Properties

Label 6026.2.a.i.1.11
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.932148 q^{3}\) \(+1.00000 q^{4}\) \(-0.513090 q^{5}\) \(+0.932148 q^{6}\) \(+0.0983188 q^{7}\) \(-1.00000 q^{8}\) \(-2.13110 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.932148 q^{3}\) \(+1.00000 q^{4}\) \(-0.513090 q^{5}\) \(+0.932148 q^{6}\) \(+0.0983188 q^{7}\) \(-1.00000 q^{8}\) \(-2.13110 q^{9}\) \(+0.513090 q^{10}\) \(+1.76350 q^{11}\) \(-0.932148 q^{12}\) \(+1.94413 q^{13}\) \(-0.0983188 q^{14}\) \(+0.478276 q^{15}\) \(+1.00000 q^{16}\) \(+0.106083 q^{17}\) \(+2.13110 q^{18}\) \(+5.57408 q^{19}\) \(-0.513090 q^{20}\) \(-0.0916477 q^{21}\) \(-1.76350 q^{22}\) \(+1.00000 q^{23}\) \(+0.932148 q^{24}\) \(-4.73674 q^{25}\) \(-1.94413 q^{26}\) \(+4.78294 q^{27}\) \(+0.0983188 q^{28}\) \(-2.46668 q^{29}\) \(-0.478276 q^{30}\) \(-6.26753 q^{31}\) \(-1.00000 q^{32}\) \(-1.64384 q^{33}\) \(-0.106083 q^{34}\) \(-0.0504464 q^{35}\) \(-2.13110 q^{36}\) \(-7.32825 q^{37}\) \(-5.57408 q^{38}\) \(-1.81222 q^{39}\) \(+0.513090 q^{40}\) \(-6.09707 q^{41}\) \(+0.0916477 q^{42}\) \(+4.09661 q^{43}\) \(+1.76350 q^{44}\) \(+1.09345 q^{45}\) \(-1.00000 q^{46}\) \(-3.63401 q^{47}\) \(-0.932148 q^{48}\) \(-6.99033 q^{49}\) \(+4.73674 q^{50}\) \(-0.0988850 q^{51}\) \(+1.94413 q^{52}\) \(+0.949157 q^{53}\) \(-4.78294 q^{54}\) \(-0.904833 q^{55}\) \(-0.0983188 q^{56}\) \(-5.19587 q^{57}\) \(+2.46668 q^{58}\) \(+15.1915 q^{59}\) \(+0.478276 q^{60}\) \(-6.05297 q^{61}\) \(+6.26753 q^{62}\) \(-0.209527 q^{63}\) \(+1.00000 q^{64}\) \(-0.997513 q^{65}\) \(+1.64384 q^{66}\) \(+9.31760 q^{67}\) \(+0.106083 q^{68}\) \(-0.932148 q^{69}\) \(+0.0504464 q^{70}\) \(+11.6016 q^{71}\) \(+2.13110 q^{72}\) \(+3.21738 q^{73}\) \(+7.32825 q^{74}\) \(+4.41534 q^{75}\) \(+5.57408 q^{76}\) \(+0.173385 q^{77}\) \(+1.81222 q^{78}\) \(+4.67534 q^{79}\) \(-0.513090 q^{80}\) \(+1.93489 q^{81}\) \(+6.09707 q^{82}\) \(+6.74942 q^{83}\) \(-0.0916477 q^{84}\) \(-0.0544301 q^{85}\) \(-4.09661 q^{86}\) \(+2.29931 q^{87}\) \(-1.76350 q^{88}\) \(-7.62846 q^{89}\) \(-1.09345 q^{90}\) \(+0.191144 q^{91}\) \(+1.00000 q^{92}\) \(+5.84226 q^{93}\) \(+3.63401 q^{94}\) \(-2.86001 q^{95}\) \(+0.932148 q^{96}\) \(+10.6127 q^{97}\) \(+6.99033 q^{98}\) \(-3.75819 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.932148 −0.538176 −0.269088 0.963116i \(-0.586722\pi\)
−0.269088 + 0.963116i \(0.586722\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.513090 −0.229461 −0.114730 0.993397i \(-0.536600\pi\)
−0.114730 + 0.993397i \(0.536600\pi\)
\(6\) 0.932148 0.380548
\(7\) 0.0983188 0.0371610 0.0185805 0.999827i \(-0.494085\pi\)
0.0185805 + 0.999827i \(0.494085\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.13110 −0.710367
\(10\) 0.513090 0.162253
\(11\) 1.76350 0.531715 0.265857 0.964012i \(-0.414345\pi\)
0.265857 + 0.964012i \(0.414345\pi\)
\(12\) −0.932148 −0.269088
\(13\) 1.94413 0.539204 0.269602 0.962972i \(-0.413108\pi\)
0.269602 + 0.962972i \(0.413108\pi\)
\(14\) −0.0983188 −0.0262768
\(15\) 0.478276 0.123490
\(16\) 1.00000 0.250000
\(17\) 0.106083 0.0257289 0.0128644 0.999917i \(-0.495905\pi\)
0.0128644 + 0.999917i \(0.495905\pi\)
\(18\) 2.13110 0.502305
\(19\) 5.57408 1.27878 0.639391 0.768882i \(-0.279186\pi\)
0.639391 + 0.768882i \(0.279186\pi\)
\(20\) −0.513090 −0.114730
\(21\) −0.0916477 −0.0199992
\(22\) −1.76350 −0.375979
\(23\) 1.00000 0.208514
\(24\) 0.932148 0.190274
\(25\) −4.73674 −0.947348
\(26\) −1.94413 −0.381275
\(27\) 4.78294 0.920478
\(28\) 0.0983188 0.0185805
\(29\) −2.46668 −0.458051 −0.229025 0.973420i \(-0.573554\pi\)
−0.229025 + 0.973420i \(0.573554\pi\)
\(30\) −0.478276 −0.0873208
\(31\) −6.26753 −1.12568 −0.562841 0.826565i \(-0.690292\pi\)
−0.562841 + 0.826565i \(0.690292\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.64384 −0.286156
\(34\) −0.106083 −0.0181931
\(35\) −0.0504464 −0.00852700
\(36\) −2.13110 −0.355183
\(37\) −7.32825 −1.20476 −0.602379 0.798210i \(-0.705780\pi\)
−0.602379 + 0.798210i \(0.705780\pi\)
\(38\) −5.57408 −0.904236
\(39\) −1.81222 −0.290187
\(40\) 0.513090 0.0811266
\(41\) −6.09707 −0.952202 −0.476101 0.879391i \(-0.657950\pi\)
−0.476101 + 0.879391i \(0.657950\pi\)
\(42\) 0.0916477 0.0141415
\(43\) 4.09661 0.624727 0.312363 0.949963i \(-0.398879\pi\)
0.312363 + 0.949963i \(0.398879\pi\)
\(44\) 1.76350 0.265857
\(45\) 1.09345 0.163001
\(46\) −1.00000 −0.147442
\(47\) −3.63401 −0.530075 −0.265038 0.964238i \(-0.585384\pi\)
−0.265038 + 0.964238i \(0.585384\pi\)
\(48\) −0.932148 −0.134544
\(49\) −6.99033 −0.998619
\(50\) 4.73674 0.669876
\(51\) −0.0988850 −0.0138467
\(52\) 1.94413 0.269602
\(53\) 0.949157 0.130377 0.0651884 0.997873i \(-0.479235\pi\)
0.0651884 + 0.997873i \(0.479235\pi\)
\(54\) −4.78294 −0.650876
\(55\) −0.904833 −0.122008
\(56\) −0.0983188 −0.0131384
\(57\) −5.19587 −0.688210
\(58\) 2.46668 0.323891
\(59\) 15.1915 1.97777 0.988885 0.148683i \(-0.0475035\pi\)
0.988885 + 0.148683i \(0.0475035\pi\)
\(60\) 0.478276 0.0617451
\(61\) −6.05297 −0.775004 −0.387502 0.921869i \(-0.626662\pi\)
−0.387502 + 0.921869i \(0.626662\pi\)
\(62\) 6.26753 0.795977
\(63\) −0.209527 −0.0263980
\(64\) 1.00000 0.125000
\(65\) −0.997513 −0.123726
