Properties

Label 8034.2.a.o.1.6
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 1.6
Root \(-0.761570\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.28276 q^{5}\) \(+1.00000 q^{6}\) \(-3.26302 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.28276 q^{5}\) \(+1.00000 q^{6}\) \(-3.26302 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-3.28276 q^{10}\) \(+3.43964 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+3.26302 q^{14}\) \(-3.28276 q^{15}\) \(+1.00000 q^{16}\) \(-4.30990 q^{17}\) \(-1.00000 q^{18}\) \(-4.26302 q^{19}\) \(+3.28276 q^{20}\) \(+3.26302 q^{21}\) \(-3.43964 q^{22}\) \(+0.898821 q^{23}\) \(+1.00000 q^{24}\) \(+5.77652 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(-3.26302 q^{28}\) \(+1.85461 q^{29}\) \(+3.28276 q^{30}\) \(+0.0760444 q^{31}\) \(-1.00000 q^{32}\) \(-3.43964 q^{33}\) \(+4.30990 q^{34}\) \(-10.7117 q^{35}\) \(+1.00000 q^{36}\) \(+6.10764 q^{37}\) \(+4.26302 q^{38}\) \(-1.00000 q^{39}\) \(-3.28276 q^{40}\) \(-10.4552 q^{41}\) \(-3.26302 q^{42}\) \(-4.03388 q^{43}\) \(+3.43964 q^{44}\) \(+3.28276 q^{45}\) \(-0.898821 q^{46}\) \(+8.58105 q^{47}\) \(-1.00000 q^{48}\) \(+3.64729 q^{49}\) \(-5.77652 q^{50}\) \(+4.30990 q^{51}\) \(+1.00000 q^{52}\) \(-0.879007 q^{53}\) \(+1.00000 q^{54}\) \(+11.2915 q^{55}\) \(+3.26302 q^{56}\) \(+4.26302 q^{57}\) \(-1.85461 q^{58}\) \(-8.39658 q^{59}\) \(-3.28276 q^{60}\) \(+6.04443 q^{61}\) \(-0.0760444 q^{62}\) \(-3.26302 q^{63}\) \(+1.00000 q^{64}\) \(+3.28276 q^{65}\) \(+3.43964 q^{66}\) \(+2.20686 q^{67}\) \(-4.30990 q^{68}\) \(-0.898821 q^{69}\) \(+10.7117 q^{70}\) \(-9.35352 q^{71}\) \(-1.00000 q^{72}\) \(+7.76041 q^{73}\) \(-6.10764 q^{74}\) \(-5.77652 q^{75}\) \(-4.26302 q^{76}\) \(-11.2236 q^{77}\) \(+1.00000 q^{78}\) \(-12.7124 q^{79}\) \(+3.28276 q^{80}\) \(+1.00000 q^{81}\) \(+10.4552 q^{82}\) \(-5.25414 q^{83}\) \(+3.26302 q^{84}\) \(-14.1484 q^{85}\) \(+4.03388 q^{86}\) \(-1.85461 q^{87}\) \(-3.43964 q^{88}\) \(-13.0095 q^{89}\) \(-3.28276 q^{90}\) \(-3.26302 q^{91}\) \(+0.898821 q^{92}\) \(-0.0760444 q^{93}\) \(-8.58105 q^{94}\) \(-13.9945 q^{95}\) \(+1.00000 q^{96}\) \(-0.220152 q^{97}\) \(-3.64729 q^{98}\) \(+3.43964 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 3.28276 1.46810 0.734048 0.679098i \(-0.237629\pi\)
0.734048 + 0.679098i \(0.237629\pi\)
\(6\) 1.00000 0.408248
\(7\) −3.26302 −1.23331 −0.616653 0.787235i \(-0.711512\pi\)
−0.616653 + 0.787235i \(0.711512\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −3.28276 −1.03810
\(11\) 3.43964 1.03709 0.518545 0.855050i \(-0.326474\pi\)
0.518545 + 0.855050i \(0.326474\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 3.26302 0.872079
\(15\) −3.28276 −0.847605
\(16\) 1.00000 0.250000
\(17\) −4.30990 −1.04530 −0.522652 0.852546i \(-0.675057\pi\)
−0.522652 + 0.852546i \(0.675057\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.26302 −0.978004 −0.489002 0.872283i \(-0.662639\pi\)
−0.489002 + 0.872283i \(0.662639\pi\)
\(20\) 3.28276 0.734048
\(21\) 3.26302 0.712049
\(22\) −3.43964 −0.733333
\(23\) 0.898821 0.187417 0.0937085 0.995600i \(-0.470128\pi\)
0.0937085 + 0.995600i \(0.470128\pi\)
\(24\) 1.00000 0.204124
\(25\) 5.77652 1.15530
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −3.26302 −0.616653
\(29\) 1.85461 0.344392 0.172196 0.985063i \(-0.444914\pi\)
0.172196 + 0.985063i \(0.444914\pi\)
\(30\) 3.28276 0.599347
\(31\) 0.0760444 0.0136580 0.00682899 0.999977i \(-0.497826\pi\)
0.00682899 + 0.999977i \(0.497826\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.43964 −0.598764
\(34\) 4.30990 0.739141
\(35\) −10.7117 −1.81061
\(36\) 1.00000 0.166667
\(37\) 6.10764 1.00409 0.502045 0.864841i \(-0.332581\pi\)
0.502045 + 0.864841i \(0.332581\pi\)
\(38\) 4.26302 0.691553
\(39\) −1.00000 −0.160128
\(40\) −3.28276 −0.519050
\(41\) −10.4552 −1.63283 −0.816417 0.577463i \(-0.804043\pi\)
−0.816417 + 0.577463i \(0.804043\pi\)
\(42\) −3.26302 −0.503495
\(43\) −4.03388 −0.615161 −0.307580 0.951522i \(-0.599519\pi\)
−0.307580 + 0.951522i \(0.599519\pi\)
\(44\) 3.43964 0.518545
\(45\) 3.28276 0.489365
\(46\) −0.898821 −0.132524
\(47\) 8.58105 1.25167 0.625837 0.779954i \(-0.284757\pi\)
0.625837 + 0.779954i \(0.284757\pi\)
\(48\) −1.00000 −0.144338
\(49\) 3.64729 0.521042
\(50\) −5.77652 −0.816923
\(51\) 4.30990 0.603506
\(52\) 1.00000 0.138675
\(53\) −0.879007 −0.120741 −0.0603704 0.998176i \(-0.519228\pi\)
−0.0603704 + 0.998176i \(0.519228\pi\)
\(54\) 1.00000 0.136083
\(55\) 11.2915 1.52255
\(56\) 3.26302 0.436039
\(57\) 4.26302 0.564651
\(58\) −1.85461 −0.243522
\(59\) −8.39658 −1.09314 −0.546571 0.837413i \(-0.684067\pi\)
−0.546571 + 0.837413i \(0.684067\pi\)
\(60\) −3.28276 −0.423803
\(61\) 6.04443 0.773910 0.386955 0.922099i \(-0.373527\pi\)
0.386955 + 0.922099i \(0.373527\pi\)
\(62\) −0.0760444 −0.00965765
\(63\) −3.26302 −0.411102
\(64\) 1.00000 0.125000
\(65\) 3.28276 0.407176
\(66\) 3.43964 0.423390
\(67\) 2.20686 0.269611 0.134805 0.990872i \(-0.456959\pi\)
0.134805 + 0.990872i \(0.456959\pi\)
\(68\) −4.30990 −0.522652
\(69\) −0.898821 −0.108205
\(70\) 10.7117 1.28029
