Properties

Label 4015.2.a.h.1.9
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.82541 q^{2}\) \(+0.572536 q^{3}\) \(+1.33213 q^{4}\) \(+1.00000 q^{5}\) \(-1.04512 q^{6}\) \(-3.97729 q^{7}\) \(+1.21914 q^{8}\) \(-2.67220 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.82541 q^{2}\) \(+0.572536 q^{3}\) \(+1.33213 q^{4}\) \(+1.00000 q^{5}\) \(-1.04512 q^{6}\) \(-3.97729 q^{7}\) \(+1.21914 q^{8}\) \(-2.67220 q^{9}\) \(-1.82541 q^{10}\) \(+1.00000 q^{11}\) \(+0.762693 q^{12}\) \(-5.95658 q^{13}\) \(+7.26019 q^{14}\) \(+0.572536 q^{15}\) \(-4.88969 q^{16}\) \(+0.0624446 q^{17}\) \(+4.87787 q^{18}\) \(+7.47082 q^{19}\) \(+1.33213 q^{20}\) \(-2.27714 q^{21}\) \(-1.82541 q^{22}\) \(-4.78206 q^{23}\) \(+0.698000 q^{24}\) \(+1.00000 q^{25}\) \(+10.8732 q^{26}\) \(-3.24754 q^{27}\) \(-5.29826 q^{28}\) \(+0.732323 q^{29}\) \(-1.04512 q^{30}\) \(+2.17635 q^{31}\) \(+6.48743 q^{32}\) \(+0.572536 q^{33}\) \(-0.113987 q^{34}\) \(-3.97729 q^{35}\) \(-3.55972 q^{36}\) \(-6.76150 q^{37}\) \(-13.6373 q^{38}\) \(-3.41036 q^{39}\) \(+1.21914 q^{40}\) \(-7.30658 q^{41}\) \(+4.15672 q^{42}\) \(-0.257853 q^{43}\) \(+1.33213 q^{44}\) \(-2.67220 q^{45}\) \(+8.72923 q^{46}\) \(+4.16410 q^{47}\) \(-2.79952 q^{48}\) \(+8.81880 q^{49}\) \(-1.82541 q^{50}\) \(+0.0357518 q^{51}\) \(-7.93494 q^{52}\) \(-10.8555 q^{53}\) \(+5.92810 q^{54}\) \(+1.00000 q^{55}\) \(-4.84886 q^{56}\) \(+4.27732 q^{57}\) \(-1.33679 q^{58}\) \(-2.87196 q^{59}\) \(+0.762693 q^{60}\) \(-2.48748 q^{61}\) \(-3.97273 q^{62}\) \(+10.6281 q^{63}\) \(-2.06285 q^{64}\) \(-5.95658 q^{65}\) \(-1.04512 q^{66}\) \(+6.77358 q^{67}\) \(+0.0831843 q^{68}\) \(-2.73790 q^{69}\) \(+7.26019 q^{70}\) \(-11.3027 q^{71}\) \(-3.25778 q^{72}\) \(+1.00000 q^{73}\) \(+12.3425 q^{74}\) \(+0.572536 q^{75}\) \(+9.95211 q^{76}\) \(-3.97729 q^{77}\) \(+6.22531 q^{78}\) \(+16.8072 q^{79}\) \(-4.88969 q^{80}\) \(+6.15727 q^{81}\) \(+13.3375 q^{82}\) \(+4.36026 q^{83}\) \(-3.03345 q^{84}\) \(+0.0624446 q^{85}\) \(+0.470688 q^{86}\) \(+0.419281 q^{87}\) \(+1.21914 q^{88}\) \(-7.39881 q^{89}\) \(+4.87787 q^{90}\) \(+23.6910 q^{91}\) \(-6.37033 q^{92}\) \(+1.24604 q^{93}\) \(-7.60119 q^{94}\) \(+7.47082 q^{95}\) \(+3.71429 q^{96}\) \(-6.04749 q^{97}\) \(-16.0979 q^{98}\) \(-2.67220 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82541 −1.29076 −0.645381 0.763861i \(-0.723301\pi\)
−0.645381 + 0.763861i \(0.723301\pi\)
\(3\) 0.572536 0.330554 0.165277 0.986247i \(-0.447148\pi\)
0.165277 + 0.986247i \(0.447148\pi\)
\(4\) 1.33213 0.666065
\(5\) 1.00000 0.447214
\(6\) −1.04512 −0.426666
\(7\) −3.97729 −1.50327 −0.751636 0.659578i \(-0.770735\pi\)
−0.751636 + 0.659578i \(0.770735\pi\)
\(8\) 1.21914 0.431030
\(9\) −2.67220 −0.890734
\(10\) −1.82541 −0.577246
\(11\) 1.00000 0.301511
\(12\) 0.762693 0.220171
\(13\) −5.95658 −1.65206 −0.826028 0.563628i \(-0.809405\pi\)
−0.826028 + 0.563628i \(0.809405\pi\)
\(14\) 7.26019 1.94037
\(15\) 0.572536 0.147828
\(16\) −4.88969 −1.22242
\(17\) 0.0624446 0.0151450 0.00757252 0.999971i \(-0.497590\pi\)
0.00757252 + 0.999971i \(0.497590\pi\)
\(18\) 4.87787 1.14973
\(19\) 7.47082 1.71392 0.856962 0.515380i \(-0.172349\pi\)
0.856962 + 0.515380i \(0.172349\pi\)
\(20\) 1.33213 0.297873
\(21\) −2.27714 −0.496913
\(22\) −1.82541 −0.389179
\(23\) −4.78206 −0.997129 −0.498564 0.866853i \(-0.666139\pi\)
−0.498564 + 0.866853i \(0.666139\pi\)
\(24\) 0.698000 0.142479
\(25\) 1.00000 0.200000
\(26\) 10.8732 2.13241
\(27\) −3.24754 −0.624990
\(28\) −5.29826 −1.00128
\(29\) 0.732323 0.135989 0.0679945 0.997686i \(-0.478340\pi\)
0.0679945 + 0.997686i \(0.478340\pi\)
\(30\) −1.04512 −0.190811
\(31\) 2.17635 0.390883 0.195442 0.980715i \(-0.437386\pi\)
0.195442 + 0.980715i \(0.437386\pi\)
\(32\) 6.48743 1.14683
\(33\) 0.572536 0.0996658
\(34\) −0.113987 −0.0195486
\(35\) −3.97729 −0.672284
\(36\) −3.55972 −0.593287
\(37\) −6.76150 −1.11158 −0.555792 0.831322i \(-0.687585\pi\)
−0.555792 + 0.831322i \(0.687585\pi\)
\(38\) −13.6373 −2.21227
\(39\) −3.41036 −0.546094
\(40\) 1.21914 0.192762
\(41\) −7.30658 −1.14110 −0.570548 0.821264i \(-0.693269\pi\)
−0.570548 + 0.821264i \(0.693269\pi\)
\(42\) 4.15672 0.641396
\(43\) −0.257853 −0.0393222 −0.0196611 0.999807i \(-0.506259\pi\)
−0.0196611 + 0.999807i \(0.506259\pi\)
\(44\) 1.33213 0.200826
\(45\) −2.67220 −0.398348
\(46\) 8.72923 1.28706
\(47\) 4.16410 0.607396 0.303698 0.952768i \(-0.401779\pi\)
0.303698 + 0.952768i \(0.401779\pi\)
\(48\) −2.79952 −0.404077
\(49\) 8.81880 1.25983
\(50\) −1.82541 −0.258152
\(51\) 0.0357518 0.00500625
\(52\) −7.93494 −1.10038
\(53\) −10.8555 −1.49111 −0.745557 0.666442i \(-0.767816\pi\)
−0.745557 + 0.666442i \(0.767816\pi\)
\(54\) 5.92810 0.806713
\(55\) 1.00000 0.134840
\(56\) −4.84886 −0.647956
\(57\) 4.27732 0.566544
\(58\) −1.33679 −0.175529
\(59\) −2.87196 −0.373897 −0.186949 0.982370i \(-0.559860\pi\)
−0.186949 + 0.982370i \(0.559860\pi\)
\(60\) 0.762693 0.0984633
\(61\) −2.48748 −0.318489 −0.159245 0.987239i \(-0.550906\pi\)
−0.159245 + 0.987239i \(0.550906\pi\)
\(62\) −3.97273 −0.504537
\(63\) 10.6281 1.33902
\(64\) −2.06285 −0.257856
\(65\) −5.95658 −0.738822
