Properties

Label 4015.2.a.h.1.18
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 1.18
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.199490 q^{2}\) \(-3.23393 q^{3}\) \(-1.96020 q^{4}\) \(+1.00000 q^{5}\) \(+0.645135 q^{6}\) \(-5.08849 q^{7}\) \(+0.790020 q^{8}\) \(+7.45829 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.199490 q^{2}\) \(-3.23393 q^{3}\) \(-1.96020 q^{4}\) \(+1.00000 q^{5}\) \(+0.645135 q^{6}\) \(-5.08849 q^{7}\) \(+0.790020 q^{8}\) \(+7.45829 q^{9}\) \(-0.199490 q^{10}\) \(+1.00000 q^{11}\) \(+6.33916 q^{12}\) \(+1.81391 q^{13}\) \(+1.01510 q^{14}\) \(-3.23393 q^{15}\) \(+3.76281 q^{16}\) \(+2.44895 q^{17}\) \(-1.48785 q^{18}\) \(-3.81160 q^{19}\) \(-1.96020 q^{20}\) \(+16.4558 q^{21}\) \(-0.199490 q^{22}\) \(+1.59753 q^{23}\) \(-2.55487 q^{24}\) \(+1.00000 q^{25}\) \(-0.361857 q^{26}\) \(-14.4178 q^{27}\) \(+9.97449 q^{28}\) \(-0.667100 q^{29}\) \(+0.645135 q^{30}\) \(-0.936457 q^{31}\) \(-2.33068 q^{32}\) \(-3.23393 q^{33}\) \(-0.488540 q^{34}\) \(-5.08849 q^{35}\) \(-14.6198 q^{36}\) \(-9.86168 q^{37}\) \(+0.760375 q^{38}\) \(-5.86606 q^{39}\) \(+0.790020 q^{40}\) \(+1.75199 q^{41}\) \(-3.28277 q^{42}\) \(-1.98661 q^{43}\) \(-1.96020 q^{44}\) \(+7.45829 q^{45}\) \(-0.318690 q^{46}\) \(+8.88010 q^{47}\) \(-12.1686 q^{48}\) \(+18.8928 q^{49}\) \(-0.199490 q^{50}\) \(-7.91971 q^{51}\) \(-3.55564 q^{52}\) \(-7.64714 q^{53}\) \(+2.87620 q^{54}\) \(+1.00000 q^{55}\) \(-4.02001 q^{56}\) \(+12.3264 q^{57}\) \(+0.133080 q^{58}\) \(-11.6715 q^{59}\) \(+6.33916 q^{60}\) \(-4.97347 q^{61}\) \(+0.186814 q^{62}\) \(-37.9514 q^{63}\) \(-7.06067 q^{64}\) \(+1.81391 q^{65}\) \(+0.645135 q^{66}\) \(-13.1510 q^{67}\) \(-4.80043 q^{68}\) \(-5.16628 q^{69}\) \(+1.01510 q^{70}\) \(+7.86330 q^{71}\) \(+5.89220 q^{72}\) \(+1.00000 q^{73}\) \(+1.96730 q^{74}\) \(-3.23393 q^{75}\) \(+7.47151 q^{76}\) \(-5.08849 q^{77}\) \(+1.17022 q^{78}\) \(-3.69416 q^{79}\) \(+3.76281 q^{80}\) \(+24.2512 q^{81}\) \(-0.349504 q^{82}\) \(-15.6546 q^{83}\) \(-32.2568 q^{84}\) \(+2.44895 q^{85}\) \(+0.396308 q^{86}\) \(+2.15735 q^{87}\) \(+0.790020 q^{88}\) \(+1.50523 q^{89}\) \(-1.48785 q^{90}\) \(-9.23009 q^{91}\) \(-3.13148 q^{92}\) \(+3.02843 q^{93}\) \(-1.77149 q^{94}\) \(-3.81160 q^{95}\) \(+7.53726 q^{96}\) \(-2.22058 q^{97}\) \(-3.76891 q^{98}\) \(+7.45829 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.199490 −0.141061 −0.0705303 0.997510i \(-0.522469\pi\)
−0.0705303 + 0.997510i \(0.522469\pi\)
\(3\) −3.23393 −1.86711 −0.933554 0.358436i \(-0.883310\pi\)
−0.933554 + 0.358436i \(0.883310\pi\)
\(4\) −1.96020 −0.980102
\(5\) 1.00000 0.447214
\(6\) 0.645135 0.263375
\(7\) −5.08849 −1.92327 −0.961635 0.274332i \(-0.911543\pi\)
−0.961635 + 0.274332i \(0.911543\pi\)
\(8\) 0.790020 0.279314
\(9\) 7.45829 2.48610
\(10\) −0.199490 −0.0630842
\(11\) 1.00000 0.301511
\(12\) 6.33916 1.82996
\(13\) 1.81391 0.503089 0.251545 0.967846i \(-0.419062\pi\)
0.251545 + 0.967846i \(0.419062\pi\)
\(14\) 1.01510 0.271298
\(15\) −3.23393 −0.834996
\(16\) 3.76281 0.940702
\(17\) 2.44895 0.593957 0.296978 0.954884i \(-0.404021\pi\)
0.296978 + 0.954884i \(0.404021\pi\)
\(18\) −1.48785 −0.350690
\(19\) −3.81160 −0.874441 −0.437220 0.899354i \(-0.644037\pi\)
−0.437220 + 0.899354i \(0.644037\pi\)
\(20\) −1.96020 −0.438315
\(21\) 16.4558 3.59095
\(22\) −0.199490 −0.0425314
\(23\) 1.59753 0.333107 0.166554 0.986032i \(-0.446736\pi\)
0.166554 + 0.986032i \(0.446736\pi\)
\(24\) −2.55487 −0.521510
\(25\) 1.00000 0.200000
\(26\) −0.361857 −0.0709660
\(27\) −14.4178 −2.77470
\(28\) 9.97449 1.88500
\(29\) −0.667100 −0.123877 −0.0619387 0.998080i \(-0.519728\pi\)
−0.0619387 + 0.998080i \(0.519728\pi\)
\(30\) 0.645135 0.117785
\(31\) −0.936457 −0.168193 −0.0840963 0.996458i \(-0.526800\pi\)
−0.0840963 + 0.996458i \(0.526800\pi\)
\(32\) −2.33068 −0.412010
\(33\) −3.23393 −0.562955
\(34\) −0.488540 −0.0837838
\(35\) −5.08849 −0.860112
\(36\) −14.6198 −2.43663
\(37\) −9.86168 −1.62125 −0.810625 0.585565i \(-0.800873\pi\)
−0.810625 + 0.585565i \(0.800873\pi\)
\(38\) 0.760375 0.123349
\(39\) −5.86606 −0.939322
\(40\) 0.790020 0.124913
\(41\) 1.75199 0.273615 0.136807 0.990598i \(-0.456316\pi\)
0.136807 + 0.990598i \(0.456316\pi\)
\(42\) −3.28277 −0.506542
\(43\) −1.98661 −0.302955 −0.151478 0.988461i \(-0.548403\pi\)
−0.151478 + 0.988461i \(0.548403\pi\)
\(44\) −1.96020 −0.295512
\(45\) 7.45829 1.11182
\(46\) −0.318690 −0.0469883
\(47\) 8.88010 1.29530 0.647648 0.761940i \(-0.275753\pi\)
0.647648 + 0.761940i \(0.275753\pi\)
\(48\) −12.1686 −1.75639
\(49\) 18.8928 2.69897