\(71\) −9.35352 −1.11006 −0.555029 0.831831i \(-0.687293\pi\)
−0.555029 + 0.831831i \(0.687293\pi\)
\(72\) −1.00000 −0.117851
\(73\) 7.76041 0.908287 0.454144 0.890929i \(-0.349945\pi\)
0.454144 + 0.890929i \(0.349945\pi\)
\(74\) −6.10764 −0.709999
\(75\) −5.77652 −0.667015
\(76\) −4.26302 −0.489002
\(77\) −11.2236 −1.27905
\(78\) 1.00000 0.113228
\(79\) −12.7124 −1.43026 −0.715129 0.698993i \(-0.753632\pi\)
−0.715129 + 0.698993i \(0.753632\pi\)
\(80\) 3.28276 0.367024
\(81\) 1.00000 0.111111
\(82\) 10.4552 1.15459
\(83\) −5.25414 −0.576717 −0.288358 0.957523i \(-0.593109\pi\)
−0.288358 + 0.957523i \(0.593109\pi\)
\(84\) 3.26302 0.356025
\(85\) −14.1484 −1.53461
\(86\) 4.03388 0.434985
\(87\) −1.85461 −0.198835
\(88\) −3.43964 −0.366667
\(89\) −13.0095 −1.37900 −0.689501 0.724284i \(-0.742170\pi\)
−0.689501 + 0.724284i \(0.742170\pi\)
\(90\) −3.28276 −0.346033
\(91\) −3.26302 −0.342057
\(92\) 0.898821 0.0937085
\(93\) −0.0760444 −0.00788544
\(94\) −8.58105 −0.885067
\(95\) −13.9945 −1.43580
\(96\) 1.00000 0.102062
\(97\) −0.220152 −0.0223531 −0.0111765 0.999938i \(-0.503558\pi\)
−0.0111765 + 0.999938i \(0.503558\pi\)
\(98\) −3.64729 −0.368432
\(99\) 3.43964 0.345697
\(100\) 5.77652 0.577652
\(101\) −6.97473 −0.694011 −0.347006 0.937863i \(-0.612801\pi\)
−0.347006 + 0.937863i \(0.612801\pi\)
\(102\) −4.30990 −0.426744
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 10.7117 1.04536
\(106\) 0.879007 0.0853767
\(107\) 12.5778 1.21594 0.607970 0.793960i \(-0.291984\pi\)
0.607970 + 0.793960i \(0.291984\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 18.9579 1.81584 0.907920 0.419144i \(-0.137670\pi\)
0.907920 + 0.419144i \(0.137670\pi\)
\(110\) −11.2915 −1.07660
\(111\) −6.10764 −0.579712
\(112\) −3.26302 −0.308326
\(113\) −3.10165 −0.291779 −0.145890 0.989301i \(-0.546604\pi\)
−0.145890 + 0.989301i \(0.546604\pi\)
\(114\) −4.26302 −0.399268
\(115\) 2.95061 0.275146
\(116\) 1.85461 0.172196
\(117\) 1.00000 0.0924500
\(118\) 8.39658 0.772968
\(119\) 14.0633 1.28918
\(120\) 3.28276 0.299674
\(121\) 0.831115 0.0755559
\(122\) −6.04443 −0.547237
\(123\) 10.4552 0.942717
\(124\) 0.0760444 0.00682899
\(125\) 2.54912 0.228000
\(126\) 3.26302 0.290693
\(127\) −10.7269 −0.951859 −0.475930 0.879483i \(-0.657888\pi\)
−0.475930 + 0.879483i \(0.657888\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.03388 0.355163
\(130\) −3.28276 −0.287917
\(131\) 5.95551 0.520335 0.260168 0.965563i \(-0.416222\pi\)
0.260168 + 0.965563i \(0.416222\pi\)
\(132\) −3.43964 −0.299382
\(133\) 13.9103 1.20618
\(134\) −2.20686 −0.190644
\(135\) −3.28276 −0.282535
\(136\) 4.30990 0.369571
\(137\) 20.6100 1.76083 0.880417 0.474201i \(-0.157263\pi\)
0.880417 + 0.474201i \(0.157263\pi\)
\(138\) 0.898821 0.0765127
\(139\) −8.49965 −0.720931 −0.360466 0.932772i \(-0.617382\pi\)
−0.360466 + 0.932772i \(0.617382\pi\)
\(140\) −10.7117 −0.905305
\(141\) −8.58105 −0.722655
\(142\) 9.35352 0.784930
\(143\) 3.43964 0.287637
\(144\) 1.00000 0.0833333
\(145\) 6.08824 0.505601
\(146\) −7.76041 −0.642256
\(147\) −3.64729 −0.300824
\(148\) 6.10764 0.502045
\(149\) −17.4883 −1.43270 −0.716350 0.697741i \(-0.754189\pi\)
−0.716350 + 0.697741i \(0.754189\pi\)
\(150\) 5.77652 0.471651
\(151\) −12.6784 −1.03176 −0.515879 0.856662i \(-0.672534\pi\)
−0.515879 + 0.856662i \(0.672534\pi\)
\(152\) 4.26302 0.345777
\(153\) −4.30990 −0.348435
\(154\) 11.2236 0.904424
\(155\) 0.249636 0.0200512
\(156\) −1.00000 −0.0800641
\(157\) −6.28656 −0.501722 −0.250861 0.968023i \(-0.580714\pi\)
−0.250861 + 0.968023i \(0.580714\pi\)
\(158\) 12.7124 1.01134
\(159\) 0.879007 0.0697098
\(160\) −3.28276 −0.259525
\(161\) −2.93287 −0.231142
\(162\) −1.00000 −0.0785674
\(163\) −11.1403 −0.872579 −0.436289 0.899806i \(-0.643708\pi\)
−0.436289 + 0.899806i \(0.643708\pi\)
\(164\) −10.4552 −0.816417
\(165\) −11.2915 −0.879043
\(166\) 5.25414 0.407800
\(167\) −2.48103 −0.191988 −0.0959938 0.995382i \(-0.530603\pi\)
−0.0959938 + 0.995382i \(0.530603\pi\)
\(168\) −3.26302 −0.251747
\(169\) 1.00000 0.0769231
\(170\) 14.1484 1.08513
\(171\) −4.26302 −0.326001
\(172\) −4.03388 −0.307580
\(173\) 21.7190 1.65126 0.825632 0.564209i \(-0.190819\pi\)
0.825632 + 0.564209i \(0.190819\pi\)
\(174\) 1.85461 0.140598
\(175\) −18.8489 −1.42484
\(176\) 3.43964 0.259273
\(177\) 8.39658 0.631126
\(178\) 13.0095 0.975102
\(179\) −2.68391 −0.200605 −0.100303 0.994957i \(-0.531981\pi\)
−0.100303 + 0.994957i \(0.531981\pi\)
\(180\) 3.28276 0.244683
\(181\) −8.98763 −0.668046 −0.334023 0.942565i \(-0.608406\pi\)
−0.334023 + 0.942565i \(0.608406\pi\)
\(182\) 3.26302 0.241871
\(183\) −6.04443 −0.446817
\(184\) −0.898821 −0.0662619
\(185\) 20.0499 1.47410
\(186\) 0.0760444 0.00557585
\(187\) −14.8245 −1.08407
\(188\) 8.58105 0.625837
\(189\) 3.26302 0.237350
\(190\) 13.9945 1.01527
\(191\) −20.8937 −1.51181 −0.755906 0.654680i \(-0.772803\pi\)
−0.755906 + 0.654680i \(0.772803\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −7.84674 −0.564820 −0.282410 0.959294i \(-0.591134\pi\)
−0.282410 + 0.959294i \(0.591134\pi\)
\(194\) 0.220152 0.0158060
\(195\) −3.28276 −0.235083