\(66\) −1.04512 −0.128645
\(67\) 6.77358 0.827525 0.413762 0.910385i \(-0.364214\pi\)
0.413762 + 0.910385i \(0.364214\pi\)
\(68\) 0.0831843 0.0100876
\(69\) −2.73790 −0.329605
\(70\) 7.26019 0.867758
\(71\) −11.3027 −1.34139 −0.670694 0.741734i \(-0.734004\pi\)
−0.670694 + 0.741734i \(0.734004\pi\)
\(72\) −3.25778 −0.383933
\(73\) 1.00000 0.117041
\(74\) 12.3425 1.43479
\(75\) 0.572536 0.0661108
\(76\) 9.95211 1.14158
\(77\) −3.97729 −0.453254
\(78\) 6.22531 0.704877
\(79\) 16.8072 1.89095 0.945477 0.325689i \(-0.105596\pi\)
0.945477 + 0.325689i \(0.105596\pi\)
\(80\) −4.88969 −0.546684
\(81\) 6.15727 0.684141
\(82\) 13.3375 1.47288
\(83\) 4.36026 0.478601 0.239300 0.970946i \(-0.423082\pi\)
0.239300 + 0.970946i \(0.423082\pi\)
\(84\) −3.03345 −0.330976
\(85\) 0.0624446 0.00677307
\(86\) 0.470688 0.0507556
\(87\) 0.419281 0.0449517
\(88\) 1.21914 0.129960
\(89\) −7.39881 −0.784272 −0.392136 0.919907i \(-0.628264\pi\)
−0.392136 + 0.919907i \(0.628264\pi\)
\(90\) 4.87787 0.514173
\(91\) 23.6910 2.48349
\(92\) −6.37033 −0.664153
\(93\) 1.24604 0.129208
\(94\) −7.60119 −0.784003
\(95\) 7.47082 0.766490
\(96\) 3.71429 0.379088
\(97\) −6.04749 −0.614029 −0.307015 0.951705i \(-0.599330\pi\)
−0.307015 + 0.951705i \(0.599330\pi\)
\(98\) −16.0979 −1.62614
\(99\) −2.67220 −0.268566
\(100\) 1.33213 0.133213
\(101\) −0.909194 −0.0904682 −0.0452341 0.998976i \(-0.514403\pi\)
−0.0452341 + 0.998976i \(0.514403\pi\)
\(102\) −0.0652618 −0.00646188
\(103\) −4.44462 −0.437942 −0.218971 0.975731i \(-0.570270\pi\)
−0.218971 + 0.975731i \(0.570270\pi\)
\(104\) −7.26188 −0.712086
\(105\) −2.27714 −0.222226
\(106\) 19.8157 1.92467
\(107\) 0.851123 0.0822812 0.0411406 0.999153i \(-0.486901\pi\)
0.0411406 + 0.999153i \(0.486901\pi\)
\(108\) −4.32615 −0.416284
\(109\) 6.65383 0.637321 0.318661 0.947869i \(-0.396767\pi\)
0.318661 + 0.947869i \(0.396767\pi\)
\(110\) −1.82541 −0.174046
\(111\) −3.87120 −0.367438
\(112\) 19.4477 1.83763
\(113\) 19.6307 1.84670 0.923349 0.383963i \(-0.125441\pi\)
0.923349 + 0.383963i \(0.125441\pi\)
\(114\) −7.80786 −0.731273
\(115\) −4.78206 −0.445930
\(116\) 0.975550 0.0905775
\(117\) 15.9172 1.47154
\(118\) 5.24251 0.482612
\(119\) −0.248360 −0.0227671
\(120\) 0.698000 0.0637184
\(121\) 1.00000 0.0909091
\(122\) 4.54068 0.411094
\(123\) −4.18329 −0.377194
\(124\) 2.89918 0.260354
\(125\) 1.00000 0.0894427
\(126\) −19.4007 −1.72835
\(127\) −2.12927 −0.188942 −0.0944709 0.995528i \(-0.530116\pi\)
−0.0944709 + 0.995528i \(0.530116\pi\)
\(128\) −9.20930 −0.813995
\(129\) −0.147630 −0.0129981
\(130\) 10.8732 0.953643
\(131\) 18.4138 1.60882 0.804409 0.594075i \(-0.202482\pi\)
0.804409 + 0.594075i \(0.202482\pi\)
\(132\) 0.762693 0.0663839
\(133\) −29.7136 −2.57649
\(134\) −12.3646 −1.06814
\(135\) −3.24754 −0.279504
\(136\) 0.0761285 0.00652796
\(137\) 10.3749 0.886390 0.443195 0.896425i \(-0.353845\pi\)
0.443195 + 0.896425i \(0.353845\pi\)
\(138\) 4.99780 0.425441
\(139\) −3.80781 −0.322975 −0.161487 0.986875i \(-0.551629\pi\)
−0.161487 + 0.986875i \(0.551629\pi\)
\(140\) −5.29826 −0.447785
\(141\) 2.38410 0.200777
\(142\) 20.6322 1.73141
\(143\) −5.95658 −0.498114
\(144\) 13.0662 1.08885
\(145\) 0.732323 0.0608161
\(146\) −1.82541 −0.151072
\(147\) 5.04908 0.416441
\(148\) −9.00720 −0.740387
\(149\) −3.31198 −0.271328 −0.135664 0.990755i \(-0.543317\pi\)
−0.135664 + 0.990755i \(0.543317\pi\)
\(150\) −1.04512 −0.0853333
\(151\) 9.71443 0.790549 0.395275 0.918563i \(-0.370649\pi\)
0.395275 + 0.918563i \(0.370649\pi\)
\(152\) 9.10795 0.738752
\(153\) −0.166865 −0.0134902
\(154\) 7.26019 0.585042
\(155\) 2.17635 0.174808
\(156\) −4.54304 −0.363734
\(157\) 10.4139 0.831121 0.415561 0.909566i \(-0.363585\pi\)
0.415561 + 0.909566i \(0.363585\pi\)
\(158\) −30.6800 −2.44077
\(159\) −6.21515 −0.492894
\(160\) 6.48743 0.512876
\(161\) 19.0196 1.49896
\(162\) −11.2396 −0.883063
\(163\) −13.6348 −1.06796 −0.533979 0.845498i \(-0.679304\pi\)
−0.533979 + 0.845498i \(0.679304\pi\)
\(164\) −9.73332 −0.760045
\(165\) 0.572536 0.0445719
\(166\) −7.95927 −0.617760
\(167\) 25.1067 1.94282 0.971409 0.237413i \(-0.0762994\pi\)
0.971409 + 0.237413i \(0.0762994\pi\)
\(168\) −2.77615 −0.214184
\(169\) 22.4808 1.72929
\(170\) −0.113987 −0.00874241
\(171\) −19.9635 −1.52665
\(172\) −0.343494 −0.0261912
\(173\) 9.43336 0.717205 0.358602 0.933490i \(-0.383253\pi\)
0.358602 + 0.933490i \(0.383253\pi\)
\(174\) −0.765361 −0.0580219
\(175\) −3.97729 −0.300655
\(176\) −4.88969 −0.368574
\(177\) −1.64430 −0.123593
\(178\) 13.5059 1.01231
\(179\) −23.4176 −1.75032 −0.875158 0.483838i \(-0.839243\pi\)
−0.875158 + 0.483838i \(0.839243\pi\)
\(180\) −3.55972 −0.265326
\(181\) −4.13000 −0.306980 −0.153490 0.988150i \(-0.549051\pi\)
−0.153490 + 0.988150i \(0.549051\pi\)
\(182\) −43.2458 −3.20560
\(183\) −1.42417 −0.105278
\(184\) −5.82999 −0.429792
\(185\) −6.76150 −0.497115
\(186\) −2.27453 −0.166777
\(187\) 0.0624446 0.00456640
\(188\) 5.54712 0.404565
\(189\) 12.9164 0.939530
\(190\) −13.6373 −0.989356
\(191\) 14.7414 1.06665 0.533324 0.845911i \(-0.320943\pi\)
0.533324 + 0.845911i \(0.320943\pi\)
