Properties

Label 4026.2.a.bc.1.5
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.128459\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+0.871541 q^{5}\) \(+1.00000 q^{6}\) \(+1.79155 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+0.871541 q^{5}\) \(+1.00000 q^{6}\) \(+1.79155 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+0.871541 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+6.05083 q^{13}\) \(+1.79155 q^{14}\) \(+0.871541 q^{15}\) \(+1.00000 q^{16}\) \(+4.28116 q^{17}\) \(+1.00000 q^{18}\) \(-0.502442 q^{19}\) \(+0.871541 q^{20}\) \(+1.79155 q^{21}\) \(+1.00000 q^{22}\) \(-0.329122 q^{23}\) \(+1.00000 q^{24}\) \(-4.24042 q^{25}\) \(+6.05083 q^{26}\) \(+1.00000 q^{27}\) \(+1.79155 q^{28}\) \(+0.826208 q^{29}\) \(+0.871541 q^{30}\) \(+2.54242 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(+4.28116 q^{34}\) \(+1.56141 q^{35}\) \(+1.00000 q^{36}\) \(-11.6827 q^{37}\) \(-0.502442 q^{38}\) \(+6.05083 q^{39}\) \(+0.871541 q^{40}\) \(+1.92808 q^{41}\) \(+1.79155 q^{42}\) \(-4.90273 q^{43}\) \(+1.00000 q^{44}\) \(+0.871541 q^{45}\) \(-0.329122 q^{46}\) \(-9.19307 q^{47}\) \(+1.00000 q^{48}\) \(-3.79035 q^{49}\) \(-4.24042 q^{50}\) \(+4.28116 q^{51}\) \(+6.05083 q^{52}\) \(+0.198049 q^{53}\) \(+1.00000 q^{54}\) \(+0.871541 q^{55}\) \(+1.79155 q^{56}\) \(-0.502442 q^{57}\) \(+0.826208 q^{58}\) \(-5.77799 q^{59}\) \(+0.871541 q^{60}\) \(-1.00000 q^{61}\) \(+2.54242 q^{62}\) \(+1.79155 q^{63}\) \(+1.00000 q^{64}\) \(+5.27355 q^{65}\) \(+1.00000 q^{66}\) \(+3.24114 q^{67}\) \(+4.28116 q^{68}\) \(-0.329122 q^{69}\) \(+1.56141 q^{70}\) \(-7.63320 q^{71}\) \(+1.00000 q^{72}\) \(+7.93920 q^{73}\) \(-11.6827 q^{74}\) \(-4.24042 q^{75}\) \(-0.502442 q^{76}\) \(+1.79155 q^{77}\) \(+6.05083 q^{78}\) \(+12.1924 q^{79}\) \(+0.871541 q^{80}\) \(+1.00000 q^{81}\) \(+1.92808 q^{82}\) \(-5.33038 q^{83}\) \(+1.79155 q^{84}\) \(+3.73121 q^{85}\) \(-4.90273 q^{86}\) \(+0.826208 q^{87}\) \(+1.00000 q^{88}\) \(-4.51300 q^{89}\) \(+0.871541 q^{90}\) \(+10.8404 q^{91}\) \(-0.329122 q^{92}\) \(+2.54242 q^{93}\) \(-9.19307 q^{94}\) \(-0.437899 q^{95}\) \(+1.00000 q^{96}\) \(+9.53546 q^{97}\) \(-3.79035 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0.871541 0.389765 0.194883 0.980827i \(-0.437567\pi\)
0.194883 + 0.980827i \(0.437567\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.79155 0.677142 0.338571 0.940941i \(-0.390056\pi\)
0.338571 + 0.940941i \(0.390056\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0.871541 0.275606
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 6.05083 1.67820 0.839099 0.543978i \(-0.183083\pi\)
0.839099 + 0.543978i \(0.183083\pi\)
\(14\) 1.79155 0.478812
\(15\) 0.871541 0.225031
\(16\) 1.00000 0.250000
\(17\) 4.28116 1.03833 0.519167 0.854673i \(-0.326242\pi\)
0.519167 + 0.854673i \(0.326242\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.502442 −0.115268 −0.0576341 0.998338i \(-0.518356\pi\)
−0.0576341 + 0.998338i \(0.518356\pi\)
\(20\) 0.871541 0.194883
\(21\) 1.79155 0.390948
\(22\) 1.00000 0.213201
\(23\) −0.329122 −0.0686266 −0.0343133 0.999411i \(-0.510924\pi\)
−0.0343133 + 0.999411i \(0.510924\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.24042 −0.848083
\(26\) 6.05083 1.18667
\(27\) 1.00000 0.192450
\(28\) 1.79155 0.338571
\(29\) 0.826208 0.153423 0.0767115 0.997053i \(-0.475558\pi\)
0.0767115 + 0.997053i \(0.475558\pi\)
\(30\) 0.871541 0.159121
\(31\) 2.54242 0.456632 0.228316 0.973587i \(-0.426678\pi\)
0.228316 + 0.973587i \(0.426678\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 4.28116 0.734212
\(35\) 1.56141 0.263926
\(36\) 1.00000 0.166667
\(37\) −11.6827 −1.92062 −0.960310 0.278933i \(-0.910019\pi\)
−0.960310 + 0.278933i \(0.910019\pi\)
\(38\) −0.502442 −0.0815069
\(39\) 6.05083 0.968908
\(40\) 0.871541 0.137803
\(41\) 1.92808 0.301115 0.150557 0.988601i \(-0.451893\pi\)
0.150557 + 0.988601i \(0.451893\pi\)
\(42\) 1.79155 0.276442
\(43\) −4.90273 −0.747660 −0.373830 0.927497i \(-0.621956\pi\)
−0.373830 + 0.927497i \(0.621956\pi\)
\(44\) 1.00000 0.150756
\(45\) 0.871541 0.129922
\(46\) −0.329122 −0.0485264
\(47\) −9.19307 −1.34095 −0.670474 0.741933i \(-0.733909\pi\)
−0.670474 + 0.741933i \(0.733909\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.79035 −0.541479
\(50\) −4.24042 −0.599685
\(51\) 4.28116 0.599482
\(52\) 6.05083 0.839099
\(53\) 0.198049 0.0272041 0.0136020 0.999907i \(-0.495670\pi\)
0.0136020 + 0.999907i \(0.495670\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.871541 0.117519
\(56\) 1.79155 0.239406
\(57\) −0.502442 −0.0665501
\(58\) 0.826208 0.108486
\(59\) −5.77799 −0.752230 −0.376115 0.926573i \(-0.622740\pi\)
−0.376115 + 0.926573i \(0.622740\pi\)
\(60\) 0.871541 0.112515
\(61\) −1.00000 −0.128037
\(62\) 2.54242 0.322888
\(63\) 1.79155 0.225714
\(64\) 1.00000 0.125000
\(65\) 5.27355 0.654103
\(66\) 1.00000 0.123091
\(67\) 3.24114 0.395969 0.197984 0.980205i \(-0.436560\pi\)
0.197984 + 0.980205i \(0.436560\pi\)
\(68\) 4.28116 0.519167
\(69\) −0.329122 −0.0396216
\(70\) 1.56141 0.186624
\(71\) −7.63320 −0.905894 −0.452947 0.891537i \(-0.649627\pi\)