\(66\) 1.64384 0.202343
\(67\) 9.31760 1.13833 0.569163 0.822225i \(-0.307267\pi\)
0.569163 + 0.822225i \(0.307267\pi\)
\(68\) 0.106083 0.0128644
\(69\) −0.932148 −0.112217
\(70\) 0.0504464 0.00602950
\(71\) 11.6016 1.37686 0.688428 0.725305i \(-0.258301\pi\)
0.688428 + 0.725305i \(0.258301\pi\)
\(72\) 2.13110 0.251153
\(73\) 3.21738 0.376565 0.188283 0.982115i \(-0.439708\pi\)
0.188283 + 0.982115i \(0.439708\pi\)
\(74\) 7.32825 0.851892
\(75\) 4.41534 0.509840
\(76\) 5.57408 0.639391
\(77\) 0.173385 0.0197591
\(78\) 1.81222 0.205193
\(79\) 4.67534 0.526017 0.263008 0.964794i \(-0.415285\pi\)
0.263008 + 0.964794i \(0.415285\pi\)
\(80\) −0.513090 −0.0573652
\(81\) 1.93489 0.214988
\(82\) 6.09707 0.673309
\(83\) 6.74942 0.740845 0.370422 0.928863i \(-0.379213\pi\)
0.370422 + 0.928863i \(0.379213\pi\)
\(84\) −0.0916477 −0.00999958
\(85\) −0.0544301 −0.00590377
\(86\) −4.09661 −0.441748
\(87\) 2.29931 0.246512
\(88\) −1.76350 −0.187990
\(89\) −7.62846 −0.808616 −0.404308 0.914623i \(-0.632488\pi\)
−0.404308 + 0.914623i \(0.632488\pi\)
\(90\) −1.09345 −0.115259
\(91\) 0.191144 0.0200374
\(92\) 1.00000 0.104257
\(93\) 5.84226 0.605815
\(94\) 3.63401 0.374820
\(95\) −2.86001 −0.293430
\(96\) 0.932148 0.0951369
\(97\) 10.6127 1.07756 0.538779 0.842447i \(-0.318886\pi\)
0.538779 + 0.842447i \(0.318886\pi\)
\(98\) 6.99033 0.706130
\(99\) −3.75819 −0.377712
\(100\) −4.73674 −0.473674
\(101\) 2.04141 0.203128 0.101564 0.994829i \(-0.467615\pi\)
0.101564 + 0.994829i \(0.467615\pi\)
\(102\) 0.0988850 0.00979107
\(103\) −17.7356 −1.74754 −0.873770 0.486339i \(-0.838332\pi\)
−0.873770 + 0.486339i \(0.838332\pi\)
\(104\) −1.94413 −0.190637
\(105\) 0.0470235 0.00458902
\(106\) −0.949157 −0.0921902
\(107\) −13.2071 −1.27677 −0.638387 0.769715i \(-0.720398\pi\)
−0.638387 + 0.769715i \(0.720398\pi\)
\(108\) 4.78294 0.460239
\(109\) 8.85329 0.847992 0.423996 0.905664i \(-0.360627\pi\)
0.423996 + 0.905664i \(0.360627\pi\)
\(110\) 0.904833 0.0862724
\(111\) 6.83102 0.648371
\(112\) 0.0983188 0.00929026
\(113\) −3.21901 −0.302819 −0.151409 0.988471i \(-0.548381\pi\)
−0.151409 + 0.988471i \(0.548381\pi\)
\(114\) 5.19587 0.486638
\(115\) −0.513090 −0.0478459
\(116\) −2.46668 −0.229025
\(117\) −4.14313 −0.383033
\(118\) −15.1915 −1.39849
\(119\) 0.0104300 0.000956112 0
\(120\) −0.478276 −0.0436604
\(121\) −7.89007 −0.717279
\(122\) 6.05297 0.548011
\(123\) 5.68337 0.512452
\(124\) −6.26753 −0.562841
\(125\) 4.99582 0.446840
\(126\) 0.209527 0.0186662
\(127\) −16.2749 −1.44417 −0.722084 0.691805i \(-0.756816\pi\)
−0.722084 + 0.691805i \(0.756816\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.81864 −0.336213
\(130\) 0.997513 0.0874876
\(131\) 1.00000 0.0873704
\(132\) −1.64384 −0.143078
\(133\) 0.548037 0.0475209
\(134\) −9.31760 −0.804918
\(135\) −2.45408 −0.211214
\(136\) −0.106083 −0.00909654
\(137\) −12.3517 −1.05528 −0.527639 0.849469i \(-0.676923\pi\)
−0.527639 + 0.849469i \(0.676923\pi\)
\(138\) 0.932148 0.0793497
\(139\) −2.02855 −0.172060 −0.0860298 0.996293i \(-0.527418\pi\)
−0.0860298 + 0.996293i \(0.527418\pi\)
\(140\) −0.0504464 −0.00426350
\(141\) 3.38744 0.285274
\(142\) −11.6016 −0.973584
\(143\) 3.42847 0.286703
\(144\) −2.13110 −0.177592
\(145\) 1.26563 0.105105
\(146\) −3.21738 −0.266272
\(147\) 6.51602 0.537433
\(148\) −7.32825 −0.602379
\(149\) 13.1522 1.07747 0.538733 0.842476i \(-0.318903\pi\)
0.538733 + 0.842476i \(0.318903\pi\)
\(150\) −4.41534 −0.360511
\(151\) 8.60668 0.700401 0.350201 0.936675i \(-0.386113\pi\)
0.350201 + 0.936675i \(0.386113\pi\)
\(152\) −5.57408 −0.452118
\(153\) −0.226073 −0.0182770
\(154\) −0.173385 −0.0139718
\(155\) 3.21581 0.258300
\(156\) −1.81222 −0.145093
\(157\) 7.59165 0.605880 0.302940 0.953010i \(-0.402032\pi\)
0.302940 + 0.953010i \(0.402032\pi\)
\(158\) −4.67534 −0.371950
\(159\) −0.884754 −0.0701656
\(160\) 0.513090 0.0405633
\(161\) 0.0983188 0.00774861
\(162\) −1.93489 −0.152019
\(163\) −7.06902 −0.553689 −0.276844 0.960915i \(-0.589289\pi\)
−0.276844 + 0.960915i \(0.589289\pi\)
\(164\) −6.09707 −0.476101
\(165\) 0.843438 0.0656616
\(166\) −6.74942 −0.523856
\(167\) 5.77948 0.447230 0.223615 0.974678i \(-0.428214\pi\)
0.223615 + 0.974678i \(0.428214\pi\)
\(168\) 0.0916477 0.00707077
\(169\) −9.22036 −0.709259
\(170\) 0.0544301 0.00417460
\(171\) −11.8789 −0.908405
\(172\) 4.09661 0.312363
\(173\) 11.0590 0.840797 0.420398 0.907340i \(-0.361890\pi\)
0.420398 + 0.907340i \(0.361890\pi\)
\(174\) −2.29931 −0.174310
\(175\) −0.465711 −0.0352044
\(176\) 1.76350 0.132929
\(177\) −14.1608 −1.06439
\(178\) 7.62846 0.571778
\(179\) −14.1530 −1.05784 −0.528922 0.848670i \(-0.677404\pi\)
−0.528922 + 0.848670i \(0.677404\pi\)
\(180\) 1.09345 0.0815007
\(181\) 3.46254 0.257369 0.128684 0.991686i \(-0.458925\pi\)
0.128684 + 0.991686i \(0.458925\pi\)
\(182\) −0.191144 −0.0141686
\(183\) 5.64227 0.417088
\(184\) −1.00000 −0.0737210
\(185\) 3.76005 0.276445
\(186\) −5.84226 −0.428376
\(187\) 0.187077 0.0136804
\(188\) −3.63401 −0.265038
\(189\) 0.470254 0.0342059
\(190\) 2.86001 0.207487
\(191\) −0.396258 −0.0286722 −0.0143361 0.999897i \(-0.504563\pi\)
−0.0143361 + 0.999897i \(0.504563\pi\)
\(192\) −0.932148 −0.0672720