\(192\) −1.18106 −0.0852354
\(193\) −7.91989 −0.570086 −0.285043 0.958515i \(-0.592008\pi\)
−0.285043 + 0.958515i \(0.592008\pi\)
\(194\) 11.0392 0.792565
\(195\) −3.41036 −0.244221
\(196\) 11.7478 0.839128
\(197\) −19.2554 −1.37189 −0.685944 0.727655i \(-0.740610\pi\)
−0.685944 + 0.727655i \(0.740610\pi\)
\(198\) 4.87787 0.346655
\(199\) −6.98322 −0.495027 −0.247514 0.968884i \(-0.579614\pi\)
−0.247514 + 0.968884i \(0.579614\pi\)
\(200\) 1.21914 0.0862060
\(201\) 3.87812 0.273542
\(202\) 1.65965 0.116773
\(203\) −2.91266 −0.204428
\(204\) 0.0476261 0.00333449
\(205\) −7.30658 −0.510314
\(206\) 8.11327 0.565278
\(207\) 12.7786 0.888176
\(208\) 29.1258 2.01951
\(209\) 7.47082 0.516767
\(210\) 4.15672 0.286841
\(211\) −7.69662 −0.529857 −0.264929 0.964268i \(-0.585348\pi\)
−0.264929 + 0.964268i \(0.585348\pi\)
\(212\) −14.4609 −0.993179
\(213\) −6.47123 −0.443401
\(214\) −1.55365 −0.106205
\(215\) −0.257853 −0.0175854
\(216\) −3.95920 −0.269389
\(217\) −8.65595 −0.587604
\(218\) −12.1460 −0.822630
\(219\) 0.572536 0.0386884
\(220\) 1.33213 0.0898122
\(221\) −0.371956 −0.0250205
\(222\) 7.06654 0.474275
\(223\) −3.51587 −0.235440 −0.117720 0.993047i \(-0.537559\pi\)
−0.117720 + 0.993047i \(0.537559\pi\)
\(224\) −25.8023 −1.72399
\(225\) −2.67220 −0.178147
\(226\) −35.8341 −2.38365
\(227\) 19.5537 1.29782 0.648912 0.760863i \(-0.275224\pi\)
0.648912 + 0.760863i \(0.275224\pi\)
\(228\) 5.69794 0.377355
\(229\) 13.8127 0.912768 0.456384 0.889783i \(-0.349144\pi\)
0.456384 + 0.889783i \(0.349144\pi\)
\(230\) 8.72923 0.575589
\(231\) −2.27714 −0.149825
\(232\) 0.892802 0.0586153
\(233\) 10.8144 0.708473 0.354237 0.935156i \(-0.384741\pi\)
0.354237 + 0.935156i \(0.384741\pi\)
\(234\) −29.0554 −1.89941
\(235\) 4.16410 0.271636
\(236\) −3.82583 −0.249040
\(237\) 9.62271 0.625062
\(238\) 0.453359 0.0293869
\(239\) 11.5352 0.746150 0.373075 0.927801i \(-0.378303\pi\)
0.373075 + 0.927801i \(0.378303\pi\)
\(240\) −2.79952 −0.180709
\(241\) 20.2550 1.30474 0.652369 0.757902i \(-0.273775\pi\)
0.652369 + 0.757902i \(0.273775\pi\)
\(242\) −1.82541 −0.117342
\(243\) 13.2679 0.851135
\(244\) −3.31365 −0.212135
\(245\) 8.81880 0.563412
\(246\) 7.63622 0.486868
\(247\) −44.5005 −2.83150
\(248\) 2.65326 0.168482
\(249\) 2.49641 0.158203
\(250\) −1.82541 −0.115449
\(251\) 6.58326 0.415532 0.207766 0.978179i \(-0.433381\pi\)
0.207766 + 0.978179i \(0.433381\pi\)
\(252\) 14.1580 0.891872
\(253\) −4.78206 −0.300646
\(254\) 3.88679 0.243879
\(255\) 0.0357518 0.00223886
\(256\) 20.9365 1.30853
\(257\) 30.9555 1.93095 0.965475 0.260495i \(-0.0838858\pi\)
0.965475 + 0.260495i \(0.0838858\pi\)
\(258\) 0.269486 0.0167775
\(259\) 26.8924 1.67101
\(260\) −7.93494 −0.492104
\(261\) −1.95691 −0.121130
\(262\) −33.6127 −2.07660
\(263\) −22.2645 −1.37289 −0.686444 0.727182i \(-0.740829\pi\)
−0.686444 + 0.727182i \(0.740829\pi\)
\(264\) 0.698000 0.0429589
\(265\) −10.8555 −0.666846
\(266\) 54.2395 3.32564
\(267\) −4.23609 −0.259244
\(268\) 9.02330 0.551185
\(269\) 1.82765 0.111434 0.0557168 0.998447i \(-0.482256\pi\)
0.0557168 + 0.998447i \(0.482256\pi\)
\(270\) 5.92810 0.360773
\(271\) 3.99725 0.242816 0.121408 0.992603i \(-0.461259\pi\)
0.121408 + 0.992603i \(0.461259\pi\)
\(272\) −0.305335 −0.0185136
\(273\) 13.5640 0.820928
\(274\) −18.9385 −1.14412
\(275\) 1.00000 0.0603023
\(276\) −3.64725 −0.219538
\(277\) 3.93518 0.236442 0.118221 0.992987i \(-0.462281\pi\)
0.118221 + 0.992987i \(0.462281\pi\)
\(278\) 6.95083 0.416883
\(279\) −5.81564 −0.348173
\(280\) −4.84886 −0.289775
\(281\) 5.31105 0.316830 0.158415 0.987373i \(-0.449362\pi\)
0.158415 + 0.987373i \(0.449362\pi\)
\(282\) −4.35196 −0.259155
\(283\) −7.08081 −0.420911 −0.210455 0.977603i \(-0.567495\pi\)
−0.210455 + 0.977603i \(0.567495\pi\)
\(284\) −15.0567 −0.893452
\(285\) 4.27732 0.253366
\(286\) 10.8732 0.642946
\(287\) 29.0604 1.71538
\(288\) −17.3357 −1.02152
\(289\) −16.9961 −0.999771
\(290\) −1.33679 −0.0784991
\(291\) −3.46241 −0.202970
\(292\) 1.33213 0.0779571
\(293\) −4.56834 −0.266885 −0.133443 0.991057i \(-0.542603\pi\)
−0.133443 + 0.991057i \(0.542603\pi\)
\(294\) −9.21666 −0.537526
\(295\) −2.87196 −0.167212
\(296\) −8.24319 −0.479126
\(297\) −3.24754 −0.188442
\(298\) 6.04572 0.350219
\(299\) 28.4847 1.64731
\(300\) 0.762693 0.0440341
\(301\) 1.02555 0.0591120
\(302\) −17.7328 −1.02041
\(303\) −0.520547 −0.0299046
\(304\) −36.5300 −2.09514
\(305\) −2.48748 −0.142433
\(306\) 0.304597 0.0174126
\(307\) −22.1111 −1.26194 −0.630972 0.775805i \(-0.717344\pi\)
−0.630972 + 0.775805i \(0.717344\pi\)
\(308\) −5.29826 −0.301897
\(309\) −2.54471 −0.144763
\(310\) −3.97273 −0.225636
\(311\) −5.55131 −0.314786 −0.157393 0.987536i \(-0.550309\pi\)
−0.157393 + 0.987536i \(0.550309\pi\)
\(312\) −4.15769 −0.235383
\(313\) −29.5115 −1.66809 −0.834045 0.551697i \(-0.813981\pi\)
−0.834045 + 0.551697i \(0.813981\pi\)
\(314\) −19.0097 −1.07278
\(315\) 10.6281 0.598826
\(316\) 22.3893 1.25950
\(317\) −5.42841 −0.304890 −0.152445 0.988312i \(-0.548715\pi\)
−0.152445 + 0.988312i \(0.548715\pi\)
\(318\) 11.3452 0.636208
\(319\) 0.732323 0.0410022
