8.25526 0.544336
\(231\) −2.12432 −0.139770
\(232\) 5.31836 0.349168
\(233\) −19.7448 −1.29353 −0.646763 0.762691i \(-0.723878\pi\)
−0.646763 + 0.762691i \(0.723878\pi\)
\(234\) 1.11255 0.0727294
\(235\) 10.9712 0.715679
\(236\) 14.0138 0.912220
\(237\) 26.7323 1.73645
\(238\) −1.24893 −0.0809564
\(239\) −10.7899 −0.697940 −0.348970 0.937134i \(-0.613469\pi\)
−0.348970 + 0.937134i \(0.613469\pi\)
\(240\) 5.48037 0.353757
\(241\) −23.0471 −1.48459 −0.742296 0.670072i \(-0.766263\pi\)
−0.742296 + 0.670072i \(0.766263\pi\)
\(242\) −9.93787 −0.638831
\(243\) −2.00008 −0.128305
\(244\) −2.49991 −0.160040
\(245\) 17.9459 1.14652
\(246\) −16.4355 −1.04789
\(247\) −31.8083 −2.02392
\(248\) 1.59392 0.101214
\(249\) 29.2675 1.85476
\(250\) −2.28620 −0.144592
\(251\) 20.7041 1.30683 0.653417 0.756999i \(-0.273335\pi\)
0.653417 + 0.756999i \(0.273335\pi\)
\(252\) −0.237145 −0.0149387
\(253\) −2.60105 −0.163527
\(254\) 7.81182 0.490157
\(255\) −5.56362 −0.348408
\(256\) 1.00000 0.0625000
\(257\) −9.13962 −0.570114 −0.285057 0.958511i \(-0.592013\pi\)
−0.285057 + 0.958511i \(0.592013\pi\)
\(258\) −7.61018 −0.473789
\(259\) −5.35740 −0.332892
\(260\) 18.8784 1.17079
\(261\) −1.02518 −0.0634571
\(262\) 5.85723 0.361861
\(263\) −7.00486 −0.431938 −0.215969 0.976400i \(-0.569291\pi\)
−0.215969 + 0.976400i \(0.569291\pi\)
\(264\) −1.72674 −0.106274
\(265\) −5.63532 −0.346175
\(266\) 6.78012 0.415716
\(267\) −7.47663 −0.457562
\(268\) −3.50881 −0.214335
\(269\) 25.2611 1.54020 0.770098 0.637925i \(-0.220207\pi\)
0.770098 + 0.637925i \(0.220207\pi\)
\(270\) −17.4975 −1.06487
\(271\) 17.9345 1.08944 0.544722 0.838616i \(-0.316635\pi\)
0.544722 + 0.838616i \(0.316635\pi\)
\(272\) −1.01519 −0.0615550
\(273\) 11.8967 0.720022
\(274\) −4.58587 −0.277043
\(275\) 5.87331 0.354174
\(276\) 4.22863 0.254534
\(277\) −29.9909 −1.80198 −0.900991 0.433839i \(-0.857159\pi\)
−0.900991 + 0.433839i \(0.857159\pi\)
\(278\) −9.70172 −0.581871
\(279\) −0.307247 −0.0183944
\(280\) −4.02404 −0.240482
\(281\) 16.9433 1.01075 0.505376 0.862899i \(-0.331354\pi\)
0.505376 + 0.862899i \(0.331354\pi\)
\(282\) 5.61981 0.334655
\(283\) 15.5126 0.922131 0.461065 0.887366i \(-0.347467\pi\)
0.461065 + 0.887366i \(0.347467\pi\)
\(284\) −8.10150 −0.480736
\(285\) 30.2034 1.78909
\(286\) −5.94817 −0.351723
\(287\) 12.0680 0.712350
\(288\) −0.192762 −0.0113586
\(289\) −15.9694 −0.939376
\(290\) −17.3960 −1.02153
\(291\) 8.88137 0.520635
\(292\) 14.1753 0.829545
\(293\) −14.3968 −0.841073 −0.420536 0.907276i \(-0.638158\pi\)
−0.420536 + 0.907276i \(0.638158\pi\)
\(294\) 9.19252 0.536119
\(295\) −45.8380 −2.66879
\(296\) −4.35474 −0.253114
\(297\) 5.51308 0.319902
\(298\) −6.58321 −0.381355
\(299\) 14.5665 0.842403
\(300\) −9.54848 −0.551282
\(301\) 5.58788 0.322080
\(302\) 21.8645 1.25816
\(303\) −6.73187 −0.386736
\(304\) 5.51119 0.316089
\(305\) 8.17702 0.468215
\(306\) 0.195691 0.0111869
\(307\) 1.51151 0.0862665 0.0431332 0.999069i \(-0.486266\pi\)
0.0431332 + 0.999069i \(0.486266\pi\)
\(308\) 1.26789 0.0722445
\(309\) −7.84019 −0.446013
\(310\) −5.21358 −0.296112
\(311\) −12.4486 −0.705896 −0.352948 0.935643i \(-0.614821\pi\)
−0.352948 + 0.935643i \(0.614821\pi\)
\(312\) 9.67019 0.547467
\(313\) 4.24020 0.239670 0.119835 0.992794i \(-0.461763\pi\)
0.119835 + 0.992794i \(0.461763\pi\)
\(314\) −2.72442 −0.153748
\(315\) 0.775684 0.0437048
\(316\) −15.9550 −0.897538
\(317\) −25.0957 −1.40952 −0.704758 0.709448i \(-0.748944\pi\)
−0.704758 + 0.709448i \(0.748944\pi\)
\(318\) −2.88660 −0.161873
\(319\) 5.48108 0.306882
\(320\) −3.27092 −0.182850
\(321\) 23.5260 1.31309
\(322\) −3.10493 −0.173031
