Properties

Label 8034.2.a.o.1.3
Level 8034
Weight 2
Character 8034.1
Self dual Yes
Analytic conductor 64.152
Analytic rank 1
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.27539\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.55242 q^{5}\) \(+1.00000 q^{6}\) \(+1.37822 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.55242 q^{5}\) \(+1.00000 q^{6}\) \(+1.37822 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+2.55242 q^{10}\) \(+4.10597 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(-1.37822 q^{14}\) \(+2.55242 q^{15}\) \(+1.00000 q^{16}\) \(+3.57390 q^{17}\) \(-1.00000 q^{18}\) \(+0.378218 q^{19}\) \(-2.55242 q^{20}\) \(-1.37822 q^{21}\) \(-4.10597 q^{22}\) \(+3.65040 q^{23}\) \(+1.00000 q^{24}\) \(+1.51486 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(+1.37822 q^{28}\) \(-0.329406 q^{29}\) \(-2.55242 q^{30}\) \(-7.41763 q^{31}\) \(-1.00000 q^{32}\) \(-4.10597 q^{33}\) \(-3.57390 q^{34}\) \(-3.51779 q^{35}\) \(+1.00000 q^{36}\) \(-6.88409 q^{37}\) \(-0.378218 q^{38}\) \(-1.00000 q^{39}\) \(+2.55242 q^{40}\) \(-7.85728 q^{41}\) \(+1.37822 q^{42}\) \(-2.74031 q^{43}\) \(+4.10597 q^{44}\) \(-2.55242 q^{45}\) \(-3.65040 q^{46}\) \(-2.13101 q^{47}\) \(-1.00000 q^{48}\) \(-5.10052 q^{49}\) \(-1.51486 q^{50}\) \(-3.57390 q^{51}\) \(+1.00000 q^{52}\) \(-10.1230 q^{53}\) \(+1.00000 q^{54}\) \(-10.4802 q^{55}\) \(-1.37822 q^{56}\) \(-0.378218 q^{57}\) \(+0.329406 q^{58}\) \(+8.34165 q^{59}\) \(+2.55242 q^{60}\) \(-0.317128 q^{61}\) \(+7.41763 q^{62}\) \(+1.37822 q^{63}\) \(+1.00000 q^{64}\) \(-2.55242 q^{65}\) \(+4.10597 q^{66}\) \(+3.12773 q^{67}\) \(+3.57390 q^{68}\) \(-3.65040 q^{69}\) \(+3.51779 q^{70}\) \(+8.40081 q^{71}\) \(-1.00000 q^{72}\) \(+2.15179 q^{73}\) \(+6.88409 q^{74}\) \(-1.51486 q^{75}\) \(+0.378218 q^{76}\) \(+5.65892 q^{77}\) \(+1.00000 q^{78}\) \(-5.79457 q^{79}\) \(-2.55242 q^{80}\) \(+1.00000 q^{81}\) \(+7.85728 q^{82}\) \(-1.11990 q^{83}\) \(-1.37822 q^{84}\) \(-9.12209 q^{85}\) \(+2.74031 q^{86}\) \(+0.329406 q^{87}\) \(-4.10597 q^{88}\) \(+0.259370 q^{89}\) \(+2.55242 q^{90}\) \(+1.37822 q^{91}\) \(+3.65040 q^{92}\) \(+7.41763 q^{93}\) \(+2.13101 q^{94}\) \(-0.965372 q^{95}\) \(+1.00000 q^{96}\) \(+4.63686 q^{97}\) \(+5.10052 q^{98}\) \(+4.10597 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.55242 −1.14148 −0.570739 0.821132i \(-0.693343\pi\)
−0.570739 + 0.821132i \(0.693343\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.37822 0.520917 0.260459 0.965485i \(-0.416126\pi\)
0.260459 + 0.965485i \(0.416126\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.55242 0.807147
\(11\) 4.10597 1.23800 0.618998 0.785392i \(-0.287539\pi\)
0.618998 + 0.785392i \(0.287539\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) −1.37822 −0.368344
\(15\) 2.55242 0.659033
\(16\) 1.00000 0.250000
\(17\) 3.57390 0.866797 0.433399 0.901202i \(-0.357314\pi\)
0.433399 + 0.901202i \(0.357314\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0.378218 0.0867691 0.0433846 0.999058i \(-0.486186\pi\)
0.0433846 + 0.999058i \(0.486186\pi\)
\(20\) −2.55242 −0.570739
\(21\) −1.37822 −0.300752
\(22\) −4.10597 −0.875396
\(23\) 3.65040 0.761161 0.380580 0.924748i \(-0.375724\pi\)
0.380580 + 0.924748i \(0.375724\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.51486 0.302972
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 1.37822 0.260459
\(29\) −0.329406 −0.0611692 −0.0305846 0.999532i \(-0.509737\pi\)
−0.0305846 + 0.999532i \(0.509737\pi\)
\(30\) −2.55242 −0.466006
\(31\) −7.41763 −1.33225 −0.666123 0.745842i \(-0.732047\pi\)
−0.666123 + 0.745842i \(0.732047\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.10597 −0.714757
\(34\) −3.57390 −0.612918
\(35\) −3.51779 −0.594616
\(36\) 1.00000 0.166667
\(37\) −6.88409 −1.13174 −0.565869 0.824495i \(-0.691459\pi\)
−0.565869 + 0.824495i \(0.691459\pi\)
\(38\) −0.378218 −0.0613550
\(39\) −1.00000 −0.160128
\(40\) 2.55242 0.403573
\(41\) −7.85728 −1.22710 −0.613550 0.789656i \(-0.710259\pi\)
−0.613550 + 0.789656i \(0.710259\pi\)
\(42\) 1.37822 0.212664
\(43\) −2.74031 −0.417893 −0.208947 0.977927i \(-0.567003\pi\)
−0.208947 + 0.977927i \(0.567003\pi\)
\(44\) 4.10597 0.618998
\(45\) −2.55242 −0.380493
\(46\) −3.65040 −0.538222
\(47\) −2.13101 −0.310840 −0.155420 0.987849i \(-0.549673\pi\)
−0.155420 + 0.987849i \(0.549673\pi\)
\(48\) −1.00000 −0.144338
\(49\) −5.10052 −0.728645
\(50\) −1.51486 −0.214234
\(51\) −3.57390 −0.500446
\(52\) 1.00000 0.138675
\(53\) −10.1230 −1.39050 −0.695251 0.718767i \(-0.744707\pi\)
−0.695251 + 0.718767i \(0.744707\pi\)
\(54\) 1.00000 0.136083
\(55\) −10.4802 −1.41315
\(56\) −1.37822 −0.184172
\(57\) −0.378218 −0.0500962
\(58\) 0.329406 0.0432532
\(59\) 8.34165 1.08599 0.542995 0.839736i \(-0.317290\pi\)
0.542995 + 0.839736i \(0.317290\pi\)
\(60\) 2.55242 0.329516
\(61\) −0.317128 −0.0406041 −0.0203020 0.999794i \(-0.506463\pi\)
−0.0203020 + 0.999794i \(0.506463\pi\)
\(62\) 7.41763 0.942040
\(63\) 1.37822 0.173639
\(64\) 1.00000 0.125000
\(65\) −2.55242 −0.316589
\(66\) 4.10597 0.505410
\(67\) 3.12773 0.382113 0.191056 0.981579i \(-0.438809\pi\)
0.191056 + 0.981579i \(0.438809\pi\)