−0.452947 + 0.891537i \(0.649627\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.93920 0.929213 0.464607 0.885517i \(-0.346196\pi\)
0.464607 + 0.885517i \(0.346196\pi\)
\(74\) −11.6827 −1.35808
\(75\) −4.24042 −0.489641
\(76\) −0.502442 −0.0576341
\(77\) 1.79155 0.204166
\(78\) 6.05083 0.685122
\(79\) 12.1924 1.37176 0.685878 0.727717i \(-0.259418\pi\)
0.685878 + 0.727717i \(0.259418\pi\)
\(80\) 0.871541 0.0974413
\(81\) 1.00000 0.111111
\(82\) 1.92808 0.212920
\(83\) −5.33038 −0.585085 −0.292543 0.956252i \(-0.594501\pi\)
−0.292543 + 0.956252i \(0.594501\pi\)
\(84\) 1.79155 0.195474
\(85\) 3.73121 0.404706
\(86\) −4.90273 −0.528675
\(87\) 0.826208 0.0885788
\(88\) 1.00000 0.106600
\(89\) −4.51300 −0.478377 −0.239189 0.970973i \(-0.576881\pi\)
−0.239189 + 0.970973i \(0.576881\pi\)
\(90\) 0.871541 0.0918685
\(91\) 10.8404 1.13638
\(92\) −0.329122 −0.0343133
\(93\) 2.54242 0.263637
\(94\) −9.19307 −0.948193
\(95\) −0.437899 −0.0449275
\(96\) 1.00000 0.102062
\(97\) 9.53546 0.968179 0.484090 0.875018i \(-0.339151\pi\)
0.484090 + 0.875018i \(0.339151\pi\)
\(98\) −3.79035 −0.382883
\(99\) 1.00000 0.100504
\(100\) −4.24042 −0.424042
\(101\) −0.178769 −0.0177882 −0.00889411 0.999960i \(-0.502831\pi\)
−0.00889411 + 0.999960i \(0.502831\pi\)
\(102\) 4.28116 0.423898
\(103\) −1.56415 −0.154120 −0.0770600 0.997026i \(-0.524553\pi\)
−0.0770600 + 0.997026i \(0.524553\pi\)
\(104\) 6.05083 0.593333
\(105\) 1.56141 0.152378
\(106\) 0.198049 0.0192362
\(107\) −3.77496 −0.364939 −0.182470 0.983211i \(-0.558409\pi\)
−0.182470 + 0.983211i \(0.558409\pi\)
\(108\) 1.00000 0.0962250
\(109\) 0.168419 0.0161316 0.00806582 0.999967i \(-0.497433\pi\)
0.00806582 + 0.999967i \(0.497433\pi\)
\(110\) 0.871541 0.0830982
\(111\) −11.6827 −1.10887
\(112\) 1.79155 0.169285
\(113\) 12.0336 1.13203 0.566013 0.824396i \(-0.308485\pi\)
0.566013 + 0.824396i \(0.308485\pi\)
\(114\) −0.502442 −0.0470580
\(115\) −0.286843 −0.0267483
\(116\) 0.826208 0.0767115
\(117\) 6.05083 0.559399
\(118\) −5.77799 −0.531907
\(119\) 7.66990 0.703099
\(120\) 0.871541 0.0795605
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) 1.92808 0.173849
\(124\) 2.54242 0.228316
\(125\) −8.05340 −0.720318
\(126\) 1.79155 0.159604
\(127\) 13.2035 1.17162 0.585810 0.810448i \(-0.300776\pi\)
0.585810 + 0.810448i \(0.300776\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.90273 −0.431661
\(130\) 5.27355 0.462521
\(131\) −0.292814 −0.0255832 −0.0127916 0.999918i \(-0.504072\pi\)
−0.0127916 + 0.999918i \(0.504072\pi\)
\(132\) 1.00000 0.0870388
\(133\) −0.900150 −0.0780529
\(134\) 3.24114 0.279992
\(135\) 0.871541 0.0750103
\(136\) 4.28116 0.367106
\(137\) −13.4359 −1.14791 −0.573954 0.818887i \(-0.694591\pi\)
−0.573954 + 0.818887i \(0.694591\pi\)
\(138\) −0.329122 −0.0280167
\(139\) −18.9380 −1.60630 −0.803150 0.595777i \(-0.796844\pi\)
−0.803150 + 0.595777i \(0.796844\pi\)
\(140\) 1.56141 0.131963
\(141\) −9.19307 −0.774196
\(142\) −7.63320 −0.640564
\(143\) 6.05083 0.505996
\(144\) 1.00000 0.0833333
\(145\) 0.720074 0.0597989
\(146\) 7.93920 0.657053
\(147\) −3.79035 −0.312623
\(148\) −11.6827 −0.960310
\(149\) 21.5424 1.76482 0.882412 0.470478i \(-0.155918\pi\)
0.882412 + 0.470478i \(0.155918\pi\)
\(150\) −4.24042 −0.346228
\(151\) 7.30147 0.594185 0.297093 0.954849i \(-0.403983\pi\)
0.297093 + 0.954849i \(0.403983\pi\)
\(152\) −0.502442 −0.0407535
\(153\) 4.28116 0.346111
\(154\) 1.79155 0.144367
\(155\) 2.21582 0.177979
\(156\) 6.05083 0.484454
\(157\) −16.8390 −1.34390 −0.671950 0.740597i \(-0.734543\pi\)
−0.671950 + 0.740597i \(0.734543\pi\)
\(158\) 12.1924 0.969978
\(159\) 0.198049 0.0157063
\(160\) 0.871541 0.0689014
\(161\) −0.589638 −0.0464700
\(162\) 1.00000 0.0785674
\(163\) 19.9962 1.56622 0.783111 0.621882i \(-0.213632\pi\)
0.783111 + 0.621882i \(0.213632\pi\)
\(164\) 1.92808 0.150557
\(165\) 0.871541 0.0678494
\(166\) −5.33038 −0.413718
\(167\) −5.96323 −0.461448 −0.230724 0.973019i \(-0.574109\pi\)
−0.230724 + 0.973019i \(0.574109\pi\)
\(168\) 1.79155 0.138221
\(169\) 23.6126 1.81635
\(170\) 3.73121 0.286170
\(171\) −0.502442 −0.0384227
\(172\) −4.90273 −0.373830
\(173\) 2.13158 0.162061 0.0810307 0.996712i \(-0.474179\pi\)
0.0810307 + 0.996712i \(0.474179\pi\)
\(174\) 0.826208 0.0626347
\(175\) −7.59691 −0.574273
\(176\) 1.00000 0.0753778
\(177\) −5.77799 −0.434300
\(178\) −4.51300 −0.338264
\(179\) 4.23721 0.316704 0.158352 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(180\) 0.871541 0.0649609
\(181\) 18.4965 1.37483 0.687417 0.726263i \(-0.258745\pi\)
0.687417 + 0.726263i \(0.258745\pi\)
\(182\) 10.8404 0.803541
\(183\) −1.00000 −0.0739221
\(184\) −0.329122 −0.0242632
\(185\) −10.1819 −0.748591
\(186\) 2.54242 0.186419
\(187\) 4.28116 0.313069
\(188\) −9.19307 −0.670474
\(189\) 1.79155 0.130316
\(190\) −0.437899 −0.0317686
\(191\) −15.3727 −1.11233 −0.556165 0.831072i \(-0.687728\pi\)
−0.556165 + 0.831072i \(0.687728\pi\)
\(192\) 1.00000 0.0721688
\(193\) 7.25371 0.522133 0.261067 0.965321i \(-0.415926\pi\)
0.261067 + 0.965321i \(0.415926\pi\)
\(194\) 9.53546 0.684606
\(195\) 5.27355 0.377647