\(50\) −0.199490 −0.0282121
\(51\) −7.91971 −1.10898
\(52\) −3.55564 −0.493079
\(53\) −7.64714 −1.05041 −0.525207 0.850974i \(-0.676012\pi\)
−0.525207 + 0.850974i \(0.676012\pi\)
\(54\) 2.87620 0.391401
\(55\) 1.00000 0.134840
\(56\) −4.02001 −0.537197
\(57\) 12.3264 1.63268
\(58\) 0.133080 0.0174742
\(59\) −11.6715 −1.51950 −0.759749 0.650216i \(-0.774678\pi\)
−0.759749 + 0.650216i \(0.774678\pi\)
\(60\) 6.33916 0.818382
\(61\) −4.97347 −0.636787 −0.318394 0.947959i \(-0.603143\pi\)
−0.318394 + 0.947959i \(0.603143\pi\)
\(62\) 0.186814 0.0237253
\(63\) −37.9514 −4.78143
\(64\) −7.06067 −0.882583
\(65\) 1.81391 0.224988
\(66\) 0.645135 0.0794107
\(67\) −13.1510 −1.60665 −0.803323 0.595543i \(-0.796937\pi\)
−0.803323 + 0.595543i \(0.796937\pi\)
\(68\) −4.80043 −0.582138
\(69\) −5.16628 −0.621947
\(70\) 1.01510 0.121328
\(71\) 7.86330 0.933202 0.466601 0.884468i \(-0.345478\pi\)
0.466601 + 0.884468i \(0.345478\pi\)
\(72\) 5.89220 0.694402
\(73\) 1.00000 0.117041
\(74\) 1.96730 0.228694
\(75\) −3.23393 −0.373422
\(76\) 7.47151 0.857041
\(77\) −5.08849 −0.579888
\(78\) 1.17022 0.132501
\(79\) −3.69416 −0.415626 −0.207813 0.978169i \(-0.566635\pi\)
−0.207813 + 0.978169i \(0.566635\pi\)
\(80\) 3.76281 0.420695
\(81\) 24.2512 2.69458
\(82\) −0.349504 −0.0385962
\(83\) −15.6546 −1.71831 −0.859157 0.511712i \(-0.829011\pi\)
−0.859157 + 0.511712i \(0.829011\pi\)
\(84\) −32.2568 −3.51950
\(85\) 2.44895 0.265625
\(86\) 0.396308 0.0427350
\(87\) 2.15735 0.231293
\(88\) 0.790020 0.0842164
\(89\) 1.50523 0.159554 0.0797772 0.996813i \(-0.474579\pi\)
0.0797772 + 0.996813i \(0.474579\pi\)
\(90\) −1.48785 −0.156833
\(91\) −9.23009 −0.967576
\(92\) −3.13148 −0.326479
\(93\) 3.02843 0.314034
\(94\) −1.77149 −0.182715
\(95\) −3.81160 −0.391062
\(96\) 7.53726 0.769268
\(97\) −2.22058 −0.225465 −0.112733 0.993625i \(-0.535960\pi\)
−0.112733 + 0.993625i \(0.535960\pi\)
\(98\) −3.76891 −0.380718
\(99\) 7.45829 0.749586
\(100\) −1.96020 −0.196020
\(101\) −12.3903 −1.23289 −0.616443 0.787400i \(-0.711427\pi\)
−0.616443 + 0.787400i \(0.711427\pi\)
\(102\) 1.57990 0.156434
\(103\) 10.5134 1.03592 0.517959 0.855405i \(-0.326692\pi\)
0.517959 + 0.855405i \(0.326692\pi\)
\(104\) 1.43303 0.140520
\(105\) 16.4558 1.60592
\(106\) 1.52553 0.148172
\(107\) −0.303178 −0.0293093 −0.0146546 0.999893i \(-0.504665\pi\)
−0.0146546 + 0.999893i \(0.504665\pi\)
\(108\) 28.2618 2.71949
\(109\) 16.3308 1.56421 0.782104 0.623148i \(-0.214146\pi\)
0.782104 + 0.623148i \(0.214146\pi\)
\(110\) −0.199490 −0.0190206
\(111\) 31.8920 3.02705
\(112\) −19.1470 −1.80922
\(113\) 6.10228 0.574054 0.287027 0.957922i \(-0.407333\pi\)
0.287027 + 0.957922i \(0.407333\pi\)
\(114\) −2.45900 −0.230306
\(115\) 1.59753 0.148970
\(116\) 1.30765 0.121412
\(117\) 13.5287 1.25073
\(118\) 2.32834 0.214341
\(119\) −12.4614 −1.14234
\(120\) −2.55487 −0.233226
\(121\) 1.00000 0.0909091
\(122\) 0.992155 0.0898255
\(123\) −5.66580 −0.510868
\(124\) 1.83565 0.164846
\(125\) 1.00000 0.0894427
\(126\) 7.57093 0.674472
\(127\) −17.9997 −1.59722 −0.798608 0.601851i \(-0.794430\pi\)
−0.798608 + 0.601851i \(0.794430\pi\)
\(128\) 6.06989 0.536508
\(129\) 6.42455 0.565650
\(130\) −0.361857 −0.0317370
\(131\) 4.98491 0.435534 0.217767 0.976001i \(-0.430123\pi\)
0.217767 + 0.976001i \(0.430123\pi\)
\(132\) 6.33916 0.551753
\(133\) 19.3953 1.68179
\(134\) 2.62348 0.226635
\(135\) −14.4178 −1.24088
\(136\) 1.93472 0.165901
\(137\) −8.45540 −0.722394 −0.361197 0.932490i \(-0.617632\pi\)
−0.361197 + 0.932490i \(0.617632\pi\)
\(138\) 1.03062 0.0877322
\(139\) 19.4886 1.65301 0.826503 0.562933i \(-0.190327\pi\)
0.826503 + 0.562933i \(0.190327\pi\)
\(140\) 9.97449 0.842998
\(141\) −28.7176 −2.41846
\(142\) −1.56865 −0.131638
\(143\) 1.81391 0.151687
\(144\) 28.0641 2.33867
\(145\) −0.667100 −0.0553996
\(146\) −0.199490 −0.0165099
\(147\) −61.0979 −5.03927
\(148\) 19.3309 1.58899
\(149\) 17.9370 1.46946 0.734728 0.678362i \(-0.237310\pi\)
0.734728 + 0.678362i \(0.237310\pi\)
\(150\) 0.645135 0.0526751
\(151\) 19.1038 1.55464 0.777322 0.629103i \(-0.216578\pi\)
0.777322 + 0.629103i \(0.216578\pi\)
\(152\) −3.01124 −0.244244
\(153\) 18.2649 1.47663
\(154\) 1.01510 0.0817993
\(155\) −0.936457 −0.0752180
\(156\) 11.4987 0.920631
\(157\) −9.88667 −0.789042 −0.394521 0.918887i \(-0.629089\pi\)
−0.394521 + 0.918887i \(0.629089\pi\)
\(158\) 0.736947 0.0586284
\(159\) 24.7303 1.96124
\(160\) −2.33068 −0.184257
\(161\) −8.12900 −0.640655
\(162\) −4.83786 −0.380098
\(163\) 6.03179 0.472447 0.236223 0.971699i \(-0.424090\pi\)
0.236223 + 0.971699i \(0.424090\pi\)