\(193\) −3.64510 −0.262380 −0.131190 0.991357i \(-0.541880\pi\)
−0.131190 + 0.991357i \(0.541880\pi\)
\(194\) −10.6127 −0.761948
\(195\) 0.929829 0.0665864
\(196\) −6.99033 −0.499310
\(197\) 26.3209 1.87528 0.937642 0.347603i \(-0.113004\pi\)
0.937642 + 0.347603i \(0.113004\pi\)
\(198\) 3.75819 0.267083
\(199\) −21.1271 −1.49766 −0.748831 0.662761i \(-0.769385\pi\)
−0.748831 + 0.662761i \(0.769385\pi\)
\(200\) 4.73674 0.334938
\(201\) −8.68538 −0.612620
\(202\) −2.04141 −0.143633
\(203\) −0.242521 −0.0170216
\(204\) −0.0988850 −0.00692333
\(205\) 3.12834 0.218493
\(206\) 17.7356 1.23570
\(207\) −2.13110 −0.148122
\(208\) 1.94413 0.134801
\(209\) 9.82989 0.679947
\(210\) −0.0470235 −0.00324493
\(211\) −5.02165 −0.345705 −0.172852 0.984948i \(-0.555298\pi\)
−0.172852 + 0.984948i \(0.555298\pi\)
\(212\) 0.949157 0.0651884
\(213\) −10.8144 −0.740990
\(214\) 13.2071 0.902816
\(215\) −2.10193 −0.143350
\(216\) −4.78294 −0.325438
\(217\) −0.616216 −0.0418315
\(218\) −8.85329 −0.599621
\(219\) −2.99907 −0.202658
\(220\) −0.904833 −0.0610038
\(221\) 0.206239 0.0138731
\(222\) −6.83102 −0.458468
\(223\) −2.98097 −0.199621 −0.0998103 0.995006i \(-0.531824\pi\)
−0.0998103 + 0.995006i \(0.531824\pi\)
\(224\) −0.0983188 −0.00656920
\(225\) 10.0945 0.672964
\(226\) 3.21901 0.214125
\(227\) −27.8779 −1.85032 −0.925160 0.379576i \(-0.876070\pi\)
−0.925160 + 0.379576i \(0.876070\pi\)
\(228\) −5.19587 −0.344105
\(229\) 8.67574 0.573309 0.286655 0.958034i \(-0.407457\pi\)
0.286655 + 0.958034i \(0.407457\pi\)
\(230\) 0.513090 0.0338321
\(231\) −0.161621 −0.0106339
\(232\) 2.46668 0.161945
\(233\) 2.48734 0.162951 0.0814756 0.996675i \(-0.474037\pi\)
0.0814756 + 0.996675i \(0.474037\pi\)
\(234\) 4.14313 0.270845
\(235\) 1.86457 0.121631
\(236\) 15.1915 0.988885
\(237\) −4.35811 −0.283089
\(238\) −0.0104300 −0.000676073 0
\(239\) 10.8334 0.700757 0.350379 0.936608i \(-0.386053\pi\)
0.350379 + 0.936608i \(0.386053\pi\)
\(240\) 0.478276 0.0308726
\(241\) −30.2691 −1.94980 −0.974901 0.222638i \(-0.928533\pi\)
−0.974901 + 0.222638i \(0.928533\pi\)
\(242\) 7.89007 0.507193
\(243\) −16.1524 −1.03618
\(244\) −6.05297 −0.387502
\(245\) 3.58667 0.229144
\(246\) −5.68337 −0.362358
\(247\) 10.8367 0.689525
\(248\) 6.26753 0.397989
\(249\) −6.29145 −0.398705
\(250\) −4.99582 −0.315964
\(251\) −16.4332 −1.03726 −0.518628 0.855000i \(-0.673557\pi\)
−0.518628 + 0.855000i \(0.673557\pi\)
\(252\) −0.209527 −0.0131990
\(253\) 1.76350 0.110870
\(254\) 16.2749 1.02118
\(255\) 0.0507369 0.00317727
\(256\) 1.00000 0.0625000
\(257\) −14.9307 −0.931351 −0.465676 0.884956i \(-0.654189\pi\)
−0.465676 + 0.884956i \(0.654189\pi\)
\(258\) 3.81864 0.237738
\(259\) −0.720505 −0.0447700
\(260\) −0.997513 −0.0618631
\(261\) 5.25674 0.325384
\(262\) −1.00000 −0.0617802
\(263\) 15.7074 0.968558 0.484279 0.874914i \(-0.339082\pi\)
0.484279 + 0.874914i \(0.339082\pi\)
\(264\) 1.64384 0.101171
\(265\) −0.487003 −0.0299163
\(266\) −0.548037 −0.0336023
\(267\) 7.11086 0.435177
\(268\) 9.31760 0.569163
\(269\) 25.6443 1.56356 0.781779 0.623556i \(-0.214313\pi\)
0.781779 + 0.623556i \(0.214313\pi\)
\(270\) 2.45408 0.149351
\(271\) −17.1604 −1.04242 −0.521209 0.853429i \(-0.674519\pi\)
−0.521209 + 0.853429i \(0.674519\pi\)
\(272\) 0.106083 0.00643222
\(273\) −0.178175 −0.0107836
\(274\) 12.3517 0.746194
\(275\) −8.35323 −0.503719
\(276\) −0.932148 −0.0561087
\(277\) −30.4299 −1.82835 −0.914177 0.405316i \(-0.867162\pi\)
−0.914177 + 0.405316i \(0.867162\pi\)
\(278\) 2.02855 0.121665
\(279\) 13.3567 0.799647
\(280\) 0.0504464 0.00301475
\(281\) 6.51695 0.388769 0.194384 0.980925i \(-0.437729\pi\)
0.194384 + 0.980925i \(0.437729\pi\)
\(282\) −3.38744 −0.201719
\(283\) 12.6219 0.750296 0.375148 0.926965i \(-0.377592\pi\)
0.375148 + 0.926965i \(0.377592\pi\)
\(284\) 11.6016 0.688428
\(285\) 2.66595 0.157917
\(286\) −3.42847 −0.202730
\(287\) −0.599457 −0.0353848
\(288\) 2.13110 0.125576
\(289\) −16.9887 −0.999338
\(290\) −1.26563 −0.0743202
\(291\) −9.89261 −0.579915
\(292\) 3.21738 0.188283
\(293\) −15.3701 −0.897932 −0.448966 0.893549i \(-0.648208\pi\)
−0.448966 + 0.893549i \(0.648208\pi\)
\(294\) −6.51602 −0.380022
\(295\) −7.79462 −0.453821
\(296\) 7.32825 0.425946
\(297\) 8.43471 0.489432
\(298\) −13.1522 −0.761884
\(299\) 1.94413 0.112432
\(300\) 4.41534 0.254920
\(301\) 0.402774 0.0232155
\(302\) −8.60668 −0.495259
\(303\) −1.90290 −0.109319
\(304\) 5.57408 0.319696
\(305\) 3.10572 0.177833
\(306\) 0.226073 0.0129238
\(307\) 15.7267 0.897570 0.448785 0.893640i \(-0.351857\pi\)
0.448785 + 0.893640i \(0.351857\pi\)
\(308\) 0.173385 0.00987953
\(309\) 16.5322 0.940484
\(310\) −3.21581 −0.182646
\(311\) −34.4984 −1.95622 −0.978112 0.208079i \(-0.933279\pi\)
−0.978112 + 0.208079i \(0.933279\pi\)
\(312\) 1.81222 0.102596
\(313\) −4.63612 −0.262049 −0.131025 0.991379i \(-0.541827\pi\)
−0.131025 + 0.991379i \(0.541827\pi\)
\(314\) −7.59165 −0.428422
\(315\) 0.107506 0.00605730
\(316\) 4.67534 0.263008
\(317\) 21.8326 1.22624 0.613119 0.789990i \(-0.289914\pi\)
0.613119 + 0.789990i \(0.289914\pi\)
\(318\) 0.884754 0.0496146
\(319\) −4.34998 −0.243552
\(320\) −0.513090 −0.0286826
\(321\) 12.3109 0.687129