\(196\) 3.64729 0.260521
\(197\) −12.3894 −0.882705 −0.441353 0.897334i \(-0.645501\pi\)
−0.441353 + 0.897334i \(0.645501\pi\)
\(198\) −3.43964 −0.244444
\(199\) −4.38042 −0.310520 −0.155260 0.987874i \(-0.549622\pi\)
−0.155260 + 0.987874i \(0.549622\pi\)
\(200\) −5.77652 −0.408461
\(201\) −2.20686 −0.155660
\(202\) 6.97473 0.490740
\(203\) −6.05162 −0.424741
\(204\) 4.30990 0.301753
\(205\) −34.3220 −2.39715
\(206\) −1.00000 −0.0696733
\(207\) 0.898821 0.0624723
\(208\) 1.00000 0.0693375
\(209\) −14.6632 −1.01428
\(210\) −10.7117 −0.739178
\(211\) −9.73052 −0.669876 −0.334938 0.942240i \(-0.608715\pi\)
−0.334938 + 0.942240i \(0.608715\pi\)
\(212\) −0.879007 −0.0603704
\(213\) 9.35352 0.640892
\(214\) −12.5778 −0.859799
\(215\) −13.2423 −0.903115
\(216\) 1.00000 0.0680414
\(217\) −0.248134 −0.0168445
\(218\) −18.9579 −1.28399
\(219\) −7.76041 −0.524400
\(220\) 11.2915 0.761274
\(221\) −4.30990 −0.289915
\(222\) 6.10764 0.409918
\(223\) −1.97961 −0.132564 −0.0662822 0.997801i \(-0.521114\pi\)
−0.0662822 + 0.997801i \(0.521114\pi\)
\(224\) 3.26302 0.218020
\(225\) 5.77652 0.385101
\(226\) 3.10165 0.206319
\(227\) −15.6688 −1.03998 −0.519988 0.854173i \(-0.674064\pi\)
−0.519988 + 0.854173i \(0.674064\pi\)
\(228\) 4.26302 0.282325
\(229\) 25.9643 1.71577 0.857885 0.513841i \(-0.171778\pi\)
0.857885 + 0.513841i \(0.171778\pi\)
\(230\) −2.95061 −0.194558
\(231\) 11.2236 0.738459
\(232\) −1.85461 −0.121761
\(233\) −1.78245 −0.116772 −0.0583860 0.998294i \(-0.518595\pi\)
−0.0583860 + 0.998294i \(0.518595\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 28.1695 1.83758
\(236\) −8.39658 −0.546571
\(237\) 12.7124 0.825759
\(238\) −14.0633 −0.911587
\(239\) 3.14850 0.203660 0.101830 0.994802i \(-0.467530\pi\)
0.101830 + 0.994802i \(0.467530\pi\)
\(240\) −3.28276 −0.211901
\(241\) −15.0632 −0.970303 −0.485152 0.874430i \(-0.661236\pi\)
−0.485152 + 0.874430i \(0.661236\pi\)
\(242\) −0.831115 −0.0534261
\(243\) −1.00000 −0.0641500
\(244\) 6.04443 0.386955
\(245\) 11.9732 0.764939
\(246\) −10.4552 −0.666601
\(247\) −4.26302 −0.271249
\(248\) −0.0760444 −0.00482883
\(249\) 5.25414 0.332968
\(250\) −2.54912 −0.161221
\(251\) −6.66166 −0.420481 −0.210240 0.977650i \(-0.567425\pi\)
−0.210240 + 0.977650i \(0.567425\pi\)
\(252\) −3.26302 −0.205551
\(253\) 3.09162 0.194368
\(254\) 10.7269 0.673066
\(255\) 14.1484 0.886005
\(256\) 1.00000 0.0625000
\(257\) 2.53517 0.158139 0.0790696 0.996869i \(-0.474805\pi\)
0.0790696 + 0.996869i \(0.474805\pi\)
\(258\) −4.03388 −0.251138
\(259\) −19.9294 −1.23835
\(260\) 3.28276 0.203588
\(261\) 1.85461 0.114797
\(262\) −5.95551 −0.367932
\(263\) 30.3814 1.87340 0.936698 0.350138i \(-0.113865\pi\)
0.936698 + 0.350138i \(0.113865\pi\)
\(264\) 3.43964 0.211695
\(265\) −2.88557 −0.177259
\(266\) −13.9103 −0.852896
\(267\) 13.0095 0.796168
\(268\) 2.20686 0.134805
\(269\) 14.9780 0.913222 0.456611 0.889666i \(-0.349063\pi\)
0.456611 + 0.889666i \(0.349063\pi\)
\(270\) 3.28276 0.199782
\(271\) 22.7307 1.38079 0.690395 0.723433i \(-0.257437\pi\)
0.690395 + 0.723433i \(0.257437\pi\)
\(272\) −4.30990 −0.261326
\(273\) 3.26302 0.197487
\(274\) −20.6100 −1.24510
\(275\) 19.8691 1.19815
\(276\) −0.898821 −0.0541026
\(277\) 16.0879 0.966628 0.483314 0.875447i \(-0.339433\pi\)
0.483314 + 0.875447i \(0.339433\pi\)
\(278\) 8.49965 0.509775
\(279\) 0.0760444 0.00455266
\(280\) 10.7117 0.640147
\(281\) 7.59780 0.453246 0.226623 0.973983i \(-0.427231\pi\)
0.226623 + 0.973983i \(0.427231\pi\)
\(282\) 8.58105 0.510994
\(283\) −21.7133 −1.29072 −0.645361 0.763878i \(-0.723293\pi\)
−0.645361 + 0.763878i \(0.723293\pi\)
\(284\) −9.35352 −0.555029
\(285\) 13.9945 0.828961
\(286\) −3.43964 −0.203390
\(287\) 34.1156 2.01378
\(288\) −1.00000 −0.0589256
\(289\) 1.57522 0.0926601
\(290\) −6.08824 −0.357514
\(291\) 0.220152 0.0129055
\(292\) 7.76041 0.454144
\(293\) 3.95009 0.230767 0.115383 0.993321i \(-0.463190\pi\)
0.115383 + 0.993321i \(0.463190\pi\)
\(294\) 3.64729 0.212714
\(295\) −27.5640 −1.60484
\(296\) −6.10764 −0.354999
\(297\) −3.43964 −0.199588
\(298\) 17.4883 1.01307
\(299\) 0.898821 0.0519801
\(300\) −5.77652 −0.333507
\(301\) 13.1626 0.758681
\(302\) 12.6784 0.729563
\(303\) 6.97473 0.400687
\(304\) −4.26302 −0.244501
\(305\) 19.8424 1.13617
\(306\) 4.30990 0.246380
\(307\) −31.6335 −1.80542 −0.902711 0.430248i \(-0.858426\pi\)
−0.902711 + 0.430248i \(0.858426\pi\)
\(308\) −11.2236 −0.639524
\(309\) −1.00000 −0.0568880
\(310\) −0.249636 −0.0141784
\(311\) −4.11144 −0.233138 −0.116569 0.993183i \(-0.537190\pi\)
−0.116569 + 0.993183i \(0.537190\pi\)
\(312\) 1.00000 0.0566139
\(313\) −1.23314 −0.0697009 −0.0348505 0.999393i \(-0.511095\pi\)
−0.0348505 + 0.999393i \(0.511095\pi\)
\(314\) 6.28656 0.354771
\(315\) −10.7117 −0.603537
\(316\) −12.7124 −0.715129
\(317\) −11.2352 −0.631032 −0.315516 0.948920i \(-0.602178\pi\)
−0.315516 + 0.948920i \(0.602178\pi\)
\(318\) −0.879007 −0.0492922
\(319\) 6.37919 0.357166
\(320\) 3.28276 0.183512
\(321\) −12.5778 −0.702023
\(322\) 2.93287 0.163442
\(323\) 18.3732 1.02231
\(324\) 1.00000 0.0555556
\(325\) 5.77652 0.320424
\(326\) 11.1403 0.617006