\(164\) −3.43425 −0.268170
\(165\) −3.23393 −0.251761
\(166\) 3.12293 0.242386
\(167\) −7.84550 −0.607103 −0.303551 0.952815i \(-0.598172\pi\)
−0.303551 + 0.952815i \(0.598172\pi\)
\(168\) 13.0004 1.00300
\(169\) −9.70972 −0.746901
\(170\) −0.488540 −0.0374693
\(171\) −28.4280 −2.17394
\(172\) 3.89416 0.296927
\(173\) −5.16279 −0.392520 −0.196260 0.980552i \(-0.562880\pi\)
−0.196260 + 0.980552i \(0.562880\pi\)
\(174\) −0.430370 −0.0326263
\(175\) −5.08849 −0.384654
\(176\) 3.76281 0.283632
\(177\) 37.7448 2.83707
\(178\) −0.300278 −0.0225068
\(179\) −19.1713 −1.43293 −0.716467 0.697621i \(-0.754242\pi\)
−0.716467 + 0.697621i \(0.754242\pi\)
\(180\) −14.6198 −1.08969
\(181\) −8.14103 −0.605118 −0.302559 0.953131i \(-0.597841\pi\)
−0.302559 + 0.953131i \(0.597841\pi\)
\(182\) 1.84131 0.136487
\(183\) 16.0838 1.18895
\(184\) 1.26208 0.0930416
\(185\) −9.86168 −0.725045
\(186\) −0.604141 −0.0442978
\(187\) 2.44895 0.179085
\(188\) −17.4068 −1.26952
\(189\) 73.3648 5.33650
\(190\) 0.760375 0.0551634
\(191\) 3.40543 0.246408 0.123204 0.992381i \(-0.460683\pi\)
0.123204 + 0.992381i \(0.460683\pi\)
\(192\) 22.8337 1.64788
\(193\) −13.0471 −0.939148 −0.469574 0.882893i \(-0.655592\pi\)
−0.469574 + 0.882893i \(0.655592\pi\)
\(194\) 0.442982 0.0318043
\(195\) −5.86606 −0.420078
\(196\) −37.0337 −2.64526
\(197\) −21.8240 −1.55490 −0.777449 0.628946i \(-0.783487\pi\)
−0.777449 + 0.628946i \(0.783487\pi\)
\(198\) −1.48785 −0.105737
\(199\) 13.8430 0.981303 0.490651 0.871356i \(-0.336759\pi\)
0.490651 + 0.871356i \(0.336759\pi\)
\(200\) 0.790020 0.0558629
\(201\) 42.5293 2.99978
\(202\) 2.47175 0.173911
\(203\) 3.39453 0.238250
\(204\) 15.5242 1.08691
\(205\) 1.75199 0.122364
\(206\) −2.09732 −0.146127
\(207\) 11.9148 0.828136
\(208\) 6.82541 0.473257
\(209\) −3.81160 −0.263654
\(210\) −3.28277 −0.226532
\(211\) 5.68107 0.391101 0.195551 0.980694i \(-0.437351\pi\)
0.195551 + 0.980694i \(0.437351\pi\)
\(212\) 14.9899 1.02951
\(213\) −25.4293 −1.74239
\(214\) 0.0604808 0.00413438
\(215\) −1.98661 −0.135486
\(216\) −11.3903 −0.775014
\(217\) 4.76515 0.323480
\(218\) −3.25783 −0.220648
\(219\) −3.23393 −0.218529
\(220\) −1.96020 −0.132157
\(221\) 4.44218 0.298813
\(222\) −6.36212 −0.426998
\(223\) 15.6168 1.04578 0.522889 0.852401i \(-0.324854\pi\)
0.522889 + 0.852401i \(0.324854\pi\)
\(224\) 11.8597 0.792407
\(225\) 7.45829 0.497219
\(226\) −1.21734 −0.0809764
\(227\) 17.6442 1.17109 0.585543 0.810641i \(-0.300881\pi\)
0.585543 + 0.810641i \(0.300881\pi\)
\(228\) −24.1623 −1.60019
\(229\) 1.85113 0.122326 0.0611631 0.998128i \(-0.480519\pi\)
0.0611631 + 0.998128i \(0.480519\pi\)
\(230\) −0.318690 −0.0210138
\(231\) 16.4558 1.08271
\(232\) −0.527022 −0.0346007
\(233\) 17.6958 1.15929 0.579644 0.814870i \(-0.303192\pi\)
0.579644 + 0.814870i \(0.303192\pi\)
\(234\) −2.69883 −0.176428
\(235\) 8.88010 0.579274
\(236\) 22.8785 1.48926
\(237\) 11.9467 0.776018
\(238\) 2.48593 0.161139
\(239\) −13.3055 −0.860663 −0.430331 0.902671i \(-0.641603\pi\)
−0.430331 + 0.902671i \(0.641603\pi\)
\(240\) −12.1686 −0.785483
\(241\) 17.2767 1.11289 0.556446 0.830884i \(-0.312165\pi\)
0.556446 + 0.830884i \(0.312165\pi\)
\(242\) −0.199490 −0.0128237
\(243\) −35.1732 −2.25636
\(244\) 9.74901 0.624116
\(245\) 18.8928 1.20701
\(246\) 1.13027 0.0720634
\(247\) −6.91391 −0.439922
\(248\) −0.739820 −0.0469786
\(249\) 50.6258 3.20828
\(250\) −0.199490 −0.0126168
\(251\) −16.6467 −1.05073 −0.525367 0.850876i \(-0.676072\pi\)
−0.525367 + 0.850876i \(0.676072\pi\)
\(252\) 74.3926 4.68629
\(253\) 1.59753 0.100436
\(254\) 3.59076 0.225304
\(255\) −7.91971 −0.495952
\(256\) 12.9105 0.806903
\(257\) −20.2119 −1.26078 −0.630392 0.776277i \(-0.717106\pi\)
−0.630392 + 0.776277i \(0.717106\pi\)
\(258\) −1.28163 −0.0797910
\(259\) 50.1811 3.11810
\(260\) −3.55564 −0.220511
\(261\) −4.97542 −0.307971
\(262\) −0.994439 −0.0614366
\(263\) 2.81916 0.173837 0.0869183 0.996215i \(-0.472298\pi\)
0.0869183 + 0.996215i \(0.472298\pi\)
\(264\) −2.55487 −0.157241
\(265\) −7.64714 −0.469760
\(266\) −3.86916 −0.237234
\(267\) −4.86781 −0.297905
\(268\) 25.7786 1.57468
\(269\) −7.89372 −0.481289 −0.240644 0.970613i \(-0.577359\pi\)
−0.240644 + 0.970613i \(0.577359\pi\)
\(270\) 2.87620 0.175040
\(271\) −5.05602 −0.307131 −0.153566 0.988138i \(-0.549076\pi\)
−0.153566 + 0.988138i \(0.549076\pi\)
\(272\) 9.21491 0.558736
\(273\) 29.8494 1.80657
\(274\) 1.68677 0.101901
\(275\) 1.00000 0.0603023
\(276\) 10.1270 0.609572
\(277\) 9.11389 0.547601 0.273800 0.961787i \(-0.411719\pi\)
0.273800 + 0.961787i \(0.411719\pi\)