\(323\) −5.59491 −0.311309
\(324\) −8.38456 −0.465809
\(325\) −32.8920 −1.82452
\(326\) −1.91800 −0.106228
\(327\) −14.5747 −0.805983
\(328\) 9.80940 0.541634
\(329\) −4.12642 −0.227497
\(330\) 5.64805 0.310915
\(331\) 34.4643 1.89433 0.947165 0.320748i \(-0.103934\pi\)
0.947165 + 0.320748i \(0.103934\pi\)
\(332\) −17.4681 −0.958689
\(333\) 0.839429 0.0460004
\(334\) −12.2075 −0.667964
\(335\) 11.4770 0.627058
\(336\) −2.06125 −0.112451
\(337\) −31.3283 −1.70656 −0.853279 0.521454i \(-0.825390\pi\)
−0.853279 + 0.521454i \(0.825390\pi\)
\(338\) 20.3112 1.10479
\(339\) −8.52588 −0.463062
\(340\) 3.32061 0.180085
\(341\) 1.64268 0.0889564
\(342\) −1.06235 −0.0574453
\(343\) −15.3615 −0.829441
\(344\) 4.54208 0.244893
\(345\) −13.8315 −0.744665
\(346\) 5.60069 0.301095
\(347\) −25.0147 −1.34286 −0.671429 0.741069i \(-0.734319\pi\)
−0.671429 + 0.741069i \(0.734319\pi\)
\(348\) −8.91082 −0.477670
\(349\) −10.6112 −0.568004 −0.284002 0.958824i \(-0.591662\pi\)
−0.284002 + 0.958824i \(0.591662\pi\)
\(350\) 7.01111 0.374759
\(351\) −30.8746 −1.64796
\(352\) 1.03060 0.0549309
\(353\) 26.2076 1.39489 0.697446 0.716637i \(-0.254320\pi\)
0.697446 + 0.716637i \(0.254320\pi\)
\(354\) −23.4798 −1.24794
\(355\) 26.4994 1.40644
\(356\) 4.46238 0.236505
\(357\) 2.09257 0.110750
\(358\) −18.0700 −0.955031
\(359\) −14.9153 −0.787199 −0.393600 0.919282i \(-0.628770\pi\)
−0.393600 + 0.919282i \(0.628770\pi\)
\(360\) 0.630511 0.0332309
\(361\) 11.3732 0.598591
\(362\) 8.65449 0.454870
\(363\) 16.6507 0.873936
\(364\) −7.10047 −0.372166
\(365\) −46.3662 −2.42692
\(366\) 4.18855 0.218939
\(367\) −29.2307 −1.52583 −0.762914 0.646500i \(-0.776232\pi\)
−0.762914 + 0.646500i \(0.776232\pi\)
\(368\) −2.52383 −0.131564
\(369\) −1.89088 −0.0984355
\(370\) 14.2440 0.740511
\(371\) 2.11953 0.110041
\(372\) −2.67058 −0.138463
\(373\) −26.7645 −1.38582 −0.692908 0.721026i \(-0.743671\pi\)
−0.692908 + 0.721026i \(0.743671\pi\)
\(374\) −1.04625 −0.0541004
\(375\) 3.83048 0.197805
\(376\) −3.35414 −0.172977
\(377\) −30.6954 −1.58089
\(378\) 6.58110 0.338495
\(379\) 0.719383 0.0369522 0.0184761 0.999829i \(-0.494119\pi\)
0.0184761 + 0.999829i \(0.494119\pi\)
\(380\) −18.0267 −0.924750
\(381\) −13.0886 −0.670547
\(382\) −18.3055 −0.936590
\(383\) 35.7180 1.82510 0.912552 0.408961i \(-0.134109\pi\)
0.912552 + 0.408961i \(0.134109\pi\)
\(384\) −1.67548 −0.0855015
\(385\) −4.14716 −0.211359
\(386\) 5.78081 0.294235
\(387\) −0.875543 −0.0445064
\(388\) −5.30079 −0.269107
\(389\) −4.52778 −0.229568 −0.114784 0.993390i \(-0.536618\pi\)
−0.114784 + 0.993390i \(0.536618\pi\)
\(390\) −31.6305 −1.60167
\(391\) 2.56217 0.129575
\(392\) −5.48649 −0.277110
\(393\) −9.81368 −0.495035
\(394\) 0.432448 0.0217864
\(395\) 52.1875 2.62584
\(396\) −0.198660 −0.00998305
\(397\) 7.07292 0.354980 0.177490 0.984123i \(-0.443202\pi\)
0.177490 + 0.984123i \(0.443202\pi\)
\(398\) −6.98443 −0.350098
\(399\) −11.3600 −0.568710
\(400\) 5.69895 0.284947
\(401\) 11.4434 0.571457 0.285728 0.958311i \(-0.407765\pi\)
0.285728 + 0.958311i \(0.407765\pi\)
\(402\) 5.87894 0.293215
\(403\) −9.19943 −0.458256
\(404\) 4.01787 0.199897
\(405\) 27.4252 1.36277
\(406\) 6.54290 0.324719
\(407\) −4.48797 −0.222461
\(408\) 1.70093 0.0842087
\(409\) −23.4154 −1.15782 −0.578909 0.815392i \(-0.696521\pi\)
−0.578909 + 0.815392i \(0.696521\pi\)
\(410\) −32.0858 −1.58461
\(411\) 7.68355 0.379001
\(412\) 4.67937 0.230536
\(413\) 17.2404 0.848345
\(414\) 0.486500 0.0239102
\(415\) 57.1370 2.80474
\(416\) −5.77159 −0.282975
\(417\) 16.2551 0.796014
\(418\) 5.67981 0.277809
\(419\) 35.3483 1.72688 0.863438 0.504455i \(-0.168307\pi\)