\(196\) −3.79035 −0.270739
\(197\) 2.95332 0.210416 0.105208 0.994450i \(-0.466449\pi\)
0.105208 + 0.994450i \(0.466449\pi\)
\(198\) 1.00000 0.0710669
\(199\) 8.65655 0.613646 0.306823 0.951767i \(-0.400734\pi\)
0.306823 + 0.951767i \(0.400734\pi\)
\(200\) −4.24042 −0.299843
\(201\) 3.24114 0.228613
\(202\) −0.178769 −0.0125782
\(203\) 1.48019 0.103889
\(204\) 4.28116 0.299741
\(205\) 1.68040 0.117364
\(206\) −1.56415 −0.108979
\(207\) −0.329122 −0.0228755
\(208\) 6.05083 0.419550
\(209\) −0.502442 −0.0347547
\(210\) 1.56141 0.107747
\(211\) −20.5222 −1.41281 −0.706403 0.707810i \(-0.749683\pi\)
−0.706403 + 0.707810i \(0.749683\pi\)
\(212\) 0.198049 0.0136020
\(213\) −7.63320 −0.523018
\(214\) −3.77496 −0.258051
\(215\) −4.27293 −0.291412
\(216\) 1.00000 0.0680414
\(217\) 4.55487 0.309205
\(218\) 0.168419 0.0114068
\(219\) 7.93920 0.536481
\(220\) 0.871541 0.0587593
\(221\) 25.9046 1.74253
\(222\) −11.6827 −0.784090
\(223\) −21.0135 −1.40717 −0.703584 0.710612i \(-0.748418\pi\)
−0.703584 + 0.710612i \(0.748418\pi\)
\(224\) 1.79155 0.119703
\(225\) −4.24042 −0.282694
\(226\) 12.0336 0.800464
\(227\) −27.1121 −1.79949 −0.899747 0.436412i \(-0.856249\pi\)
−0.899747 + 0.436412i \(0.856249\pi\)
\(228\) −0.502442 −0.0332751
\(229\) 16.6742 1.10186 0.550932 0.834550i \(-0.314272\pi\)
0.550932 + 0.834550i \(0.314272\pi\)
\(230\) −0.286843 −0.0189139
\(231\) 1.79155 0.117875
\(232\) 0.826208 0.0542432
\(233\) 7.53921 0.493910 0.246955 0.969027i \(-0.420570\pi\)
0.246955 + 0.969027i \(0.420570\pi\)
\(234\) 6.05083 0.395555
\(235\) −8.01214 −0.522655
\(236\) −5.77799 −0.376115
\(237\) 12.1924 0.791984
\(238\) 7.66990 0.497166
\(239\) −26.0180 −1.68297 −0.841483 0.540284i \(-0.818317\pi\)
−0.841483 + 0.540284i \(0.818317\pi\)
\(240\) 0.871541 0.0562577
\(241\) −23.7245 −1.52823 −0.764114 0.645082i \(-0.776823\pi\)
−0.764114 + 0.645082i \(0.776823\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −3.30345 −0.211050
\(246\) 1.92808 0.122930
\(247\) −3.04019 −0.193443
\(248\) 2.54242 0.161444
\(249\) −5.33038 −0.337799
\(250\) −8.05340 −0.509342
\(251\) 17.2264 1.08732 0.543661 0.839305i \(-0.317038\pi\)
0.543661 + 0.839305i \(0.317038\pi\)
\(252\) 1.79155 0.112857
\(253\) −0.329122 −0.0206917
\(254\) 13.2035 0.828461
\(255\) 3.73121 0.233657
\(256\) 1.00000 0.0625000
\(257\) 14.9836 0.934649 0.467325 0.884086i \(-0.345218\pi\)
0.467325 + 0.884086i \(0.345218\pi\)
\(258\) −4.90273 −0.305231
\(259\) −20.9301 −1.30053
\(260\) 5.27355 0.327052
\(261\) 0.826208 0.0511410
\(262\) −0.292814 −0.0180901
\(263\) 6.28404 0.387490 0.193745 0.981052i \(-0.437936\pi\)
0.193745 + 0.981052i \(0.437936\pi\)
\(264\) 1.00000 0.0615457
\(265\) 0.172607 0.0106032
\(266\) −0.900150 −0.0551918
\(267\) −4.51300 −0.276191
\(268\) 3.24114 0.197984
\(269\) −19.9982 −1.21931 −0.609655 0.792666i \(-0.708692\pi\)
−0.609655 + 0.792666i \(0.708692\pi\)
\(270\) 0.871541 0.0530403
\(271\) 5.33390 0.324011 0.162006 0.986790i \(-0.448204\pi\)
0.162006 + 0.986790i \(0.448204\pi\)
\(272\) 4.28116 0.259583
\(273\) 10.8404 0.656089
\(274\) −13.4359 −0.811694
\(275\) −4.24042 −0.255707
\(276\) −0.329122 −0.0198108
\(277\) −13.2945 −0.798791 −0.399396 0.916779i \(-0.630780\pi\)
−0.399396 + 0.916779i \(0.630780\pi\)
\(278\) −18.9380 −1.13583
\(279\) 2.54242 0.152211
\(280\) 1.56141 0.0933120
\(281\) 0.315638 0.0188294 0.00941471 0.999956i \(-0.497003\pi\)
0.00941471 + 0.999956i \(0.497003\pi\)
\(282\) −9.19307 −0.547440
\(283\) 0.146911 0.00873297 0.00436648 0.999990i \(-0.498610\pi\)
0.00436648 + 0.999990i \(0.498610\pi\)
\(284\) −7.63320 −0.452947
\(285\) −0.437899 −0.0259389
\(286\) 6.05083 0.357793
\(287\) 3.45424 0.203898
\(288\) 1.00000 0.0589256
\(289\) 1.32831 0.0781358
\(290\) 0.720074 0.0422842
\(291\) 9.53546 0.558979
\(292\) 7.93920 0.464607
\(293\) −31.8915 −1.86312 −0.931560 0.363587i \(-0.881552\pi\)
−0.931560 + 0.363587i \(0.881552\pi\)
\(294\) −3.79035 −0.221058
\(295\) −5.03576 −0.293193
\(296\) −11.6827 −0.679042
\(297\) 1.00000 0.0580259
\(298\) 21.5424 1.24792
\(299\) −1.99146 −0.115169
\(300\) −4.24042 −0.244821
\(301\) −8.78349 −0.506272
\(302\) 7.30147 0.420152
\(303\) −0.178769 −0.0102700
\(304\) −0.502442 −0.0288170
\(305\) −0.871541 −0.0499043
\(306\) 4.28116 0.244737
\(307\) 3.27266 0.186781 0.0933903 0.995630i \(-0.470230\pi\)
0.0933903 + 0.995630i \(0.470230\pi\)
\(308\) 1.79155 0.102083
\(309\) −1.56415 −0.0889812
\(310\) 2.21582 0.125850
\(311\) 11.1080 0.629877 0.314938 0.949112i \(-0.398016\pi\)
0.314938 + 0.949112i \(0.398016\pi\)
\(312\) 6.05083 0.342561
\(313\) −21.1941 −1.19796 −0.598981 0.800763i \(-0.704428\pi\)
−0.598981 + 0.800763i \(0.704428\pi\)
\(314\) −16.8390 −0.950280
\(315\) 1.56141 0.0879754
\(316\) 12.1924 0.685878
\(317\) −10.5636 −0.593310 −0.296655 0.954985i \(-0.595871\pi\)
−0.296655 + 0.954985i \(0.595871\pi\)
\(318\) 0.198049 0.0111060
\(319\) 0.826208 0.0462588
\(320\) 0.871541 0.0487206
\(321\) −3.77496 −0.210698
\(322\) −0.589638 −0.0328592
\(323\) −2.15104 −0.119687
\(324\) 1.00000 0.0555556
\(325\) −25.6580 −1.42325
\(326\) 19.9962 1.10749
\(327\) 0.168419 0.00931360