\(322\) −0.0983188 −0.00547909
\(323\) 0.591315 0.0329017
\(324\) 1.93489 0.107494
\(325\) −9.20883 −0.510814
\(326\) 7.06902 0.391517
\(327\) −8.25258 −0.456369
\(328\) 6.09707 0.336654
\(329\) −0.357292 −0.0196981
\(330\) −0.843438 −0.0464297
\(331\) 6.75135 0.371088 0.185544 0.982636i \(-0.440595\pi\)
0.185544 + 0.982636i \(0.440595\pi\)
\(332\) 6.74942 0.370422
\(333\) 15.6172 0.855820
\(334\) −5.77948 −0.316239
\(335\) −4.78077 −0.261201
\(336\) −0.0916477 −0.00499979
\(337\) −7.77881 −0.423739 −0.211869 0.977298i \(-0.567955\pi\)
−0.211869 + 0.977298i \(0.567955\pi\)
\(338\) 9.22036 0.501522
\(339\) 3.00059 0.162970
\(340\) −0.0544301 −0.00295189
\(341\) −11.0528 −0.598541
\(342\) 11.8789 0.642339
\(343\) −1.37551 −0.0742707
\(344\) −4.09661 −0.220874
\(345\) 0.478276 0.0257495
\(346\) −11.0590 −0.594533
\(347\) 3.94396 0.211723 0.105862 0.994381i \(-0.466240\pi\)
0.105862 + 0.994381i \(0.466240\pi\)
\(348\) 2.29931 0.123256
\(349\) −17.2435 −0.923023 −0.461511 0.887134i \(-0.652693\pi\)
−0.461511 + 0.887134i \(0.652693\pi\)
\(350\) 0.465711 0.0248933
\(351\) 9.29866 0.496326
\(352\) −1.76350 −0.0939948
\(353\) −2.61370 −0.139113 −0.0695565 0.997578i \(-0.522158\pi\)
−0.0695565 + 0.997578i \(0.522158\pi\)
\(354\) 14.1608 0.752636
\(355\) −5.95266 −0.315934
\(356\) −7.62846 −0.404308
\(357\) −0.00972226 −0.000514556 0
\(358\) 14.1530 0.748009
\(359\) 0.221086 0.0116685 0.00583423 0.999983i \(-0.498143\pi\)
0.00583423 + 0.999983i \(0.498143\pi\)
\(360\) −1.09345 −0.0576297
\(361\) 12.0704 0.635284
\(362\) −3.46254 −0.181987
\(363\) 7.35472 0.386022
\(364\) 0.191144 0.0100187
\(365\) −1.65080 −0.0864070
\(366\) −5.64227 −0.294926
\(367\) −2.70938 −0.141429 −0.0707143 0.997497i \(-0.522528\pi\)
−0.0707143 + 0.997497i \(0.522528\pi\)
\(368\) 1.00000 0.0521286
\(369\) 12.9935 0.676413
\(370\) −3.76005 −0.195476
\(371\) 0.0933200 0.00484493
\(372\) 5.84226 0.302907
\(373\) −12.7238 −0.658815 −0.329408 0.944188i \(-0.606849\pi\)
−0.329408 + 0.944188i \(0.606849\pi\)
\(374\) −0.187077 −0.00967353
\(375\) −4.65684 −0.240478
\(376\) 3.63401 0.187410
\(377\) −4.79554 −0.246983
\(378\) −0.470254 −0.0241872
\(379\) −17.5973 −0.903914 −0.451957 0.892040i \(-0.649274\pi\)
−0.451957 + 0.892040i \(0.649274\pi\)
\(380\) −2.86001 −0.146715
\(381\) 15.1707 0.777216
\(382\) 0.396258 0.0202743
\(383\) −6.01438 −0.307321 −0.153660 0.988124i \(-0.549106\pi\)
−0.153660 + 0.988124i \(0.549106\pi\)
\(384\) 0.932148 0.0475685
\(385\) −0.0889621 −0.00453393
\(386\) 3.64510 0.185530
\(387\) −8.73028 −0.443785
\(388\) 10.6127 0.538779
\(389\) −24.6541 −1.25001 −0.625007 0.780619i \(-0.714904\pi\)
−0.625007 + 0.780619i \(0.714904\pi\)
\(390\) −0.929829 −0.0470837
\(391\) 0.106083 0.00536484
\(392\) 6.99033 0.353065
\(393\) −0.932148 −0.0470206
\(394\) −26.3209 −1.32603
\(395\) −2.39887 −0.120700
\(396\) −3.75819 −0.188856
\(397\) −20.0548 −1.00652 −0.503261 0.864134i \(-0.667867\pi\)
−0.503261 + 0.864134i \(0.667867\pi\)
\(398\) 21.1271 1.05901
\(399\) −0.510852 −0.0255746
\(400\) −4.73674 −0.236837
\(401\) −34.0924 −1.70249 −0.851247 0.524765i \(-0.824153\pi\)
−0.851247 + 0.524765i \(0.824153\pi\)
\(402\) 8.68538 0.433188
\(403\) −12.1849 −0.606972
\(404\) 2.04141 0.101564
\(405\) −0.992773 −0.0493313
\(406\) 0.242521 0.0120361
\(407\) −12.9234 −0.640587
\(408\) 0.0988850 0.00489554
\(409\) 12.5220 0.619171 0.309585 0.950872i \(-0.399810\pi\)
0.309585 + 0.950872i \(0.399810\pi\)
\(410\) −3.12834 −0.154498
\(411\) 11.5136 0.567925
\(412\) −17.7356 −0.873770
\(413\) 1.49361 0.0734960
\(414\) 2.13110 0.104738
\(415\) −3.46306 −0.169995
\(416\) −1.94413 −0.0953187
\(417\) 1.89091 0.0925983
\(418\) −9.82989 −0.480795
\(419\) −24.1069 −1.17770 −0.588849 0.808243i \(-0.700419\pi\)
−0.588849 + 0.808243i \(0.700419\pi\)
\(420\) 0.0470235 0.00229451
\(421\) −14.3417 −0.698972 −0.349486 0.936942i \(-0.613644\pi\)
−0.349486 + 0.936942i \(0.613644\pi\)
\(422\) 5.02165 0.244450
\(423\) 7.74445 0.376548
\(424\) −0.949157 −0.0460951
\(425\) −0.502487 −0.0243742
\(426\) 10.8144 0.523959
\(427\) −0.595121 −0.0287999
\(428\) −13.2071 −0.638387
\(429\) −3.19584 −0.154297
\(430\) 2.10193 0.101364
\(431\) 20.7787 1.00088 0.500438 0.865773i \(-0.333172\pi\)
0.500438 + 0.865773i \(0.333172\pi\)
\(432\) 4.78294 0.230120
\(433\) −28.2502 −1.35762 −0.678810 0.734314i \(-0.737504\pi\)
−0.678810 + 0.734314i \(0.737504\pi\)
\(434\) 0.616216 0.0295793
\(435\) −1.17975 −0.0565648
\(436\) 8.85329 0.423996
\(437\) 5.57408 0.266645
\(438\) 2.99907 0.143301
\(439\) −11.0153 −0.525731 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(440\) 0.904833 0.0431362
\(441\) 14.8971 0.709386
\(442\) −0.206239 −0.00980978
\(443\) 5.22423 0.248211 0.124105 0.992269i \(-0.460394\pi\)
0.124105 + 0.992269i \(0.460394\pi\)
\(444\) 6.83102 0.324186
\(445\) 3.91409 0.185546
\(446\) 2.98097 0.141153
\(447\) −12.2598 −0.579866
\(448\) 0.0983188 0.00464513
\(449\) −40.2241 −1.89829 −0.949147 0.314833i \(-0.898052\pi\)
−0.949147 + 0.314833i \(0.898052\pi\)
\(450\) −10.0945 −0.475858
\(451\) −10.7522 −0.506300
\(452\) −3.21901 −0.151409
\(453\) −8.02269 −0.376939
\(454\) 27.8779 1.30837
\(455\) −0.0980743 −0.00459779