\(68\) 3.57390 0.433399
\(69\) −3.65040 −0.439456
\(70\) 3.51779 0.420457
\(71\) 8.40081 0.996992 0.498496 0.866892i \(-0.333886\pi\)
0.498496 + 0.866892i \(0.333886\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.15179 0.251848 0.125924 0.992040i \(-0.459810\pi\)
0.125924 + 0.992040i \(0.459810\pi\)
\(74\) 6.88409 0.800259
\(75\) −1.51486 −0.174921
\(76\) 0.378218 0.0433846
\(77\) 5.65892 0.644894
\(78\) 1.00000 0.113228
\(79\) −5.79457 −0.651940 −0.325970 0.945380i \(-0.605691\pi\)
−0.325970 + 0.945380i \(0.605691\pi\)
\(80\) −2.55242 −0.285370
\(81\) 1.00000 0.111111
\(82\) 7.85728 0.867691
\(83\) −1.11990 −0.122925 −0.0614625 0.998109i \(-0.519576\pi\)
−0.0614625 + 0.998109i \(0.519576\pi\)
\(84\) −1.37822 −0.150376
\(85\) −9.12209 −0.989430
\(86\) 2.74031 0.295495
\(87\) 0.329406 0.0353161
\(88\) −4.10597 −0.437698
\(89\) 0.259370 0.0274932 0.0137466 0.999906i \(-0.495624\pi\)
0.0137466 + 0.999906i \(0.495624\pi\)
\(90\) 2.55242 0.269049
\(91\) 1.37822 0.144476
\(92\) 3.65040 0.380580
\(93\) 7.41763 0.769173
\(94\) 2.13101 0.219797
\(95\) −0.965372 −0.0990451
\(96\) 1.00000 0.102062
\(97\) 4.63686 0.470802 0.235401 0.971898i \(-0.424360\pi\)
0.235401 + 0.971898i \(0.424360\pi\)
\(98\) 5.10052 0.515230
\(99\) 4.10597 0.412665
\(100\) 1.51486 0.151486
\(101\) −15.5977 −1.55203 −0.776014 0.630715i \(-0.782762\pi\)
−0.776014 + 0.630715i \(0.782762\pi\)
\(102\) 3.57390 0.353868
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 3.51779 0.343302
\(106\) 10.1230 0.983233
\(107\) 10.0618 0.972714 0.486357 0.873760i \(-0.338325\pi\)
0.486357 + 0.873760i \(0.338325\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 11.4816 1.09974 0.549869 0.835251i \(-0.314678\pi\)
0.549869 + 0.835251i \(0.314678\pi\)
\(110\) 10.4802 0.999245
\(111\) 6.88409 0.653409
\(112\) 1.37822 0.130229
\(113\) 4.69080 0.441273 0.220637 0.975356i \(-0.429186\pi\)
0.220637 + 0.975356i \(0.429186\pi\)
\(114\) 0.378218 0.0354233
\(115\) −9.31736 −0.868848
\(116\) −0.329406 −0.0305846
\(117\) 1.00000 0.0924500
\(118\) −8.34165 −0.767911
\(119\) 4.92561 0.451530
\(120\) −2.55242 −0.233003
\(121\) 5.85898 0.532635
\(122\) 0.317128 0.0287114
\(123\) 7.85728 0.708467
\(124\) −7.41763 −0.666123
\(125\) 8.89555 0.795642
\(126\) −1.37822 −0.122781
\(127\) −18.9176 −1.67867 −0.839335 0.543615i \(-0.817055\pi\)
−0.839335 + 0.543615i \(0.817055\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.74031 0.241271
\(130\) 2.55242 0.223862
\(131\) 14.9131 1.30297 0.651483 0.758663i \(-0.274147\pi\)
0.651483 + 0.758663i \(0.274147\pi\)
\(132\) −4.10597 −0.357379
\(133\) 0.521267 0.0451995
\(134\) −3.12773 −0.270194
\(135\) 2.55242 0.219678
\(136\) −3.57390 −0.306459
\(137\) 17.1905 1.46868 0.734341 0.678781i \(-0.237491\pi\)
0.734341 + 0.678781i \(0.237491\pi\)
\(138\) 3.65040 0.310743
\(139\) 18.1741 1.54150 0.770752 0.637135i \(-0.219881\pi\)
0.770752 + 0.637135i \(0.219881\pi\)
\(140\) −3.51779 −0.297308
\(141\) 2.13101 0.179463
\(142\) −8.40081 −0.704980
\(143\) 4.10597 0.343358
\(144\) 1.00000 0.0833333
\(145\) 0.840784 0.0698233
\(146\) −2.15179 −0.178083
\(147\) 5.10052 0.420683
\(148\) −6.88409 −0.565869
\(149\) −7.54334 −0.617975 −0.308987 0.951066i \(-0.599990\pi\)
−0.308987 + 0.951066i \(0.599990\pi\)
\(150\) 1.51486 0.123688
\(151\) −22.2535 −1.81096 −0.905481 0.424386i \(-0.860490\pi\)
−0.905481 + 0.424386i \(0.860490\pi\)
\(152\) −0.378218 −0.0306775
\(153\) 3.57390 0.288932
\(154\) −5.65892 −0.456009
\(155\) 18.9329 1.52073
\(156\) −1.00000 −0.0800641
\(157\) −11.8126 −0.942746 −0.471373 0.881934i \(-0.656242\pi\)
−0.471373 + 0.881934i \(0.656242\pi\)
\(158\) 5.79457 0.460992
\(159\) 10.1230 0.802806
\(160\) 2.55242 0.201787
\(161\) 5.03104 0.396502
\(162\) −1.00000 −0.0785674
\(163\) −5.81167 −0.455205 −0.227603 0.973754i \(-0.573089\pi\)
−0.227603 + 0.973754i \(0.573089\pi\)
\(164\) −7.85728 −0.613550
\(165\) 10.4802 0.815880
\(166\) 1.11990 0.0869211
\(167\) −8.49879 −0.657656 −0.328828 0.944390i \(-0.606654\pi\)
−0.328828 + 0.944390i \(0.606654\pi\)
\(168\) 1.37822 0.106332
\(169\) 1.00000 0.0769231
\(170\) 9.12209 0.699632
\(171\) 0.378218 0.0289230
\(172\) −2.74031 −0.208947
\(173\) −16.5832 −1.26080 −0.630398 0.776272i \(-0.717108\pi\)
−0.630398 + 0.776272i \(0.717108\pi\)
\(174\) −0.329406 −0.0249722
\(175\) 2.08781 0.157823
\(176\) 4.10597 0.309499
\(177\) −8.34165 −0.626997
\(178\) −0.259370 −0.0194406
\(179\) −14.9667 −1.11866 −0.559331 0.828945i \(-0.688942\pi\)
−0.559331 + 0.828945i \(0.688942\pi\)
\(180\) −2.55242 −0.190246
\(181\) −15.9377 −1.18464 −0.592319 0.805704i \(-0.701787\pi\)
−0.592319 + 0.805704i \(0.701787\pi\)
\(182\) −1.37822 −0.102160
\(183\) 0.317128 0.0234428
\(184\) −3.65040 −0.269111
\(185\) 17.5711 1.29185
\(186\) −7.41763 −0.543887
\(187\) 14.6743 1.07309
\(188\) −2.13101 −0.155420
\(189\) −1.37822 −0.100251
\(190\) 0.965372 0.0700354
\(191\) 14.0461 1.01634 0.508170 0.861257i \(-0.330322\pi\)
0.508170 + 0.861257i \(0.330322\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −9.70946 −0.698902 −0.349451 0.936955i \(-0.613632\pi\)
−0.349451 + 0.936955i \(0.613632\pi\)