0.863438 + 0.504455i \(0.168307\pi\)
\(420\) 6.74221 0.328986
\(421\) −39.0439 −1.90288 −0.951442 0.307827i \(-0.900398\pi\)
−0.951442 + 0.307827i \(0.900398\pi\)
\(422\) −6.16999 −0.300350
\(423\) 0.646553 0.0314365
\(424\) 1.72285 0.0836690
\(425\) −5.78552 −0.280639
\(426\) 13.5739 0.657658
\(427\) −3.07551 −0.148834
\(428\) −14.0413 −0.678712
\(429\) 9.96606 0.481166
\(430\) −14.8568 −0.716459
\(431\) 11.8228 0.569482 0.284741 0.958604i \(-0.408092\pi\)
0.284741 + 0.958604i \(0.408092\pi\)
\(432\) 5.34941 0.257374
\(433\) −14.0008 −0.672834 −0.336417 0.941713i \(-0.609215\pi\)
−0.336417 + 0.941713i \(0.609215\pi\)
\(434\) 1.96091 0.0941267
\(435\) 29.1466 1.39747
\(436\) 8.69881 0.416598
\(437\) −13.9093 −0.665373
\(438\) −23.7504 −1.13484
\(439\) −36.1255 −1.72418 −0.862089 0.506757i \(-0.830844\pi\)
−0.862089 + 0.506757i \(0.830844\pi\)
\(440\) −3.37100 −0.160706
\(441\) 1.05759 0.0503614
\(442\) 5.85926 0.278697
\(443\) −20.5890 −0.978213 −0.489107 0.872224i \(-0.662677\pi\)
−0.489107 + 0.872224i \(0.662677\pi\)
\(444\) 7.29628 0.346266
\(445\) −14.5961 −0.691921
\(446\) −21.9244 −1.03815
\(447\) 11.0300 0.521703
\(448\) 1.23025 0.0581237
\(449\) 16.1228 0.760881 0.380441 0.924805i \(-0.375772\pi\)
0.380441 + 0.924805i \(0.375772\pi\)
\(450\) −1.09854 −0.0517858
\(451\) 10.1095 0.476039
\(452\) 5.08862 0.239348
\(453\) −36.6335 −1.72119
\(454\) 11.0850 0.520246
\(455\) 23.2251 1.08881
\(456\) −9.23390 −0.432417
\(457\) 22.1163 1.03456 0.517280 0.855816i \(-0.326945\pi\)
0.517280 + 0.855816i \(0.326945\pi\)
\(458\) −10.7911 −0.504236
\(459\) −5.43068 −0.253482
\(460\) 8.25526 0.384903
\(461\) 15.6986 0.731158 0.365579 0.930780i \(-0.380871\pi\)
0.365579 + 0.930780i \(0.380871\pi\)
\(462\) −2.12432 −0.0988323
\(463\) −37.5351 −1.74440 −0.872201 0.489147i \(-0.837308\pi\)
−0.872201 + 0.489147i \(0.837308\pi\)
\(464\) 5.31836 0.246899
\(465\) 8.73526 0.405088
\(466\) −19.7448 −0.914661
\(467\) 34.9749 1.61844 0.809222 0.587502i \(-0.199889\pi\)
0.809222 + 0.587502i \(0.199889\pi\)
\(468\) 1.11255 0.0514274
\(469\) −4.31670 −0.199327
\(470\) 10.9712 0.506062
\(471\) 4.56471 0.210331
\(472\) 14.0138 0.645037
\(473\) 4.68105 0.215235
\(474\) 26.7323 1.22785
\(475\) 31.4080 1.44110
\(476\) −1.24893 −0.0572448
\(477\) −0.332101 −0.0152059
\(478\) −10.7899 −0.493518
\(479\) −39.9938 −1.82736 −0.913681 0.406433i \(-0.866773\pi\)
−0.913681 + 0.406433i \(0.866773\pi\)
\(480\) 5.48037 0.250144
\(481\) 25.1337 1.14600
\(482\) −23.0471 −1.04977
\(483\) 5.20226 0.236711
\(484\) −9.93787 −0.451721
\(485\) 17.3385 0.787299
\(486\) −2.00008 −0.0907253
\(487\) 32.6062 1.47753 0.738764 0.673964i \(-0.235410\pi\)
0.738764 + 0.673964i \(0.235410\pi\)
\(488\) −2.49991 −0.113166
\(489\) 3.21358 0.145323
\(490\) 17.9459 0.810714
\(491\) 1.15726 0.0522263 0.0261131 0.999659i \(-0.491687\pi\)
0.0261131 + 0.999659i \(0.491687\pi\)
\(492\) −16.4355 −0.740968
\(493\) −5.39916 −0.243166
\(494\) −31.8083 −1.43112
\(495\) 0.649802 0.0292064
\(496\) 1.59392 0.0715690
\(497\) −9.96684 −0.447074
\(498\) 29.2675 1.31151
\(499\) −0.648504 −0.0290310 −0.0145155 0.999895i \(-0.504621\pi\)
−0.0145155 + 0.999895i \(0.504621\pi\)
\(500\) −2.28620 −0.102242
\(501\) 20.4534 0.913792
\(502\) 20.7041 0.924071
\(503\) −34.3028 −1.52949 −0.764743 0.644336i \(-0.777134\pi\)
−0.764743 + 0.644336i \(0.777134\pi\)
\(504\) −0.237145 −0.0105633
\(505\) −13.1422 −0.584818
\(506\) −2.60105 −0.115631
\(507\) −34.0311 −1.51137
\(508\) 7.81182 0.346593
\(509\) −8.63106 −0.382565 −0.191283 0.981535i \(-0.561265\pi\)
−0.191283 + 0.981535i \(0.561265\pi\)
\(510\) −5.56362 −0.246361
\(511\) 17.4391 0.771459