\(456\) 5.19587 0.243319
\(457\) 9.25575 0.432966 0.216483 0.976286i \(-0.430541\pi\)
0.216483 + 0.976286i \(0.430541\pi\)
\(458\) −8.67574 −0.405391
\(459\) 0.507389 0.0236829
\(460\) −0.513090 −0.0239229
\(461\) 20.0758 0.935023 0.467511 0.883987i \(-0.345151\pi\)
0.467511 + 0.883987i \(0.345151\pi\)
\(462\) 0.161621 0.00751927
\(463\) 13.5756 0.630914 0.315457 0.948940i \(-0.397842\pi\)
0.315457 + 0.948940i \(0.397842\pi\)
\(464\) −2.46668 −0.114513
\(465\) −2.99761 −0.139011
\(466\) −2.48734 −0.115224
\(467\) 38.9289 1.80141 0.900707 0.434427i \(-0.143049\pi\)
0.900707 + 0.434427i \(0.143049\pi\)
\(468\) −4.14313 −0.191516
\(469\) 0.916096 0.0423014
\(470\) −1.86457 −0.0860064
\(471\) −7.07654 −0.326070
\(472\) −15.1915 −0.699247
\(473\) 7.22436 0.332176
\(474\) 4.35811 0.200174
\(475\) −26.4030 −1.21145
\(476\) 0.0104300 0.000478056 0
\(477\) −2.02275 −0.0926153
\(478\) −10.8334 −0.495510
\(479\) −10.4185 −0.476034 −0.238017 0.971261i \(-0.576497\pi\)
−0.238017 + 0.971261i \(0.576497\pi\)
\(480\) −0.478276 −0.0218302
\(481\) −14.2471 −0.649610
\(482\) 30.2691 1.37872
\(483\) −0.0916477 −0.00417011
\(484\) −7.89007 −0.358640
\(485\) −5.44527 −0.247257
\(486\) 16.1524 0.732689
\(487\) −12.3536 −0.559797 −0.279898 0.960030i \(-0.590301\pi\)
−0.279898 + 0.960030i \(0.590301\pi\)
\(488\) 6.05297 0.274005
\(489\) 6.58937 0.297982
\(490\) −3.58667 −0.162029
\(491\) −2.11026 −0.0952345 −0.0476173 0.998866i \(-0.515163\pi\)
−0.0476173 + 0.998866i \(0.515163\pi\)
\(492\) 5.68337 0.256226
\(493\) −0.261673 −0.0117851
\(494\) −10.8367 −0.487568
\(495\) 1.92829 0.0866702
\(496\) −6.26753 −0.281420
\(497\) 1.14065 0.0511654
\(498\) 6.29145 0.281927
\(499\) 13.5076 0.604682 0.302341 0.953200i \(-0.402232\pi\)
0.302341 + 0.953200i \(0.402232\pi\)
\(500\) 4.99582 0.223420
\(501\) −5.38733 −0.240688
\(502\) 16.4332 0.733451
\(503\) −24.2987 −1.08342 −0.541712 0.840564i \(-0.682224\pi\)
−0.541712 + 0.840564i \(0.682224\pi\)
\(504\) 0.209527 0.00933309
\(505\) −1.04743 −0.0466099
\(506\) −1.76350 −0.0783971
\(507\) 8.59474 0.381706
\(508\) −16.2749 −0.722084
\(509\) 6.59346 0.292250 0.146125 0.989266i \(-0.453320\pi\)
0.146125 + 0.989266i \(0.453320\pi\)
\(510\) −0.0507369 −0.00224667
\(511\) 0.316329 0.0139936
\(512\) −1.00000 −0.0441942
\(513\) 26.6605 1.17709
\(514\) 14.9307 0.658565
\(515\) 9.09995 0.400992
\(516\) −3.81864 −0.168106
\(517\) −6.40857 −0.281849
\(518\) 0.720505 0.0316572
\(519\) −10.3086 −0.452496
\(520\) 0.997513 0.0437438
\(521\) −9.01633 −0.395013 −0.197506 0.980302i \(-0.563284\pi\)
−0.197506 + 0.980302i \(0.563284\pi\)
\(522\) −5.25674 −0.230081
\(523\) −18.4767 −0.807931 −0.403965 0.914774i \(-0.632368\pi\)
−0.403965 + 0.914774i \(0.632368\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0.434111 0.0189462
\(526\) −15.7074 −0.684874
\(527\) −0.664878 −0.0289625
\(528\) −1.64384 −0.0715390
\(529\) 1.00000 0.0434783
\(530\) 0.487003 0.0211540
\(531\) −32.3747 −1.40494
\(532\) 0.548037 0.0237604
\(533\) −11.8535 −0.513431
\(534\) −7.11086 −0.307717
\(535\) 6.77641 0.292970
\(536\) −9.31760 −0.402459
\(537\) 13.1927 0.569306
\(538\) −25.6443 −1.10560
\(539\) −12.3274 −0.530980
\(540\) −2.45408 −0.105607
\(541\) −0.125397 −0.00539124 −0.00269562 0.999996i \(-0.500858\pi\)
−0.00269562 + 0.999996i \(0.500858\pi\)
\(542\) 17.1604 0.737101
\(543\) −3.22760 −0.138510
\(544\) −0.106083 −0.00454827
\(545\) −4.54254 −0.194581
\(546\) 0.178175 0.00762518
\(547\) 24.9486 1.06673 0.533363 0.845887i \(-0.320928\pi\)
0.533363 + 0.845887i \(0.320928\pi\)
\(548\) −12.3517 −0.527639
\(549\) 12.8995 0.550537
\(550\) 8.35323 0.356183
\(551\) −13.7495 −0.585747
\(552\) 0.932148 0.0396748
\(553\) 0.459674 0.0195473
\(554\) 30.4299 1.29284
\(555\) −3.50492 −0.148776
\(556\) −2.02855 −0.0860298
\(557\) −34.5318 −1.46316 −0.731579 0.681757i \(-0.761216\pi\)
−0.731579 + 0.681757i \(0.761216\pi\)
\(558\) −13.3567 −0.565436
\(559\) 7.96433 0.336855
\(560\) −0.0504464 −0.00213175
\(561\) −0.174383 −0.00736248
\(562\) −6.51695 −0.274901
\(563\) 8.18846 0.345102 0.172551 0.985001i \(-0.444799\pi\)
0.172551 + 0.985001i \(0.444799\pi\)
\(564\) 3.38744 0.142637
\(565\) 1.65164 0.0694850
\(566\) −12.6219 −0.530539
\(567\) 0.190236 0.00798917
\(568\) −11.6016 −0.486792
\(569\) −31.6922 −1.32861 −0.664303 0.747463i \(-0.731272\pi\)
−0.664303 + 0.747463i \(0.731272\pi\)
\(570\) −2.66595 −0.111664
\(571\) 12.5688 0.525986 0.262993 0.964798i \(-0.415290\pi\)
0.262993 + 0.964798i \(0.415290\pi\)
\(572\) 3.42847 0.143351
\(573\) 0.369371 0.0154307
\(574\) 0.599457 0.0250208
\(575\) −4.73674 −0.197536
\(576\) −2.13110 −0.0887959
\(577\) 29.8320 1.24192 0.620962 0.783840i \(-0.286742\pi\)
0.620962 + 0.783840i \(0.286742\pi\)
\(578\) 16.9887 0.706639
\(579\) 3.39777 0.141206
\(580\) 1.26563 0.0525523
\(581\) 0.663595 0.0275305
\(582\) 9.89261 0.410062
\(583\) 1.67384 0.0693232
\(584\) −3.21738 −0.133136
\(585\) 2.12580 0.0878910
\(586\) 15.3701 0.634934
\(587\) 12.0481 0.497279 0.248640 0.968596i \(-0.420017\pi\)
0.248640 + 0.968596i \(0.420017\pi\)
\(588\) 6.51602 0.268716
\(589\) −34.9357 −1.43950
\(590\) 7.79462 0.320900
\(591\) −24.5349 −1.00923
\(592\) −7.32825 −0.301189