\(320\) −2.06285 −0.115317
\(321\) 0.487299 0.0271984
\(322\) −34.7187 −1.93479
\(323\) 0.466512 0.0259574
\(324\) 8.20229 0.455683
\(325\) −5.95658 −0.330411
\(326\) 24.8891 1.37848
\(327\) 3.80956 0.210669
\(328\) −8.90773 −0.491847
\(329\) −16.5618 −0.913081
\(330\) −1.04512 −0.0575317
\(331\) 19.6653 1.08090 0.540452 0.841375i \(-0.318253\pi\)
0.540452 + 0.841375i \(0.318253\pi\)
\(332\) 5.80844 0.318779
\(333\) 18.0681 0.990125
\(334\) −45.8302 −2.50771
\(335\) 6.77358 0.370080
\(336\) 11.1345 0.607437
\(337\) 0.894802 0.0487430 0.0243715 0.999703i \(-0.492242\pi\)
0.0243715 + 0.999703i \(0.492242\pi\)
\(338\) −41.0367 −2.23210
\(339\) 11.2393 0.610433
\(340\) 0.0831843 0.00451130
\(341\) 2.17635 0.117856
\(342\) 36.4417 1.97054
\(343\) −7.23388 −0.390593
\(344\) −0.314358 −0.0169490
\(345\) −2.73790 −0.147404
\(346\) −17.2198 −0.925741
\(347\) 31.9613 1.71577 0.857885 0.513842i \(-0.171778\pi\)
0.857885 + 0.513842i \(0.171778\pi\)
\(348\) 0.558538 0.0299408
\(349\) 11.9587 0.640134 0.320067 0.947395i \(-0.396295\pi\)
0.320067 + 0.947395i \(0.396295\pi\)
\(350\) 7.26019 0.388073
\(351\) 19.3442 1.03252
\(352\) 6.48743 0.345781
\(353\) −24.1558 −1.28568 −0.642841 0.766000i \(-0.722244\pi\)
−0.642841 + 0.766000i \(0.722244\pi\)
\(354\) 3.00153 0.159529
\(355\) −11.3027 −0.599887
\(356\) −9.85618 −0.522376
\(357\) −0.142195 −0.00752576
\(358\) 42.7468 2.25924
\(359\) 11.1170 0.586734 0.293367 0.956000i \(-0.405224\pi\)
0.293367 + 0.956000i \(0.405224\pi\)
\(360\) −3.25778 −0.171700
\(361\) 36.8131 1.93753
\(362\) 7.53895 0.396238
\(363\) 0.572536 0.0300504
\(364\) 31.5595 1.65417
\(365\) 1.00000 0.0523424
\(366\) 2.59970 0.135889
\(367\) −23.1866 −1.21033 −0.605167 0.796099i \(-0.706893\pi\)
−0.605167 + 0.796099i \(0.706893\pi\)
\(368\) 23.3828 1.21891
\(369\) 19.5247 1.01641
\(370\) 12.3425 0.641657
\(371\) 43.1753 2.24155
\(372\) 1.65989 0.0860610
\(373\) 25.8037 1.33607 0.668034 0.744131i \(-0.267136\pi\)
0.668034 + 0.744131i \(0.267136\pi\)
\(374\) −0.113987 −0.00589413
\(375\) 0.572536 0.0295657
\(376\) 5.07660 0.261806
\(377\) −4.36214 −0.224661
\(378\) −23.5778 −1.21271
\(379\) 6.12477 0.314608 0.157304 0.987550i \(-0.449720\pi\)
0.157304 + 0.987550i \(0.449720\pi\)
\(380\) 9.95211 0.510532
\(381\) −1.21908 −0.0624555
\(382\) −26.9091 −1.37679
\(383\) −33.0109 −1.68678 −0.843389 0.537303i \(-0.819443\pi\)
−0.843389 + 0.537303i \(0.819443\pi\)
\(384\) −5.27266 −0.269069
\(385\) −3.97729 −0.202701
\(386\) 14.4571 0.735846
\(387\) 0.689035 0.0350256
\(388\) −8.05604 −0.408984
\(389\) −4.29868 −0.217952 −0.108976 0.994044i \(-0.534757\pi\)
−0.108976 + 0.994044i \(0.534757\pi\)
\(390\) 6.22531 0.315231
\(391\) −0.298614 −0.0151015
\(392\) 10.7513 0.543024
\(393\) 10.5426 0.531802
\(394\) 35.1490 1.77078
\(395\) 16.8072 0.845660
\(396\) −3.55972 −0.178883
\(397\) 8.96942 0.450162 0.225081 0.974340i \(-0.427735\pi\)
0.225081 + 0.974340i \(0.427735\pi\)
\(398\) 12.7473 0.638962
\(399\) −17.0121 −0.851670
\(400\) −4.88969 −0.244484
\(401\) 16.7718 0.837544 0.418772 0.908091i \(-0.362461\pi\)
0.418772 + 0.908091i \(0.362461\pi\)
\(402\) −7.07917 −0.353077
\(403\) −12.9636 −0.645762
\(404\) −1.21116 −0.0602577
\(405\) 6.15727 0.305957
\(406\) 5.31680 0.263868
\(407\) −6.76150 −0.335155
\(408\) 0.0435863 0.00215784
\(409\) 31.2333 1.54439 0.772194 0.635387i \(-0.219160\pi\)
0.772194 + 0.635387i \(0.219160\pi\)
\(410\) 13.3375 0.658694
\(411\) 5.94002 0.293000
\(412\) −5.92082 −0.291698
\(413\) 11.4226 0.562070
\(414\) −23.3263 −1.14642
\(415\) 4.36026 0.214037
\(416\) −38.6428 −1.89462
\(417\) −2.18011 −0.106761
\(418\) −13.6373 −0.667023
\(419\) 26.8418 1.31131 0.655655 0.755061i \(-0.272393\pi\)
0.655655 + 0.755061i \(0.272393\pi\)
\(420\) −3.03345 −0.148017
\(421\) −19.5493 −0.952775 −0.476387 0.879235i \(-0.658054\pi\)
−0.476387 + 0.879235i \(0.658054\pi\)
\(422\) 14.0495 0.683919
\(423\) −11.1273 −0.541028
\(424\) −13.2343 −0.642715
\(425\) 0.0624446 0.00302901
\(426\) 11.8127 0.572325
\(427\) 9.89342 0.478776
\(428\) 1.13381 0.0548047
\(429\) −3.41036 −0.164654
\(430\) 0.470688 0.0226986
\(431\) 12.2264 0.588924 0.294462 0.955663i \(-0.404860\pi\)
0.294462 + 0.955663i \(0.404860\pi\)
\(432\) 15.8795 0.764001
\(433\) 27.9346 1.34245 0.671226 0.741253i \(-0.265768\pi\)
0.671226 + 0.741253i \(0.265768\pi\)
\(434\) 15.8007 0.758457
\(435\) 0.419281 0.0201030
\(436\) 8.86377 0.424498
\(437\) −35.7259 −1.70900
\(438\) −1.04512 −0.0499375
\(439\) 25.5208 1.21804 0.609020 0.793155i \(-0.291563\pi\)
0.609020 + 0.793155i \(0.291563\pi\)
\(440\) 1.21914 0.0581201
\(441\) −23.5656 −1.12217
\(442\) 0.678973 0.0322954
\(443\) 25.0811 1.19164 0.595819 0.803119i \(-0.296828\pi\)
0.595819 + 0.803119i \(0.296828\pi\)
\(444\) −5.15695 −0.244738
\(445\) −7.39881 −0.350737
\(446\) 6.41792 0.303897
\(447\) −1.89623 −0.0896884
\(448\) 8.20454 0.387628
\(449\) 18.2120 0.859477 0.429738 0.902953i \(-0.358606\pi\)
0.429738 + 0.902953i \(0.358606\pi\)
\(450\) 4.87787 0.229945
\(451\) −7.30658 −0.344054
\(452\) 26.1506 1.23002
\(453\) 5.56186 0.261319
\(454\) −35.6936 −1.67518
\(455\) 23.6910 1.11065