\(278\) −3.88779 −0.233174
\(279\) −6.98436 −0.418143
\(280\) −4.02001 −0.240242
\(281\) 15.1470 0.903597 0.451798 0.892120i \(-0.350783\pi\)
0.451798 + 0.892120i \(0.350783\pi\)
\(282\) 5.72887 0.341149
\(283\) 11.3872 0.676901 0.338450 0.940984i \(-0.390097\pi\)
0.338450 + 0.940984i \(0.390097\pi\)
\(284\) −15.4137 −0.914633
\(285\) 12.3264 0.730155
\(286\) −0.361857 −0.0213971
\(287\) −8.91498 −0.526235
\(288\) −17.3829 −1.02430
\(289\) −11.0027 −0.647216
\(290\) 0.133080 0.00781470
\(291\) 7.18118 0.420968
\(292\) −1.96020 −0.114712
\(293\) 24.6240 1.43855 0.719275 0.694725i \(-0.244474\pi\)
0.719275 + 0.694725i \(0.244474\pi\)
\(294\) 12.1884 0.710842
\(295\) −11.6715 −0.679540
\(296\) −7.79093 −0.452838
\(297\) −14.4178 −0.836604
\(298\) −3.57825 −0.207282
\(299\) 2.89777 0.167583
\(300\) 6.33916 0.365991
\(301\) 10.1089 0.582665
\(302\) −3.81101 −0.219299
\(303\) 40.0695 2.30193
\(304\) −14.3423 −0.822588
\(305\) −4.97347 −0.284780
\(306\) −3.64367 −0.208295
\(307\) 6.02662 0.343958 0.171979 0.985101i \(-0.444984\pi\)
0.171979 + 0.985101i \(0.444984\pi\)
\(308\) 9.97449 0.568349
\(309\) −33.9997 −1.93417
\(310\) 0.186814 0.0106103
\(311\) −32.9998 −1.87125 −0.935624 0.352998i \(-0.885162\pi\)
−0.935624 + 0.352998i \(0.885162\pi\)
\(312\) −4.63431 −0.262366
\(313\) −7.42152 −0.419489 −0.209745 0.977756i \(-0.567263\pi\)
−0.209745 + 0.977756i \(0.567263\pi\)
\(314\) 1.97229 0.111303
\(315\) −37.9514 −2.13832
\(316\) 7.24131 0.407356
\(317\) −17.6516 −0.991415 −0.495707 0.868490i \(-0.665091\pi\)
−0.495707 + 0.868490i \(0.665091\pi\)
\(318\) −4.93344 −0.276653
\(319\) −0.667100 −0.0373504
\(320\) −7.06067 −0.394703
\(321\) 0.980454 0.0547236
\(322\) 1.62165 0.0903712
\(323\) −9.33440 −0.519380
\(324\) −47.5373 −2.64096
\(325\) 1.81391 0.100618
\(326\) −1.20328 −0.0666436
\(327\) −52.8127 −2.92055
\(328\) 1.38411 0.0764245
\(329\) −45.1863 −2.49120
\(330\) 0.645135 0.0355135
\(331\) 35.4038 1.94597 0.972986 0.230865i \(-0.0741557\pi\)
0.972986 + 0.230865i \(0.0741557\pi\)
\(332\) 30.6862 1.68412
\(333\) −73.5512 −4.03058
\(334\) 1.56510 0.0856382
\(335\) −13.1510 −0.718514
\(336\) 61.9201 3.37802
\(337\) 3.52978 0.192279 0.0961396 0.995368i \(-0.469350\pi\)
0.0961396 + 0.995368i \(0.469350\pi\)
\(338\) 1.93699 0.105358
\(339\) −19.7343 −1.07182
\(340\) −4.80043 −0.260340
\(341\) −0.936457 −0.0507120
\(342\) 5.67109 0.306658
\(343\) −60.5163 −3.26757
\(344\) −1.56946 −0.0846197
\(345\) −5.16628 −0.278143
\(346\) 1.02992 0.0553690
\(347\) 15.2212 0.817118 0.408559 0.912732i \(-0.366031\pi\)
0.408559 + 0.912732i \(0.366031\pi\)
\(348\) −4.22885 −0.226690
\(349\) −15.8857 −0.850341 −0.425171 0.905113i \(-0.639786\pi\)
−0.425171 + 0.905113i \(0.639786\pi\)
\(350\) 1.01510 0.0542595
\(351\) −26.1526 −1.39592
\(352\) −2.33068 −0.124226
\(353\) 14.0821 0.749517 0.374758 0.927122i \(-0.377726\pi\)
0.374758 + 0.927122i \(0.377726\pi\)
\(354\) −7.52969 −0.400199
\(355\) 7.86330 0.417341
\(356\) −2.95056 −0.156379
\(357\) 40.2994 2.13287
\(358\) 3.82449 0.202130
\(359\) 8.88663 0.469018 0.234509 0.972114i \(-0.424652\pi\)
0.234509 + 0.972114i \(0.424652\pi\)
\(360\) 5.89220 0.310546
\(361\) −4.47172 −0.235353
\(362\) 1.62405 0.0853583
\(363\) −3.23393 −0.169737
\(364\) 18.0929 0.948323
\(365\) 1.00000 0.0523424
\(366\) −3.20856 −0.167714
\(367\) 23.6621 1.23515 0.617575 0.786512i \(-0.288115\pi\)
0.617575 + 0.786512i \(0.288115\pi\)
\(368\) 6.01118 0.313354
\(369\) 13.0668 0.680232
\(370\) 1.96730 0.102275
\(371\) 38.9124 2.02023
\(372\) −5.93635 −0.307785
\(373\) 24.0619 1.24588 0.622939 0.782271i \(-0.285939\pi\)
0.622939 + 0.782271i \(0.285939\pi\)
\(374\) −0.488540 −0.0252618
\(375\) −3.23393 −0.166999
\(376\) 7.01546 0.361795
\(377\) −1.21006 −0.0623213
\(378\) −14.6355 −0.752770
\(379\) −26.9520 −1.38443 −0.692215 0.721692i \(-0.743365\pi\)
−0.692215 + 0.721692i \(0.743365\pi\)
\(380\) 7.47151 0.383280
\(381\) 58.2098 2.98218
\(382\) −0.679348 −0.0347585
\(383\) 6.83061 0.349028 0.174514 0.984655i \(-0.444165\pi\)
0.174514 + 0.984655i \(0.444165\pi\)
\(384\) −19.6296 −1.00172
\(385\) −5.08849 −0.259334
\(386\) 2.60275 0.132477
\(387\) −14.8167 −0.753176
\(388\) 4.35278 0.220979
\(389\) 17.9698 0.911104 0.455552 0.890209i \(-0.349442\pi\)
0.455552 + 0.890209i \(0.349442\pi\)
\(390\) 1.17022 0.0592564
\(391\) 3.91225 0.197851
\(392\) 14.9257 0.753860
\(393\) −16.1208 −0.813189
\(394\) 4.35367 0.219335
\(395\) −3.69416 −0.185873
\(396\) −14.6198 −0.734671
\(397\) 7.53954 0.378399 0.189199 0.981939i \(-0.439411\pi\)
0.189199 + 0.981939i \(0.439411\pi\)