\(327\) −18.9579 −1.04838
\(328\) 10.4552 0.577294
\(329\) −28.0001 −1.54370
\(330\) 11.2915 0.621577
\(331\) −12.0823 −0.664101 −0.332050 0.943262i \(-0.607740\pi\)
−0.332050 + 0.943262i \(0.607740\pi\)
\(332\) −5.25414 −0.288358
\(333\) 6.10764 0.334697
\(334\) 2.48103 0.135756
\(335\) 7.24459 0.395814
\(336\) 3.26302 0.178012
\(337\) 11.5507 0.629206 0.314603 0.949223i \(-0.398129\pi\)
0.314603 + 0.949223i \(0.398129\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 3.10165 0.168459
\(340\) −14.1484 −0.767303
\(341\) 0.261565 0.0141646
\(342\) 4.26302 0.230518
\(343\) 10.9399 0.590702
\(344\) 4.03388 0.217492
\(345\) −2.95061 −0.158856
\(346\) −21.7190 −1.16762
\(347\) −1.65725 −0.0889661 −0.0444830 0.999010i \(-0.514164\pi\)
−0.0444830 + 0.999010i \(0.514164\pi\)
\(348\) −1.85461 −0.0994175
\(349\) 2.13379 0.114219 0.0571094 0.998368i \(-0.481812\pi\)
0.0571094 + 0.998368i \(0.481812\pi\)
\(350\) 18.8489 1.00752
\(351\) −1.00000 −0.0533761
\(352\) −3.43964 −0.183333
\(353\) 2.11532 0.112587 0.0562935 0.998414i \(-0.482072\pi\)
0.0562935 + 0.998414i \(0.482072\pi\)
\(354\) −8.39658 −0.446273
\(355\) −30.7054 −1.62967
\(356\) −13.0095 −0.689501
\(357\) −14.0633 −0.744308
\(358\) 2.68391 0.141849
\(359\) −24.6758 −1.30234 −0.651169 0.758933i \(-0.725721\pi\)
−0.651169 + 0.758933i \(0.725721\pi\)
\(360\) −3.28276 −0.173017
\(361\) −0.826669 −0.0435089
\(362\) 8.98763 0.472380
\(363\) −0.831115 −0.0436222
\(364\) −3.26302 −0.171029
\(365\) 25.4756 1.33345
\(366\) 6.04443 0.315948
\(367\) 28.4209 1.48356 0.741780 0.670643i \(-0.233982\pi\)
0.741780 + 0.670643i \(0.233982\pi\)
\(368\) 0.898821 0.0468543
\(369\) −10.4552 −0.544278
\(370\) −20.0499 −1.04235
\(371\) 2.86822 0.148910
\(372\) −0.0760444 −0.00394272
\(373\) −18.1734 −0.940982 −0.470491 0.882405i \(-0.655923\pi\)
−0.470491 + 0.882405i \(0.655923\pi\)
\(374\) 14.8245 0.766556
\(375\) −2.54912 −0.131636
\(376\) −8.58105 −0.442534
\(377\) 1.85461 0.0955172
\(378\) −3.26302 −0.167832
\(379\) 10.2512 0.526571 0.263285 0.964718i \(-0.415194\pi\)
0.263285 + 0.964718i \(0.415194\pi\)
\(380\) −13.9945 −0.717901
\(381\) 10.7269 0.549556
\(382\) 20.8937 1.06901
\(383\) 25.1009 1.28259 0.641297 0.767293i \(-0.278397\pi\)
0.641297 + 0.767293i \(0.278397\pi\)
\(384\) 1.00000 0.0510310
\(385\) −36.8444 −1.87777
\(386\) 7.84674 0.399388
\(387\) −4.03388 −0.205054
\(388\) −0.220152 −0.0111765
\(389\) −10.0350 −0.508795 −0.254398 0.967100i \(-0.581877\pi\)
−0.254398 + 0.967100i \(0.581877\pi\)
\(390\) 3.28276 0.166229
\(391\) −3.87382 −0.195908
\(392\) −3.64729 −0.184216
\(393\) −5.95551 −0.300416
\(394\) 12.3894 0.624167
\(395\) −41.7318 −2.09975
\(396\) 3.43964 0.172848
\(397\) 32.7780 1.64508 0.822540 0.568707i \(-0.192556\pi\)
0.822540 + 0.568707i \(0.192556\pi\)
\(398\) 4.38042 0.219571
\(399\) −13.9103 −0.696387
\(400\) 5.77652 0.288826
\(401\) −2.15080 −0.107406 −0.0537029 0.998557i \(-0.517102\pi\)
−0.0537029 + 0.998557i \(0.517102\pi\)
\(402\) 2.20686 0.110068
\(403\) 0.0760444 0.00378804
\(404\) −6.97473 −0.347006
\(405\) 3.28276 0.163122
\(406\) 6.05162 0.300337
\(407\) 21.0081 1.04133
\(408\) −4.30990 −0.213372
\(409\) −24.9692 −1.23465 −0.617324 0.786709i \(-0.711783\pi\)
−0.617324 + 0.786709i \(0.711783\pi\)
\(410\) 34.3220 1.69504
\(411\) −20.6100 −1.01662
\(412\) 1.00000 0.0492665
\(413\) 27.3982 1.34818
\(414\) −0.898821 −0.0441746
\(415\) −17.2481 −0.846675
\(416\) −1.00000 −0.0490290
\(417\) 8.49965 0.416230
\(418\) 14.6632 0.717203
\(419\) −11.6865 −0.570923 −0.285462 0.958390i \(-0.592147\pi\)
−0.285462 + 0.958390i \(0.592147\pi\)
\(420\) 10.7117 0.522678
\(421\) 10.0040 0.487565 0.243782 0.969830i \(-0.421612\pi\)
0.243782 + 0.969830i \(0.421612\pi\)
\(422\) 9.73052 0.473674
\(423\) 8.58105 0.417225
\(424\) 0.879007 0.0426883
\(425\) −24.8962 −1.20764
\(426\) −9.35352 −0.453179
\(427\) −19.7231 −0.954468
\(428\) 12.5778 0.607970
\(429\) −3.43964 −0.166067
\(430\) 13.2423 0.638599
\(431\) 7.96361 0.383594 0.191797 0.981435i \(-0.438569\pi\)
0.191797 + 0.981435i \(0.438569\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 20.0637 0.964198 0.482099 0.876117i \(-0.339875\pi\)
0.482099 + 0.876117i \(0.339875\pi\)
\(434\) 0.248134 0.0119108
\(435\) −6.08824 −0.291909
\(436\) 18.9579 0.907920
\(437\) −3.83169 −0.183295
\(438\) 7.76041 0.370807
\(439\) −24.6906 −1.17842 −0.589208 0.807981i \(-0.700560\pi\)
−0.589208 + 0.807981i \(0.700560\pi\)
\(440\) −11.2915 −0.538302
\(441\) 3.64729 0.173681
\(442\) 4.30990 0.205001
\(443\) −35.2903 −1.67669 −0.838347 0.545136i \(-0.816478\pi\)
−0.838347 + 0.545136i \(0.816478\pi\)
\(444\) −6.10764 −0.289856
\(445\) −42.7070 −2.02451
\(446\) 1.97961 0.0937372
\(447\) 17.4883 0.827170
\(448\) −3.26302 −0.154163
\(449\) −15.5411 −0.733428 −0.366714 0.930334i \(-0.619517\pi\)
−0.366714 + 0.930334i \(0.619517\pi\)
\(450\) −5.77652 −0.272308
\(451\) −35.9622 −1.69340
\(452\) −3.10165 −0.145890
\(453\) 12.6784 0.595685
\(454\) 15.6688 0.735375
\(455\) −10.7117 −0.502173
\(456\) −4.26302 −0.199634
\(457\) −37.2104 −1.74063 −0.870314 0.492497i \(-0.836084\pi\)