\(328\) 1.92808 0.106460
\(329\) −16.4698 −0.908012
\(330\) 0.871541 0.0479768
\(331\) 26.7220 1.46877 0.734387 0.678731i \(-0.237470\pi\)
0.734387 + 0.678731i \(0.237470\pi\)
\(332\) −5.33038 −0.292543
\(333\) −11.6827 −0.640207
\(334\) −5.96323 −0.326293
\(335\) 2.82479 0.154335
\(336\) 1.79155 0.0977370
\(337\) 14.8452 0.808669 0.404335 0.914611i \(-0.367503\pi\)
0.404335 + 0.914611i \(0.367503\pi\)
\(338\) 23.6126 1.28435
\(339\) 12.0336 0.653576
\(340\) 3.73121 0.202353
\(341\) 2.54242 0.137680
\(342\) −0.502442 −0.0271690
\(343\) −19.3314 −1.04380
\(344\) −4.90273 −0.264338
\(345\) −0.286843 −0.0154431
\(346\) 2.13158 0.114595
\(347\) 32.2966 1.73377 0.866887 0.498504i \(-0.166117\pi\)
0.866887 + 0.498504i \(0.166117\pi\)
\(348\) 0.826208 0.0442894
\(349\) 19.0687 1.02073 0.510363 0.859959i \(-0.329511\pi\)
0.510363 + 0.859959i \(0.329511\pi\)
\(350\) −7.59691 −0.406072
\(351\) 6.05083 0.322969
\(352\) 1.00000 0.0533002
\(353\) −24.7218 −1.31581 −0.657905 0.753101i \(-0.728557\pi\)
−0.657905 + 0.753101i \(0.728557\pi\)
\(354\) −5.77799 −0.307097
\(355\) −6.65265 −0.353086
\(356\) −4.51300 −0.239189
\(357\) 7.66990 0.405934
\(358\) 4.23721 0.223944
\(359\) 29.6397 1.56432 0.782162 0.623075i \(-0.214117\pi\)
0.782162 + 0.623075i \(0.214117\pi\)
\(360\) 0.871541 0.0459343
\(361\) −18.7476 −0.986713
\(362\) 18.4965 0.972154
\(363\) 1.00000 0.0524864
\(364\) 10.8404 0.568189
\(365\) 6.91934 0.362175
\(366\) −1.00000 −0.0522708
\(367\) −2.72541 −0.142265 −0.0711325 0.997467i \(-0.522661\pi\)
−0.0711325 + 0.997467i \(0.522661\pi\)
\(368\) −0.329122 −0.0171567
\(369\) 1.92808 0.100372
\(370\) −10.1819 −0.529334
\(371\) 0.354814 0.0184210
\(372\) 2.54242 0.131818
\(373\) 25.8653 1.33926 0.669628 0.742696i \(-0.266453\pi\)
0.669628 + 0.742696i \(0.266453\pi\)
\(374\) 4.28116 0.221373
\(375\) −8.05340 −0.415876
\(376\) −9.19307 −0.474097
\(377\) 4.99924 0.257474
\(378\) 1.79155 0.0921474
\(379\) −29.8825 −1.53496 −0.767479 0.641074i \(-0.778489\pi\)
−0.767479 + 0.641074i \(0.778489\pi\)
\(380\) −0.437899 −0.0224638
\(381\) 13.2035 0.676435
\(382\) −15.3727 −0.786536
\(383\) −32.6319 −1.66741 −0.833705 0.552210i \(-0.813785\pi\)
−0.833705 + 0.552210i \(0.813785\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.56141 0.0795768
\(386\) 7.25371 0.369204
\(387\) −4.90273 −0.249220
\(388\) 9.53546 0.484090
\(389\) −24.7562 −1.25519 −0.627595 0.778540i \(-0.715961\pi\)
−0.627595 + 0.778540i \(0.715961\pi\)
\(390\) 5.27355 0.267037
\(391\) −1.40902 −0.0712573
\(392\) −3.79035 −0.191442
\(393\) −0.292814 −0.0147705
\(394\) 2.95332 0.148786
\(395\) 10.6262 0.534663
\(396\) 1.00000 0.0502519
\(397\) −8.25865 −0.414490 −0.207245 0.978289i \(-0.566450\pi\)
−0.207245 + 0.978289i \(0.566450\pi\)
\(398\) 8.65655 0.433914
\(399\) −0.900150 −0.0450639
\(400\) −4.24042 −0.212021
\(401\) 10.5654 0.527613 0.263807 0.964576i \(-0.415022\pi\)
0.263807 + 0.964576i \(0.415022\pi\)
\(402\) 3.24114 0.161653
\(403\) 15.3837 0.766319
\(404\) −0.178769 −0.00889411
\(405\) 0.871541 0.0433072
\(406\) 1.48019 0.0734607
\(407\) −11.6827 −0.579089
\(408\) 4.28116 0.211949
\(409\) 31.0066 1.53318 0.766590 0.642137i \(-0.221952\pi\)
0.766590 + 0.642137i \(0.221952\pi\)
\(410\) 1.68040 0.0829889
\(411\) −13.4359 −0.662745
\(412\) −1.56415 −0.0770600
\(413\) −10.3516 −0.509367
\(414\) −0.329122 −0.0161755
\(415\) −4.64565 −0.228046
\(416\) 6.05083 0.296666
\(417\) −18.9380 −0.927397
\(418\) −0.502442 −0.0245753
\(419\) −6.83731 −0.334024 −0.167012 0.985955i \(-0.553412\pi\)
−0.167012 + 0.985955i \(0.553412\pi\)
\(420\) 1.56141 0.0761890
\(421\) 27.9306 1.36125 0.680627 0.732630i \(-0.261707\pi\)
0.680627 + 0.732630i \(0.261707\pi\)
\(422\) −20.5222 −0.999004
\(423\) −9.19307 −0.446982
\(424\) 0.198049 0.00961809
\(425\) −18.1539 −0.880593
\(426\) −7.63320 −0.369830
\(427\) −1.79155 −0.0866991
\(428\) −3.77496 −0.182470
\(429\) 6.05083 0.292137
\(430\) −4.27293 −0.206059
\(431\) −39.8994 −1.92189 −0.960943 0.276746i \(-0.910744\pi\)
−0.960943 + 0.276746i \(0.910744\pi\)
\(432\) 1.00000 0.0481125
\(433\) 40.2106 1.93240 0.966200 0.257795i \(-0.0829959\pi\)
0.966200 + 0.257795i \(0.0829959\pi\)
\(434\) 4.55487 0.218641
\(435\) 0.720074 0.0345249
\(436\) 0.168419 0.00806582
\(437\) 0.165365 0.00791047
\(438\) 7.93920 0.379350
\(439\) 3.05387 0.145753 0.0728767 0.997341i \(-0.476782\pi\)
0.0728767 + 0.997341i \(0.476782\pi\)
\(440\) 0.871541 0.0415491
\(441\) −3.79035 −0.180493
\(442\) 25.9046 1.23215
\(443\) 24.4029 1.15942 0.579709 0.814824i \(-0.303166\pi\)
0.579709 + 0.814824i \(0.303166\pi\)
\(444\) −11.6827 −0.554435
\(445\) −3.93327 −0.186455
\(446\) −21.0135 −0.995018
\(447\) 21.5424 1.01892
\(448\) 1.79155 0.0846427
\(449\) 20.0453 0.945995 0.472998 0.881064i \(-0.343172\pi\)
0.472998 + 0.881064i \(0.343172\pi\)
\(450\) −4.24042 −0.199895
\(451\) 1.92808 0.0907895
\(452\) 12.0336 0.566013
\(453\) 7.30147 0.343053
\(454\) −27.1121 −1.27243
\(455\) 9.44782 0.442921
\(456\) −0.502442 −0.0235290
\(457\) −19.3350 −0.904451 −0.452226 0.891904i \(-0.649370\pi\)
−0.452226 + 0.891904i \(0.649370\pi\)
\(458\) 16.6742 0.779136