\(456\) 5.21463 0.244198
\(457\) 36.5873 1.71148 0.855740 0.517406i \(-0.173102\pi\)
0.855740 + 0.517406i \(0.173102\pi\)
\(458\) −25.2139 −1.17817
\(459\) −0.202791 −0.00946549
\(460\) −6.37033 −0.297018
\(461\) −23.3861 −1.08920 −0.544599 0.838696i \(-0.683318\pi\)
−0.544599 + 0.838696i \(0.683318\pi\)
\(462\) 4.15672 0.193388
\(463\) −8.83736 −0.410707 −0.205354 0.978688i \(-0.565834\pi\)
−0.205354 + 0.978688i \(0.565834\pi\)
\(464\) −3.58083 −0.166236
\(465\) 1.24604 0.0577836
\(466\) −19.7407 −0.914470
\(467\) 12.9354 0.598577 0.299288 0.954163i \(-0.403251\pi\)
0.299288 + 0.954163i \(0.403251\pi\)
\(468\) 21.2038 0.980144
\(469\) −26.9405 −1.24400
\(470\) −7.60119 −0.350617
\(471\) 5.96235 0.274730
\(472\) −3.50131 −0.161161
\(473\) −0.257853 −0.0118561
\(474\) −17.5654 −0.806806
\(475\) 7.47082 0.342785
\(476\) −0.330848 −0.0151644
\(477\) 29.0080 1.32819
\(478\) −21.0565 −0.963102
\(479\) 4.01427 0.183417 0.0917084 0.995786i \(-0.470767\pi\)
0.0917084 + 0.995786i \(0.470767\pi\)
\(480\) 3.71429 0.169533
\(481\) 40.2754 1.83640
\(482\) −36.9737 −1.68411
\(483\) 10.8894 0.495486
\(484\) 1.33213 0.0605514
\(485\) −6.04749 −0.274602
\(486\) −24.2194 −1.09861
\(487\) 30.9263 1.40140 0.700702 0.713454i \(-0.252870\pi\)
0.700702 + 0.713454i \(0.252870\pi\)
\(488\) −3.03258 −0.137278
\(489\) −7.80641 −0.353018
\(490\) −16.0979 −0.727231
\(491\) 10.0248 0.452411 0.226206 0.974080i \(-0.427368\pi\)
0.226206 + 0.974080i \(0.427368\pi\)
\(492\) −5.57268 −0.251236
\(493\) 0.0457296 0.00205956
\(494\) 81.2318 3.65479
\(495\) −2.67220 −0.120107
\(496\) −10.6417 −0.477825
\(497\) 44.9542 2.01647
\(498\) −4.55697 −0.204203
\(499\) −30.4536 −1.36329 −0.681645 0.731683i \(-0.738735\pi\)
−0.681645 + 0.731683i \(0.738735\pi\)
\(500\) 1.33213 0.0595747
\(501\) 14.3745 0.642206
\(502\) −12.0172 −0.536353
\(503\) −16.2335 −0.723814 −0.361907 0.932214i \(-0.617874\pi\)
−0.361907 + 0.932214i \(0.617874\pi\)
\(504\) 12.9571 0.577156
\(505\) −0.909194 −0.0404586
\(506\) 8.72923 0.388062
\(507\) 12.8711 0.571624
\(508\) −2.83646 −0.125848
\(509\) 32.5441 1.44249 0.721245 0.692680i \(-0.243570\pi\)
0.721245 + 0.692680i \(0.243570\pi\)
\(510\) −0.0652618 −0.00288984
\(511\) −3.97729 −0.175945
\(512\) −19.7991 −0.875005
\(513\) −24.2618 −1.07118
\(514\) −56.5065 −2.49240
\(515\) −4.44462 −0.195853
\(516\) −0.196663 −0.00865759
\(517\) 4.16410 0.183137
\(518\) −49.0897 −2.15688
\(519\) 5.40094 0.237075
\(520\) −7.26188 −0.318455
\(521\) −26.2947 −1.15199 −0.575995 0.817453i \(-0.695385\pi\)
−0.575995 + 0.817453i \(0.695385\pi\)
\(522\) 3.57218 0.156350
\(523\) −30.2378 −1.32221 −0.661103 0.750295i \(-0.729911\pi\)
−0.661103 + 0.750295i \(0.729911\pi\)
\(524\) 24.5296 1.07158
\(525\) −2.27714 −0.0993826
\(526\) 40.6419 1.77207
\(527\) 0.135901 0.00591994
\(528\) −2.79952 −0.121834
\(529\) −0.131891 −0.00573437
\(530\) 19.8157 0.860740
\(531\) 7.67446 0.333043
\(532\) −39.5824 −1.71611
\(533\) 43.5222 1.88516
\(534\) 7.73261 0.334623
\(535\) 0.851123 0.0367973
\(536\) 8.25792 0.356688
\(537\) −13.4074 −0.578574
\(538\) −3.33621 −0.143834
\(539\) 8.81880 0.379853
\(540\) −4.32615 −0.186168
\(541\) −2.56772 −0.110395 −0.0551974 0.998475i \(-0.517579\pi\)
−0.0551974 + 0.998475i \(0.517579\pi\)
\(542\) −7.29663 −0.313417
\(543\) −2.36457 −0.101474
\(544\) 0.405105 0.0173687
\(545\) 6.65383 0.285019
\(546\) −24.7598 −1.05962
\(547\) 39.2263 1.67720 0.838598 0.544751i \(-0.183376\pi\)
0.838598 + 0.544751i \(0.183376\pi\)
\(548\) 13.8208 0.590393
\(549\) 6.64705 0.283689
\(550\) −1.82541 −0.0778358
\(551\) 5.47105 0.233075
\(552\) −3.33788 −0.142070
\(553\) −66.8469 −2.84262
\(554\) −7.18333 −0.305190
\(555\) −3.87120 −0.164323
\(556\) −5.07251 −0.215122
\(557\) −15.4127 −0.653058 −0.326529 0.945187i \(-0.605879\pi\)
−0.326529 + 0.945187i \(0.605879\pi\)
\(558\) 10.6159 0.449409
\(559\) 1.53592 0.0649625
\(560\) 19.4477 0.821815
\(561\) 0.0357518 0.00150944
\(562\) −9.69485 −0.408953
\(563\) −18.1899 −0.766614 −0.383307 0.923621i \(-0.625215\pi\)
−0.383307 + 0.923621i \(0.625215\pi\)
\(564\) 3.17593 0.133731
\(565\) 19.6307 0.825868
\(566\) 12.9254 0.543295
\(567\) −24.4892 −1.02845
\(568\) −13.7796 −0.578179
\(569\) −5.28963 −0.221753 −0.110876 0.993834i \(-0.535366\pi\)
−0.110876 + 0.993834i \(0.535366\pi\)
\(570\) −7.80786 −0.327035
\(571\) 19.3654 0.810419 0.405209 0.914224i \(-0.367199\pi\)
0.405209 + 0.914224i \(0.367199\pi\)
\(572\) −7.93494 −0.331776
\(573\) 8.43998 0.352585
\(574\) −53.0472 −2.21415
\(575\) −4.78206 −0.199426
\(576\) 5.51235 0.229681
\(577\) 2.29948 0.0957285 0.0478642 0.998854i \(-0.484759\pi\)
0.0478642 + 0.998854i \(0.484759\pi\)
\(578\) 31.0249 1.29047
\(579\) −4.53443 −0.188444
\(580\) 0.975550 0.0405075
\(581\) −17.3420 −0.719467
\(582\) 6.32032 0.261986
\(583\) −10.8555 −0.449588
\(584\) 1.21914 0.0504482
\(585\) 15.9172 0.658094
\(586\) 8.33910 0.344485
\(587\) −26.0625 −1.07571 −0.537857 0.843036i \(-0.680766\pi\)
−0.537857 + 0.843036i \(0.680766\pi\)
\(588\) 6.72604 0.277377
\(589\) 16.2591 0.669944
\(590\) 5.24251 0.215831
\(591\) −11.0244 −0.453483
\(592\) 33.0616 1.35882