\(194\) −4.63686 −0.332907
\(195\) 2.55242 0.182783
\(196\) −5.10052 −0.364323
\(197\) 10.6953 0.762006 0.381003 0.924574i \(-0.375579\pi\)
0.381003 + 0.924574i \(0.375579\pi\)
\(198\) −4.10597 −0.291799
\(199\) −4.21109 −0.298516 −0.149258 0.988798i \(-0.547689\pi\)
−0.149258 + 0.988798i \(0.547689\pi\)
\(200\) −1.51486 −0.107117
\(201\) −3.12773 −0.220613
\(202\) 15.5977 1.09745
\(203\) −0.453994 −0.0318641
\(204\) −3.57390 −0.250223
\(205\) 20.0551 1.40071
\(206\) −1.00000 −0.0696733
\(207\) 3.65040 0.253720
\(208\) 1.00000 0.0693375
\(209\) 1.55295 0.107420
\(210\) −3.51779 −0.242751
\(211\) −21.1987 −1.45938 −0.729690 0.683778i \(-0.760336\pi\)
−0.729690 + 0.683778i \(0.760336\pi\)
\(212\) −10.1230 −0.695251
\(213\) −8.40081 −0.575614
\(214\) −10.0618 −0.687813
\(215\) 6.99442 0.477016
\(216\) 1.00000 0.0680414
\(217\) −10.2231 −0.693990
\(218\) −11.4816 −0.777632
\(219\) −2.15179 −0.145405
\(220\) −10.4802 −0.706573
\(221\) 3.57390 0.240406
\(222\) −6.88409 −0.462030
\(223\) 9.75733 0.653399 0.326700 0.945128i \(-0.394063\pi\)
0.326700 + 0.945128i \(0.394063\pi\)
\(224\) −1.37822 −0.0920861
\(225\) 1.51486 0.100991
\(226\) −4.69080 −0.312027
\(227\) 26.6880 1.77135 0.885673 0.464310i \(-0.153698\pi\)
0.885673 + 0.464310i \(0.153698\pi\)
\(228\) −0.378218 −0.0250481
\(229\) −21.0379 −1.39022 −0.695112 0.718902i \(-0.744645\pi\)
−0.695112 + 0.718902i \(0.744645\pi\)
\(230\) 9.31736 0.614368
\(231\) −5.65892 −0.372330
\(232\) 0.329406 0.0216266
\(233\) −8.73734 −0.572402 −0.286201 0.958170i \(-0.592393\pi\)
−0.286201 + 0.958170i \(0.592393\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 5.43923 0.354816
\(236\) 8.34165 0.542995
\(237\) 5.79457 0.376398
\(238\) −4.92561 −0.319280
\(239\) −17.3130 −1.11988 −0.559942 0.828532i \(-0.689177\pi\)
−0.559942 + 0.828532i \(0.689177\pi\)
\(240\) 2.55242 0.164758
\(241\) 19.3299 1.24515 0.622574 0.782561i \(-0.286087\pi\)
0.622574 + 0.782561i \(0.286087\pi\)
\(242\) −5.85898 −0.376630
\(243\) −1.00000 −0.0641500
\(244\) −0.317128 −0.0203020
\(245\) 13.0187 0.831732
\(246\) −7.85728 −0.500962
\(247\) 0.378218 0.0240654
\(248\) 7.41763 0.471020
\(249\) 1.11990 0.0709708
\(250\) −8.89555 −0.562604
\(251\) 11.1871 0.706125 0.353063 0.935600i \(-0.385140\pi\)
0.353063 + 0.935600i \(0.385140\pi\)
\(252\) 1.37822 0.0868196
\(253\) 14.9884 0.942314
\(254\) 18.9176 1.18700
\(255\) 9.12209 0.571248
\(256\) 1.00000 0.0625000
\(257\) −25.3163 −1.57919 −0.789594 0.613629i \(-0.789709\pi\)
−0.789594 + 0.613629i \(0.789709\pi\)
\(258\) −2.74031 −0.170604
\(259\) −9.48777 −0.589542
\(260\) −2.55242 −0.158295
\(261\) −0.329406 −0.0203897
\(262\) −14.9131 −0.921336
\(263\) −22.2746 −1.37351 −0.686754 0.726890i \(-0.740965\pi\)
−0.686754 + 0.726890i \(0.740965\pi\)
\(264\) 4.10597 0.252705
\(265\) 25.8382 1.58723
\(266\) −0.521267 −0.0319609
\(267\) −0.259370 −0.0158732
\(268\) 3.12773 0.191056
\(269\) 23.4427 1.42933 0.714663 0.699469i \(-0.246580\pi\)
0.714663 + 0.699469i \(0.246580\pi\)
\(270\) −2.55242 −0.155335
\(271\) 14.7770 0.897638 0.448819 0.893623i \(-0.351845\pi\)
0.448819 + 0.893623i \(0.351845\pi\)
\(272\) 3.57390 0.216699
\(273\) −1.37822 −0.0834135
\(274\) −17.1905 −1.03851
\(275\) 6.21997 0.375078
\(276\) −3.65040 −0.219728
\(277\) 0.941275 0.0565557 0.0282779 0.999600i \(-0.490998\pi\)
0.0282779 + 0.999600i \(0.490998\pi\)
\(278\) −18.1741 −1.09001
\(279\) −7.41763 −0.444082
\(280\) 3.51779 0.210228
\(281\) −8.44093 −0.503543 −0.251772 0.967787i \(-0.581013\pi\)
−0.251772 + 0.967787i \(0.581013\pi\)
\(282\) −2.13101 −0.126900
\(283\) 0.458757 0.0272703 0.0136351 0.999907i \(-0.495660\pi\)
0.0136351 + 0.999907i \(0.495660\pi\)
\(284\) 8.40081 0.498496
\(285\) 0.965372 0.0571837
\(286\) −4.10597 −0.242791
\(287\) −10.8290 −0.639218
\(288\) −1.00000 −0.0589256
\(289\) −4.22727 −0.248663
\(290\) −0.840784 −0.0493726
\(291\) −4.63686 −0.271818
\(292\) 2.15179 0.125924
\(293\) −5.81927 −0.339965 −0.169983 0.985447i \(-0.554371\pi\)
−0.169983 + 0.985447i \(0.554371\pi\)
\(294\) −5.10052 −0.297468
\(295\) −21.2914 −1.23963
\(296\) 6.88409 0.400130
\(297\) −4.10597 −0.238252
\(298\) 7.54334 0.436974
\(299\) 3.65040 0.211108
\(300\) −1.51486 −0.0874605
\(301\) −3.77674 −0.217688
\(302\) 22.2535 1.28054
\(303\) 15.5977 0.896064
\(304\) 0.378218 0.0216923
\(305\) 0.809445 0.0463487
\(306\) −3.57390 −0.204306
\(307\) −15.4051 −0.879214 −0.439607 0.898190i \(-0.644882\pi\)
−0.439607 + 0.898190i \(0.644882\pi\)
\(308\) 5.65892 0.322447
\(309\) −1.00000 −0.0568880
\(310\) −18.9329 −1.07532
\(311\) 21.3489 1.21058 0.605292 0.796004i \(-0.293056\pi\)
0.605292 + 0.796004i \(0.293056\pi\)
\(312\) 1.00000 0.0566139
\(313\) −0.467785 −0.0264408 −0.0132204 0.999913i \(-0.504208\pi\)
−0.0132204 + 0.999913i \(0.504208\pi\)
\(314\) 11.8126 0.666622
\(315\) −3.51779 −0.198205
\(316\) −5.79457 −0.325970
\(317\) 17.6599 0.991881 0.495941 0.868356i \(-0.334823\pi\)
0.495941 + 0.868356i \(0.334823\pi\)
\(318\) −10.1230 −0.567670
\(319\) −1.35253 −0.0757273
\(320\) −2.55242 −0.142685
\(321\) −10.0618 −0.561597
\(322\) −5.03104 −0.280369
\(323\) 1.35171 0.0752112
\(324\) 1.00000 0.0555556