\(398\) −2.76153 −0.138423
\(399\) −62.7230 −3.14008
\(400\) 3.76281 0.188140
\(401\) 12.6850 0.633459 0.316730 0.948516i \(-0.397415\pi\)
0.316730 + 0.948516i \(0.397415\pi\)
\(402\) −8.48416 −0.423151
\(403\) −1.69865 −0.0846159
\(404\) 24.2876 1.20835
\(405\) 24.2512 1.20505
\(406\) −0.677175 −0.0336076
\(407\) −9.86168 −0.488825
\(408\) −6.25673 −0.309754
\(409\) 34.1896 1.69057 0.845283 0.534319i \(-0.179432\pi\)
0.845283 + 0.534319i \(0.179432\pi\)
\(410\) −0.349504 −0.0172608
\(411\) 27.3442 1.34879
\(412\) −20.6085 −1.01531
\(413\) 59.3903 2.92241
\(414\) −2.37688 −0.116817
\(415\) −15.6546 −0.768453
\(416\) −4.22765 −0.207278
\(417\) −63.0249 −3.08634
\(418\) 0.760375 0.0371912
\(419\) −4.80104 −0.234546 −0.117273 0.993100i \(-0.537415\pi\)
−0.117273 + 0.993100i \(0.537415\pi\)
\(420\) −32.2568 −1.57397
\(421\) −1.52853 −0.0744961 −0.0372481 0.999306i \(-0.511859\pi\)
−0.0372481 + 0.999306i \(0.511859\pi\)
\(422\) −1.13332 −0.0551690
\(423\) 66.2303 3.22023
\(424\) −6.04139 −0.293396
\(425\) 2.44895 0.118791
\(426\) 5.07289 0.245783
\(427\) 25.3075 1.22471
\(428\) 0.594290 0.0287261
\(429\) −5.86606 −0.283216
\(430\) 0.396308 0.0191117
\(431\) 2.87906 0.138679 0.0693396 0.997593i \(-0.477911\pi\)
0.0693396 + 0.997593i \(0.477911\pi\)
\(432\) −54.2513 −2.61017
\(433\) 7.12162 0.342243 0.171122 0.985250i \(-0.445261\pi\)
0.171122 + 0.985250i \(0.445261\pi\)
\(434\) −0.950600 −0.0456302
\(435\) 2.15735 0.103437
\(436\) −32.0117 −1.53308
\(437\) −6.08913 −0.291282
\(438\) 0.645135 0.0308258
\(439\) 27.2069 1.29851 0.649257 0.760569i \(-0.275080\pi\)
0.649257 + 0.760569i \(0.275080\pi\)
\(440\) 0.790020 0.0376627
\(441\) 140.908 6.70989
\(442\) −0.886168 −0.0421507
\(443\) −28.6887 −1.36304 −0.681521 0.731798i \(-0.738681\pi\)
−0.681521 + 0.731798i \(0.738681\pi\)
\(444\) −62.5147 −2.96682
\(445\) 1.50523 0.0713549
\(446\) −3.11539 −0.147518
\(447\) −58.0069 −2.74363
\(448\) 35.9282 1.69745
\(449\) 9.30793 0.439268 0.219634 0.975582i \(-0.429514\pi\)
0.219634 + 0.975582i \(0.429514\pi\)
\(450\) −1.48785 −0.0701380
\(451\) 1.75199 0.0824979
\(452\) −11.9617 −0.562632
\(453\) −61.7803 −2.90269
\(454\) −3.51984 −0.165194
\(455\) −9.23009 −0.432713
\(456\) 9.73813 0.456030
\(457\) −29.0463 −1.35873 −0.679365 0.733801i \(-0.737745\pi\)
−0.679365 + 0.733801i \(0.737745\pi\)
\(458\) −0.369282 −0.0172554
\(459\) −35.3083 −1.64805
\(460\) −3.13148 −0.146006
\(461\) −0.818568 −0.0381245 −0.0190623 0.999818i \(-0.506068\pi\)
−0.0190623 + 0.999818i \(0.506068\pi\)
\(462\) −3.28277 −0.152728
\(463\) 15.8732 0.737691 0.368845 0.929491i \(-0.379753\pi\)
0.368845 + 0.929491i \(0.379753\pi\)
\(464\) −2.51017 −0.116532
\(465\) 3.02843 0.140440
\(466\) −3.53012 −0.163530
\(467\) 11.5405 0.534032 0.267016 0.963692i \(-0.413962\pi\)
0.267016 + 0.963692i \(0.413962\pi\)
\(468\) −26.5190 −1.22584
\(469\) 66.9186 3.09002
\(470\) −1.77149 −0.0817127
\(471\) 31.9728 1.47323
\(472\) −9.22071 −0.424418
\(473\) −1.98661 −0.0913444
\(474\) −2.38323 −0.109466
\(475\) −3.81160 −0.174888
\(476\) 24.4270 1.11961
\(477\) −57.0345 −2.61143
\(478\) 2.65432 0.121406
\(479\) −26.6661 −1.21841 −0.609203 0.793015i \(-0.708510\pi\)
−0.609203 + 0.793015i \(0.708510\pi\)
\(480\) 7.53726 0.344027
\(481\) −17.8882 −0.815633
\(482\) −3.44653 −0.156985
\(483\) 26.2886 1.19617
\(484\) −1.96020 −0.0891002
\(485\) −2.22058 −0.100831
\(486\) 7.01670 0.318284
\(487\) 30.7891 1.39519 0.697595 0.716493i \(-0.254254\pi\)
0.697595 + 0.716493i \(0.254254\pi\)
\(488\) −3.92914 −0.177864
\(489\) −19.5064 −0.882109
\(490\) −3.76891 −0.170262
\(491\) −35.6631 −1.60945 −0.804726 0.593647i \(-0.797688\pi\)
−0.804726 + 0.593647i \(0.797688\pi\)
\(492\) 11.1061 0.500703
\(493\) −1.63369 −0.0735778
\(494\) 1.37925 0.0620556
\(495\) 7.45829 0.335225
\(496\) −3.52371 −0.158219
\(497\) −40.0124 −1.79480
\(498\) −10.0993 −0.452562
\(499\) −34.7460 −1.55544 −0.777722 0.628609i \(-0.783625\pi\)
−0.777722 + 0.628609i \(0.783625\pi\)
\(500\) −1.96020 −0.0876630
\(501\) 25.3718 1.13353
\(502\) 3.32086 0.148217
\(503\) −19.7827 −0.882065 −0.441032 0.897491i \(-0.645388\pi\)
−0.441032 + 0.897491i \(0.645388\pi\)
\(504\) −29.9824 −1.33552
\(505\) −12.3903 −0.551363
\(506\) −0.318690 −0.0141675
\(507\) 31.4005 1.39455
\(508\) 35.2831 1.56544
\(509\) 27.4381 1.21617 0.608087 0.793871i \(-0.291937\pi\)
0.608087 + 0.793871i \(0.291937\pi\)
\(510\) 1.57990 0.0699592
\(511\) −5.08849 −0.225102
\(512\) −14.7153 −0.650330
\(513\) 54.9548 2.42631
\(514\) 4.03207 0.177847
\(515\) 10.5134 0.463277
\(516\) −12.5934 −0.554395