\(593\) −17.4884 −0.718162 −0.359081 0.933306i \(-0.616910\pi\)
−0.359081 + 0.933306i \(0.616910\pi\)
\(594\) 5.92810 0.243233
\(595\) −0.248360 −0.0101818
\(596\) −4.41198 −0.180722
\(597\) −3.99815 −0.163633
\(598\) −51.9963 −2.12629
\(599\) 2.78712 0.113878 0.0569392 0.998378i \(-0.481866\pi\)
0.0569392 + 0.998378i \(0.481866\pi\)
\(600\) 0.698000 0.0284957
\(601\) 8.31497 0.339175 0.169587 0.985515i \(-0.445756\pi\)
0.169587 + 0.985515i \(0.445756\pi\)
\(602\) −1.87206 −0.0762995
\(603\) −18.1004 −0.737104
\(604\) 12.9409 0.526557
\(605\) 1.00000 0.0406558
\(606\) 0.950212 0.0385997
\(607\) −24.6354 −0.999921 −0.499960 0.866048i \(-0.666652\pi\)
−0.499960 + 0.866048i \(0.666652\pi\)
\(608\) 48.4664 1.96557
\(609\) −1.66760 −0.0675746
\(610\) 4.54068 0.183847
\(611\) −24.8037 −1.00345
\(612\) −0.222285 −0.00898535
\(613\) 22.5277 0.909886 0.454943 0.890521i \(-0.349660\pi\)
0.454943 + 0.890521i \(0.349660\pi\)
\(614\) 40.3618 1.62887
\(615\) −4.18329 −0.168686
\(616\) −4.84886 −0.195366
\(617\) 6.83978 0.275359 0.137680 0.990477i \(-0.456036\pi\)
0.137680 + 0.990477i \(0.456036\pi\)
\(618\) 4.64514 0.186855
\(619\) 18.7575 0.753929 0.376965 0.926228i \(-0.376968\pi\)
0.376965 + 0.926228i \(0.376968\pi\)
\(620\) 2.89918 0.116434
\(621\) 15.5299 0.623195
\(622\) 10.1334 0.406314
\(623\) 29.4272 1.17897
\(624\) 16.6756 0.667558
\(625\) 1.00000 0.0400000
\(626\) 53.8707 2.15311
\(627\) 4.27732 0.170820
\(628\) 13.8727 0.553581
\(629\) −0.422219 −0.0168350
\(630\) −19.4007 −0.772942
\(631\) −26.5216 −1.05581 −0.527903 0.849305i \(-0.677022\pi\)
−0.527903 + 0.849305i \(0.677022\pi\)
\(632\) 20.4902 0.815058
\(633\) −4.40660 −0.175146
\(634\) 9.90909 0.393540
\(635\) −2.12927 −0.0844973
\(636\) −8.27940 −0.328299
\(637\) −52.5298 −2.08131
\(638\) −1.33679 −0.0529241
\(639\) 30.2032 1.19482
\(640\) −9.20930 −0.364030
\(641\) 25.1651 0.993962 0.496981 0.867761i \(-0.334442\pi\)
0.496981 + 0.867761i \(0.334442\pi\)
\(642\) −0.889522 −0.0351066
\(643\) 22.4622 0.885824 0.442912 0.896565i \(-0.353945\pi\)
0.442912 + 0.896565i \(0.353945\pi\)
\(644\) 25.3366 0.998403
\(645\) −0.147630 −0.00581293
\(646\) −0.851577 −0.0335048
\(647\) 27.1996 1.06933 0.534663 0.845065i \(-0.320438\pi\)
0.534663 + 0.845065i \(0.320438\pi\)
\(648\) 7.50656 0.294885
\(649\) −2.87196 −0.112734
\(650\) 10.8732 0.426482
\(651\) −4.95585 −0.194235
\(652\) −18.1633 −0.711330
\(653\) 30.0406 1.17558 0.587790 0.809014i \(-0.299998\pi\)
0.587790 + 0.809014i \(0.299998\pi\)
\(654\) −6.95402 −0.271924
\(655\) 18.4138 0.719486
\(656\) 35.7269 1.39490
\(657\) −2.67220 −0.104253
\(658\) 30.2321 1.17857
\(659\) 0.302425 0.0117808 0.00589040 0.999983i \(-0.498125\pi\)
0.00589040 + 0.999983i \(0.498125\pi\)
\(660\) 0.762693 0.0296878
\(661\) 8.75991 0.340721 0.170360 0.985382i \(-0.445507\pi\)
0.170360 + 0.985382i \(0.445507\pi\)
\(662\) −35.8973 −1.39519
\(663\) −0.212958 −0.00827061
\(664\) 5.31575 0.206291
\(665\) −29.7136 −1.15224
\(666\) −32.9817 −1.27802
\(667\) −3.50201 −0.135598
\(668\) 33.4455 1.29404
\(669\) −2.01297 −0.0778257
\(670\) −12.3646 −0.477685
\(671\) −2.48748 −0.0960281
\(672\) −14.7728 −0.569872
\(673\) 12.7795 0.492615 0.246307 0.969192i \(-0.420783\pi\)
0.246307 + 0.969192i \(0.420783\pi\)
\(674\) −1.63338 −0.0629156
\(675\) −3.24754 −0.124998
\(676\) 29.9474 1.15182
\(677\) 34.1423 1.31220 0.656098 0.754675i \(-0.272206\pi\)
0.656098 + 0.754675i \(0.272206\pi\)
\(678\) −20.5163 −0.787924
\(679\) 24.0526 0.923053
\(680\) 0.0761285 0.00291939
\(681\) 11.1952 0.429001
\(682\) −3.97273 −0.152124
\(683\) −43.5086 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(684\) −26.5940 −1.01685
\(685\) 10.3749 0.396406
\(686\) 13.2048 0.504162
\(687\) 7.90827 0.301719
\(688\) 1.26082 0.0480683
\(689\) 64.6614 2.46340
\(690\) 4.99780 0.190263
\(691\) −49.1993 −1.87163 −0.935815 0.352493i \(-0.885334\pi\)
−0.935815 + 0.352493i \(0.885334\pi\)
\(692\) 12.5665 0.477705
\(693\) 10.6281 0.403729
\(694\) −58.3425 −2.21465
\(695\) −3.80781 −0.144439
\(696\) 0.511161 0.0193755
\(697\) −0.456257 −0.0172819
\(698\) −21.8295 −0.826260
\(699\) 6.19162 0.234189
\(700\) −5.29826 −0.200256
\(701\) −9.77682 −0.369266 −0.184633 0.982808i \(-0.559110\pi\)
−0.184633 + 0.982808i \(0.559110\pi\)
\(702\) −35.3112 −1.33274
\(703\) −50.5139 −1.90517
\(704\) −2.06285 −0.0777466
\(705\) 2.38410 0.0897903
\(706\) 44.0942 1.65951
\(707\) 3.61612 0.135998
\(708\) −2.19042 −0.0823212
\(709\) −28.7367 −1.07923 −0.539615 0.841912i \(-0.681430\pi\)
−0.539615 + 0.841912i \(0.681430\pi\)
\(710\) 20.6322 0.774311
\(711\) −44.9121 −1.68434
\(712\) −9.02016 −0.338045
\(713\) −10.4074 −0.389761
\(714\) 0.259565 0.00971396
\(715\) −5.95658 −0.222763
\(716\) −31.1953 −1.16582
\(717\) 6.60432 0.246643
\(718\) −20.2931 −0.757334
\(719\) −13.2386 −0.493715 −0.246858 0.969052i \(-0.579398\pi\)
−0.246858 + 0.969052i \(0.579398\pi\)
\(720\) 13.0662 0.486950
\(721\) 17.6775 0.658345
\(722\) −67.1991 −2.50089
\(723\) 11.5967 0.431286
\(724\) −5.50170 −0.204469
\(725\) 0.732323 0.0271978
\(726\) −1.04512 −0.0387879
\(727\) 34.8059 1.29088 0.645439 0.763812i \(-0.276675\pi\)