\(512\) 1.00000 0.0441942
\(513\) 29.4816 1.30165
\(514\) −9.13962 −0.403132
\(515\) −15.3059 −0.674457
\(516\) −7.61018 −0.335019
\(517\) −3.45677 −0.152028
\(518\) −5.35740 −0.235390
\(519\) −9.38384 −0.411905
\(520\) 18.8784 0.827874
\(521\) 6.11582 0.267939 0.133970 0.990985i \(-0.457228\pi\)
0.133970 + 0.990985i \(0.457228\pi\)
\(522\) −1.02518 −0.0448709
\(523\) −31.2719 −1.36743 −0.683713 0.729751i \(-0.739636\pi\)
−0.683713 + 0.729751i \(0.739636\pi\)
\(524\) 5.85723 0.255874
\(525\) −11.7470 −0.512680
\(526\) −7.00486 −0.305426
\(527\) −1.61813 −0.0704869
\(528\) −1.72674 −0.0751469
\(529\) −16.6303 −0.723056
\(530\) −5.63532 −0.244782
\(531\) −2.70133 −0.117228
\(532\) 6.78012 0.293956
\(533\) −56.6158 −2.45230
\(534\) −7.47663 −0.323545
\(535\) 45.9281 1.98564
\(536\) −3.50881 −0.151557
\(537\) 30.2760 1.30651
\(538\) 25.2611 1.08908
\(539\) −5.65436 −0.243550
\(540\) −17.4975 −0.752974
\(541\) −4.39429 −0.188925 −0.0944626 0.995528i \(-0.530113\pi\)
−0.0944626 + 0.995528i \(0.530113\pi\)
\(542\) 17.9345 0.770354
\(543\) −14.5004 −0.622274
\(544\) −1.01519 −0.0435259
\(545\) −28.4532 −1.21880
\(546\) 11.8967 0.509132
\(547\) −12.2016 −0.521702 −0.260851 0.965379i \(-0.584003\pi\)
−0.260851 + 0.965379i \(0.584003\pi\)
\(548\) −4.58587 −0.195899
\(549\) 0.481889 0.0205665
\(550\) 5.87331 0.250439
\(551\) 29.3105 1.24867
\(552\) 4.22863 0.179983
\(553\) −19.6286 −0.834691
\(554\) −29.9909 −1.27419
\(555\) −23.8656 −1.01304
\(556\) −9.70172 −0.411445
\(557\) 20.2470 0.857892 0.428946 0.903330i \(-0.358885\pi\)
0.428946 + 0.903330i \(0.358885\pi\)
\(558\) −0.307247 −0.0130068
\(559\) −26.2150 −1.10878
\(560\) −4.02404 −0.170047
\(561\) 1.75297 0.0740107
\(562\) 16.9433 0.714709
\(563\) 9.06236 0.381933 0.190966 0.981597i \(-0.438838\pi\)
0.190966 + 0.981597i \(0.438838\pi\)
\(564\) 5.61981 0.236637
\(565\) −16.6445 −0.700238
\(566\) 15.5126 0.652045
\(567\) −10.3151 −0.433192
\(568\) −8.10150 −0.339932
\(569\) 13.4297 0.563002 0.281501 0.959561i \(-0.409168\pi\)
0.281501 + 0.959561i \(0.409168\pi\)
\(570\) 30.2034 1.26508
\(571\) 29.8524 1.24929 0.624643 0.780911i \(-0.285245\pi\)
0.624643 + 0.780911i \(0.285245\pi\)
\(572\) −5.94817 −0.248706
\(573\) 30.6705 1.28128
\(574\) 12.0680 0.503708
\(575\) −14.3832 −0.599820
\(576\) −0.192762 −0.00803177
\(577\) 42.7212 1.77850 0.889252 0.457417i \(-0.151225\pi\)
0.889252 + 0.457417i \(0.151225\pi\)
\(578\) −15.9694 −0.664239
\(579\) −9.68564 −0.402521
\(580\) −17.3960 −0.722328
\(581\) −21.4901 −0.891560
\(582\) 8.88137 0.368145
\(583\) 1.77556 0.0735363
\(584\) 14.1753 0.586577
\(585\) −3.63905 −0.150456
\(586\) −14.3968 −0.594728
\(587\) −36.5357 −1.50799 −0.753994 0.656881i \(-0.771875\pi\)
−0.753994 + 0.656881i \(0.771875\pi\)
\(588\) 9.19252 0.379093
\(589\) 8.78438 0.361954
\(590\) −45.8380 −1.88712
\(591\) −0.724558 −0.0298044
\(592\) −4.35474 −0.178979
\(593\) −44.0021 −1.80695 −0.903475 0.428641i \(-0.858993\pi\)
−0.903475 + 0.428641i \(0.858993\pi\)
\(594\) 5.51308 0.226205
\(595\) 4.08517 0.167476
\(596\) −6.58321 −0.269659
\(597\) 11.7023 0.478943
\(598\) 14.5665 0.595669
\(599\) 27.5899 1.12729 0.563646 0.826016i \(-0.309398\pi\)
0.563646 + 0.826016i \(0.309398\pi\)
\(600\) −9.54848 −0.389815
\(601\) −11.1967 −0.456725 −0.228362 0.973576i \(-0.573337\pi\)
−0.228362 + 0.973576i \(0.573337\pi\)
\(602\) 5.58788 0.227745
\(603\) 0.676367 0.0275438
\(604\) 21.8645 0.889653
\(605\) 32.5060 1.32156
\(606\) −6.73187 −0.273463
\(607\) 17.8311 0.723742 0.361871 0.932228i \(-0.382138\pi\)
0.361871 + 0.932228i \(0.382138\pi\)
\(608\) 5.51119 0.223508
\(609\) −10.9625 −0.444223