\(325\) 1.51486 0.0840293
\(326\) 5.81167 0.321879
\(327\) −11.4816 −0.634934
\(328\) 7.85728 0.433846
\(329\) −2.93699 −0.161922
\(330\) −10.4802 −0.576914
\(331\) −14.5394 −0.799155 −0.399578 0.916699i \(-0.630843\pi\)
−0.399578 + 0.916699i \(0.630843\pi\)
\(332\) −1.11990 −0.0614625
\(333\) −6.88409 −0.377246
\(334\) 8.49879 0.465033
\(335\) −7.98328 −0.436173
\(336\) −1.37822 −0.0751879
\(337\) −27.2491 −1.48435 −0.742177 0.670204i \(-0.766207\pi\)
−0.742177 + 0.670204i \(0.766207\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −4.69080 −0.254769
\(340\) −9.12209 −0.494715
\(341\) −30.4566 −1.64932
\(342\) −0.378218 −0.0204517
\(343\) −16.6771 −0.900481
\(344\) 2.74031 0.147748
\(345\) 9.31736 0.501630
\(346\) 16.5832 0.891517
\(347\) −6.74311 −0.361989 −0.180994 0.983484i \(-0.557932\pi\)
−0.180994 + 0.983484i \(0.557932\pi\)
\(348\) 0.329406 0.0176580
\(349\) −9.28940 −0.497250 −0.248625 0.968600i \(-0.579979\pi\)
−0.248625 + 0.968600i \(0.579979\pi\)
\(350\) −2.08781 −0.111598
\(351\) −1.00000 −0.0533761
\(352\) −4.10597 −0.218849
\(353\) 9.67070 0.514719 0.257360 0.966316i \(-0.417147\pi\)
0.257360 + 0.966316i \(0.417147\pi\)
\(354\) 8.34165 0.443354
\(355\) −21.4424 −1.13804
\(356\) 0.259370 0.0137466
\(357\) −4.92561 −0.260691
\(358\) 14.9667 0.791013
\(359\) −3.21503 −0.169683 −0.0848413 0.996394i \(-0.527038\pi\)
−0.0848413 + 0.996394i \(0.527038\pi\)
\(360\) 2.55242 0.134524
\(361\) −18.8570 −0.992471
\(362\) 15.9377 0.837666
\(363\) −5.85898 −0.307517
\(364\) 1.37822 0.0722382
\(365\) −5.49228 −0.287479
\(366\) −0.317128 −0.0165766
\(367\) 13.5101 0.705224 0.352612 0.935770i \(-0.385294\pi\)
0.352612 + 0.935770i \(0.385294\pi\)
\(368\) 3.65040 0.190290
\(369\) −7.85728 −0.409034
\(370\) −17.5711 −0.913478
\(371\) −13.9517 −0.724336
\(372\) 7.41763 0.384586
\(373\) −8.16869 −0.422959 −0.211479 0.977382i \(-0.567828\pi\)
−0.211479 + 0.977382i \(0.567828\pi\)
\(374\) −14.6743 −0.758790
\(375\) −8.89555 −0.459364
\(376\) 2.13101 0.109898
\(377\) −0.329406 −0.0169653
\(378\) 1.37822 0.0708879
\(379\) −5.83245 −0.299593 −0.149797 0.988717i \(-0.547862\pi\)
−0.149797 + 0.988717i \(0.547862\pi\)
\(380\) −0.965372 −0.0495225
\(381\) 18.9176 0.969180
\(382\) −14.0461 −0.718661
\(383\) 10.4854 0.535779 0.267890 0.963450i \(-0.413674\pi\)
0.267890 + 0.963450i \(0.413674\pi\)
\(384\) 1.00000 0.0510310
\(385\) −14.4440 −0.736132
\(386\) 9.70946 0.494199
\(387\) −2.74031 −0.139298
\(388\) 4.63686 0.235401
\(389\) −1.54358 −0.0782628 −0.0391314 0.999234i \(-0.512459\pi\)
−0.0391314 + 0.999234i \(0.512459\pi\)
\(390\) −2.55242 −0.129247
\(391\) 13.0461 0.659772
\(392\) 5.10052 0.257615
\(393\) −14.9131 −0.752268
\(394\) −10.6953 −0.538820
\(395\) 14.7902 0.744176
\(396\) 4.10597 0.206333
\(397\) 25.3759 1.27358 0.636790 0.771038i \(-0.280262\pi\)
0.636790 + 0.771038i \(0.280262\pi\)
\(398\) 4.21109 0.211083
\(399\) −0.521267 −0.0260960
\(400\) 1.51486 0.0757430
\(401\) −18.4808 −0.922887 −0.461444 0.887170i \(-0.652668\pi\)
−0.461444 + 0.887170i \(0.652668\pi\)
\(402\) 3.12773 0.155997
\(403\) −7.41763 −0.369499
\(404\) −15.5977 −0.776014
\(405\) −2.55242 −0.126831
\(406\) 0.453994 0.0225313
\(407\) −28.2659 −1.40109
\(408\) 3.57390 0.176934
\(409\) 5.38841 0.266440 0.133220 0.991086i \(-0.457468\pi\)
0.133220 + 0.991086i \(0.457468\pi\)
\(410\) −20.0551 −0.990450
\(411\) −17.1905 −0.847944
\(412\) 1.00000 0.0492665
\(413\) 11.4966 0.565711
\(414\) −3.65040 −0.179407
\(415\) 2.85846 0.140316
\(416\) −1.00000 −0.0490290
\(417\) −18.1741 −0.889988
\(418\) −1.55295 −0.0759573
\(419\) −17.1706 −0.838840 −0.419420 0.907792i \(-0.637767\pi\)
−0.419420 + 0.907792i \(0.637767\pi\)
\(420\) 3.51779 0.171651
\(421\) −27.6057 −1.34542 −0.672710 0.739906i \(-0.734870\pi\)
−0.672710 + 0.739906i \(0.734870\pi\)
\(422\) 21.1987 1.03194
\(423\) −2.13101 −0.103613
\(424\) 10.1230 0.491616
\(425\) 5.41395 0.262615
\(426\) 8.40081 0.407020
\(427\) −0.437072 −0.0211514
\(428\) 10.0618 0.486357
\(429\) −4.10597 −0.198238
\(430\) −6.99442 −0.337301
\(431\) −6.25335 −0.301213 −0.150607 0.988594i \(-0.548123\pi\)
−0.150607 + 0.988594i \(0.548123\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −15.4271 −0.741380 −0.370690 0.928757i \(-0.620879\pi\)
−0.370690 + 0.928757i \(0.620879\pi\)
\(434\) 10.2231 0.490725
\(435\) −0.840784 −0.0403125
\(436\) 11.4816 0.549869
\(437\) 1.38065 0.0660453
\(438\) 2.15179 0.102817
\(439\) 10.2796 0.490617 0.245309 0.969445i \(-0.421111\pi\)
0.245309 + 0.969445i \(0.421111\pi\)
\(440\) 10.4802 0.499622
\(441\) −5.10052 −0.242882
\(442\) −3.57390 −0.169993
\(443\) 29.9234 1.42170 0.710852 0.703342i \(-0.248310\pi\)
0.710852 + 0.703342i \(0.248310\pi\)
\(444\) 6.88409 0.326704
\(445\) −0.662023 −0.0313829
\(446\) −9.75733 −0.462023
\(447\) 7.54334 0.356788
\(448\) 1.37822 0.0651147
\(449\) −6.67530 −0.315027 −0.157513 0.987517i \(-0.550348\pi\)
−0.157513 + 0.987517i \(0.550348\pi\)
\(450\) −1.51486 −0.0714112
\(451\) −32.2617 −1.51915
\(452\) 4.69080 0.220637
\(453\) 22.2535 1.04556
\(454\) −26.6880 −1.25253
\(455\) −3.51779 −0.164917
\(456\) 0.378218 0.0177117