0.645439 + 0.763812i \(0.276675\pi\)
\(728\) 28.8826 1.07046
\(729\) −10.8755 −0.402795
\(730\) −1.82541 −0.0675615
\(731\) −0.0161015 −0.000595536 0
\(732\) −1.89719 −0.0701220
\(733\) −5.28451 −0.195188 −0.0975939 0.995226i \(-0.531115\pi\)
−0.0975939 + 0.995226i \(0.531115\pi\)
\(734\) 42.3252 1.56225
\(735\) 5.04908 0.186238
\(736\) −31.0233 −1.14353
\(737\) 6.77358 0.249508
\(738\) −35.6406 −1.31195
\(739\) 30.0845 1.10668 0.553338 0.832957i \(-0.313354\pi\)
0.553338 + 0.832957i \(0.313354\pi\)
\(740\) −9.00720 −0.331111
\(741\) −25.4782 −0.935963
\(742\) −78.8127 −2.89331
\(743\) −17.0901 −0.626977 −0.313488 0.949592i \(-0.601498\pi\)
−0.313488 + 0.949592i \(0.601498\pi\)
\(744\) 1.51909 0.0556926
\(745\) −3.31198 −0.121341
\(746\) −47.1025 −1.72454
\(747\) −11.6515 −0.426306
\(748\) 0.0831843 0.00304152
\(749\) −3.38516 −0.123691
\(750\) −1.04512 −0.0381622
\(751\) 4.79269 0.174888 0.0874439 0.996169i \(-0.472130\pi\)
0.0874439 + 0.996169i \(0.472130\pi\)
\(752\) −20.3611 −0.742494
\(753\) 3.76916 0.137356
\(754\) 7.96270 0.289984
\(755\) 9.71443 0.353544
\(756\) 17.2063 0.625788
\(757\) −1.66572 −0.0605415 −0.0302707 0.999542i \(-0.509637\pi\)
−0.0302707 + 0.999542i \(0.509637\pi\)
\(758\) −11.1802 −0.406084
\(759\) −2.73790 −0.0993796
\(760\) 9.10795 0.330380
\(761\) 16.3328 0.592064 0.296032 0.955178i \(-0.404336\pi\)
0.296032 + 0.955178i \(0.404336\pi\)
\(762\) 2.22533 0.0806151
\(763\) −26.4642 −0.958068
\(764\) 19.6374 0.710458
\(765\) −0.166865 −0.00603300
\(766\) 60.2585 2.17723
\(767\) 17.1070 0.617700
\(768\) 11.9869 0.432540
\(769\) −8.43323 −0.304110 −0.152055 0.988372i \(-0.548589\pi\)
−0.152055 + 0.988372i \(0.548589\pi\)
\(770\) 7.26019 0.261639
\(771\) 17.7231 0.638283
\(772\) −10.5503 −0.379715
\(773\) 15.7987 0.568239 0.284119 0.958789i \(-0.408299\pi\)
0.284119 + 0.958789i \(0.408299\pi\)
\(774\) −1.25777 −0.0452097
\(775\) 2.17635 0.0781767
\(776\) −7.37271 −0.264665
\(777\) 15.3969 0.552360
\(778\) 7.84686 0.281324
\(779\) −54.5862 −1.95575
\(780\) −4.54304 −0.162667
\(781\) −11.3027 −0.404444
\(782\) 0.545093 0.0194925
\(783\) −2.37825 −0.0849917
\(784\) −43.1212 −1.54004
\(785\) 10.4139 0.371689
\(786\) −19.2445 −0.686429
\(787\) −25.2856 −0.901334 −0.450667 0.892692i \(-0.648814\pi\)
−0.450667 + 0.892692i \(0.648814\pi\)
\(788\) −25.6507 −0.913767
\(789\) −12.7472 −0.453814
\(790\) −30.6800 −1.09155
\(791\) −78.0767 −2.77609
\(792\) −3.25778 −0.115760
\(793\) 14.8169 0.526162
\(794\) −16.3729 −0.581052
\(795\) −6.21515 −0.220429
\(796\) −9.30256 −0.329721
\(797\) 14.5872 0.516704 0.258352 0.966051i \(-0.416821\pi\)
0.258352 + 0.966051i \(0.416821\pi\)
\(798\) 31.0541 1.09930
\(799\) 0.260025 0.00919903
\(800\) 6.48743 0.229365
\(801\) 19.7711 0.698578
\(802\) −30.6155 −1.08107
\(803\) 1.00000 0.0352892
\(804\) 5.16616 0.182197
\(805\) 19.0196 0.670354
\(806\) 23.6639 0.833524
\(807\) 1.04639 0.0368348
\(808\) −1.10843 −0.0389945
\(809\) −30.7364 −1.08064 −0.540318 0.841461i \(-0.681696\pi\)
−0.540318 + 0.841461i \(0.681696\pi\)
\(810\) −11.2396 −0.394918
\(811\) −45.9306 −1.61284 −0.806421 0.591341i \(-0.798599\pi\)
−0.806421 + 0.591341i \(0.798599\pi\)
\(812\) −3.88004 −0.136163
\(813\) 2.28857 0.0802637
\(814\) 12.3425 0.432605
\(815\) −13.6348 −0.477605
\(816\) −0.174815 −0.00611975
\(817\) −1.92637 −0.0673952
\(818\) −57.0137 −1.99344
\(819\) −63.3071 −2.21213
\(820\) −9.73332 −0.339902
\(821\) −36.1425 −1.26138 −0.630690 0.776035i \(-0.717228\pi\)
−0.630690 + 0.776035i \(0.717228\pi\)
\(822\) −10.8430 −0.378193
\(823\) −50.0757 −1.74553 −0.872765 0.488141i \(-0.837675\pi\)
−0.872765 + 0.488141i \(0.837675\pi\)
\(824\) −5.41860 −0.188766
\(825\) 0.572536 0.0199332
\(826\) −20.8510 −0.725498
\(827\) 12.2115 0.424635 0.212318 0.977201i \(-0.431899\pi\)
0.212318 + 0.977201i \(0.431899\pi\)
\(828\) 17.0228 0.591584
\(829\) −5.31050 −0.184441 −0.0922206 0.995739i \(-0.529396\pi\)
−0.0922206 + 0.995739i \(0.529396\pi\)
\(830\) −7.95927 −0.276270
\(831\) 2.25303 0.0781569
\(832\) 12.2875 0.425993
\(833\) 0.550686 0.0190801
\(834\) 3.97960 0.137802
\(835\) 25.1067 0.868854
\(836\) 9.95211 0.344201
\(837\) −7.06778 −0.244298
\(838\) −48.9974 −1.69259
\(839\) −7.69701 −0.265730 −0.132865 0.991134i \(-0.542418\pi\)
−0.132865 + 0.991134i \(0.542418\pi\)
\(840\) −2.77615 −0.0957861
\(841\) −28.4637 −0.981507
\(842\) 35.6855 1.22981
\(843\) 3.04077 0.104730
\(844\) −10.2529 −0.352920
\(845\) 22.4808 0.773363
\(846\) 20.3119 0.698338
\(847\) −3.97729 −0.136661
\(848\) 53.0799 1.82277
\(849\) −4.05402 −0.139134
\(850\) −0.113987 −0.00390973
\(851\) 32.3339 1.10839
\(852\) −8.62052 −0.295334
\(853\) −33.6697 −1.15283 −0.576414 0.817158i \(-0.695549\pi\)
−0.576414 + 0.817158i \(0.695549\pi\)
\(854\) −18.0596 −0.617986
\(855\) −19.9635 −0.682739
\(856\) 1.03764 0.0354657
\(857\) −20.3732 −0.695936 −0.347968 0.937506i \(-0.613128\pi\)
−0.347968 + 0.937506i \(0.613128\pi\)
\(858\) 6.22531 0.212528
\(859\) −46.9767 −1.60282 −0.801411 0.598113i \(-0.795917\pi\)
−0.801411 + 0.598113i \(0.795917\pi\)
\(860\) −0.343494 −0.0117130