\(593\) −31.5007 −1.29358 −0.646789 0.762669i \(-0.723889\pi\)
−0.646789 + 0.762669i \(0.723889\pi\)
\(594\) −8.43471 −0.346080
\(595\) −0.00535150 −0.000219390 0
\(596\) 13.1522 0.538733
\(597\) 19.6936 0.806006
\(598\) −1.94413 −0.0795013
\(599\) −42.6727 −1.74356 −0.871780 0.489898i \(-0.837034\pi\)
−0.871780 + 0.489898i \(0.837034\pi\)
\(600\) −4.41534 −0.180256
\(601\) −0.490616 −0.0200126 −0.0100063 0.999950i \(-0.503185\pi\)
−0.0100063 + 0.999950i \(0.503185\pi\)
\(602\) −0.402774 −0.0164158
\(603\) −19.8567 −0.808629
\(604\) 8.60668 0.350201
\(605\) 4.04832 0.164587
\(606\) 1.90290 0.0773000
\(607\) −1.21928 −0.0494892 −0.0247446 0.999694i \(-0.507877\pi\)
−0.0247446 + 0.999694i \(0.507877\pi\)
\(608\) −5.57408 −0.226059
\(609\) 0.226065 0.00916063
\(610\) −3.10572 −0.125747
\(611\) −7.06499 −0.285819
\(612\) −0.226073 −0.00913848
\(613\) −30.8954 −1.24786 −0.623928 0.781482i \(-0.714464\pi\)
−0.623928 + 0.781482i \(0.714464\pi\)
\(614\) −15.7267 −0.634678
\(615\) −2.91608 −0.117588
\(616\) −0.173385 −0.00698588
\(617\) 17.8401 0.718216 0.359108 0.933296i \(-0.383081\pi\)
0.359108 + 0.933296i \(0.383081\pi\)
\(618\) −16.5322 −0.665022
\(619\) 16.4586 0.661526 0.330763 0.943714i \(-0.392694\pi\)
0.330763 + 0.943714i \(0.392694\pi\)
\(620\) 3.21581 0.129150
\(621\) 4.78294 0.191933
\(622\) 34.4984 1.38326
\(623\) −0.750022 −0.0300490
\(624\) −1.81222 −0.0725467
\(625\) 21.1204 0.844816
\(626\) 4.63612 0.185297
\(627\) −9.16291 −0.365931
\(628\) 7.59165 0.302940
\(629\) −0.777403 −0.0309971
\(630\) −0.107506 −0.00428316
\(631\) −29.7876 −1.18583 −0.592913 0.805266i \(-0.702022\pi\)
−0.592913 + 0.805266i \(0.702022\pi\)
\(632\) −4.67534 −0.185975
\(633\) 4.68092 0.186050
\(634\) −21.8326 −0.867082
\(635\) 8.35051 0.331380
\(636\) −0.884754 −0.0350828
\(637\) −13.5901 −0.538460
\(638\) 4.34998 0.172218
\(639\) −24.7242 −0.978072
\(640\) 0.513090 0.0202817
\(641\) 3.80678 0.150359 0.0751795 0.997170i \(-0.476047\pi\)
0.0751795 + 0.997170i \(0.476047\pi\)
\(642\) −12.3109 −0.485874
\(643\) −26.2794 −1.03636 −0.518179 0.855272i \(-0.673390\pi\)
−0.518179 + 0.855272i \(0.673390\pi\)
\(644\) 0.0983188 0.00387430
\(645\) 1.95931 0.0771476
\(646\) −0.591315 −0.0232650
\(647\) 31.8279 1.25128 0.625642 0.780110i \(-0.284837\pi\)
0.625642 + 0.780110i \(0.284837\pi\)
\(648\) −1.93489 −0.0760097
\(649\) 26.7903 1.05161
\(650\) 9.20883 0.361200
\(651\) 0.574405 0.0225127
\(652\) −7.06902 −0.276844
\(653\) 36.8484 1.44199 0.720994 0.692941i \(-0.243685\pi\)
0.720994 + 0.692941i \(0.243685\pi\)
\(654\) 8.25258 0.322701
\(655\) −0.513090 −0.0200481
\(656\) −6.09707 −0.238051
\(657\) −6.85655 −0.267500
\(658\) 0.357292 0.0139287
\(659\) −38.4786 −1.49891 −0.749456 0.662054i \(-0.769685\pi\)
−0.749456 + 0.662054i \(0.769685\pi\)
\(660\) 0.843438 0.0328308
\(661\) −21.2349 −0.825940 −0.412970 0.910745i \(-0.635509\pi\)
−0.412970 + 0.910745i \(0.635509\pi\)
\(662\) −6.75135 −0.262399
\(663\) −0.192245 −0.00746618
\(664\) −6.74942 −0.261928
\(665\) −0.281192 −0.0109042
\(666\) −15.6172 −0.605156
\(667\) −2.46668 −0.0955102
\(668\) 5.77948 0.223615
\(669\) 2.77871 0.107431
\(670\) 4.78077 0.184697
\(671\) −10.6744 −0.412081
\(672\) 0.0916477 0.00353539
\(673\) 11.7931 0.454589 0.227294 0.973826i \(-0.427012\pi\)
0.227294 + 0.973826i \(0.427012\pi\)
\(674\) 7.77881 0.299628
\(675\) −22.6556 −0.872013
\(676\) −9.22036 −0.354629
\(677\) 35.9761 1.38267 0.691336 0.722533i \(-0.257022\pi\)
0.691336 + 0.722533i \(0.257022\pi\)
\(678\) −3.00059 −0.115237
\(679\) 1.04343 0.0400431
\(680\) 0.0544301 0.00208730
\(681\) 25.9863 0.995798
\(682\) 11.0528 0.423233
\(683\) 3.99954 0.153038 0.0765192 0.997068i \(-0.475619\pi\)
0.0765192 + 0.997068i \(0.475619\pi\)
\(684\) −11.8789 −0.454202
\(685\) 6.33754 0.242145
\(686\) 1.37551 0.0525173
\(687\) −8.08708 −0.308541
\(688\) 4.09661 0.156182
\(689\) 1.84528 0.0702997
\(690\) −0.478276 −0.0182076
\(691\) 15.8844 0.604272 0.302136 0.953265i \(-0.402300\pi\)
0.302136 + 0.953265i \(0.402300\pi\)
\(692\) 11.0590 0.420398
\(693\) −0.369501 −0.0140362
\(694\) −3.94396 −0.149711
\(695\) 1.04083 0.0394809
\(696\) −2.29931 −0.0871551
\(697\) −0.646795 −0.0244991
\(698\) 17.2435 0.652676
\(699\) −2.31857 −0.0876964
\(700\) −0.465711 −0.0176022
\(701\) 0.670179 0.0253123 0.0126562 0.999920i \(-0.495971\pi\)
0.0126562 + 0.999920i \(0.495971\pi\)
\(702\) −9.29866 −0.350955
\(703\) −40.8483 −1.54062
\(704\) 1.76350 0.0664643
\(705\) −1.73806 −0.0654591
\(706\) 2.61370 0.0983678
\(707\) 0.200709 0.00754845
\(708\) −14.1608 −0.532194
\(709\) 27.8747 1.04685 0.523427 0.852070i \(-0.324653\pi\)
0.523427 + 0.852070i \(0.324653\pi\)
\(710\) 5.95266 0.223399
\(711\) −9.96362 −0.373665
\(712\) 7.62846 0.285889
\(713\) −6.26753 −0.234721
\(714\) 0.00972226 0.000363846 0
\(715\) −1.75911 −0.0657870
\(716\) −14.1530 −0.528922
\(717\) −10.0984 −0.377131
\(718\) −0.221086 −0.00825084
\(719\) −37.7795 −1.40894 −0.704469 0.709734i \(-0.748815\pi\)
−0.704469 + 0.709734i \(0.748815\pi\)
\(720\) 1.09345 0.0407503
\(721\) −1.74374 −0.0649404
\(722\) −12.0704 −0.449214
\(723\) 28.2152 1.04934
\(724\) 3.46254 0.128684
\(725\) 11.6840 0.433933
\(726\) −7.35472 −0.272959