\(457\) −5.76757 −0.269796 −0.134898 0.990860i \(-0.543071\pi\)
−0.134898 + 0.990860i \(0.543071\pi\)
\(458\) 21.0379 0.983036
\(459\) −3.57390 −0.166815
\(460\) −9.31736 −0.434424
\(461\) 10.8327 0.504528 0.252264 0.967658i \(-0.418825\pi\)
0.252264 + 0.967658i \(0.418825\pi\)
\(462\) 5.65892 0.263277
\(463\) −11.7791 −0.547420 −0.273710 0.961812i \(-0.588251\pi\)
−0.273710 + 0.961812i \(0.588251\pi\)
\(464\) −0.329406 −0.0152923
\(465\) −18.9329 −0.877994
\(466\) 8.73734 0.404749
\(467\) 33.0283 1.52837 0.764184 0.644998i \(-0.223142\pi\)
0.764184 + 0.644998i \(0.223142\pi\)
\(468\) 1.00000 0.0462250
\(469\) 4.31069 0.199049
\(470\) −5.43923 −0.250893
\(471\) 11.8126 0.544295
\(472\) −8.34165 −0.383955
\(473\) −11.2516 −0.517350
\(474\) −5.79457 −0.266154
\(475\) 0.572947 0.0262886
\(476\) 4.92561 0.225765
\(477\) −10.1230 −0.463500
\(478\) 17.3130 0.791877
\(479\) −19.4169 −0.887179 −0.443589 0.896230i \(-0.646295\pi\)
−0.443589 + 0.896230i \(0.646295\pi\)
\(480\) −2.55242 −0.116502
\(481\) −6.88409 −0.313887
\(482\) −19.3299 −0.880453
\(483\) −5.03104 −0.228920
\(484\) 5.85898 0.266317
\(485\) −11.8352 −0.537410
\(486\) 1.00000 0.0453609
\(487\) 12.6915 0.575107 0.287554 0.957765i \(-0.407158\pi\)
0.287554 + 0.957765i \(0.407158\pi\)
\(488\) 0.317128 0.0143557
\(489\) 5.81167 0.262813
\(490\) −13.0187 −0.588124
\(491\) −14.4170 −0.650629 −0.325315 0.945606i \(-0.605470\pi\)
−0.325315 + 0.945606i \(0.605470\pi\)
\(492\) 7.85728 0.354233
\(493\) −1.17726 −0.0530213
\(494\) −0.378218 −0.0170168
\(495\) −10.4802 −0.471048
\(496\) −7.41763 −0.333062
\(497\) 11.5781 0.519351
\(498\) −1.11990 −0.0501839
\(499\) 13.4253 0.600998 0.300499 0.953782i \(-0.402847\pi\)
0.300499 + 0.953782i \(0.402847\pi\)
\(500\) 8.89555 0.397821
\(501\) 8.49879 0.379698
\(502\) −11.1871 −0.499306
\(503\) 22.0217 0.981900 0.490950 0.871188i \(-0.336650\pi\)
0.490950 + 0.871188i \(0.336650\pi\)
\(504\) −1.37822 −0.0613907
\(505\) 39.8119 1.77161
\(506\) −14.9884 −0.666317
\(507\) −1.00000 −0.0444116
\(508\) −18.9176 −0.839335
\(509\) −1.19058 −0.0527714 −0.0263857 0.999652i \(-0.508400\pi\)
−0.0263857 + 0.999652i \(0.508400\pi\)
\(510\) −9.12209 −0.403933
\(511\) 2.96564 0.131192
\(512\) −1.00000 −0.0441942
\(513\) −0.378218 −0.0166987
\(514\) 25.3163 1.11666
\(515\) −2.55242 −0.112473
\(516\) 2.74031 0.120635
\(517\) −8.74985 −0.384818
\(518\) 9.48777 0.416869
\(519\) 16.5832 0.727921
\(520\) 2.55242 0.111931
\(521\) −14.7616 −0.646718 −0.323359 0.946276i \(-0.604812\pi\)
−0.323359 + 0.946276i \(0.604812\pi\)
\(522\) 0.329406 0.0144177
\(523\) 34.5063 1.50885 0.754427 0.656384i \(-0.227915\pi\)
0.754427 + 0.656384i \(0.227915\pi\)
\(524\) 14.9131 0.651483
\(525\) −2.08781 −0.0911194
\(526\) 22.2746 0.971217
\(527\) −26.5098 −1.15479
\(528\) −4.10597 −0.178689
\(529\) −9.67459 −0.420634
\(530\) −25.8382 −1.12234
\(531\) 8.34165 0.361997
\(532\) 0.521267 0.0225998
\(533\) −7.85728 −0.340336
\(534\) 0.259370 0.0112241
\(535\) −25.6820 −1.11033
\(536\) −3.12773 −0.135097
\(537\) 14.9667 0.645859
\(538\) −23.4427 −1.01069
\(539\) −20.9426 −0.902060
\(540\) 2.55242 0.109839
\(541\) −17.0031 −0.731020 −0.365510 0.930807i \(-0.619105\pi\)
−0.365510 + 0.930807i \(0.619105\pi\)
\(542\) −14.7770 −0.634726
\(543\) 15.9377 0.683951
\(544\) −3.57390 −0.153230
\(545\) −29.3059 −1.25533
\(546\) 1.37822 0.0589823
\(547\) 36.4996 1.56061 0.780306 0.625398i \(-0.215063\pi\)
0.780306 + 0.625398i \(0.215063\pi\)
\(548\) 17.1905 0.734341
\(549\) −0.317128 −0.0135347
\(550\) −6.21997 −0.265220
\(551\) −0.124587 −0.00530760
\(552\) 3.65040 0.155371
\(553\) −7.98618 −0.339607
\(554\) −0.941275 −0.0399909
\(555\) −17.5711 −0.745852
\(556\) 18.1741 0.770752
\(557\) −43.3356 −1.83619 −0.918094 0.396363i \(-0.870272\pi\)
−0.918094 + 0.396363i \(0.870272\pi\)
\(558\) 7.41763 0.314013
\(559\) −2.74031 −0.115903
\(560\) −3.51779 −0.148654
\(561\) −14.6743 −0.619550
\(562\) 8.44093 0.356059
\(563\) −37.0062 −1.55962 −0.779812 0.626014i \(-0.784685\pi\)
−0.779812 + 0.626014i \(0.784685\pi\)
\(564\) 2.13101 0.0897316
\(565\) −11.9729 −0.503704
\(566\) −0.458757 −0.0192830
\(567\) 1.37822 0.0578797
\(568\) −8.40081 −0.352490
\(569\) −20.9891 −0.879910 −0.439955 0.898020i \(-0.645006\pi\)
−0.439955 + 0.898020i \(0.645006\pi\)
\(570\) −0.965372 −0.0404350
\(571\) −13.1783 −0.551495 −0.275748 0.961230i \(-0.588925\pi\)
−0.275748 + 0.961230i \(0.588925\pi\)
\(572\) 4.10597 0.171679
\(573\) −14.0461 −0.586784
\(574\) 10.8290 0.451995
\(575\) 5.52984 0.230610
\(576\) 1.00000 0.0416667
\(577\) −31.5512 −1.31349 −0.656746 0.754112i \(-0.728068\pi\)
−0.656746 + 0.754112i \(0.728068\pi\)
\(578\) 4.22727 0.175831
\(579\) 9.70946 0.403512
\(580\) 0.840784 0.0349117
\(581\) −1.54347 −0.0640338
\(582\) 4.63686 0.192204
\(583\) −41.5647 −1.72144
\(584\) −2.15179 −0.0890417
\(585\) −2.55242 −0.105530
\(586\) 5.81927 0.240392
\(587\) −28.2823 −1.16734 −0.583668 0.811992i \(-0.698383\pi\)
−0.583668 + 0.811992i \(0.698383\pi\)
\(588\) 5.10052 0.210342
\(589\) −2.80548 −0.115598
\(590\) 21.2914 0.876553
\(591\) −10.6953 −0.439945
\(592\) −6.88409 −0.282934