\(610\) 8.17702 0.331078
\(611\) 19.3587 0.783171
\(612\) 0.195691 0.00791033
\(613\) −38.3484 −1.54888 −0.774438 0.632650i \(-0.781967\pi\)
−0.774438 + 0.632650i \(0.781967\pi\)
\(614\) 1.51151 0.0609996
\(615\) 53.7592 2.16778
\(616\) 1.26789 0.0510846
\(617\) 5.29385 0.213123 0.106561 0.994306i \(-0.466016\pi\)
0.106561 + 0.994306i \(0.466016\pi\)
\(618\) −7.84019 −0.315379
\(619\) −36.8198 −1.47991 −0.739955 0.672656i \(-0.765153\pi\)
−0.739955 + 0.672656i \(0.765153\pi\)
\(620\) −5.21358 −0.209383
\(621\) −13.5010 −0.541777
\(622\) −12.4486 −0.499144
\(623\) 5.48982 0.219945
\(624\) 9.67019 0.387117
\(625\) −21.0167 −0.840670
\(626\) 4.24020 0.169473
\(627\) −9.51642 −0.380049
\(628\) −2.72442 −0.108716
\(629\) 4.42089 0.176272
\(630\) 0.775684 0.0309040
\(631\) 6.39195 0.254460 0.127230 0.991873i \(-0.459391\pi\)
0.127230 + 0.991873i \(0.459391\pi\)
\(632\) −15.9550 −0.634655
\(633\) 10.3377 0.410887
\(634\) −25.0957 −0.996678
\(635\) −25.5519 −1.01399
\(636\) −2.88660 −0.114461
\(637\) 31.6658 1.25464
\(638\) 5.48108 0.216998
\(639\) 1.56167 0.0617785
\(640\) −3.27092 −0.129295
\(641\) −2.33826 −0.0923556 −0.0461778 0.998933i \(-0.514704\pi\)
−0.0461778 + 0.998933i \(0.514704\pi\)
\(642\) 23.5260 0.928495
\(643\) −1.92774 −0.0760227 −0.0380114 0.999277i \(-0.512102\pi\)
−0.0380114 + 0.999277i \(0.512102\pi\)
\(644\) −3.10493 −0.122352
\(645\) 24.8923 0.980134
\(646\) −5.59491 −0.220129
\(647\) −36.1916 −1.42284 −0.711419 0.702768i \(-0.751947\pi\)
−0.711419 + 0.702768i \(0.751947\pi\)
\(648\) −8.38456 −0.329376
\(649\) 14.4426 0.566920
\(650\) −32.8920 −1.29013
\(651\) −3.28547 −0.128768
\(652\) −1.91800 −0.0751147
\(653\) 6.01108 0.235232 0.117616 0.993059i \(-0.462475\pi\)
0.117616 + 0.993059i \(0.462475\pi\)
\(654\) −14.5747 −0.569916
\(655\) −19.1586 −0.748587
\(656\) 9.80940 0.382993
\(657\) −2.73246 −0.106603
\(658\) −4.12642 −0.160865
\(659\) 25.2506 0.983626 0.491813 0.870701i \(-0.336334\pi\)
0.491813 + 0.870701i \(0.336334\pi\)
\(660\) 5.64805 0.219850
\(661\) −40.7724 −1.58586 −0.792932 0.609310i \(-0.791447\pi\)
−0.792932 + 0.609310i \(0.791447\pi\)
\(662\) 34.4643 1.33949
\(663\) −9.81709 −0.381264
\(664\) −17.4681 −0.677895
\(665\) −22.1773 −0.859998
\(666\) 0.839429 0.0325272
\(667\) −13.4227 −0.519727
\(668\) −12.2075 −0.472322
\(669\) 36.7339 1.42022
\(670\) 11.4770 0.443397
\(671\) −2.57640 −0.0994608
\(672\) −2.06125 −0.0795146
\(673\) −38.1955 −1.47233 −0.736165 0.676802i \(-0.763365\pi\)
−0.736165 + 0.676802i \(0.763365\pi\)
\(674\) −31.3283 −1.20672
\(675\) 30.4860 1.17341
\(676\) 20.3112 0.781201
\(677\) 32.9447 1.26617 0.633084 0.774083i \(-0.281789\pi\)
0.633084 + 0.774083i \(0.281789\pi\)
\(678\) −8.52588 −0.327435
\(679\) −6.52127 −0.250263
\(680\) 3.32061 0.127340
\(681\) −18.5728 −0.711710
\(682\) 1.64268 0.0629016
\(683\) 3.55360 0.135975 0.0679873 0.997686i \(-0.478342\pi\)
0.0679873 + 0.997686i \(0.478342\pi\)
\(684\) −1.06235 −0.0406200
\(685\) 15.0000 0.573122
\(686\) −15.3615 −0.586503
\(687\) 18.0803 0.689807
\(688\) 4.54208 0.173165
\(689\) −9.94359 −0.378820
\(690\) −13.8315 −0.526557
\(691\) −3.58738 −0.136470 −0.0682352 0.997669i \(-0.521737\pi\)
−0.0682352 + 0.997669i \(0.521737\pi\)
\(692\) 5.60069 0.212906
\(693\) −0.244401 −0.00928402
\(694\) −25.0147 −0.949544
\(695\) 31.7336 1.20372
\(696\) −8.91082 −0.337764
\(697\) −9.95842 −0.377202
\(698\) −10.6112 −0.401639
\(699\) 33.0821 1.25128
\(700\) 7.01111 0.264995
\(701\) 45.0840 1.70280 0.851399 0.524519i \(-0.175755\pi\)
0.851399 + 0.524519i \(0.175755\pi\)
\(702\) −30.8746 −1.16529
\(703\) −23.9998 −0.905169
\(704\) 1.03060 0.0388420