\(727\) −32.1529 −1.19249 −0.596243 0.802804i \(-0.703341\pi\)
−0.596243 + 0.802804i \(0.703341\pi\)
\(728\) −0.191144 −0.00708428
\(729\) 9.25179 0.342659
\(730\) 1.65080 0.0610990
\(731\) 0.434580 0.0160735
\(732\) 5.64227 0.208544
\(733\) 8.83362 0.326277 0.163139 0.986603i \(-0.447838\pi\)
0.163139 + 0.986603i \(0.447838\pi\)
\(734\) 2.70938 0.100005
\(735\) −3.34331 −0.123320
\(736\) −1.00000 −0.0368605
\(737\) 16.4316 0.605265
\(738\) −12.9935 −0.478296
\(739\) −32.1232 −1.18167 −0.590835 0.806793i \(-0.701201\pi\)
−0.590835 + 0.806793i \(0.701201\pi\)
\(740\) 3.76005 0.138222
\(741\) −10.1014 −0.371086
\(742\) −0.0933200 −0.00342588
\(743\) −0.361862 −0.0132754 −0.00663772 0.999978i \(-0.502113\pi\)
−0.00663772 + 0.999978i \(0.502113\pi\)
\(744\) −5.84226 −0.214188
\(745\) −6.74824 −0.247236
\(746\) 12.7238 0.465853
\(747\) −14.3837 −0.526271
\(748\) 0.187077 0.00684022
\(749\) −1.29850 −0.0474462
\(750\) 4.65684 0.170044
\(751\) 4.90666 0.179047 0.0895233 0.995985i \(-0.471466\pi\)
0.0895233 + 0.995985i \(0.471466\pi\)
\(752\) −3.63401 −0.132519
\(753\) 15.3182 0.558226
\(754\) 4.79554 0.174643
\(755\) −4.41600 −0.160715
\(756\) 0.470254 0.0171030
\(757\) −11.8860 −0.432005 −0.216003 0.976393i \(-0.569302\pi\)
−0.216003 + 0.976393i \(0.569302\pi\)
\(758\) 17.5973 0.639164
\(759\) −1.64384 −0.0596677
\(760\) 2.86001 0.103743
\(761\) 24.8316 0.900143 0.450072 0.892993i \(-0.351398\pi\)
0.450072 + 0.892993i \(0.351398\pi\)
\(762\) −15.1707 −0.549575
\(763\) 0.870446 0.0315122
\(764\) −0.396258 −0.0143361
\(765\) 0.115996 0.00419384
\(766\) 6.01438 0.217309
\(767\) 29.5343 1.06642
\(768\) −0.932148 −0.0336360
\(769\) 7.65492 0.276043 0.138022 0.990429i \(-0.455926\pi\)
0.138022 + 0.990429i \(0.455926\pi\)
\(770\) 0.0889621 0.00320597
\(771\) 13.9176 0.501231
\(772\) −3.64510 −0.131190
\(773\) 39.9471 1.43680 0.718399 0.695632i \(-0.244875\pi\)
0.718399 + 0.695632i \(0.244875\pi\)
\(774\) 8.73028 0.313803
\(775\) 29.6877 1.06641
\(776\) −10.6127 −0.380974
\(777\) 0.671618 0.0240941
\(778\) 24.6541 0.883893
\(779\) −33.9856 −1.21766
\(780\) 0.929829 0.0332932
\(781\) 20.4594 0.732094
\(782\) −0.106083 −0.00379352
\(783\) −11.7980 −0.421626
\(784\) −6.99033 −0.249655
\(785\) −3.89520 −0.139026
\(786\) 0.932148 0.0332486
\(787\) −8.27965 −0.295138 −0.147569 0.989052i \(-0.547145\pi\)
−0.147569 + 0.989052i \(0.547145\pi\)
\(788\) 26.3209 0.937642
\(789\) −14.6416 −0.521255
\(790\) 2.39887 0.0853479
\(791\) −0.316489 −0.0112531
\(792\) 3.75819 0.133542
\(793\) −11.7678 −0.417885
\(794\) 20.0548 0.711719
\(795\) 0.453958 0.0161002
\(796\) −21.1271 −0.748831
\(797\) −14.4902 −0.513268 −0.256634 0.966509i \(-0.582614\pi\)
−0.256634 + 0.966509i \(0.582614\pi\)
\(798\) 0.510852 0.0180840
\(799\) −0.385507 −0.0136382
\(800\) 4.73674 0.167469
\(801\) 16.2570 0.574414
\(802\) 34.0924 1.20384
\(803\) 5.67384 0.200225
\(804\) −8.68538 −0.306310
\(805\) −0.0504464 −0.00177800
\(806\) 12.1849 0.429194
\(807\) −23.9042 −0.841469
\(808\) −2.04141 −0.0718167
\(809\) 18.9987 0.667960 0.333980 0.942580i \(-0.391608\pi\)
0.333980 + 0.942580i \(0.391608\pi\)
\(810\) 0.992773 0.0348825
\(811\) −43.9705 −1.54401 −0.772007 0.635614i \(-0.780747\pi\)
−0.772007 + 0.635614i \(0.780747\pi\)
\(812\) −0.242521 −0.00851082
\(813\) 15.9960 0.561004
\(814\) 12.9234 0.452964
\(815\) 3.62704 0.127050
\(816\) −0.0988850 −0.00346167
\(817\) 22.8348 0.798889
\(818\) −12.5220 −0.437820
\(819\) −0.407348 −0.0142339
\(820\) 3.12834 0.109247
\(821\) −31.2007 −1.08891 −0.544456 0.838790i \(-0.683264\pi\)
−0.544456 + 0.838790i \(0.683264\pi\)
\(822\) −11.5136 −0.401584
\(823\) −15.0831 −0.525764 −0.262882 0.964828i \(-0.584673\pi\)
−0.262882 + 0.964828i \(0.584673\pi\)
\(824\) 17.7356 0.617849
\(825\) 7.78645 0.271089
\(826\) −1.49361 −0.0519695
\(827\) 29.7431 1.03427 0.517135 0.855904i \(-0.326999\pi\)
0.517135 + 0.855904i \(0.326999\pi\)
\(828\) −2.13110 −0.0740609
\(829\) −16.9184 −0.587600 −0.293800 0.955867i \(-0.594920\pi\)
−0.293800 + 0.955867i \(0.594920\pi\)
\(830\) 3.46306 0.120204
\(831\) 28.3651 0.983976
\(832\) 1.94413 0.0674005
\(833\) −0.741555 −0.0256934
\(834\) −1.89091 −0.0654769
\(835\) −2.96540 −0.102622
\(836\) 9.82989 0.339974
\(837\) −29.9772 −1.03617
\(838\) 24.1069 0.832758
\(839\) 41.7923 1.44283 0.721416 0.692502i \(-0.243492\pi\)
0.721416 + 0.692502i \(0.243492\pi\)
\(840\) −0.0470235 −0.00162246
\(841\) −22.9155 −0.790189
\(842\) 14.3417 0.494248
\(843\) −6.07476 −0.209226
\(844\) −5.02165 −0.172852
\(845\) 4.73088 0.162747
\(846\) −7.74445 −0.266260
\(847\) −0.775743 −0.0266548
\(848\) 0.949157 0.0325942
\(849\) −11.7655 −0.403791
\(850\) 0.502487 0.0172352
\(851\) −7.32825 −0.251209
\(852\) −10.8144 −0.370495
\(853\) 16.6582 0.570364 0.285182 0.958473i \(-0.407946\pi\)
0.285182 + 0.958473i \(0.407946\pi\)
\(854\) 0.595121 0.0203646
\(855\) 6.09496 0.208443
\(856\) 13.2071 0.451408
\(857\) −24.2190 −0.827306 −0.413653 0.910435i \(-0.635747\pi\)
−0.413653 + 0.910435i \(0.635747\pi\)
\(858\) 3.19584 0.109104
\(859\) −36.8280 −1.25656 −0.628278 0.777989i \(-0.716240\pi\)
−0.628278 + 0.777989i \(0.716240\pi\)
\(860\) −2.10193 −0.0716751