\(517\) 8.88010 0.390546
\(518\) −10.0106 −0.439841
\(519\) 16.6961 0.732877
\(520\) 1.43303 0.0628424
\(521\) 18.5762 0.813837 0.406918 0.913465i \(-0.366603\pi\)
0.406918 + 0.913465i \(0.366603\pi\)
\(522\) 0.992546 0.0434426
\(523\) 41.3607 1.80858 0.904289 0.426921i \(-0.140402\pi\)
0.904289 + 0.426921i \(0.140402\pi\)
\(524\) −9.77144 −0.426867
\(525\) 16.4558 0.718191
\(526\) −0.562393 −0.0245215
\(527\) −2.29333 −0.0998991
\(528\) −12.1686 −0.529572
\(529\) −20.4479 −0.889040
\(530\) 1.52553 0.0662646
\(531\) −87.0493 −3.77762
\(532\) −38.0187 −1.64832
\(533\) 3.17796 0.137653
\(534\) 0.971079 0.0420227
\(535\) −0.303178 −0.0131075
\(536\) −10.3895 −0.448759
\(537\) 61.9987 2.67544
\(538\) 1.57472 0.0678908
\(539\) 18.8928 0.813769
\(540\) 28.2618 1.21619
\(541\) 8.82640 0.379477 0.189738 0.981835i \(-0.439236\pi\)
0.189738 + 0.981835i \(0.439236\pi\)
\(542\) 1.00862 0.0433241
\(543\) 26.3275 1.12982
\(544\) −5.70771 −0.244716
\(545\) 16.3308 0.699535
\(546\) −5.95466 −0.254836
\(547\) −17.8087 −0.761443 −0.380722 0.924690i \(-0.624324\pi\)
−0.380722 + 0.924690i \(0.624324\pi\)
\(548\) 16.5743 0.708019
\(549\) −37.0935 −1.58311
\(550\) −0.199490 −0.00850627
\(551\) 2.54272 0.108323
\(552\) −4.08147 −0.173719
\(553\) 18.7977 0.799360
\(554\) −1.81813 −0.0772449
\(555\) 31.8920 1.35374
\(556\) −38.2017 −1.62011
\(557\) 24.5953 1.04214 0.521069 0.853515i \(-0.325534\pi\)
0.521069 + 0.853515i \(0.325534\pi\)
\(558\) 1.39331 0.0589835
\(559\) −3.60354 −0.152413
\(560\) −19.1470 −0.809109
\(561\) −7.91971 −0.334370
\(562\) −3.02168 −0.127462
\(563\) 44.0996 1.85858 0.929288 0.369356i \(-0.120422\pi\)
0.929288 + 0.369356i \(0.120422\pi\)
\(564\) 56.2924 2.37034
\(565\) 6.10228 0.256725
\(566\) −2.27164 −0.0954840
\(567\) −123.402 −5.18240
\(568\) 6.21217 0.260657
\(569\) 32.8125 1.37557 0.687785 0.725915i \(-0.258583\pi\)
0.687785 + 0.725915i \(0.258583\pi\)
\(570\) −2.45900 −0.102996
\(571\) −41.2285 −1.72536 −0.862679 0.505752i \(-0.831215\pi\)
−0.862679 + 0.505752i \(0.831215\pi\)
\(572\) −3.55564 −0.148669
\(573\) −11.0129 −0.460071
\(574\) 1.77845 0.0742310
\(575\) 1.59753 0.0666214
\(576\) −52.6605 −2.19419
\(577\) −21.2172 −0.883282 −0.441641 0.897192i \(-0.645604\pi\)
−0.441641 + 0.897192i \(0.645604\pi\)
\(578\) 2.19492 0.0912966
\(579\) 42.1932 1.75349
\(580\) 1.30765 0.0542973
\(581\) 79.6582 3.30478
\(582\) −1.43257 −0.0593820
\(583\) −7.64714 −0.316712
\(584\) 0.790020 0.0326913
\(585\) 13.5287 0.559342
\(586\) −4.91224 −0.202923
\(587\) 20.4094 0.842388 0.421194 0.906971i \(-0.361611\pi\)
0.421194 + 0.906971i \(0.361611\pi\)
\(588\) 119.764 4.93899
\(589\) 3.56940 0.147074
\(590\) 2.32834 0.0958564
\(591\) 70.5774 2.90316
\(592\) −37.1076 −1.52511
\(593\) 3.96830 0.162959 0.0814793 0.996675i \(-0.474036\pi\)
0.0814793 + 0.996675i \(0.474036\pi\)
\(594\) 2.87620 0.118012
\(595\) −12.4614 −0.510869
\(596\) −35.1602 −1.44022
\(597\) −44.7672 −1.83220
\(598\) −0.578076 −0.0236393
\(599\) −38.4890 −1.57262 −0.786310 0.617833i \(-0.788011\pi\)
−0.786310 + 0.617833i \(0.788011\pi\)
\(600\) −2.55487 −0.104302
\(601\) 2.95147 0.120393 0.0601965 0.998187i \(-0.480827\pi\)
0.0601965 + 0.998187i \(0.480827\pi\)
\(602\) −2.01661 −0.0821910
\(603\) −98.0837 −3.99428
\(604\) −37.4473 −1.52371
\(605\) 1.00000 0.0406558
\(606\) −7.99345 −0.324712
\(607\) 31.0687 1.26104 0.630521 0.776173i \(-0.282841\pi\)
0.630521 + 0.776173i \(0.282841\pi\)
\(608\) 8.88362 0.360278
\(609\) −10.9777 −0.444838
\(610\) 0.992155 0.0401712
\(611\) 16.1077 0.651649
\(612\) −35.8030 −1.44725
\(613\) −24.5415 −0.991224 −0.495612 0.868544i \(-0.665056\pi\)
−0.495612 + 0.868544i \(0.665056\pi\)
\(614\) −1.20225 −0.0485189
\(615\) −5.66580 −0.228467
\(616\) −4.02001 −0.161971
\(617\) −23.0002 −0.925955 −0.462977 0.886370i \(-0.653219\pi\)
−0.462977 + 0.886370i \(0.653219\pi\)
\(618\) 6.78259 0.272836
\(619\) 23.6831 0.951905 0.475952 0.879471i \(-0.342103\pi\)
0.475952 + 0.879471i \(0.342103\pi\)
\(620\) 1.83565 0.0737213
\(621\) −23.0328 −0.924273
\(622\) 6.58313 0.263959
\(623\) −7.65937 −0.306866
\(624\) −22.0729 −0.883622
\(625\) 1.00000 0.0400000
\(626\) 1.48052 0.0591734
\(627\) 12.3264 0.492270
\(628\) 19.3799 0.773341
\(629\) −24.1507 −0.962952
\(630\) 7.57093 0.301633
\(631\) 26.1281 1.04014 0.520071 0.854123i \(-0.325905\pi\)
0.520071 + 0.854123i \(0.325905\pi\)
\(632\) −2.91846 −0.116090
\(633\) −18.3722 −0.730229
\(634\) 3.52132 0.139850
\(635\) −17.9997 −0.714297
\(636\) −48.4764 −1.92221
\(637\) 34.2699 1.35782
\(638\) 0.133080 0.00526867
\(639\) 58.6468 2.32003