\(593\) 3.23446 0.132823 0.0664117 0.997792i \(-0.478845\pi\)
0.0664117 + 0.997792i \(0.478845\pi\)
\(594\) 4.10597 0.168470
\(595\) −12.5722 −0.515411
\(596\) −7.54334 −0.308987
\(597\) 4.21109 0.172348
\(598\) −3.65040 −0.149276
\(599\) −16.7633 −0.684930 −0.342465 0.939531i \(-0.611262\pi\)
−0.342465 + 0.939531i \(0.611262\pi\)
\(600\) 1.51486 0.0618439
\(601\) 28.5348 1.16396 0.581980 0.813203i \(-0.302278\pi\)
0.581980 + 0.813203i \(0.302278\pi\)
\(602\) 3.77674 0.153929
\(603\) 3.12773 0.127371
\(604\) −22.2535 −0.905481
\(605\) −14.9546 −0.607991
\(606\) −15.5977 −0.633613
\(607\) 38.5489 1.56465 0.782327 0.622868i \(-0.214033\pi\)
0.782327 + 0.622868i \(0.214033\pi\)
\(608\) −0.378218 −0.0153388
\(609\) 0.453994 0.0183968
\(610\) −0.809445 −0.0327735
\(611\) −2.13101 −0.0862114
\(612\) 3.57390 0.144466
\(613\) 23.7566 0.959522 0.479761 0.877399i \(-0.340723\pi\)
0.479761 + 0.877399i \(0.340723\pi\)
\(614\) 15.4051 0.621698
\(615\) −20.0551 −0.808699
\(616\) −5.65892 −0.228004
\(617\) −2.88539 −0.116161 −0.0580807 0.998312i \(-0.518498\pi\)
−0.0580807 + 0.998312i \(0.518498\pi\)
\(618\) 1.00000 0.0402259
\(619\) −25.6125 −1.02945 −0.514727 0.857354i \(-0.672107\pi\)
−0.514727 + 0.857354i \(0.672107\pi\)
\(620\) 18.9329 0.760365
\(621\) −3.65040 −0.146485
\(622\) −21.3489 −0.856012
\(623\) 0.357469 0.0143217
\(624\) −1.00000 −0.0400320
\(625\) −30.2795 −1.21118
\(626\) 0.467785 0.0186964
\(627\) −1.55295 −0.0620189
\(628\) −11.8126 −0.471373
\(629\) −24.6030 −0.980987
\(630\) 3.51779 0.140152
\(631\) −2.46911 −0.0982939 −0.0491469 0.998792i \(-0.515650\pi\)
−0.0491469 + 0.998792i \(0.515650\pi\)
\(632\) 5.79457 0.230496
\(633\) 21.1987 0.842574
\(634\) −17.6599 −0.701366
\(635\) 48.2858 1.91616
\(636\) 10.1230 0.401403
\(637\) −5.10052 −0.202090
\(638\) 1.35253 0.0535473
\(639\) 8.40081 0.332331
\(640\) 2.55242 0.100893
\(641\) 41.5397 1.64072 0.820360 0.571847i \(-0.193773\pi\)
0.820360 + 0.571847i \(0.193773\pi\)
\(642\) 10.0618 0.397109
\(643\) −6.01921 −0.237374 −0.118687 0.992932i \(-0.537869\pi\)
−0.118687 + 0.992932i \(0.537869\pi\)
\(644\) 5.03104 0.198251
\(645\) −6.99442 −0.275405
\(646\) −1.35171 −0.0531824
\(647\) −6.66297 −0.261949 −0.130974 0.991386i \(-0.541811\pi\)
−0.130974 + 0.991386i \(0.541811\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 34.2505 1.34445
\(650\) −1.51486 −0.0594177
\(651\) 10.2231 0.400675
\(652\) −5.81167 −0.227603
\(653\) 44.0181 1.72256 0.861282 0.508128i \(-0.169662\pi\)
0.861282 + 0.508128i \(0.169662\pi\)
\(654\) 11.4816 0.448966
\(655\) −38.0646 −1.48731
\(656\) −7.85728 −0.306775
\(657\) 2.15179 0.0839494
\(658\) 2.93699 0.114496
\(659\) 36.7419 1.43126 0.715631 0.698479i \(-0.246139\pi\)
0.715631 + 0.698479i \(0.246139\pi\)
\(660\) 10.4802 0.407940
\(661\) −19.5472 −0.760298 −0.380149 0.924925i \(-0.624127\pi\)
−0.380149 + 0.924925i \(0.624127\pi\)
\(662\) 14.5394 0.565088
\(663\) −3.57390 −0.138799
\(664\) 1.11990 0.0434605
\(665\) −1.33049 −0.0515943
\(666\) 6.88409 0.266753
\(667\) −1.20246 −0.0465596
\(668\) −8.49879 −0.328828
\(669\) −9.75733 −0.377240
\(670\) 7.98328 0.308421
\(671\) −1.30212 −0.0502677
\(672\) 1.37822 0.0531659
\(673\) 14.6908 0.566289 0.283144 0.959077i \(-0.408622\pi\)
0.283144 + 0.959077i \(0.408622\pi\)
\(674\) 27.2491 1.04960
\(675\) −1.51486 −0.0583070
\(676\) 1.00000 0.0384615
\(677\) 26.6253 1.02329 0.511646 0.859196i \(-0.329036\pi\)
0.511646 + 0.859196i \(0.329036\pi\)
\(678\) 4.69080 0.180149
\(679\) 6.39061 0.245249
\(680\) 9.12209 0.349816
\(681\) −26.6880 −1.02269
\(682\) 30.4566 1.16624
\(683\) 15.9055 0.608607 0.304303 0.952575i \(-0.401576\pi\)
0.304303 + 0.952575i \(0.401576\pi\)
\(684\) 0.378218 0.0144615
\(685\) −43.8774 −1.67647
\(686\) 16.6771 0.636736
\(687\) 21.0379 0.802646
\(688\) −2.74031 −0.104473
\(689\) −10.1230 −0.385656
\(690\) −9.31736 −0.354706
\(691\) 48.6228 1.84970 0.924849 0.380335i \(-0.124191\pi\)
0.924849 + 0.380335i \(0.124191\pi\)
\(692\) −16.5832 −0.630398
\(693\) 5.65892 0.214965
\(694\) 6.74311 0.255965
\(695\) −46.3879 −1.75959
\(696\) −0.329406 −0.0124861
\(697\) −28.0811 −1.06365
\(698\) 9.28940 0.351609
\(699\) 8.73734 0.330477
\(700\) 2.08781 0.0789117
\(701\) −15.0542 −0.568588 −0.284294 0.958737i \(-0.591759\pi\)
−0.284294 + 0.958737i \(0.591759\pi\)
\(702\) 1.00000 0.0377426
\(703\) −2.60369 −0.0981999
\(704\) 4.10597 0.154750
\(705\) −5.43923 −0.204853
\(706\) −9.67070 −0.363962
\(707\) −21.4970 −0.808479
\(708\) −8.34165 −0.313498
\(709\) 31.3168 1.17613 0.588063 0.808815i \(-0.299891\pi\)
0.588063 + 0.808815i \(0.299891\pi\)
\(710\) 21.4424 0.804719
\(711\) −5.79457 −0.217313
\(712\) −0.259370 −0.00972032
\(713\) −27.0773 −1.01405
\(714\) 4.92561 0.184336
\(715\) −10.4802 −0.391936
\(716\) −14.9667 −0.559331
\(717\) 17.3130 0.646565
\(718\) 3.21503 0.119984
\(719\) −52.9418 −1.97440 −0.987198 0.159500i \(-0.949012\pi\)
−0.987198 + 0.159500i \(0.949012\pi\)
\(720\) −2.55242 −0.0951232
\(721\) 1.37822 0.0513275
\(722\) 18.8570 0.701783
\(723\) −19.3299 −0.718886
\(724\) −15.9377 −0.592319
\(725\) −0.499005 −0.0185326
\(726\) 5.85898 0.217447
\(727\) 5.87787 0.217998 0.108999 0.994042i \(-0.465235\pi\)