\(705\) −18.3820 −0.692305
\(706\) 26.2076 0.986338
\(707\) 4.94297 0.185900
\(708\) −23.4798 −0.882427
\(709\) 34.6108 1.29984 0.649919 0.760004i \(-0.274803\pi\)
0.649919 + 0.760004i \(0.274803\pi\)
\(710\) 26.4994 0.994505
\(711\) 3.07552 0.115341
\(712\) 4.46238 0.167235
\(713\) −4.02278 −0.150654
\(714\) 2.09257 0.0783123
\(715\) 19.4560 0.727614
\(716\) −18.0700 −0.675309
\(717\) 18.0783 0.675145
\(718\) −14.9153 −0.556634
\(719\) −32.9516 −1.22889 −0.614443 0.788961i \(-0.710619\pi\)
−0.614443 + 0.788961i \(0.710619\pi\)
\(720\) 0.630511 0.0234978
\(721\) 5.75677 0.214393
\(722\) 11.3732 0.423268
\(723\) 38.6149 1.43611
\(724\) 8.65449 0.321642
\(725\) 30.3091 1.12565
\(726\) 16.6507 0.617966
\(727\) −2.89091 −0.107218 −0.0536089 0.998562i \(-0.517072\pi\)
−0.0536089 + 0.998562i \(0.517072\pi\)
\(728\) −7.10047 −0.263161
\(729\) 28.5048 1.05573
\(730\) −46.3662 −1.71609
\(731\) −4.61108 −0.170547
\(732\) 4.18855 0.154813
\(733\) 51.0512 1.88562 0.942810 0.333331i \(-0.108172\pi\)
0.942810 + 0.333331i \(0.108172\pi\)
\(734\) −29.2307 −1.07892
\(735\) −30.0680 −1.10908
\(736\) −2.52383 −0.0930296
\(737\) −3.61616 −0.133203
\(738\) −1.89088 −0.0696044
\(739\) 8.30753 0.305597 0.152799 0.988257i \(-0.451171\pi\)
0.152799 + 0.988257i \(0.451171\pi\)
\(740\) 14.2440 0.523620
\(741\) 53.2943 1.95781
\(742\) 2.11953 0.0778104
\(743\) 18.5948 0.682177 0.341088 0.940031i \(-0.389204\pi\)
0.341088 + 0.940031i \(0.389204\pi\)
\(744\) −2.67058 −0.0979082
\(745\) 21.5332 0.788915
\(746\) −26.7645 −0.979920
\(747\) 3.36720 0.123199
\(748\) −1.04625 −0.0382547
\(749\) −17.2743 −0.631188
\(750\) 3.83048 0.139869
\(751\) −23.6909 −0.864492 −0.432246 0.901756i \(-0.642279\pi\)
−0.432246 + 0.901756i \(0.642279\pi\)
\(752\) −3.35414 −0.122313
\(753\) −34.6894 −1.26415
\(754\) −30.6954 −1.11786
\(755\) −71.5171 −2.60277
\(756\) 6.58110 0.239352
\(757\) −8.22004 −0.298762 −0.149381 0.988780i \(-0.547728\pi\)
−0.149381 + 0.988780i \(0.547728\pi\)
\(758\) 0.719383 0.0261292
\(759\) 4.35801 0.158186
\(760\) −18.0267 −0.653897
\(761\) −37.3385 −1.35352 −0.676760 0.736203i \(-0.736617\pi\)
−0.676760 + 0.736203i \(0.736617\pi\)
\(762\) −13.0886 −0.474148
\(763\) 10.7017 0.387427
\(764\) −18.3055 −0.662269
\(765\) −0.640089 −0.0231425
\(766\) 35.7180 1.29054
\(767\) −80.8818 −2.92047
\(768\) −1.67548 −0.0604587
\(769\) 23.9716 0.864438 0.432219 0.901769i \(-0.357731\pi\)
0.432219 + 0.901769i \(0.357731\pi\)
\(770\) −4.14716 −0.149453
\(771\) 15.3133 0.551494
\(772\) 5.78081 0.208056
\(773\) 26.5916 0.956432 0.478216 0.878242i \(-0.341284\pi\)
0.478216 + 0.878242i \(0.341284\pi\)
\(774\) −0.875543 −0.0314707
\(775\) 9.08365 0.326294
\(776\) −5.30079 −0.190287
\(777\) 8.97622 0.322020
\(778\) −4.52778 −0.162329
\(779\) 54.0615 1.93695
\(780\) −31.6305 −1.13255
\(781\) −8.34938 −0.298764
\(782\) 2.56217 0.0916230
\(783\) 28.4501 1.01672
\(784\) −5.48649 −0.195946
\(785\) 8.91136 0.318060
\(786\) −9.81368 −0.350042
\(787\) 3.73496 0.133137 0.0665685 0.997782i \(-0.478795\pi\)
0.0665685 + 0.997782i \(0.478795\pi\)
\(788\) 0.432448 0.0154053
\(789\) 11.7365 0.417831
\(790\) 52.1875 1.85675
\(791\) 6.26025 0.222589
\(792\) −0.198660 −0.00705908
\(793\) 14.4285 0.512370
\(794\) 7.07292 0.251008
\(795\) 9.44187 0.334868
\(796\) −6.98443 −0.247557
\(797\) 10.1986 0.361254 0.180627 0.983552i \(-0.442187\pi\)
0.180627 + 0.983552i \(0.442187\pi\)
\(798\) −11.3600 −0.402139
\(799\) 3.40510 0.120464
\(800\) 5.69895 0.201488
\(801\) −0.860178 −0.0303929
\(802\) 11.4434 0.404081
\(803\) 14.6090 0.515540
\(804\) 5.87894 0.207334
\(805\) 10.1560 0.357952
\(806\) −9.19943 −0.324036