\(640\) 6.06989 0.239934
\(641\) −5.61450 −0.221759 −0.110880 0.993834i \(-0.535367\pi\)
−0.110880 + 0.993834i \(0.535367\pi\)
\(642\) −0.195591 −0.00771934
\(643\) −39.9459 −1.57531 −0.787655 0.616116i \(-0.788705\pi\)
−0.787655 + 0.616116i \(0.788705\pi\)
\(644\) 15.9345 0.627907
\(645\) 6.42455 0.252967
\(646\) 1.86212 0.0732640
\(647\) −25.0996 −0.986768 −0.493384 0.869811i \(-0.664240\pi\)
−0.493384 + 0.869811i \(0.664240\pi\)
\(648\) 19.1589 0.752634
\(649\) −11.6715 −0.458146
\(650\) −0.361857 −0.0141932
\(651\) −15.4102 −0.603972
\(652\) −11.8235 −0.463046
\(653\) 22.6910 0.887966 0.443983 0.896035i \(-0.353565\pi\)
0.443983 + 0.896035i \(0.353565\pi\)
\(654\) 10.5356 0.411974
\(655\) 4.98491 0.194777
\(656\) 6.59239 0.257390
\(657\) 7.45829 0.290975
\(658\) 9.01421 0.351411
\(659\) −38.9264 −1.51636 −0.758178 0.652047i \(-0.773910\pi\)
−0.758178 + 0.652047i \(0.773910\pi\)
\(660\) 6.33916 0.246751
\(661\) −1.79011 −0.0696274 −0.0348137 0.999394i \(-0.511084\pi\)
−0.0348137 + 0.999394i \(0.511084\pi\)
\(662\) −7.06271 −0.274500
\(663\) −14.3657 −0.557916
\(664\) −12.3674 −0.479950
\(665\) 19.3953 0.752117
\(666\) 14.6727 0.568556
\(667\) −1.06571 −0.0412644
\(668\) 15.3788 0.595023
\(669\) −50.5036 −1.95258
\(670\) 2.62348 0.101354
\(671\) −4.97347 −0.191999
\(672\) −38.3533 −1.47951
\(673\) 15.7767 0.608148 0.304074 0.952648i \(-0.401653\pi\)
0.304074 + 0.952648i \(0.401653\pi\)
\(674\) −0.704154 −0.0271230
\(675\) −14.4178 −0.554940
\(676\) 19.0330 0.732039
\(677\) −23.8678 −0.917314 −0.458657 0.888614i \(-0.651669\pi\)
−0.458657 + 0.888614i \(0.651669\pi\)
\(678\) 3.93680 0.151192
\(679\) 11.2994 0.433631
\(680\) 1.93472 0.0741930
\(681\) −57.0600 −2.18655
\(682\) 0.186814 0.00715346
\(683\) 20.2845 0.776165 0.388083 0.921625i \(-0.373137\pi\)
0.388083 + 0.921625i \(0.373137\pi\)
\(684\) 55.7247 2.13069
\(685\) −8.45540 −0.323064
\(686\) 12.0724 0.460926
\(687\) −5.98642 −0.228396
\(688\) −7.47523 −0.284990
\(689\) −13.8712 −0.528452
\(690\) 1.03062 0.0392351
\(691\) 9.55265 0.363400 0.181700 0.983354i \(-0.441840\pi\)
0.181700 + 0.983354i \(0.441840\pi\)
\(692\) 10.1201 0.384709
\(693\) −37.9514 −1.44166
\(694\) −3.03648 −0.115263
\(695\) 19.4886 0.739246
\(696\) 1.70435 0.0646033
\(697\) 4.29052 0.162515
\(698\) 3.16903 0.119950
\(699\) −57.2268 −2.16452
\(700\) 9.97449 0.377000
\(701\) 32.7484 1.23689 0.618445 0.785828i \(-0.287763\pi\)
0.618445 + 0.785828i \(0.287763\pi\)
\(702\) 5.21718 0.196910
\(703\) 37.5888 1.41769
\(704\) −7.06067 −0.266109
\(705\) −28.7176 −1.08157
\(706\) −2.80924 −0.105727
\(707\) 63.0482 2.37117
\(708\) −73.9874 −2.78062
\(709\) −28.6857 −1.07732 −0.538658 0.842525i \(-0.681068\pi\)
−0.538658 + 0.842525i \(0.681068\pi\)
\(710\) −1.56865 −0.0588703
\(711\) −27.5521 −1.03329
\(712\) 1.18916 0.0445658
\(713\) −1.49601 −0.0560262
\(714\) −8.03932 −0.300864
\(715\) 1.81391 0.0678365
\(716\) 37.5797 1.40442
\(717\) 43.0291 1.60695
\(718\) −1.77279 −0.0661600
\(719\) −27.9305 −1.04163 −0.520816 0.853669i \(-0.674372\pi\)
−0.520816 + 0.853669i \(0.674372\pi\)
\(720\) 28.0641 1.04589
\(721\) −53.4975 −1.99235
\(722\) 0.892062 0.0331991
\(723\) −55.8717 −2.07789
\(724\) 15.9581 0.593077
\(725\) −0.667100 −0.0247755
\(726\) 0.645135 0.0239432
\(727\) 43.8990 1.62812 0.814062 0.580778i \(-0.197252\pi\)
0.814062 + 0.580778i \(0.197252\pi\)
\(728\) −7.29196 −0.270258
\(729\) 40.9941 1.51830
\(730\) −0.199490 −0.00738345
\(731\) −4.86510 −0.179942
\(732\) −31.5276 −1.16529
\(733\) 11.5712 0.427391 0.213696 0.976900i \(-0.431450\pi\)
0.213696 + 0.976900i \(0.431450\pi\)
\(734\) −4.72034 −0.174231
\(735\) −61.0979 −2.25363
\(736\) −3.72332 −0.137244
\(737\) −13.1510 −0.484422
\(738\) −2.60670 −0.0959539
\(739\) 7.11325 0.261665 0.130833 0.991404i \(-0.458235\pi\)
0.130833 + 0.991404i \(0.458235\pi\)
\(740\) 19.3309 0.710618
\(741\) 22.3591 0.821381
\(742\) −7.76263 −0.284975
\(743\) 33.9716 1.24630 0.623148 0.782104i \(-0.285853\pi\)
0.623148 + 0.782104i \(0.285853\pi\)
\(744\) 2.39252 0.0877142
\(745\) 17.9370 0.657160
\(746\) −4.80010 −0.175744
\(747\) −116.756 −4.27189
\(748\) −4.80043 −0.175521
\(749\) 1.54272 0.0563697
\(750\) 0.645135 0.0235570
\(751\) −14.1515 −0.516396 −0.258198 0.966092i \(-0.583129\pi\)
−0.258198 + 0.966092i \(0.583129\pi\)
\(752\) 33.4141 1.21849
\(753\) 53.8344 1.96183
\(754\) 0.241395 0.00879108
\(755\) 19.1038 0.695258
\(756\) −143.810 −5.23032
\(757\) −28.2459 −1.02661 −0.513307 0.858205i \(-0.671580\pi\)
−0.513307 + 0.858205i \(0.671580\pi\)
\(758\) 5.37664 0.195288