0.108999 + 0.994042i \(0.465235\pi\)
\(728\) −1.37822 −0.0510802
\(729\) 1.00000 0.0370370
\(730\) 5.49228 0.203278
\(731\) −9.79358 −0.362229
\(732\) 0.317128 0.0117214
\(733\) 35.8254 1.32324 0.661622 0.749838i \(-0.269869\pi\)
0.661622 + 0.749838i \(0.269869\pi\)
\(734\) −13.5101 −0.498668
\(735\) −13.0187 −0.480201
\(736\) −3.65040 −0.134555
\(737\) 12.8423 0.473054
\(738\) 7.85728 0.289230
\(739\) −10.0672 −0.370327 −0.185164 0.982708i \(-0.559281\pi\)
−0.185164 + 0.982708i \(0.559281\pi\)
\(740\) 17.5711 0.645927
\(741\) −0.378218 −0.0138942
\(742\) 13.9517 0.512183
\(743\) 24.4390 0.896580 0.448290 0.893888i \(-0.352033\pi\)
0.448290 + 0.893888i \(0.352033\pi\)
\(744\) −7.41763 −0.271944
\(745\) 19.2538 0.705405
\(746\) 8.16869 0.299077
\(747\) −1.11990 −0.0409750
\(748\) 14.6743 0.536546
\(749\) 13.8674 0.506704
\(750\) 8.89555 0.324820
\(751\) −11.2872 −0.411874 −0.205937 0.978565i \(-0.566024\pi\)
−0.205937 + 0.978565i \(0.566024\pi\)
\(752\) −2.13101 −0.0777099
\(753\) −11.1871 −0.407682
\(754\) 0.329406 0.0119963
\(755\) 56.8003 2.06717
\(756\) −1.37822 −0.0501253
\(757\) −31.1159 −1.13093 −0.565464 0.824773i \(-0.691303\pi\)
−0.565464 + 0.824773i \(0.691303\pi\)
\(758\) 5.83245 0.211844
\(759\) −14.9884 −0.544045
\(760\) 0.965372 0.0350177
\(761\) 43.0335 1.55996 0.779982 0.625802i \(-0.215228\pi\)
0.779982 + 0.625802i \(0.215228\pi\)
\(762\) −18.9176 −0.685314
\(763\) 15.8241 0.572873
\(764\) 14.0461 0.508170
\(765\) −9.12209 −0.329810
\(766\) −10.4854 −0.378853
\(767\) 8.34165 0.301199
\(768\) −1.00000 −0.0360844
\(769\) 6.89994 0.248818 0.124409 0.992231i \(-0.460296\pi\)
0.124409 + 0.992231i \(0.460296\pi\)
\(770\) 14.4440 0.520524
\(771\) 25.3163 0.911745
\(772\) −9.70946 −0.349451
\(773\) 13.3315 0.479499 0.239750 0.970835i \(-0.422935\pi\)
0.239750 + 0.970835i \(0.422935\pi\)
\(774\) 2.74031 0.0984984
\(775\) −11.2367 −0.403633
\(776\) −4.63686 −0.166454
\(777\) 9.48777 0.340372
\(778\) 1.54358 0.0553402
\(779\) −2.97176 −0.106474
\(780\) 2.55242 0.0913914
\(781\) 34.4935 1.23427
\(782\) −13.0461 −0.466529
\(783\) 0.329406 0.0117720
\(784\) −5.10052 −0.182161
\(785\) 30.1507 1.07612
\(786\) 14.9131 0.531934
\(787\) −22.2913 −0.794597 −0.397299 0.917689i \(-0.630052\pi\)
−0.397299 + 0.917689i \(0.630052\pi\)
\(788\) 10.6953 0.381003
\(789\) 22.2746 0.792995
\(790\) −14.7902 −0.526212
\(791\) 6.46495 0.229867
\(792\) −4.10597 −0.145899
\(793\) −0.317128 −0.0112615
\(794\) −25.3759 −0.900556
\(795\) −25.8382 −0.916386
\(796\) −4.21109 −0.149258
\(797\) −50.1769 −1.77736 −0.888678 0.458532i \(-0.848375\pi\)
−0.888678 + 0.458532i \(0.848375\pi\)
\(798\) 0.521267 0.0184526
\(799\) −7.61600 −0.269435
\(800\) −1.51486 −0.0535584
\(801\) 0.259370 0.00916441
\(802\) 18.4808 0.652580
\(803\) 8.83519 0.311787
\(804\) −3.12773 −0.110306
\(805\) −12.8414 −0.452598
\(806\) 7.41763 0.261275
\(807\) −23.4427 −0.825221
\(808\) 15.5977 0.548725
\(809\) −47.5700 −1.67247 −0.836235 0.548371i \(-0.815248\pi\)
−0.836235 + 0.548371i \(0.815248\pi\)
\(810\) 2.55242 0.0896830
\(811\) −31.1647 −1.09434 −0.547171 0.837021i \(-0.684295\pi\)
−0.547171 + 0.837021i \(0.684295\pi\)
\(812\) −0.453994 −0.0159321
\(813\) −14.7770 −0.518251
\(814\) 28.2659 0.990718
\(815\) 14.8338 0.519607
\(816\) −3.57390 −0.125111
\(817\) −1.03643 −0.0362602
\(818\) −5.38841 −0.188401
\(819\) 1.37822 0.0481588
\(820\) 20.0551 0.700354
\(821\) −7.31853 −0.255418 −0.127709 0.991812i \(-0.540762\pi\)
−0.127709 + 0.991812i \(0.540762\pi\)
\(822\) 17.1905 0.599587
\(823\) −14.1340 −0.492682 −0.246341 0.969183i \(-0.579228\pi\)
−0.246341 + 0.969183i \(0.579228\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −6.21997 −0.216552
\(826\) −11.4966 −0.400018
\(827\) −32.4299 −1.12770 −0.563850 0.825877i \(-0.690680\pi\)
−0.563850 + 0.825877i \(0.690680\pi\)
\(828\) 3.65040 0.126860
\(829\) 20.4679 0.710881 0.355440 0.934699i \(-0.384331\pi\)
0.355440 + 0.934699i \(0.384331\pi\)
\(830\) −2.85846 −0.0992185
\(831\) −0.941275 −0.0326525
\(832\) 1.00000 0.0346688
\(833\) −18.2287 −0.631587
\(834\) 18.1741 0.629316
\(835\) 21.6925 0.750700
\(836\) 1.55295 0.0537099
\(837\) 7.41763 0.256391
\(838\) 17.1706 0.593150
\(839\) −13.3546 −0.461052 −0.230526 0.973066i \(-0.574045\pi\)
−0.230526 + 0.973066i \(0.574045\pi\)
\(840\) −3.51779 −0.121375
\(841\) −28.8915 −0.996258
\(842\) 27.6057 0.951356
\(843\) 8.44093 0.290721
\(844\) −21.1987 −0.729690
\(845\) −2.55242 −0.0878060
\(846\) 2.13101 0.0732656
\(847\) 8.07495 0.277459
\(848\) −10.1230 −0.347625
\(849\) −0.458757 −0.0157445
\(850\) −5.41395 −0.185697
\(851\) −25.1297 −0.861434
\(852\) −8.40081 −0.287807
\(853\) 26.5489 0.909017 0.454508 0.890742i \(-0.349815\pi\)
0.454508 + 0.890742i \(0.349815\pi\)
\(854\) 0.437072 0.0149563
\(855\) −0.965372 −0.0330150
\(856\) −10.0618 −0.343906
\(857\) −31.4250 −1.07346 −0.536728 0.843755i \(-0.680340\pi\)
−0.536728 + 0.843755i \(0.680340\pi\)
\(858\) 4.10597 0.140175
\(859\) −34.3335 −1.17144 −0.585721 0.810513i \(-0.699189\pi\)
−0.585721 + 0.810513i \(0.699189\pi\)
\(860\) 6.99442 0.238508
\(861\) 10.8290 0.369053
\(862\) 6.25335 0.212990