−0.870314 + 0.492497i \(0.836084\pi\)
\(458\) −25.9643 −1.21323
\(459\) 4.30990 0.201169
\(460\) 2.95061 0.137573
\(461\) 16.2449 0.756600 0.378300 0.925683i \(-0.376509\pi\)
0.378300 + 0.925683i \(0.376509\pi\)
\(462\) −11.2236 −0.522169
\(463\) 32.2809 1.50022 0.750110 0.661313i \(-0.230001\pi\)
0.750110 + 0.661313i \(0.230001\pi\)
\(464\) 1.85461 0.0860981
\(465\) −0.249636 −0.0115766
\(466\) 1.78245 0.0825702
\(467\) 23.2790 1.07722 0.538611 0.842555i \(-0.318949\pi\)
0.538611 + 0.842555i \(0.318949\pi\)
\(468\) 1.00000 0.0462250
\(469\) −7.20103 −0.332512
\(470\) −28.1695 −1.29936
\(471\) 6.28656 0.289669
\(472\) 8.39658 0.386484
\(473\) −13.8751 −0.637977
\(474\) −12.7124 −0.583900
\(475\) −24.6254 −1.12989
\(476\) 14.0633 0.644589
\(477\) −0.879007 −0.0402470
\(478\) −3.14850 −0.144009
\(479\) 7.50179 0.342766 0.171383 0.985205i \(-0.445176\pi\)
0.171383 + 0.985205i \(0.445176\pi\)
\(480\) 3.28276 0.149837
\(481\) 6.10764 0.278484
\(482\) 15.0632 0.686108
\(483\) 2.93287 0.133450
\(484\) 0.831115 0.0377780
\(485\) −0.722707 −0.0328164
\(486\) 1.00000 0.0453609
\(487\) −18.3043 −0.829448 −0.414724 0.909947i \(-0.636122\pi\)
−0.414724 + 0.909947i \(0.636122\pi\)
\(488\) −6.04443 −0.273619
\(489\) 11.1403 0.503783
\(490\) −11.9732 −0.540894
\(491\) 30.8152 1.39067 0.695335 0.718686i \(-0.255256\pi\)
0.695335 + 0.718686i \(0.255256\pi\)
\(492\) 10.4552 0.471358
\(493\) −7.99318 −0.359995
\(494\) 4.26302 0.191802
\(495\) 11.2915 0.507516
\(496\) 0.0760444 0.00341450
\(497\) 30.5207 1.36904
\(498\) −5.25414 −0.235444
\(499\) −29.3153 −1.31234 −0.656168 0.754615i \(-0.727824\pi\)
−0.656168 + 0.754615i \(0.727824\pi\)
\(500\) 2.54912 0.114000
\(501\) 2.48103 0.110844
\(502\) 6.66166 0.297325
\(503\) −11.5573 −0.515315 −0.257658 0.966236i \(-0.582951\pi\)
−0.257658 + 0.966236i \(0.582951\pi\)
\(504\) 3.26302 0.145346
\(505\) −22.8964 −1.01887
\(506\) −3.09162 −0.137439
\(507\) −1.00000 −0.0444116
\(508\) −10.7269 −0.475930
\(509\) 10.6860 0.473647 0.236824 0.971553i \(-0.423894\pi\)
0.236824 + 0.971553i \(0.423894\pi\)
\(510\) −14.1484 −0.626500
\(511\) −25.3224 −1.12020
\(512\) −1.00000 −0.0441942
\(513\) 4.26302 0.188217
\(514\) −2.53517 −0.111821
\(515\) 3.28276 0.144656
\(516\) 4.03388 0.177582
\(517\) 29.5157 1.29810
\(518\) 19.9294 0.875645
\(519\) −21.7190 −0.953358
\(520\) −3.28276 −0.143959
\(521\) 5.14259 0.225301 0.112651 0.993635i \(-0.464066\pi\)
0.112651 + 0.993635i \(0.464066\pi\)
\(522\) −1.85461 −0.0811740
\(523\) −11.7640 −0.514404 −0.257202 0.966358i \(-0.582801\pi\)
−0.257202 + 0.966358i \(0.582801\pi\)
\(524\) 5.95551 0.260168
\(525\) 18.8489 0.822633
\(526\) −30.3814 −1.32469
\(527\) −0.327744 −0.0142767
\(528\) −3.43964 −0.149691
\(529\) −22.1921 −0.964875
\(530\) 2.88557 0.125341
\(531\) −8.39658 −0.364381
\(532\) 13.9103 0.603089
\(533\) −10.4552 −0.452866
\(534\) −13.0095 −0.562975
\(535\) 41.2898 1.78511
\(536\) −2.20686 −0.0953218
\(537\) 2.68391 0.115819
\(538\) −14.9780 −0.645745
\(539\) 12.5454 0.540367
\(540\) −3.28276 −0.141268
\(541\) −20.5340 −0.882825 −0.441413 0.897304i \(-0.645523\pi\)
−0.441413 + 0.897304i \(0.645523\pi\)
\(542\) −22.7307 −0.976366
\(543\) 8.98763 0.385696
\(544\) 4.30990 0.184785
\(545\) 62.2343 2.66582
\(546\) −3.26302 −0.139644
\(547\) −23.1411 −0.989441 −0.494721 0.869052i \(-0.664730\pi\)
−0.494721 + 0.869052i \(0.664730\pi\)
\(548\) 20.6100 0.880417
\(549\) 6.04443 0.257970
\(550\) −19.8691 −0.847223
\(551\) −7.90623 −0.336817
\(552\) 0.898821 0.0382563
\(553\) 41.4808 1.76394
\(554\) −16.0879 −0.683509
\(555\) −20.0499 −0.851072
\(556\) −8.49965 −0.360466
\(557\) −4.31085 −0.182657 −0.0913284 0.995821i \(-0.529111\pi\)
−0.0913284 + 0.995821i \(0.529111\pi\)
\(558\) −0.0760444 −0.00321922
\(559\) −4.03388 −0.170615
\(560\) −10.7117 −0.452652
\(561\) 14.8245 0.625891
\(562\) −7.59780 −0.320494
\(563\) 30.5560 1.28778 0.643891 0.765117i \(-0.277319\pi\)
0.643891 + 0.765117i \(0.277319\pi\)
\(564\) −8.58105 −0.361327
\(565\) −10.1820 −0.428360
\(566\) 21.7133 0.912678
\(567\) −3.26302 −0.137034
\(568\) 9.35352 0.392465
\(569\) 17.5992 0.737797 0.368898 0.929470i \(-0.379735\pi\)
0.368898 + 0.929470i \(0.379735\pi\)
\(570\) −13.9945 −0.586164
\(571\) 21.3058 0.891621 0.445811 0.895127i \(-0.352916\pi\)
0.445811 + 0.895127i \(0.352916\pi\)
\(572\) 3.43964 0.143819
\(573\) 20.8937 0.872845
\(574\) −34.1156 −1.42396
\(575\) 5.19205 0.216524
\(576\) 1.00000 0.0416667
\(577\) 18.6119 0.774822 0.387411 0.921907i \(-0.373370\pi\)
0.387411 + 0.921907i \(0.373370\pi\)
\(578\) −1.57522 −0.0655206
\(579\) 7.84674 0.326099
\(580\) 6.08824 0.252800
\(581\) 17.1444 0.711268
\(582\) −0.220152 −0.00912560
\(583\) −3.02347 −0.125219
\(584\) −7.76041 −0.321128
\(585\) 3.28276 0.135725
\(586\) −3.95009 −0.163177
\(587\) −33.0387 −1.36365 −0.681827 0.731514i \(-0.738814\pi\)
−0.681827 + 0.731514i \(0.738814\pi\)
\(588\) −3.64729 −0.150412
\(589\) −0.324179 −0.0133576
\(590\) 27.5640 1.13479
\(591\) 12.3894 0.509630
\(592\) 6.10764 0.251023
\(593\) 20.1374 0.826943 0.413471 0.910517i \(-0.364316\pi\)
0.413471 + 0.910517i \(0.364316\pi\)