\(807\) −42.3245 −1.48989
\(808\) 4.01787 0.141348
\(809\) 6.66281 0.234252 0.117126 0.993117i \(-0.462632\pi\)
0.117126 + 0.993117i \(0.462632\pi\)
\(810\) 27.4252 0.963625
\(811\) −17.2188 −0.604633 −0.302317 0.953208i \(-0.597760\pi\)
−0.302317 + 0.953208i \(0.597760\pi\)
\(812\) 6.54290 0.229611
\(813\) −30.0490 −1.05386
\(814\) −4.48797 −0.157303
\(815\) 6.27364 0.219756
\(816\) 1.70093 0.0595446
\(817\) 25.0323 0.875769
\(818\) −23.4154 −0.818701
\(819\) 1.36870 0.0478264
\(820\) −32.0858 −1.12049
\(821\) 8.20969 0.286520 0.143260 0.989685i \(-0.454241\pi\)
0.143260 + 0.989685i \(0.454241\pi\)
\(822\) 7.68355 0.267994
\(823\) −19.6814 −0.686050 −0.343025 0.939326i \(-0.611451\pi\)
−0.343025 + 0.939326i \(0.611451\pi\)
\(824\) 4.67937 0.163013
\(825\) −9.84062 −0.342606
\(826\) 17.2404 0.599871
\(827\) 24.2739 0.844086 0.422043 0.906576i \(-0.361313\pi\)
0.422043 + 0.906576i \(0.361313\pi\)
\(828\) 0.486500 0.0169070
\(829\) 29.9937 1.04172 0.520862 0.853641i \(-0.325611\pi\)
0.520862 + 0.853641i \(0.325611\pi\)
\(830\) 57.1370 1.98325
\(831\) 50.2493 1.74313
\(832\) −5.77159 −0.200094
\(833\) 5.56984 0.192983
\(834\) 16.2551 0.562867
\(835\) 39.9298 1.38183
\(836\) 5.67981 0.196440
\(837\) 8.52652 0.294720
\(838\) 35.3483 1.22109
\(839\) −21.8066 −0.752848 −0.376424 0.926447i \(-0.622846\pi\)
−0.376424 + 0.926447i \(0.622846\pi\)
\(840\) 6.74221 0.232628
\(841\) −0.714999 −0.0246552
\(842\) −39.0439 −1.34554
\(843\) −28.3881 −0.977740
\(844\) −6.16999 −0.212380
\(845\) −66.4365 −2.28548
\(846\) 0.646553 0.0222290
\(847\) −12.2260 −0.420091
\(848\) 1.72285 0.0591629
\(849\) −25.9911 −0.892014
\(850\) −5.78552 −0.198442
\(851\) 10.9906 0.376753
\(852\) 13.5739 0.465035
\(853\) 25.6078 0.876794 0.438397 0.898782i \(-0.355546\pi\)
0.438397 + 0.898782i \(0.355546\pi\)
\(854\) −3.07551 −0.105242
\(855\) 3.47487 0.118838
\(856\) −14.0413 −0.479922
\(857\) −16.3062 −0.557008 −0.278504 0.960435i \(-0.589839\pi\)
−0.278504 + 0.960435i \(0.589839\pi\)
\(858\) 9.96606 0.340236
\(859\) 42.1342 1.43760 0.718800 0.695217i \(-0.244692\pi\)
0.718800 + 0.695217i \(0.244692\pi\)
\(860\) −14.8568 −0.506613
\(861\) −20.2197 −0.689085
\(862\) 11.8228 0.402685
\(863\) −39.0269 −1.32849 −0.664245 0.747515i \(-0.731247\pi\)
−0.664245 + 0.747515i \(0.731247\pi\)
\(864\) 5.34941 0.181991
\(865\) −18.3194 −0.622879
\(866\) −14.0008 −0.475765
\(867\) 26.7564 0.908695
\(868\) 1.96091 0.0665576
\(869\) −16.4431 −0.557795
\(870\) 29.1466 0.988163
\(871\) 20.2514 0.686193
\(872\) 8.69881 0.294579
\(873\) 1.02179 0.0345824
\(874\) −13.9093 −0.470490
\(875\) −2.81259 −0.0950828
\(876\) −23.7504 −0.802452
\(877\) −28.7317 −0.970200 −0.485100 0.874459i \(-0.661217\pi\)
−0.485100 + 0.874459i \(0.661217\pi\)
\(878\) −36.1255 −1.21918
\(879\) 24.1216 0.813603
\(880\) −3.37100 −0.113636
\(881\) −10.8550 −0.365715 −0.182858 0.983139i \(-0.558535\pi\)
−0.182858 + 0.983139i \(0.558535\pi\)
\(882\) 1.05759 0.0356109
\(883\) 10.2387 0.344559 0.172280 0.985048i \(-0.444887\pi\)
0.172280 + 0.985048i \(0.444887\pi\)
\(884\) 5.85926 0.197068
\(885\) 76.8008 2.58163
\(886\) −20.5890 −0.691701
\(887\) 24.3808 0.818628 0.409314 0.912394i \(-0.365768\pi\)
0.409314 + 0.912394i \(0.365768\pi\)
\(888\) 7.29628 0.244847
\(889\) 9.61046 0.322324
\(890\) −14.5961 −0.489262
\(891\) −8.64109 −0.289487
\(892\) −21.9244 −0.734083
\(893\) −18.4853 −0.618588
\(894\) 11.0300 0.368900
\(895\) 59.1057 1.97569
\(896\) 1.23025 0.0410996
\(897\) −24.4059 −0.814890
\(898\) 16.1228 0.538024
\(899\) 8.47703 0.282725
\(900\) −1.09854 −0.0366181
\(901\) −1.74902 −0.0582684
\(902\) 10.1095 0.336611
\(903\) −9.36239 −0.311561