\(863\) −13.8241 −0.470577 −0.235289 0.971926i \(-0.575604\pi\)
−0.235289 + 0.971926i \(0.575604\pi\)
\(864\) 1.00000 0.0340207
\(865\) 42.3273 1.43917
\(866\) 15.4271 0.524235
\(867\) 4.22727 0.143566
\(868\) −10.2231 −0.346995
\(869\) −23.7923 −0.807100
\(870\) 0.840784 0.0285053
\(871\) 3.12773 0.105979
\(872\) −11.4816 −0.388816
\(873\) 4.63686 0.156934
\(874\) −1.38065 −0.0467010
\(875\) 12.2600 0.414464
\(876\) −2.15179 −0.0727023
\(877\) 0.0399391 0.00134865 0.000674324 1.00000i \(-0.499785\pi\)
0.000674324 1.00000i \(0.499785\pi\)
\(878\) −10.2796 −0.346919
\(879\) 5.81927 0.196279
\(880\) −10.4802 −0.353286
\(881\) −22.9628 −0.773638 −0.386819 0.922156i \(-0.626426\pi\)
−0.386819 + 0.922156i \(0.626426\pi\)
\(882\) 5.10052 0.171743
\(883\) 2.20731 0.0742821 0.0371410 0.999310i \(-0.488175\pi\)
0.0371410 + 0.999310i \(0.488175\pi\)
\(884\) 3.57390 0.120203
\(885\) 21.2914 0.715703
\(886\) −29.9234 −1.00530
\(887\) −24.6791 −0.828644 −0.414322 0.910130i \(-0.635981\pi\)
−0.414322 + 0.910130i \(0.635981\pi\)
\(888\) −6.88409 −0.231015
\(889\) −26.0726 −0.874448
\(890\) 0.662023 0.0221911
\(891\) 4.10597 0.137555
\(892\) 9.75733 0.326700
\(893\) −0.805985 −0.0269713
\(894\) −7.54334 −0.252287
\(895\) 38.2013 1.27693
\(896\) −1.37822 −0.0460430
\(897\) −3.65040 −0.121883
\(898\) 6.67530 0.222758
\(899\) 2.44342 0.0814925
\(900\) 1.51486 0.0504953
\(901\) −36.1786 −1.20528
\(902\) 32.2617 1.07420
\(903\) 3.77674 0.125682
\(904\) −4.69080 −0.156014
\(905\) 40.6797 1.35224
\(906\) −22.2535 −0.739322
\(907\) −23.5663 −0.782508 −0.391254 0.920283i \(-0.627959\pi\)
−0.391254 + 0.920283i \(0.627959\pi\)
\(908\) 26.6880 0.885673
\(909\) −15.5977 −0.517343
\(910\) 3.51779 0.116614
\(911\) −28.0145 −0.928163 −0.464082 0.885792i \(-0.653616\pi\)
−0.464082 + 0.885792i \(0.653616\pi\)
\(912\) −0.378218 −0.0125240
\(913\) −4.59827 −0.152181
\(914\) 5.76757 0.190774
\(915\) −0.809445 −0.0267594
\(916\) −21.0379 −0.695112
\(917\) 20.5535 0.678738
\(918\) 3.57390 0.117956
\(919\) −13.9310 −0.459542 −0.229771 0.973245i \(-0.573798\pi\)
−0.229771 + 0.973245i \(0.573798\pi\)
\(920\) 9.31736 0.307184
\(921\) 15.4051 0.507614
\(922\) −10.8327 −0.356755
\(923\) 8.40081 0.276516
\(924\) −5.65892 −0.186165
\(925\) −10.4284 −0.342885
\(926\) 11.7791 0.387084
\(927\) 1.00000 0.0328443
\(928\) 0.329406 0.0108133
\(929\) −55.5699 −1.82319 −0.911594 0.411091i \(-0.865148\pi\)
−0.911594 + 0.411091i \(0.865148\pi\)
\(930\) 18.9329 0.620835
\(931\) −1.92911 −0.0632239
\(932\) −8.73734 −0.286201
\(933\) −21.3489 −0.698931
\(934\) −33.0283 −1.08072
\(935\) −37.4550 −1.22491
\(936\) −1.00000 −0.0326860
\(937\) 16.7160 0.546088 0.273044 0.962002i \(-0.411969\pi\)
0.273044 + 0.962002i \(0.411969\pi\)
\(938\) −4.31069 −0.140749
\(939\) 0.467785 0.0152656
\(940\) 5.43923 0.177408
\(941\) −2.93553 −0.0956957 −0.0478478 0.998855i \(-0.515236\pi\)
−0.0478478 + 0.998855i \(0.515236\pi\)
\(942\) −11.8126 −0.384875
\(943\) −28.6822 −0.934021
\(944\) 8.34165 0.271497
\(945\) 3.51779 0.114434
\(946\) 11.2516 0.365822
\(947\) 30.9142 1.00458 0.502288 0.864700i \(-0.332492\pi\)
0.502288 + 0.864700i \(0.332492\pi\)
\(948\) 5.79457 0.188199
\(949\) 2.15179 0.0698501
\(950\) −0.572947 −0.0185889
\(951\) −17.6599 −0.572663
\(952\) −4.92561 −0.159640
\(953\) −39.3113 −1.27342 −0.636709 0.771104i \(-0.719705\pi\)
−0.636709 + 0.771104i \(0.719705\pi\)
\(954\) 10.1230 0.327744
\(955\) −35.8516 −1.16013
\(956\) −17.3130 −0.559942
\(957\) 1.35253 0.0437212
\(958\) 19.4169 0.627330
\(959\) 23.6922 0.765062
\(960\) 2.55242 0.0823791
\(961\) 24.0213 0.774880
\(962\) 6.88409 0.221952
\(963\) 10.0618 0.324238
\(964\) 19.3299 0.622574
\(965\) 24.7827 0.797782
\(966\) 5.03104 0.161871
\(967\) 33.4298 1.07503 0.537515 0.843254i \(-0.319363\pi\)
0.537515 + 0.843254i \(0.319363\pi\)
\(968\) −5.85898 −0.188315
\(969\) −1.35171 −0.0434232
\(970\) 11.8352 0.380006
\(971\) −1.90635 −0.0611778 −0.0305889 0.999532i \(-0.509738\pi\)
−0.0305889 + 0.999532i \(0.509738\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 25.0478 0.802996
\(974\) −12.6915 −0.406662
\(975\) −1.51486 −0.0485144
\(976\) −0.317128 −0.0101510
\(977\) 22.6232 0.723781 0.361891 0.932221i \(-0.382131\pi\)
0.361891 + 0.932221i \(0.382131\pi\)
\(978\) −5.81167 −0.185837
\(979\) 1.06497 0.0340365
\(980\) 13.0187 0.415866
\(981\) 11.4816 0.366579
\(982\) 14.4170 0.460064
\(983\) −35.9535 −1.14674 −0.573369 0.819297i \(-0.694364\pi\)
−0.573369 + 0.819297i \(0.694364\pi\)
\(984\) −7.85728 −0.250481
\(985\) −27.2988 −0.869814
\(986\) 1.17726 0.0374917
\(987\) 2.93699 0.0934855
\(988\) 0.378218 0.0120327
\(989\) −10.0032 −0.318084
\(990\) 10.4802 0.333082
\(991\) −47.8301 −1.51937 −0.759686 0.650290i \(-0.774647\pi\)
−0.759686 + 0.650290i \(0.774647\pi\)
\(992\) 7.41763 0.235510
\(993\) 14.5394 0.461392
\(994\) −11.5781 −0.367236
\(995\) 10.7485 0.340750
\(996\) 1.11990 0.0354854
\(997\) −44.1437 −1.39805 −0.699023 0.715099i \(-0.746381\pi\)
−0.699023 + 0.715099i \(0.746381\pi\)
\(998\) −13.4253 −0.424970
\(999\) 6.88409 0.217803
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 \(a_p\))