\(594\) 3.43964 0.141130
\(595\) 46.1664 1.89264
\(596\) −17.4883 −0.716350
\(597\) 4.38042 0.179279
\(598\) −0.898821 −0.0367555
\(599\) −34.4796 −1.40880 −0.704399 0.709804i \(-0.748783\pi\)
−0.704399 + 0.709804i \(0.748783\pi\)
\(600\) 5.77652 0.235825
\(601\) 2.31160 0.0942922 0.0471461 0.998888i \(-0.484987\pi\)
0.0471461 + 0.998888i \(0.484987\pi\)
\(602\) −13.1626 −0.536469
\(603\) 2.20686 0.0898703
\(604\) −12.6784 −0.515879
\(605\) 2.72835 0.110923
\(606\) −6.97473 −0.283329
\(607\) −36.1744 −1.46827 −0.734136 0.679002i \(-0.762413\pi\)
−0.734136 + 0.679002i \(0.762413\pi\)
\(608\) 4.26302 0.172888
\(609\) 6.05162 0.245224
\(610\) −19.8424 −0.803397
\(611\) 8.58105 0.347152
\(612\) −4.30990 −0.174217
\(613\) −47.4639 −1.91705 −0.958524 0.285010i \(-0.908003\pi\)
−0.958524 + 0.285010i \(0.908003\pi\)
\(614\) 31.6335 1.27663
\(615\) 34.3220 1.38400
\(616\) 11.2236 0.452212
\(617\) −36.5587 −1.47180 −0.735898 0.677092i \(-0.763240\pi\)
−0.735898 + 0.677092i \(0.763240\pi\)
\(618\) 1.00000 0.0402259
\(619\) −44.8668 −1.80335 −0.901675 0.432415i \(-0.857662\pi\)
−0.901675 + 0.432415i \(0.857662\pi\)
\(620\) 0.249636 0.0100256
\(621\) −0.898821 −0.0360684
\(622\) 4.11144 0.164854
\(623\) 42.4502 1.70073
\(624\) −1.00000 −0.0400320
\(625\) −20.5144 −0.820577
\(626\) 1.23314 0.0492860
\(627\) 14.6632 0.585594
\(628\) −6.28656 −0.250861
\(629\) −26.3233 −1.04958
\(630\) 10.7117 0.426765
\(631\) −25.8508 −1.02910 −0.514552 0.857459i \(-0.672042\pi\)
−0.514552 + 0.857459i \(0.672042\pi\)
\(632\) 12.7124 0.505672
\(633\) 9.73052 0.386753
\(634\) 11.2352 0.446207
\(635\) −35.2139 −1.39742
\(636\) 0.879007 0.0348549
\(637\) 3.64729 0.144511
\(638\) −6.37919 −0.252554
\(639\) −9.35352 −0.370019
\(640\) −3.28276 −0.129763
\(641\) −44.7299 −1.76673 −0.883363 0.468690i \(-0.844726\pi\)
−0.883363 + 0.468690i \(0.844726\pi\)
\(642\) 12.5778 0.496405
\(643\) 11.7784 0.464493 0.232247 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(644\) −2.93287 −0.115571
\(645\) 13.2423 0.521414
\(646\) −18.3732 −0.722883
\(647\) 9.23873 0.363212 0.181606 0.983371i \(-0.441870\pi\)
0.181606 + 0.983371i \(0.441870\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −28.8812 −1.13369
\(650\) −5.77652 −0.226574
\(651\) 0.248134 0.00972515
\(652\) −11.1403 −0.436289
\(653\) −0.764358 −0.0299116 −0.0149558 0.999888i \(-0.504761\pi\)
−0.0149558 + 0.999888i \(0.504761\pi\)
\(654\) 18.9579 0.741313
\(655\) 19.5505 0.763901
\(656\) −10.4552 −0.408208
\(657\) 7.76041 0.302762
\(658\) 28.0001 1.09156
\(659\) −34.4761 −1.34300 −0.671499 0.741006i \(-0.734349\pi\)
−0.671499 + 0.741006i \(0.734349\pi\)
\(660\) −11.2915 −0.439521
\(661\) 29.1626 1.13429 0.567146 0.823617i \(-0.308047\pi\)
0.567146 + 0.823617i \(0.308047\pi\)
\(662\) 12.0823 0.469590
\(663\) 4.30990 0.167383
\(664\) 5.25414 0.203900
\(665\) 45.6642 1.77078
\(666\) −6.10764 −0.236666
\(667\) 1.66696 0.0645450
\(668\) −2.48103 −0.0959938
\(669\) 1.97961 0.0765361
\(670\) −7.24459 −0.279883
\(671\) 20.7907 0.802615
\(672\) −3.26302 −0.125874
\(673\) 10.4580 0.403125 0.201562 0.979476i \(-0.435398\pi\)
0.201562 + 0.979476i \(0.435398\pi\)
\(674\) −11.5507 −0.444916
\(675\) −5.77652 −0.222338
\(676\) 1.00000 0.0384615
\(677\) −31.7092 −1.21869 −0.609343 0.792907i \(-0.708567\pi\)
−0.609343 + 0.792907i \(0.708567\pi\)
\(678\) −3.10165 −0.119118
\(679\) 0.718360 0.0275681
\(680\) 14.1484 0.542565
\(681\) 15.6688 0.600431
\(682\) −0.261565 −0.0100159
\(683\) −12.2425 −0.468448 −0.234224 0.972183i \(-0.575255\pi\)
−0.234224 + 0.972183i \(0.575255\pi\)
\(684\) −4.26302 −0.163001
\(685\) 67.6578 2.58507
\(686\) −10.9399 −0.417689
\(687\) −25.9643 −0.990601
\(688\) −4.03388 −0.153790
\(689\) −0.879007 −0.0334875
\(690\) 2.95061 0.112328
\(691\) 30.0734 1.14405 0.572023 0.820238i \(-0.306159\pi\)
0.572023 + 0.820238i \(0.306159\pi\)
\(692\) 21.7190 0.825632
\(693\) −11.2236 −0.426350
\(694\) 1.65725 0.0629085
\(695\) −27.9023 −1.05840
\(696\) 1.85461 0.0702988
\(697\) 45.0610 1.70681
\(698\) −2.13379 −0.0807650
\(699\) 1.78245 0.0674183
\(700\) −18.8489 −0.712421
\(701\) −28.4612 −1.07497 −0.537483 0.843275i \(-0.680625\pi\)
−0.537483 + 0.843275i \(0.680625\pi\)
\(702\) 1.00000 0.0377426
\(703\) −26.0370 −0.982004
\(704\) 3.43964 0.129636
\(705\) −28.1695 −1.06093
\(706\) −2.11532 −0.0796110
\(707\) 22.7587 0.855928
\(708\) 8.39658 0.315563
\(709\) 8.65120 0.324903 0.162451 0.986717i \(-0.448060\pi\)
0.162451 + 0.986717i \(0.448060\pi\)
\(710\) 30.7054 1.15235
\(711\) −12.7124 −0.476752
\(712\) 13.0095 0.487551
\(713\) 0.0683503 0.00255974
\(714\) 14.0633 0.526305
\(715\) 11.2915 0.422279
\(716\) −2.68391 −0.100303
\(717\) −3.14850 −0.117583
\(718\) 24.6758 0.920892
\(719\) 22.8200 0.851043 0.425522 0.904948i \(-0.360091\pi\)
0.425522 + 0.904948i \(0.360091\pi\)
\(720\) 3.28276 0.122341
\(721\) −3.26302 −0.121521
\(722\) 0.826669 0.0307654
\(723\) 15.0632 0.560205
\(724\) −8.98763 −0.334023
\(725\) 10.7132 0.397878
\(726\) 0.831115 0.0308456
\(727\) −47.1790 −1.74977 −0.874886 0.484329i \(-0.839064\pi\)
−0.874886 + 0.484329i \(0.839064\pi\)