\(459\) 4.28116 0.199827
\(460\) −0.286843 −0.0133741
\(461\) −33.8556 −1.57681 −0.788406 0.615155i \(-0.789093\pi\)
−0.788406 + 0.615155i \(0.789093\pi\)
\(462\) 1.79155 0.0833504
\(463\) 24.0563 1.11799 0.558996 0.829170i \(-0.311187\pi\)
0.558996 + 0.829170i \(0.311187\pi\)
\(464\) 0.826208 0.0383557
\(465\) 2.21582 0.102756
\(466\) 7.53921 0.349247
\(467\) 34.5776 1.60006 0.800030 0.599960i \(-0.204817\pi\)
0.800030 + 0.599960i \(0.204817\pi\)
\(468\) 6.05083 0.279700
\(469\) 5.80667 0.268127
\(470\) −8.01214 −0.369573
\(471\) −16.8390 −0.775901
\(472\) −5.77799 −0.265953
\(473\) −4.90273 −0.225428
\(474\) 12.1924 0.560017
\(475\) 2.13056 0.0977570
\(476\) 7.66990 0.351549
\(477\) 0.198049 0.00906802
\(478\) −26.0180 −1.19004
\(479\) 15.7430 0.719315 0.359657 0.933084i \(-0.382894\pi\)
0.359657 + 0.933084i \(0.382894\pi\)
\(480\) 0.871541 0.0397802
\(481\) −70.6899 −3.22318
\(482\) −23.7245 −1.08062
\(483\) −0.589638 −0.0268295
\(484\) 1.00000 0.0454545
\(485\) 8.31055 0.377363
\(486\) 1.00000 0.0453609
\(487\) 3.71321 0.168262 0.0841308 0.996455i \(-0.473189\pi\)
0.0841308 + 0.996455i \(0.473189\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 19.9962 0.904259
\(490\) −3.30345 −0.149235
\(491\) −34.7263 −1.56718 −0.783588 0.621281i \(-0.786613\pi\)
−0.783588 + 0.621281i \(0.786613\pi\)
\(492\) 1.92808 0.0869244
\(493\) 3.53713 0.159304
\(494\) −3.04019 −0.136785
\(495\) 0.871541 0.0391729
\(496\) 2.54242 0.114158
\(497\) −13.6753 −0.613419
\(498\) −5.33038 −0.238860
\(499\) 8.45034 0.378289 0.189145 0.981949i \(-0.439429\pi\)
0.189145 + 0.981949i \(0.439429\pi\)
\(500\) −8.05340 −0.360159
\(501\) −5.96323 −0.266417
\(502\) 17.2264 0.768853
\(503\) −8.67082 −0.386613 −0.193306 0.981138i \(-0.561921\pi\)
−0.193306 + 0.981138i \(0.561921\pi\)
\(504\) 1.79155 0.0798019
\(505\) −0.155805 −0.00693323
\(506\) −0.329122 −0.0146312
\(507\) 23.6126 1.04867
\(508\) 13.2035 0.585810
\(509\) −30.2899 −1.34258 −0.671288 0.741197i \(-0.734258\pi\)
−0.671288 + 0.741197i \(0.734258\pi\)
\(510\) 3.73121 0.165221
\(511\) 14.2235 0.629209
\(512\) 1.00000 0.0441942
\(513\) −0.502442 −0.0221834
\(514\) 14.9836 0.660897
\(515\) −1.36322 −0.0600706
\(516\) −4.90273 −0.215831
\(517\) −9.19307 −0.404311
\(518\) −20.9301 −0.919616
\(519\) 2.13158 0.0935662
\(520\) 5.27355 0.231260
\(521\) −30.7393 −1.34671 −0.673356 0.739318i \(-0.735148\pi\)
−0.673356 + 0.739318i \(0.735148\pi\)
\(522\) 0.826208 0.0361621
\(523\) 31.2904 1.36823 0.684117 0.729373i \(-0.260188\pi\)
0.684117 + 0.729373i \(0.260188\pi\)
\(524\) −0.292814 −0.0127916
\(525\) −7.59691 −0.331557
\(526\) 6.28404 0.273997
\(527\) 10.8845 0.474136
\(528\) 1.00000 0.0435194
\(529\) −22.8917 −0.995290
\(530\) 0.172607 0.00749759
\(531\) −5.77799 −0.250743
\(532\) −0.900150 −0.0390265
\(533\) 11.6665 0.505331
\(534\) −4.51300 −0.195297
\(535\) −3.29003 −0.142241
\(536\) 3.24114 0.139996
\(537\) 4.23721 0.182849
\(538\) −19.9982 −0.862183
\(539\) −3.79035 −0.163262
\(540\) 0.871541 0.0375052
\(541\) 8.22017 0.353413 0.176706 0.984264i \(-0.443456\pi\)
0.176706 + 0.984264i \(0.443456\pi\)
\(542\) 5.33390 0.229111
\(543\) 18.4965 0.793760
\(544\) 4.28116 0.183553
\(545\) 0.146784 0.00628755
\(546\) 10.8404 0.463925
\(547\) −31.2358 −1.33555 −0.667773 0.744365i \(-0.732752\pi\)
−0.667773 + 0.744365i \(0.732752\pi\)
\(548\) −13.4359 −0.573954
\(549\) −1.00000 −0.0426790
\(550\) −4.24042 −0.180812
\(551\) −0.415122 −0.0176848
\(552\) −0.329122 −0.0140084
\(553\) 21.8433 0.928874
\(554\) −13.2945 −0.564831
\(555\) −10.1819 −0.432199
\(556\) −18.9380 −0.803150
\(557\) −12.4285 −0.526613 −0.263307 0.964712i \(-0.584813\pi\)
−0.263307 + 0.964712i \(0.584813\pi\)
\(558\) 2.54242 0.107629
\(559\) −29.6656 −1.25472
\(560\) 1.56141 0.0659816
\(561\) 4.28116 0.180751
\(562\) 0.315638 0.0133144
\(563\) −4.07195 −0.171612 −0.0858062 0.996312i \(-0.527347\pi\)
−0.0858062 + 0.996312i \(0.527347\pi\)
\(564\) −9.19307 −0.387098
\(565\) 10.4878 0.441225
\(566\) 0.146911 0.00617514
\(567\) 1.79155 0.0752380
\(568\) −7.63320 −0.320282
\(569\) 36.9313 1.54824 0.774120 0.633039i \(-0.218193\pi\)
0.774120 + 0.633039i \(0.218193\pi\)
\(570\) −0.437899 −0.0183416
\(571\) −22.1626 −0.927478 −0.463739 0.885972i \(-0.653492\pi\)
−0.463739 + 0.885972i \(0.653492\pi\)
\(572\) 6.05083 0.252998
\(573\) −15.3727 −0.642204
\(574\) 3.45424 0.144177
\(575\) 1.39561 0.0582011
\(576\) 1.00000 0.0416667
\(577\) −21.4524 −0.893074 −0.446537 0.894765i \(-0.647343\pi\)
−0.446537 + 0.894765i \(0.647343\pi\)
\(578\) 1.32831 0.0552503
\(579\) 7.25371 0.301454
\(580\) 0.720074 0.0298995
\(581\) −9.54964 −0.396186
\(582\) 9.53546 0.395258
\(583\) 0.198049 0.00820233
\(584\) 7.93920 0.328526
\(585\) 5.27355 0.218034
\(586\) −31.8915 −1.31743
\(587\) 41.7377 1.72270 0.861350 0.508012i \(-0.169620\pi\)
0.861350 + 0.508012i \(0.169620\pi\)
\(588\) −3.79035 −0.156311
\(589\) −1.27742 −0.0526351
\(590\) −5.03576 −0.207319
\(591\) 2.95332 0.121484
\(592\) −11.6827 −0.480155
\(593\) 5.41312 0.222290 0.111145 0.993804i \(-0.464548\pi\)
0.111145 + 0.993804i \(0.464548\pi\)