\(904\) 5.08862 0.169245
\(905\) −28.3082 −0.940996
\(906\) −36.6335 −1.21707
\(907\) 20.6024 0.684090 0.342045 0.939684i \(-0.388880\pi\)
0.342045 + 0.939684i \(0.388880\pi\)
\(908\) 11.0850 0.367870
\(909\) −0.774495 −0.0256884
\(910\) 23.2251 0.769905
\(911\) 48.1552 1.59545 0.797727 0.603019i \(-0.206036\pi\)
0.797727 + 0.603019i \(0.206036\pi\)
\(912\) −9.23390 −0.305765
\(913\) −18.0026 −0.595799
\(914\) 22.1163 0.731544
\(915\) −13.7004 −0.452923
\(916\) −10.7911 −0.356549
\(917\) 7.20583 0.237958
\(918\) −5.43068 −0.179239
\(919\) −48.9924 −1.61611 −0.808055 0.589107i \(-0.799480\pi\)
−0.808055 + 0.589107i \(0.799480\pi\)
\(920\) 8.25526 0.272168
\(921\) −2.53251 −0.0834490
\(922\) 15.6986 0.517007
\(923\) 46.7585 1.53908
\(924\) −2.12432 −0.0698850
\(925\) −24.8174 −0.815991
\(926\) −37.5351 −1.23348
\(927\) −0.902006 −0.0296258
\(928\) 5.31836 0.174584
\(929\) 32.4438 1.06445 0.532224 0.846604i \(-0.321356\pi\)
0.532224 + 0.846604i \(0.321356\pi\)
\(930\) 8.73526 0.286440
\(931\) −30.2371 −0.990982
\(932\) −19.7448 −0.646763
\(933\) 20.8574 0.682841
\(934\) 34.9749 1.14441
\(935\) 3.42221 0.111918
\(936\) 1.11255 0.0363647
\(937\) 0.965582 0.0315442 0.0157721 0.999876i \(-0.494979\pi\)
0.0157721 + 0.999876i \(0.494979\pi\)
\(938\) −4.31670 −0.140945
\(939\) −7.10438 −0.231843
\(940\) 10.9712 0.357840
\(941\) 23.3676 0.761763 0.380882 0.924624i \(-0.375621\pi\)
0.380882 + 0.924624i \(0.375621\pi\)
\(942\) 4.56471 0.148726
\(943\) −24.7573 −0.806208
\(944\) 14.0138 0.456110
\(945\) −21.5263 −0.700249
\(946\) 4.68105 0.152194
\(947\) −3.75900 −0.122151 −0.0610755 0.998133i \(-0.519453\pi\)
−0.0610755 + 0.998133i \(0.519453\pi\)
\(948\) 26.7323 0.868224
\(949\) −81.8138 −2.65579
\(950\) 31.4080 1.01901
\(951\) 42.0474 1.36348
\(952\) −1.24893 −0.0404782
\(953\) 33.5486 1.08674 0.543372 0.839492i \(-0.317147\pi\)
0.543372 + 0.839492i \(0.317147\pi\)
\(954\) −0.332101 −0.0107522
\(955\) 59.8759 1.93754
\(956\) −10.7899 −0.348970
\(957\) −9.18346 −0.296859
\(958\) −39.9938 −1.29214
\(959\) −5.64175 −0.182182
\(960\) 5.48037 0.176878
\(961\) −28.4594 −0.918046
\(962\) 25.1337 0.810344
\(963\) 2.70664 0.0872202
\(964\) −23.0471 −0.742296
\(965\) −18.9086 −0.608689
\(966\) 5.20226 0.167380
\(967\) 27.3858 0.880669 0.440335 0.897834i \(-0.354860\pi\)
0.440335 + 0.897834i \(0.354860\pi\)
\(968\) −9.93787 −0.319415
\(969\) 9.37417 0.301142
\(970\) 17.3385 0.556705
\(971\) −38.3483 −1.23065 −0.615327 0.788272i \(-0.710976\pi\)
−0.615327 + 0.788272i \(0.710976\pi\)
\(972\) −2.00008 −0.0641525
\(973\) −11.9355 −0.382635
\(974\) 32.6062 1.04477
\(975\) 55.1099 1.76493
\(976\) −2.49991 −0.0800202
\(977\) 4.20089 0.134398 0.0671991 0.997740i \(-0.478594\pi\)
0.0671991 + 0.997740i \(0.478594\pi\)
\(978\) 3.21358 0.102759
\(979\) 4.59891 0.146982
\(980\) 17.9459 0.573261
\(981\) −1.67680 −0.0535362
\(982\) 1.15726 0.0369295
\(983\) 46.6160 1.48682 0.743410 0.668835i \(-0.233207\pi\)
0.743410 + 0.668835i \(0.233207\pi\)
\(984\) −16.4355 −0.523944
\(985\) −1.41450 −0.0450699
\(986\) −5.39916 −0.171944
\(987\) 6.91375 0.220067
\(988\) −31.8083 −1.01196
\(989\) −11.4635 −0.364517
\(990\) 0.649802 0.0206521
\(991\) 5.84863 0.185788 0.0928940 0.995676i \(-0.470388\pi\)
0.0928940 + 0.995676i \(0.470388\pi\)
\(992\) 1.59392 0.0506069
\(993\) −57.7443 −1.83246
\(994\) −9.96684 −0.316129
\(995\) 22.8456 0.724253
\(996\) 29.2675 0.927378
\(997\) −13.8354 −0.438171 −0.219086 0.975706i \(-0.570307\pi\)
−0.219086 + 0.975706i \(0.570307\pi\)
\(998\) −0.648504 −0.0205280
\(999\) −23.2953 −0.737030
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 \(a_p\))