\(728\) 3.26302 0.120936
\(729\) 1.00000 0.0370370
\(730\) −25.4756 −0.942893
\(731\) 17.3856 0.643030
\(732\) −6.04443 −0.223409
\(733\) 9.75884 0.360451 0.180225 0.983625i \(-0.442317\pi\)
0.180225 + 0.983625i \(0.442317\pi\)
\(734\) −28.4209 −1.04904
\(735\) −11.9732 −0.441638
\(736\) −0.898821 −0.0331310
\(737\) 7.59080 0.279611
\(738\) 10.4552 0.384862
\(739\) −38.3408 −1.41039 −0.705195 0.709013i \(-0.749141\pi\)
−0.705195 + 0.709013i \(0.749141\pi\)
\(740\) 20.0499 0.737050
\(741\) 4.26302 0.156606
\(742\) −2.86822 −0.105296
\(743\) −1.14474 −0.0419964 −0.0209982 0.999780i \(-0.506684\pi\)
−0.0209982 + 0.999780i \(0.506684\pi\)
\(744\) 0.0760444 0.00278792
\(745\) −57.4100 −2.10334
\(746\) 18.1734 0.665375
\(747\) −5.25414 −0.192239
\(748\) −14.8245 −0.542037
\(749\) −41.0415 −1.49962
\(750\) 2.54912 0.0930808
\(751\) 12.4653 0.454865 0.227433 0.973794i \(-0.426967\pi\)
0.227433 + 0.973794i \(0.426967\pi\)
\(752\) 8.58105 0.312919
\(753\) 6.66166 0.242765
\(754\) −1.85461 −0.0675409
\(755\) −41.6203 −1.51472
\(756\) 3.26302 0.118675
\(757\) 0.935711 0.0340090 0.0170045 0.999855i \(-0.494587\pi\)
0.0170045 + 0.999855i \(0.494587\pi\)
\(758\) −10.2512 −0.372342
\(759\) −3.09162 −0.112219
\(760\) 13.9945 0.507633
\(761\) 7.60000 0.275500 0.137750 0.990467i \(-0.456013\pi\)
0.137750 + 0.990467i \(0.456013\pi\)
\(762\) −10.7269 −0.388595
\(763\) −61.8600 −2.23948
\(764\) −20.8937 −0.755906
\(765\) −14.1484 −0.511535
\(766\) −25.1009 −0.906931
\(767\) −8.39658 −0.303183
\(768\) −1.00000 −0.0360844
\(769\) −48.9605 −1.76556 −0.882780 0.469786i \(-0.844331\pi\)
−0.882780 + 0.469786i \(0.844331\pi\)
\(770\) 36.8444 1.32778
\(771\) −2.53517 −0.0913018
\(772\) −7.84674 −0.282410
\(773\) −4.51395 −0.162356 −0.0811778 0.996700i \(-0.525868\pi\)
−0.0811778 + 0.996700i \(0.525868\pi\)
\(774\) 4.03388 0.144995
\(775\) 0.439272 0.0157791
\(776\) 0.220152 0.00790300
\(777\) 19.9294 0.714961
\(778\) 10.0350 0.359773
\(779\) 44.5709 1.59692
\(780\) −3.28276 −0.117542
\(781\) −32.1727 −1.15123
\(782\) 3.87382 0.138528
\(783\) −1.85461 −0.0662783
\(784\) 3.64729 0.130260
\(785\) −20.6373 −0.736576
\(786\) 5.95551 0.212426
\(787\) −8.70267 −0.310217 −0.155108 0.987897i \(-0.549573\pi\)
−0.155108 + 0.987897i \(0.549573\pi\)
\(788\) −12.3894 −0.441353
\(789\) −30.3814 −1.08161
\(790\) 41.7318 1.48475
\(791\) 10.1208 0.359853
\(792\) −3.43964 −0.122222
\(793\) 6.04443 0.214644
\(794\) −32.7780 −1.16325
\(795\) 2.88557 0.102341
\(796\) −4.38042 −0.155260
\(797\) −36.5177 −1.29352 −0.646762 0.762692i \(-0.723877\pi\)
−0.646762 + 0.762692i \(0.723877\pi\)
\(798\) 13.9103 0.492420
\(799\) −36.9834 −1.30838
\(800\) −5.77652 −0.204231
\(801\) −13.0095 −0.459668
\(802\) 2.15080 0.0759473
\(803\) 26.6930 0.941976
\(804\) −2.20686 −0.0778300
\(805\) −9.62791 −0.339339
\(806\) −0.0760444 −0.00267855
\(807\) −14.9780 −0.527249
\(808\) 6.97473 0.245370
\(809\) 7.20570 0.253339 0.126669 0.991945i \(-0.459571\pi\)
0.126669 + 0.991945i \(0.459571\pi\)
\(810\) −3.28276 −0.115344
\(811\) −24.8192 −0.871519 −0.435759 0.900063i \(-0.643520\pi\)
−0.435759 + 0.900063i \(0.643520\pi\)
\(812\) −6.05162 −0.212370
\(813\) −22.7307 −0.797199
\(814\) −21.0081 −0.736333
\(815\) −36.5711 −1.28103
\(816\) 4.30990 0.150877
\(817\) 17.1965 0.601630
\(818\) 24.9692 0.873028
\(819\) −3.26302 −0.114019
\(820\) −34.3220 −1.19858
\(821\) 43.0666 1.50303 0.751517 0.659714i \(-0.229323\pi\)
0.751517 + 0.659714i \(0.229323\pi\)
\(822\) 20.6100 0.718857
\(823\) 28.3312 0.987562 0.493781 0.869586i \(-0.335614\pi\)
0.493781 + 0.869586i \(0.335614\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −19.8691 −0.691754
\(826\) −27.3982 −0.953306
\(827\) 5.69940 0.198188 0.0990938 0.995078i \(-0.468406\pi\)
0.0990938 + 0.995078i \(0.468406\pi\)
\(828\) 0.898821 0.0312362
\(829\) 11.8320 0.410941 0.205470 0.978663i \(-0.434128\pi\)
0.205470 + 0.978663i \(0.434128\pi\)
\(830\) 17.2481 0.598690
\(831\) −16.0879 −0.558083
\(832\) 1.00000 0.0346688
\(833\) −15.7195 −0.544647
\(834\) −8.49965 −0.294319
\(835\) −8.14462 −0.281856
\(836\) −14.6632 −0.507139
\(837\) −0.0760444 −0.00262848
\(838\) 11.6865 0.403704
\(839\) 30.6643 1.05865 0.529325 0.848419i \(-0.322445\pi\)
0.529325 + 0.848419i \(0.322445\pi\)
\(840\) −10.7117 −0.369589
\(841\) −25.5604 −0.881394
\(842\) −10.0040 −0.344760
\(843\) −7.59780 −0.261682
\(844\) −9.73052 −0.334938
\(845\) 3.28276 0.112930
\(846\) −8.58105 −0.295022
\(847\) −2.71194 −0.0931835
\(848\) −0.879007 −0.0301852
\(849\) 21.7133 0.745198
\(850\) 24.8962 0.853933
\(851\) 5.48967 0.188184
\(852\) 9.35352 0.320446
\(853\) −39.6843 −1.35876 −0.679381 0.733785i \(-0.737752\pi\)
−0.679381 + 0.733785i \(0.737752\pi\)
\(854\) 19.7231 0.674911
\(855\) −13.9945 −0.478601
\(856\) −12.5778 −0.429899
\(857\) −16.1198 −0.550643 −0.275322 0.961352i \(-0.588784\pi\)
−0.275322 + 0.961352i \(0.588784\pi\)
\(858\) 3.43964 0.117427
\(859\) 28.2736 0.964682 0.482341 0.875984i \(-0.339787\pi\)
0.482341 + 0.875984i \(0.339787\pi\)
\(860\) −13.2423 −0.451557
\(861\) −34.1156 −1.16266
\(862\) −7.96361 −0.271242