\(861\) 0.558782 0.0190433
\(862\) −20.7787 −0.707726
\(863\) 11.8916 0.404795 0.202397 0.979303i \(-0.435127\pi\)
0.202397 + 0.979303i \(0.435127\pi\)
\(864\) −4.78294 −0.162719
\(865\) −5.67424 −0.192930
\(866\) 28.2502 0.959983
\(867\) 15.8360 0.537820
\(868\) −0.616216 −0.0209157
\(869\) 8.24495 0.279691
\(870\) 1.17975 0.0399974
\(871\) 18.1146 0.613790
\(872\) −8.85329 −0.299810
\(873\) −22.6167 −0.765461
\(874\) −5.57408 −0.188546
\(875\) 0.491183 0.0166050
\(876\) −2.99907 −0.101329
\(877\) 19.3786 0.654369 0.327184 0.944961i \(-0.393900\pi\)
0.327184 + 0.944961i \(0.393900\pi\)
\(878\) 11.0153 0.371748
\(879\) 14.3272 0.483245
\(880\) −0.904833 −0.0305019
\(881\) −25.5138 −0.859582 −0.429791 0.902928i \(-0.641413\pi\)
−0.429791 + 0.902928i \(0.641413\pi\)
\(882\) −14.8971 −0.501612
\(883\) −13.8350 −0.465584 −0.232792 0.972527i \(-0.574786\pi\)
−0.232792 + 0.972527i \(0.574786\pi\)
\(884\) 0.206239 0.00693656
\(885\) 7.26574 0.244235
\(886\) −5.22423 −0.175512
\(887\) 7.10366 0.238517 0.119259 0.992863i \(-0.461948\pi\)
0.119259 + 0.992863i \(0.461948\pi\)
\(888\) −6.83102 −0.229234
\(889\) −1.60013 −0.0536668
\(890\) −3.91409 −0.131201
\(891\) 3.41218 0.114312
\(892\) −2.98097 −0.0998103
\(893\) −20.2563 −0.677851
\(894\) 12.2598 0.410027
\(895\) 7.26176 0.242734
\(896\) −0.0983188 −0.00328460
\(897\) −1.81222 −0.0605081
\(898\) 40.2241 1.34230
\(899\) 15.4600 0.515619
\(900\) 10.0945 0.336482
\(901\) 0.100689 0.00335445
\(902\) 10.7522 0.358008
\(903\) −0.375445 −0.0124940
\(904\) 3.21901 0.107063
\(905\) −1.77659 −0.0590560
\(906\) 8.02269 0.266536
\(907\) 8.42017 0.279587 0.139794 0.990181i \(-0.455356\pi\)
0.139794 + 0.990181i \(0.455356\pi\)
\(908\) −27.8779 −0.925160
\(909\) −4.35046 −0.144296
\(910\) 0.0980743 0.00325113
\(911\) 11.7259 0.388497 0.194248 0.980952i \(-0.437773\pi\)
0.194248 + 0.980952i \(0.437773\pi\)
\(912\) −5.19587 −0.172052
\(913\) 11.9026 0.393918
\(914\) −9.25575 −0.306153
\(915\) −2.89499 −0.0957054
\(916\) 8.67574 0.286655
\(917\) 0.0983188 0.00324677
\(918\) −0.507389 −0.0167463
\(919\) −45.1929 −1.49077 −0.745387 0.666632i \(-0.767735\pi\)
−0.745387 + 0.666632i \(0.767735\pi\)
\(920\) 0.513090 0.0169161
\(921\) −14.6596 −0.483051
\(922\) −20.0758 −0.661161
\(923\) 22.5550 0.742406
\(924\) −0.161621 −0.00531693
\(925\) 34.7120 1.14132
\(926\) −13.5756 −0.446123
\(927\) 37.7963 1.24139
\(928\) 2.46668 0.0809727
\(929\) −44.0576 −1.44548 −0.722742 0.691118i \(-0.757118\pi\)
−0.722742 + 0.691118i \(0.757118\pi\)
\(930\) 2.99761 0.0982954
\(931\) −38.9647 −1.27702
\(932\) 2.48734 0.0814756
\(933\) 32.1576 1.05279
\(934\) −38.9289 −1.27379
\(935\) −0.0959874 −0.00313912
\(936\) 4.14313 0.135423
\(937\) 17.9028 0.584859 0.292430 0.956287i \(-0.405536\pi\)
0.292430 + 0.956287i \(0.405536\pi\)
\(938\) −0.916096 −0.0299116
\(939\) 4.32155 0.141028
\(940\) 1.86457 0.0608157
\(941\) 12.1445 0.395900 0.197950 0.980212i \(-0.436572\pi\)
0.197950 + 0.980212i \(0.436572\pi\)
\(942\) 7.07654 0.230566
\(943\) −6.09707 −0.198548
\(944\) 15.1915 0.494442
\(945\) −0.241282 −0.00784891
\(946\) −7.22436 −0.234884
\(947\) 40.1063 1.30328 0.651640 0.758528i \(-0.274081\pi\)
0.651640 + 0.758528i \(0.274081\pi\)
\(948\) −4.35811 −0.141545
\(949\) 6.25499 0.203046
\(950\) 26.4030 0.856626
\(951\) −20.3512 −0.659932
\(952\) −0.0104300 −0.000338037 0
\(953\) 19.1677 0.620902 0.310451 0.950589i \(-0.399520\pi\)
0.310451 + 0.950589i \(0.399520\pi\)
\(954\) 2.02275 0.0654889
\(955\) 0.203316 0.00657914
\(956\) 10.8334 0.350379
\(957\) 4.05483 0.131074
\(958\) 10.4185 0.336607
\(959\) −1.21441 −0.0392152
\(960\) 0.478276 0.0154363
\(961\) 8.28193 0.267159
\(962\) 14.2471 0.459344
\(963\) 28.1456 0.906978
\(964\) −30.2691 −0.974901
\(965\) 1.87026 0.0602058
\(966\) 0.0916477 0.00294872
\(967\) 41.4739 1.33371 0.666856 0.745187i \(-0.267640\pi\)
0.666856 + 0.745187i \(0.267640\pi\)
\(968\) 7.89007 0.253597
\(969\) −0.551193 −0.0177069
\(970\) 5.44527 0.174837
\(971\) −12.3194 −0.395348 −0.197674 0.980268i \(-0.563339\pi\)
−0.197674 + 0.980268i \(0.563339\pi\)
\(972\) −16.1524 −0.518090
\(973\) −0.199445 −0.00639391
\(974\) 12.3536 0.395836
\(975\) 8.58399 0.274908
\(976\) −6.05297 −0.193751
\(977\) 2.09975 0.0671769 0.0335885 0.999436i \(-0.489306\pi\)
0.0335885 + 0.999436i \(0.489306\pi\)
\(978\) −6.58937 −0.210705
\(979\) −13.4528 −0.429953
\(980\) 3.58667 0.114572
\(981\) −18.8673 −0.602385
\(982\) 2.11026 0.0673410
\(983\) 27.1713 0.866629 0.433314 0.901243i \(-0.357344\pi\)
0.433314 + 0.901243i \(0.357344\pi\)
\(984\) −5.68337 −0.181179
\(985\) −13.5050 −0.430304
\(986\) 0.261673 0.00833335
\(987\) 0.333049 0.0106011
\(988\) 10.8367 0.344762
\(989\) 4.09661 0.130265
\(990\) −1.92829 −0.0612851
\(991\) −39.5928 −1.25771 −0.628854 0.777524i \(-0.716476\pi\)
−0.628854 + 0.777524i \(0.716476\pi\)
\(992\) 6.26753 0.198994
\(993\) −6.29325 −0.199710
\(994\) −1.14065 −0.0361794
\(995\) 10.8401 0.343655
\(996\) −6.29145 −0.199352
\(997\) −7.35412 −0.232907 −0.116454 0.993196i \(-0.537153\pi\)
−0.116454 + 0.993196i \(0.537153\pi\)
\(998\) −13.5076 −0.427575
\(999\) −35.0506 −1.10895
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 \(a_p\))