\(594\) 1.00000 0.0410305
\(595\) 6.68464 0.274043
\(596\) 21.5424 0.882412
\(597\) 8.65655 0.354289
\(598\) −1.99146 −0.0814369
\(599\) −19.5160 −0.797401 −0.398700 0.917081i \(-0.630539\pi\)
−0.398700 + 0.917081i \(0.630539\pi\)
\(600\) −4.24042 −0.173114
\(601\) 23.3839 0.953850 0.476925 0.878944i \(-0.341751\pi\)
0.476925 + 0.878944i \(0.341751\pi\)
\(602\) −8.78349 −0.357988
\(603\) 3.24114 0.131990
\(604\) 7.30147 0.297093
\(605\) 0.871541 0.0354332
\(606\) −0.178769 −0.00726201
\(607\) −5.66519 −0.229943 −0.114971 0.993369i \(-0.536678\pi\)
−0.114971 + 0.993369i \(0.536678\pi\)
\(608\) −0.502442 −0.0203767
\(609\) 1.48019 0.0599804
\(610\) −0.871541 −0.0352877
\(611\) −55.6257 −2.25038
\(612\) 4.28116 0.173056
\(613\) 30.1541 1.21791 0.608956 0.793204i \(-0.291588\pi\)
0.608956 + 0.793204i \(0.291588\pi\)
\(614\) 3.27266 0.132074
\(615\) 1.68040 0.0677602
\(616\) 1.79155 0.0721836
\(617\) 15.7985 0.636026 0.318013 0.948086i \(-0.396984\pi\)
0.318013 + 0.948086i \(0.396984\pi\)
\(618\) −1.56415 −0.0629192
\(619\) −40.3515 −1.62186 −0.810931 0.585142i \(-0.801039\pi\)
−0.810931 + 0.585142i \(0.801039\pi\)
\(620\) 2.21582 0.0889896
\(621\) −0.329122 −0.0132072
\(622\) 11.1080 0.445390
\(623\) −8.08527 −0.323929
\(624\) 6.05083 0.242227
\(625\) 14.1832 0.567328
\(626\) −21.1941 −0.847087
\(627\) −0.502442 −0.0200656
\(628\) −16.8390 −0.671950
\(629\) −50.0154 −1.99424
\(630\) 1.56141 0.0622080
\(631\) 15.3245 0.610060 0.305030 0.952343i \(-0.401333\pi\)
0.305030 + 0.952343i \(0.401333\pi\)
\(632\) 12.1924 0.484989
\(633\) −20.5222 −0.815684
\(634\) −10.5636 −0.419533
\(635\) 11.5074 0.456657
\(636\) 0.198049 0.00785314
\(637\) −22.9348 −0.908709
\(638\) 0.826208 0.0327099
\(639\) −7.63320 −0.301965
\(640\) 0.871541 0.0344507
\(641\) −4.60133 −0.181741 −0.0908707 0.995863i \(-0.528965\pi\)
−0.0908707 + 0.995863i \(0.528965\pi\)
\(642\) −3.77496 −0.148986
\(643\) 26.3732 1.04006 0.520028 0.854149i \(-0.325921\pi\)
0.520028 + 0.854149i \(0.325921\pi\)
\(644\) −0.589638 −0.0232350
\(645\) −4.27293 −0.168247
\(646\) −2.15104 −0.0846313
\(647\) −14.3028 −0.562300 −0.281150 0.959664i \(-0.590716\pi\)
−0.281150 + 0.959664i \(0.590716\pi\)
\(648\) 1.00000 0.0392837
\(649\) −5.77799 −0.226806
\(650\) −25.6580 −1.00639
\(651\) 4.55487 0.178519
\(652\) 19.9962 0.783111
\(653\) −12.7098 −0.497371 −0.248686 0.968584i \(-0.579999\pi\)
−0.248686 + 0.968584i \(0.579999\pi\)
\(654\) 0.168419 0.00658571
\(655\) −0.255199 −0.00997146
\(656\) 1.92808 0.0752787
\(657\) 7.93920 0.309738
\(658\) −16.4698 −0.642061
\(659\) −40.4796 −1.57686 −0.788430 0.615124i \(-0.789106\pi\)
−0.788430 + 0.615124i \(0.789106\pi\)
\(660\) 0.871541 0.0339247
\(661\) 18.5910 0.723104 0.361552 0.932352i \(-0.382247\pi\)
0.361552 + 0.932352i \(0.382247\pi\)
\(662\) 26.7220 1.03858
\(663\) 25.9046 1.00605
\(664\) −5.33038 −0.206859
\(665\) −0.784518 −0.0304223
\(666\) −11.6827 −0.452695
\(667\) −0.271923 −0.0105289
\(668\) −5.96323 −0.230724
\(669\) −21.0135 −0.812429
\(670\) 2.82479 0.109131
\(671\) −1.00000 −0.0386046
\(672\) 1.79155 0.0691105
\(673\) −13.3367 −0.514091 −0.257045 0.966399i \(-0.582749\pi\)
−0.257045 + 0.966399i \(0.582749\pi\)
\(674\) 14.8452 0.571815
\(675\) −4.24042 −0.163214
\(676\) 23.6126 0.908175
\(677\) 25.7955 0.991402 0.495701 0.868493i \(-0.334911\pi\)
0.495701 + 0.868493i \(0.334911\pi\)
\(678\) 12.0336 0.462148
\(679\) 17.0832 0.655595
\(680\) 3.73121 0.143085
\(681\) −27.1121 −1.03894
\(682\) 2.54242 0.0973543
\(683\) −2.30888 −0.0883468 −0.0441734 0.999024i \(-0.514065\pi\)
−0.0441734 + 0.999024i \(0.514065\pi\)
\(684\) −0.502442 −0.0192114
\(685\) −11.7100 −0.447415
\(686\) −19.3314 −0.738078
\(687\) 16.6742 0.636162
\(688\) −4.90273 −0.186915
\(689\) 1.19836 0.0456538
\(690\) −0.286843 −0.0109199
\(691\) 23.5170 0.894630 0.447315 0.894376i \(-0.352380\pi\)
0.447315 + 0.894376i \(0.352380\pi\)
\(692\) 2.13158 0.0810307
\(693\) 1.79155 0.0680553
\(694\) 32.2966 1.22596
\(695\) −16.5052 −0.626080
\(696\) 0.826208 0.0313173
\(697\) 8.25440 0.312658
\(698\) 19.0687 0.721762
\(699\) 7.53921 0.285159
\(700\) −7.59691 −0.287136
\(701\) 4.93652 0.186450 0.0932249 0.995645i \(-0.470282\pi\)
0.0932249 + 0.995645i \(0.470282\pi\)
\(702\) 6.05083 0.228374
\(703\) 5.86987 0.221387
\(704\) 1.00000 0.0376889
\(705\) −8.01214 −0.301755
\(706\) −24.7218 −0.930419
\(707\) −0.320274 −0.0120451
\(708\) −5.77799 −0.217150
\(709\) −15.8317 −0.594572 −0.297286 0.954788i \(-0.596082\pi\)
−0.297286 + 0.954788i \(0.596082\pi\)
\(710\) −6.65265 −0.249670
\(711\) 12.1924 0.457252
\(712\) −4.51300 −0.169132
\(713\) −0.836766 −0.0313371
\(714\) 7.66990 0.287039
\(715\) 5.27355 0.197220
\(716\) 4.23721 0.158352
\(717\) −26.0180 −0.971661
\(718\) 29.6397 1.10614
\(719\) −9.24628 −0.344828 −0.172414 0.985025i \(-0.555157\pi\)
−0.172414 + 0.985025i \(0.555157\pi\)
\(720\) 0.871541 0.0324804
\(721\) −2.80225 −0.104361
\(722\) −18.7476 −0.697712
\(723\) −23.7245 −0.882323
\(724\) 18.4965 0.687417
\(725\) −3.50347 −0.130115
\(726\) 1.00000 0.0371135
\(727\) 22.9494 0.851147 0.425574 0.904924i \(-0.360072\pi\)
0.425574 + 0.904924i \(0.360072\pi\)