\(861\) 16.6381 0.567026
\(862\) −22.3182 −0.760161
\(863\) 10.4335 0.355159 0.177580 0.984106i \(-0.443173\pi\)
0.177580 + 0.984106i \(0.443173\pi\)
\(864\) −21.0682 −0.716754
\(865\) 9.43336 0.320744
\(866\) −50.9922 −1.73279
\(867\) −9.73089 −0.330478
\(868\) −11.5309 −0.391383
\(869\) 16.8072 0.570144
\(870\) −0.765361 −0.0259482
\(871\) −40.3473 −1.36712
\(872\) 8.11193 0.274705
\(873\) 16.1601 0.546937
\(874\) 65.2145 2.20591
\(875\) −3.97729 −0.134457
\(876\) 0.762693 0.0257690
\(877\) 0.873478 0.0294953 0.0147476 0.999891i \(-0.495306\pi\)
0.0147476 + 0.999891i \(0.495306\pi\)
\(878\) −46.5859 −1.57220
\(879\) −2.61554 −0.0882199
\(880\) −4.88969 −0.164831
\(881\) 13.2800 0.447414 0.223707 0.974656i \(-0.428184\pi\)
0.223707 + 0.974656i \(0.428184\pi\)
\(882\) 43.0170 1.44846
\(883\) 21.7634 0.732397 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(884\) −0.495494 −0.0166653
\(885\) −1.64430 −0.0552726
\(886\) −45.7833 −1.53812
\(887\) −58.2019 −1.95423 −0.977115 0.212714i \(-0.931770\pi\)
−0.977115 + 0.212714i \(0.931770\pi\)
\(888\) −4.71953 −0.158377
\(889\) 8.46870 0.284031
\(890\) 13.5059 0.452718
\(891\) 6.15727 0.206276
\(892\) −4.68360 −0.156819
\(893\) 31.1092 1.04103
\(894\) 3.46139 0.115766
\(895\) −23.4176 −0.782765
\(896\) 36.6280 1.22366
\(897\) 16.3085 0.544526
\(898\) −33.2444 −1.10938
\(899\) 1.59379 0.0531558
\(900\) −3.55972 −0.118657
\(901\) −0.677865 −0.0225830
\(902\) 13.3375 0.444091
\(903\) 0.587167 0.0195397
\(904\) 23.9325 0.795982
\(905\) −4.13000 −0.137286
\(906\) −10.1527 −0.337301
\(907\) −11.4799 −0.381183 −0.190591 0.981669i \(-0.561041\pi\)
−0.190591 + 0.981669i \(0.561041\pi\)
\(908\) 26.0481 0.864436
\(909\) 2.42955 0.0805831
\(910\) −43.2458 −1.43359
\(911\) 24.0459 0.796676 0.398338 0.917239i \(-0.369587\pi\)
0.398338 + 0.917239i \(0.369587\pi\)
\(912\) −20.9147 −0.692556
\(913\) 4.36026 0.144304
\(914\) −66.7869 −2.20911
\(915\) −1.42417 −0.0470817
\(916\) 18.4003 0.607963
\(917\) −73.2368 −2.41849
\(918\) 0.370178 0.0122177
\(919\) −11.0686 −0.365120 −0.182560 0.983195i \(-0.558438\pi\)
−0.182560 + 0.983195i \(0.558438\pi\)
\(920\) −5.82999 −0.192209
\(921\) −12.6594 −0.417141
\(922\) 42.6893 1.40590
\(923\) 67.3256 2.21605
\(924\) −3.03345 −0.0997931
\(925\) −6.76150 −0.222317
\(926\) 16.1318 0.530125
\(927\) 11.8769 0.390089
\(928\) 4.75089 0.155956
\(929\) 58.5645 1.92144 0.960720 0.277519i \(-0.0895123\pi\)
0.960720 + 0.277519i \(0.0895123\pi\)
\(930\) −2.27453 −0.0745849
\(931\) 65.8836 2.15925
\(932\) 14.4062 0.471889
\(933\) −3.17833 −0.104054
\(934\) −23.6124 −0.772620
\(935\) 0.0624446 0.00204216
\(936\) 19.4052 0.634279
\(937\) 34.5295 1.12803 0.564016 0.825764i \(-0.309256\pi\)
0.564016 + 0.825764i \(0.309256\pi\)
\(938\) 49.1775 1.60570
\(939\) −16.8964 −0.551394
\(940\) 5.54712 0.180927
\(941\) −51.2421 −1.67045 −0.835223 0.549912i \(-0.814661\pi\)
−0.835223 + 0.549912i \(0.814661\pi\)
\(942\) −10.8837 −0.354611
\(943\) 34.9405 1.13782
\(944\) 14.0430 0.457060
\(945\) 12.9164 0.420171
\(946\) 0.470688 0.0153034
\(947\) 16.8563 0.547755 0.273878 0.961765i \(-0.411694\pi\)
0.273878 + 0.961765i \(0.411694\pi\)
\(948\) 12.8187 0.416332
\(949\) −5.95658 −0.193359
\(950\) −13.6373 −0.442453
\(951\) −3.10796 −0.100783
\(952\) −0.302785 −0.00981331
\(953\) 52.1860 1.69047 0.845234 0.534396i \(-0.179461\pi\)
0.845234 + 0.534396i \(0.179461\pi\)
\(954\) −52.9516 −1.71437
\(955\) 14.7414 0.477020
\(956\) 15.3664 0.496985
\(957\) 0.419281 0.0135534
\(958\) −7.32770 −0.236747
\(959\) −41.2640 −1.33249
\(960\) −1.18106 −0.0381184
\(961\) −26.2635 −0.847210
\(962\) −73.5192 −2.37035
\(963\) −2.27437 −0.0732907
\(964\) 26.9823 0.869041
\(965\) −7.91989 −0.254950
\(966\) −19.8777 −0.639554
\(967\) 8.20198 0.263758 0.131879 0.991266i \(-0.457899\pi\)
0.131879 + 0.991266i \(0.457899\pi\)
\(968\) 1.21914 0.0391845
\(969\) 0.267095 0.00858033
\(970\) 11.0392 0.354446
\(971\) 1.02351 0.0328460 0.0164230 0.999865i \(-0.494772\pi\)
0.0164230 + 0.999865i \(0.494772\pi\)
\(972\) 17.6746 0.566912
\(973\) 15.1448 0.485519
\(974\) −56.4532 −1.80888
\(975\) −3.41036 −0.109219
\(976\) 12.1630 0.389328
\(977\) −36.7427 −1.17550 −0.587752 0.809041i \(-0.699987\pi\)
−0.587752 + 0.809041i \(0.699987\pi\)
\(978\) 14.2499 0.455662
\(979\) −7.39881 −0.236467
\(980\) 11.7478 0.375269
\(981\) −17.7804 −0.567684
\(982\) −18.2993 −0.583955
\(983\) −7.17396 −0.228814 −0.114407 0.993434i \(-0.536497\pi\)
−0.114407 + 0.993434i \(0.536497\pi\)
\(984\) −5.10000 −0.162582
\(985\) −19.2554 −0.613527
\(986\) −0.0834753 −0.00265840
\(987\) −9.48223 −0.301823
\(988\) −59.2805 −1.88596
\(989\) 1.23307 0.0392093
\(990\) 4.87787 0.155029
\(991\) 4.28532 0.136128 0.0680639 0.997681i \(-0.478318\pi\)
0.0680639 + 0.997681i \(0.478318\pi\)
\(992\) 14.1189 0.448275
\(993\) 11.2591 0.357297
\(994\) −82.0600 −2.60279
\(995\) −6.98322 −0.221383
\(996\) 3.32554 0.105374
\(997\) 8.99158 0.284766 0.142383 0.989812i \(-0.454523\pi\)
0.142383 + 0.989812i \(0.454523\pi\)
\(998\) 55.5903 1.75968
\(999\) 21.9582 0.694728
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 \(a_p\))