\(863\) 20.4429 0.695885 0.347942 0.937516i \(-0.386880\pi\)
0.347942 + 0.937516i \(0.386880\pi\)
\(864\) 1.00000 0.0340207
\(865\) 71.2982 2.42421
\(866\) −20.0637 −0.681791
\(867\) −1.57522 −0.0534974
\(868\) −0.248134 −0.00842223
\(869\) −43.7261 −1.48331
\(870\) 6.08824 0.206411
\(871\) 2.20686 0.0747766
\(872\) −18.9579 −0.641996
\(873\) −0.220152 −0.00745102
\(874\) 3.83169 0.129609
\(875\) −8.31783 −0.281194
\(876\) −7.76041 −0.262200
\(877\) −35.9441 −1.21375 −0.606874 0.794798i \(-0.707577\pi\)
−0.606874 + 0.794798i \(0.707577\pi\)
\(878\) 24.6906 0.833266
\(879\) −3.95009 −0.133233
\(880\) 11.2915 0.380637
\(881\) 15.9209 0.536389 0.268195 0.963365i \(-0.413573\pi\)
0.268195 + 0.963365i \(0.413573\pi\)
\(882\) −3.64729 −0.122811
\(883\) −34.9059 −1.17468 −0.587339 0.809341i \(-0.699825\pi\)
−0.587339 + 0.809341i \(0.699825\pi\)
\(884\) −4.30990 −0.144958
\(885\) 27.5640 0.926553
\(886\) 35.2903 1.18560
\(887\) −3.37682 −0.113383 −0.0566913 0.998392i \(-0.518055\pi\)
−0.0566913 + 0.998392i \(0.518055\pi\)
\(888\) 6.10764 0.204959
\(889\) 35.0021 1.17393
\(890\) 42.7070 1.43154
\(891\) 3.43964 0.115232
\(892\) −1.97961 −0.0662822
\(893\) −36.5812 −1.22414
\(894\) −17.4883 −0.584897
\(895\) −8.81065 −0.294507
\(896\) 3.26302 0.109010
\(897\) −0.898821 −0.0300107
\(898\) 15.5411 0.518612
\(899\) 0.141033 0.00470370
\(900\) 5.77652 0.192551
\(901\) 3.78843 0.126211
\(902\) 35.9622 1.19741
\(903\) −13.1626 −0.438025
\(904\) 3.10165 0.103160
\(905\) −29.5042 −0.980754
\(906\) −12.6784 −0.421213
\(907\) −38.8367 −1.28955 −0.644776 0.764371i \(-0.723050\pi\)
−0.644776 + 0.764371i \(0.723050\pi\)
\(908\) −15.6688 −0.519988
\(909\) −6.97473 −0.231337
\(910\) 10.7117 0.355090
\(911\) 12.6984 0.420717 0.210358 0.977624i \(-0.432537\pi\)
0.210358 + 0.977624i \(0.432537\pi\)
\(912\) 4.26302 0.141163
\(913\) −18.0723 −0.598107
\(914\) 37.2104 1.23081
\(915\) −19.8424 −0.655971
\(916\) 25.9643 0.857885
\(917\) −19.4329 −0.641732
\(918\) −4.30990 −0.142248
\(919\) −39.0797 −1.28912 −0.644560 0.764554i \(-0.722959\pi\)
−0.644560 + 0.764554i \(0.722959\pi\)
\(920\) −2.95061 −0.0972788
\(921\) 31.6335 1.04236
\(922\) −16.2449 −0.534997
\(923\) −9.35352 −0.307875
\(924\) 11.2236 0.369230
\(925\) 35.2809 1.16003
\(926\) −32.2809 −1.06082
\(927\) 1.00000 0.0328443
\(928\) −1.85461 −0.0608805
\(929\) 50.9887 1.67288 0.836442 0.548056i \(-0.184632\pi\)
0.836442 + 0.548056i \(0.184632\pi\)
\(930\) 0.249636 0.00818588
\(931\) −15.5485 −0.509581
\(932\) −1.78245 −0.0583860
\(933\) 4.11144 0.134602
\(934\) −23.2790 −0.761711
\(935\) −48.6653 −1.59152
\(936\) −1.00000 −0.0326860
\(937\) −19.8224 −0.647569 −0.323785 0.946131i \(-0.604955\pi\)
−0.323785 + 0.946131i \(0.604955\pi\)
\(938\) 7.20103 0.235122
\(939\) 1.23314 0.0402419
\(940\) 28.1695 0.918789
\(941\) −37.7454 −1.23046 −0.615232 0.788346i \(-0.710938\pi\)
−0.615232 + 0.788346i \(0.710938\pi\)
\(942\) −6.28656 −0.204827
\(943\) −9.39738 −0.306021
\(944\) −8.39658 −0.273286
\(945\) 10.7117 0.348452
\(946\) 13.8751 0.451118
\(947\) −32.8061 −1.06606 −0.533028 0.846098i \(-0.678946\pi\)
−0.533028 + 0.846098i \(0.678946\pi\)
\(948\) 12.7124 0.412880
\(949\) 7.76041 0.251914
\(950\) 24.6254 0.798954
\(951\) 11.2352 0.364326
\(952\) −14.0633 −0.455794
\(953\) 46.6766 1.51200 0.756001 0.654570i \(-0.227150\pi\)
0.756001 + 0.654570i \(0.227150\pi\)
\(954\) 0.879007 0.0284589
\(955\) −68.5889 −2.21948
\(956\) 3.14850 0.101830
\(957\) −6.37919 −0.206210
\(958\) −7.50179 −0.242372
\(959\) −67.2509 −2.17164
\(960\) −3.28276 −0.105951
\(961\) −30.9942 −0.999813
\(962\) −6.10764 −0.196918
\(963\) 12.5778 0.405313
\(964\) −15.0632 −0.485152
\(965\) −25.7590 −0.829210
\(966\) −2.93287 −0.0943635
\(967\) 13.1433 0.422662 0.211331 0.977415i \(-0.432220\pi\)
0.211331 + 0.977415i \(0.432220\pi\)
\(968\) −0.831115 −0.0267131
\(969\) −18.3732 −0.590232
\(970\) 0.722707 0.0232047
\(971\) 6.83327 0.219290 0.109645 0.993971i \(-0.465029\pi\)
0.109645 + 0.993971i \(0.465029\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 27.7345 0.889128
\(974\) 18.3043 0.586509
\(975\) −5.77652 −0.184997
\(976\) 6.04443 0.193478
\(977\) −7.28983 −0.233222 −0.116611 0.993178i \(-0.537203\pi\)
−0.116611 + 0.993178i \(0.537203\pi\)
\(978\) −11.1403 −0.356229
\(979\) −44.7479 −1.43015
\(980\) 11.9732 0.382470
\(981\) 18.9579 0.605280
\(982\) −30.8152 −0.983352
\(983\) 11.9172 0.380098 0.190049 0.981775i \(-0.439135\pi\)
0.190049 + 0.981775i \(0.439135\pi\)
\(984\) −10.4552 −0.333301
\(985\) −40.6713 −1.29590
\(986\) 7.99318 0.254555
\(987\) 28.0001 0.891254
\(988\) −4.26302 −0.135625
\(989\) −3.62573 −0.115292
\(990\) −11.2915 −0.358868
\(991\) 2.39520 0.0760861 0.0380431 0.999276i \(-0.487888\pi\)
0.0380431 + 0.999276i \(0.487888\pi\)
\(992\) −0.0760444 −0.00241441
\(993\) 12.0823 0.383419
\(994\) −30.5207 −0.968058
\(995\) −14.3799 −0.455873
\(996\) 5.25414 0.166484
\(997\) 3.65690 0.115815 0.0579076 0.998322i \(-0.481557\pi\)
0.0579076 + 0.998322i \(0.481557\pi\)
\(998\) 29.3153 0.927961
\(999\) −6.10764 −0.193237
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 \(a_p\))