\(728\) 10.8404 0.401771
\(729\) 1.00000 0.0370370
\(730\) 6.91934 0.256096
\(731\) −20.9894 −0.776320
\(732\) −1.00000 −0.0369611
\(733\) 25.1109 0.927491 0.463745 0.885969i \(-0.346505\pi\)
0.463745 + 0.885969i \(0.346505\pi\)
\(734\) −2.72541 −0.100597
\(735\) −3.30345 −0.121849
\(736\) −0.329122 −0.0121316
\(737\) 3.24114 0.119389
\(738\) 1.92808 0.0709735
\(739\) −45.7398 −1.68257 −0.841283 0.540595i \(-0.818199\pi\)
−0.841283 + 0.540595i \(0.818199\pi\)
\(740\) −10.1819 −0.374296
\(741\) −3.04019 −0.111684
\(742\) 0.354814 0.0130256
\(743\) −29.0108 −1.06430 −0.532152 0.846649i \(-0.678617\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(744\) 2.54242 0.0932096
\(745\) 18.7751 0.687867
\(746\) 25.8653 0.946997
\(747\) −5.33038 −0.195028
\(748\) 4.28116 0.156535
\(749\) −6.76303 −0.247116
\(750\) −8.05340 −0.294069
\(751\) −17.1099 −0.624350 −0.312175 0.950025i \(-0.601057\pi\)
−0.312175 + 0.950025i \(0.601057\pi\)
\(752\) −9.19307 −0.335237
\(753\) 17.2264 0.627766
\(754\) 4.99924 0.182062
\(755\) 6.36353 0.231593
\(756\) 1.79155 0.0651580
\(757\) 51.1697 1.85980 0.929898 0.367819i \(-0.119895\pi\)
0.929898 + 0.367819i \(0.119895\pi\)
\(758\) −29.8825 −1.08538
\(759\) −0.329122 −0.0119464
\(760\) −0.437899 −0.0158843
\(761\) −4.71107 −0.170776 −0.0853881 0.996348i \(-0.527213\pi\)
−0.0853881 + 0.996348i \(0.527213\pi\)
\(762\) 13.2035 0.478312
\(763\) 0.301731 0.0109234
\(764\) −15.3727 −0.556165
\(765\) 3.73121 0.134902
\(766\) −32.6319 −1.17904
\(767\) −34.9616 −1.26239
\(768\) 1.00000 0.0360844
\(769\) 43.7160 1.57644 0.788220 0.615394i \(-0.211003\pi\)
0.788220 + 0.615394i \(0.211003\pi\)
\(770\) 1.56141 0.0562693
\(771\) 14.9836 0.539620
\(772\) 7.25371 0.261067
\(773\) 11.7670 0.423229 0.211615 0.977353i \(-0.432128\pi\)
0.211615 + 0.977353i \(0.432128\pi\)
\(774\) −4.90273 −0.176225
\(775\) −10.7809 −0.387262
\(776\) 9.53546 0.342303
\(777\) −20.9301 −0.750863
\(778\) −24.7562 −0.887554
\(779\) −0.968747 −0.0347090
\(780\) 5.27355 0.188823
\(781\) −7.63320 −0.273137
\(782\) −1.40902 −0.0503865
\(783\) 0.826208 0.0295263
\(784\) −3.79035 −0.135370
\(785\) −14.6759 −0.523805
\(786\) −0.292814 −0.0104443
\(787\) −1.27956 −0.0456114 −0.0228057 0.999740i \(-0.507260\pi\)
−0.0228057 + 0.999740i \(0.507260\pi\)
\(788\) 2.95332 0.105208
\(789\) 6.28404 0.223718
\(790\) 10.6262 0.378064
\(791\) 21.5588 0.766543
\(792\) 1.00000 0.0355335
\(793\) −6.05083 −0.214871
\(794\) −8.25865 −0.293088
\(795\) 0.172607 0.00612176
\(796\) 8.65655 0.306823
\(797\) −28.8178 −1.02078 −0.510390 0.859943i \(-0.670499\pi\)
−0.510390 + 0.859943i \(0.670499\pi\)
\(798\) −0.900150 −0.0318650
\(799\) −39.3570 −1.39235
\(800\) −4.24042 −0.149921
\(801\) −4.51300 −0.159459
\(802\) 10.5654 0.373079
\(803\) 7.93920 0.280168
\(804\) 3.24114 0.114306
\(805\) −0.513894 −0.0181124
\(806\) 15.3837 0.541869
\(807\) −19.9982 −0.703970
\(808\) −0.178769 −0.00628908
\(809\) 15.0691 0.529800 0.264900 0.964276i \(-0.414661\pi\)
0.264900 + 0.964276i \(0.414661\pi\)
\(810\) 0.871541 0.0306228
\(811\) −28.7549 −1.00972 −0.504861 0.863201i \(-0.668456\pi\)
−0.504861 + 0.863201i \(0.668456\pi\)
\(812\) 1.48019 0.0519446
\(813\) 5.33390 0.187068
\(814\) −11.6827 −0.409478
\(815\) 17.4275 0.610459
\(816\) 4.28116 0.149870
\(817\) 2.46334 0.0861814
\(818\) 31.0066 1.08412
\(819\) 10.8404 0.378793
\(820\) 1.68040 0.0586820
\(821\) 41.2780 1.44061 0.720307 0.693656i \(-0.244001\pi\)
0.720307 + 0.693656i \(0.244001\pi\)
\(822\) −13.4359 −0.468632
\(823\) −33.0229 −1.15111 −0.575554 0.817764i \(-0.695213\pi\)
−0.575554 + 0.817764i \(0.695213\pi\)
\(824\) −1.56415 −0.0544896
\(825\) −4.24042 −0.147632
\(826\) −10.3516 −0.360177
\(827\) 21.1263 0.734632 0.367316 0.930096i \(-0.380277\pi\)
0.367316 + 0.930096i \(0.380277\pi\)
\(828\) −0.329122 −0.0114378
\(829\) 20.0800 0.697409 0.348704 0.937233i \(-0.386622\pi\)
0.348704 + 0.937233i \(0.386622\pi\)
\(830\) −4.64565 −0.161253
\(831\) −13.2945 −0.461182
\(832\) 6.05083 0.209775
\(833\) −16.2271 −0.562235
\(834\) −18.9380 −0.655769
\(835\) −5.19720 −0.179856
\(836\) −0.502442 −0.0173773
\(837\) 2.54242 0.0878789
\(838\) −6.83731 −0.236191
\(839\) 11.8308 0.408443 0.204222 0.978925i \(-0.434534\pi\)
0.204222 + 0.978925i \(0.434534\pi\)
\(840\) 1.56141 0.0538737
\(841\) −28.3174 −0.976461
\(842\) 27.9306 0.962552
\(843\) 0.315638 0.0108712
\(844\) −20.5222 −0.706403
\(845\) 20.5793 0.707950
\(846\) −9.19307 −0.316064
\(847\) 1.79155 0.0615584
\(848\) 0.198049 0.00680102
\(849\) 0.146911 0.00504198
\(850\) −18.1539 −0.622673
\(851\) 3.84503 0.131806
\(852\) −7.63320 −0.261509
\(853\) 8.86844 0.303650 0.151825 0.988407i \(-0.451485\pi\)
0.151825 + 0.988407i \(0.451485\pi\)
\(854\) −1.79155 −0.0613056
\(855\) −0.437899 −0.0149758
\(856\) −3.77496 −0.129025
\(857\) 37.6326 1.28551 0.642753 0.766074i \(-0.277792\pi\)
0.642753 + 0.766074i \(0.277792\pi\)
\(858\) 6.05083 0.206572
\(859\) 43.4331 1.48192 0.740960 0.671550i \(-0.234371\pi\)
0.740960 + 0.671550i \(0.234371\pi\)
\(860\) −4.27293 −0.145706
\(861\) 3.45424 0.117720
\(862\) −39.8994 −1.35898
\(863\) −31.7604 −1.08114 −0.540568 0.841301i \(-0.681790\pi\)
−0.540568 + 0.841301i \(0.681790\pi\)
\(864\) 1.00000 0.0340207
\(865\) 1.85776 0.0631659
\(866\) 40.2106 1.36641
\(867\) 1.32831 0.0451117
\(868\) 4.55487 0.154602
\(869\) 12.1924 0.413600
\(870\) 0.720074 0.0244128
\(871\) 19.6116 0.664514
\(872\) 0.168419 0.00570339
\(873\) 9.53546 0.322726
\(874\) 0.165365 0.00559355
\(875\) −14.4281 −0.487758
\(876\) 7.93920 0.268241
\(877\) −45.6417 −1.54121 −0.770605 0.637313i \(-0.780046\pi\)
−0.770605 + 0.637313i \(0.780046\pi\)
\(878\) 3.05387 0.103063
\(879\) −31.8915 −1.07567
\(880\) 0.871541 0.0293797
\(881\) −42.3932 −1.42826 −0.714132 0.700011i \(-0.753179\pi\)
−0.714132 + 0.700011i \(0.753179\pi\)
\(882\) −3.79035 −0.127628
\(883\) −9.14185 −0.307648 −0.153824 0.988098i \(-0.549159\pi\)
−0.153824 + 0.988098i \(0.549159\pi\)
\(884\) 25.9046 0.871265
\(885\) −5.03576 −0.169275
\(886\) 24.4029 0.819832
\(887\) −27.1358 −0.911131 −0.455565 0.890202i \(-0.650563\pi\)
−0.455565 + 0.890202i \(0.650563\pi\)
\(888\) −11.6827 −0.392045
\(889\) 23.6547 0.793353
\(890\) −3.93327 −0.131843
\(891\) 1.00000 0.0335013
\(892\) −21.0135 −0.703584
\(893\) 4.61899 0.154569
\(894\) 21.5424 0.720486
\(895\) 3.69290 0.123440
\(896\) 1.79155 0.0598515
\(897\) −1.99146 −0.0664929
\(898\) 20.0453 0.668920
\(899\) 2.10057 0.0700578
\(900\) −4.24042 −0.141347
\(901\) 0.847877 0.0282469
\(902\) 1.92808 0.0641979
\(903\) −8.78349 −0.292296
\(904\) 12.0336 0.400232
\(905\) 16.1205 0.535862
\(906\) 7.30147 0.242575
\(907\) −34.4559 −1.14409 −0.572045 0.820222i \(-0.693850\pi\)
−0.572045 + 0.820222i \(0.693850\pi\)
\(908\) −27.1121 −0.899747
\(909\) −0.178769 −0.00592941
\(910\) 9.44782 0.313192
\(911\) 45.0367 1.49213 0.746067 0.665871i \(-0.231940\pi\)
0.746067 + 0.665871i \(0.231940\pi\)
\(912\) −0.502442 −0.0166375
\(913\) −5.33038 −0.176410
\(914\) −19.3350 −0.639544
\(915\) −0.871541 −0.0288123
\(916\) 16.6742 0.550932
\(917\) −0.524590 −0.0173235
\(918\) 4.28116 0.141299
\(919\) −5.52206 −0.182156 −0.0910780 0.995844i \(-0.529031\pi\)
−0.0910780 + 0.995844i \(0.529031\pi\)
\(920\) −0.286843 −0.00945694
\(921\) 3.27266 0.107838
\(922\) −33.8556 −1.11497
\(923\) −46.1872 −1.52027
\(924\) 1.79155 0.0589376
\(925\) 49.5394 1.62885
\(926\) 24.0563 0.790540
\(927\) −1.56415 −0.0513733
\(928\) 0.826208 0.0271216
\(929\) −11.5449 −0.378777 −0.189388 0.981902i \(-0.560650\pi\)
−0.189388 + 0.981902i \(0.560650\pi\)
\(930\) 2.21582 0.0726597
\(931\) 1.90443 0.0624153
\(932\) 7.53921 0.246955
\(933\) 11.1080 0.363660
\(934\) 34.5776 1.13141
\(935\) 3.73121 0.122023
\(936\) 6.05083 0.197778
\(937\) 18.9532 0.619176 0.309588 0.950871i \(-0.399809\pi\)
0.309588 + 0.950871i \(0.399809\pi\)
\(938\) 5.80667 0.189594
\(939\) −21.1941 −0.691644
\(940\) −8.01214 −0.261327
\(941\) −32.9889 −1.07541 −0.537704 0.843133i \(-0.680708\pi\)
−0.537704 + 0.843133i \(0.680708\pi\)
\(942\) −16.8390 −0.548645
\(943\) −0.634572 −0.0206645
\(944\) −5.77799 −0.188058
\(945\) 1.56141 0.0507926
\(946\) −4.90273 −0.159402
\(947\) 32.9216 1.06981 0.534904 0.844913i \(-0.320348\pi\)
0.534904 + 0.844913i \(0.320348\pi\)
\(948\) 12.1924 0.395992
\(949\) 48.0388 1.55940
\(950\) 2.13056 0.0691246
\(951\) −10.5636 −0.342547
\(952\) 7.66990 0.248583
\(953\) 38.5330 1.24821 0.624103 0.781342i \(-0.285465\pi\)
0.624103 + 0.781342i \(0.285465\pi\)
\(954\) 0.198049 0.00641206
\(955\) −13.3979 −0.433547
\(956\) −26.0180 −0.841483
\(957\) 0.826208 0.0267075
\(958\) 15.7430 0.508632
\(959\) −24.0711 −0.777297
\(960\) 0.871541 0.0281289
\(961\) −24.5361 −0.791487
\(962\) −70.6899 −2.27913
\(963\) −3.77496 −0.121646
\(964\) −23.7245 −0.764114
\(965\) 6.32191 0.203509
\(966\) −0.589638 −0.0189713
\(967\) 28.0347 0.901535 0.450767 0.892641i \(-0.351150\pi\)
0.450767 + 0.892641i \(0.351150\pi\)
\(968\) 1.00000 0.0321412
\(969\) −2.15104 −0.0691012
\(970\) 8.31055 0.266836
\(971\) −17.3290 −0.556115 −0.278057 0.960565i \(-0.589690\pi\)
−0.278057 + 0.960565i \(0.589690\pi\)
\(972\) 1.00000 0.0320750
\(973\) −33.9283 −1.08769
\(974\) 3.71321 0.118979
\(975\) −25.6580 −0.821715
\(976\) −1.00000 −0.0320092
\(977\) −2.32402 −0.0743521 −0.0371761 0.999309i \(-0.511836\pi\)
−0.0371761 + 0.999309i \(0.511836\pi\)
\(978\) 19.9962 0.639408
\(979\) −4.51300 −0.144236
\(980\) −3.30345 −0.105525
\(981\) 0.168419 0.00537721
\(982\) −34.7263 −1.10816
\(983\) −23.4849 −0.749052 −0.374526 0.927216i \(-0.622195\pi\)
−0.374526 + 0.927216i \(0.622195\pi\)
\(984\) 1.92808 0.0614648
\(985\) 2.57394 0.0820127
\(986\) 3.53713 0.112645
\(987\) −16.4698 −0.524241
\(988\) −3.04019 −0.0967215
\(989\) 1.61360 0.0513094
\(990\) 0.871541 0.0276994
\(991\) 5.88572 0.186966 0.0934830 0.995621i \(-0.470200\pi\)
0.0934830 + 0.995621i \(0.470200\pi\)
\(992\) 2.54242 0.0807219
\(993\) 26.7220 0.847997
\(994\) −13.6753 −0.433753
\(995\) 7.54454 0.239178
\(996\) −5.33038 −0.168900
\(997\) 52.4312 1.66051 0.830256 0.557382i \(-0.188194\pi\)
0.830256 + 0.557382i \(0.188194\pi\)
\(998\) 8.45034 0.267491
\(999\) −11.6827 −0.369624
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 \(a_p\))