\(759\) −5.16628 −0.187524
\(760\) −3.01124 −0.109229
\(761\) −40.9436 −1.48420 −0.742101 0.670288i \(-0.766171\pi\)
−0.742101 + 0.670288i \(0.766171\pi\)
\(762\) −11.6123 −0.420668
\(763\) −83.0993 −3.00839
\(764\) −6.67534 −0.241505
\(765\) 18.2649 0.660370
\(766\) −1.36264 −0.0492340
\(767\) −21.1711 −0.764443
\(768\) −41.7515 −1.50658
\(769\) −24.0881 −0.868641 −0.434320 0.900758i \(-0.643011\pi\)
−0.434320 + 0.900758i \(0.643011\pi\)
\(770\) 1.01510 0.0365818
\(771\) 65.3638 2.35402
\(772\) 25.5749 0.920460
\(773\) 25.0757 0.901912 0.450956 0.892546i \(-0.351083\pi\)
0.450956 + 0.892546i \(0.351083\pi\)
\(774\) 2.95578 0.106243
\(775\) −0.936457 −0.0336385
\(776\) −1.75430 −0.0629757
\(777\) −162.282 −5.82184
\(778\) −3.58479 −0.128521
\(779\) −6.67788 −0.239260
\(780\) 11.4987 0.411719
\(781\) 7.86330 0.281371
\(782\) −0.780455 −0.0279090
\(783\) 9.61810 0.343723
\(784\) 71.0899 2.53892
\(785\) −9.88667 −0.352870
\(786\) 3.21594 0.114709
\(787\) −26.3223 −0.938289 −0.469145 0.883121i \(-0.655438\pi\)
−0.469145 + 0.883121i \(0.655438\pi\)
\(788\) 42.7796 1.52396
\(789\) −9.11695 −0.324572
\(790\) 0.736947 0.0262194
\(791\) −31.0514 −1.10406
\(792\) 5.89220 0.209370
\(793\) −9.02144 −0.320361
\(794\) −1.50406 −0.0533771
\(795\) 24.7303 0.877093
\(796\) −27.1351 −0.961777
\(797\) −8.78817 −0.311293 −0.155647 0.987813i \(-0.549746\pi\)
−0.155647 + 0.987813i \(0.549746\pi\)
\(798\) 12.5126 0.442941
\(799\) 21.7469 0.769350
\(800\) −2.33068 −0.0824020
\(801\) 11.2265 0.396667
\(802\) −2.53053 −0.0893561
\(803\) 1.00000 0.0352892
\(804\) −83.3661 −2.94009
\(805\) −8.12900 −0.286510
\(806\) 0.338864 0.0119360
\(807\) 25.5277 0.898618
\(808\) −9.78862 −0.344362
\(809\) 10.8460 0.381324 0.190662 0.981656i \(-0.438936\pi\)
0.190662 + 0.981656i \(0.438936\pi\)
\(810\) −4.83786 −0.169985
\(811\) 17.3101 0.607839 0.303920 0.952698i \(-0.401705\pi\)
0.303920 + 0.952698i \(0.401705\pi\)
\(812\) −6.65398 −0.233509
\(813\) 16.3508 0.573448
\(814\) 1.96730 0.0689540
\(815\) 6.03179 0.211285
\(816\) −29.8003 −1.04322
\(817\) 7.57216 0.264916
\(818\) −6.82047 −0.238472
\(819\) −68.8406 −2.40549
\(820\) −3.43425 −0.119929
\(821\) 12.7795 0.446009 0.223005 0.974817i \(-0.428414\pi\)
0.223005 + 0.974817i \(0.428414\pi\)
\(822\) −5.45488 −0.190261
\(823\) 22.4386 0.782159 0.391079 0.920357i \(-0.372102\pi\)
0.391079 + 0.920357i \(0.372102\pi\)
\(824\) 8.30582 0.289347
\(825\) −3.23393 −0.112591
\(826\) −11.8478 −0.412236
\(827\) 36.2568 1.26077 0.630386 0.776282i \(-0.282897\pi\)
0.630386 + 0.776282i \(0.282897\pi\)
\(828\) −23.3554 −0.811658
\(829\) 4.80574 0.166910 0.0834550 0.996512i \(-0.473404\pi\)
0.0834550 + 0.996512i \(0.473404\pi\)
\(830\) 3.12293 0.108398
\(831\) −29.4737 −1.02243
\(832\) −12.8074 −0.444018
\(833\) 46.2674 1.60307
\(834\) 12.5728 0.435361
\(835\) −7.84550 −0.271505
\(836\) 7.47151 0.258408
\(837\) 13.5016 0.466684
\(838\) 0.957758 0.0330852
\(839\) −28.0417 −0.968108 −0.484054 0.875038i \(-0.660836\pi\)
−0.484054 + 0.875038i \(0.660836\pi\)
\(840\) 13.0004 0.448557
\(841\) −28.5550 −0.984654
\(842\) 0.304927 0.0105085
\(843\) −48.9844 −1.68711
\(844\) −11.1361 −0.383319
\(845\) −9.70972 −0.334024
\(846\) −13.2123 −0.454247
\(847\) −5.08849 −0.174843
\(848\) −28.7747 −0.988127
\(849\) −36.8255 −1.26385
\(850\) −0.488540 −0.0167568
\(851\) −15.7543 −0.540050
\(852\) 49.8467 1.70772
\(853\) −53.9392 −1.84684 −0.923422 0.383786i \(-0.874620\pi\)
−0.923422 + 0.383786i \(0.874620\pi\)
\(854\) −5.04858 −0.172759
\(855\) −28.4280 −0.972217
\(856\) −0.239516 −0.00818650
\(857\) −0.740933 −0.0253098 −0.0126549 0.999920i \(-0.504028\pi\)
−0.0126549 + 0.999920i \(0.504028\pi\)
\(858\) 1.17022 0.0399506
\(859\) 6.44786 0.219998 0.109999 0.993932i \(-0.464915\pi\)
0.109999 + 0.993932i \(0.464915\pi\)
\(860\) 3.89416 0.132790
\(861\) 28.8304 0.982538
\(862\) −0.574342 −0.0195622
\(863\) 17.6608 0.601182 0.300591 0.953753i \(-0.402816\pi\)
0.300591 + 0.953753i \(0.402816\pi\)
\(864\) 33.6032 1.14321
\(865\) −5.16279 −0.175540
\(866\) −1.42069 −0.0482770
\(867\) 35.5818 1.20842
\(868\) −9.34067 −0.317043
\(869\) −3.69416 −0.125316
\(870\) −0.430370 −0.0145909
\(871\) −23.8547 −0.808287
\(872\) 12.9017 0.436906
\(873\) −16.5617 −0.560528
\(874\) 1.21472 0.0410885
\(875\) −5.08849 −0.172022
\(876\) 6.33916 0.214180
\(877\) −27.5285 −0.929571 −0.464785 0.885423i \(-0.653869\pi\)
−0.464785 + 0.885423i \(0.653869\pi\)
\(878\) −5.42749 −0.183169
\(879\) −79.6323 −2.68593
\(880\) 3.76281 0.126844
\(881\) −9.19379 −0.309747 −0.154873 0.987934i \(-0.549497\pi\)
−0.154873 + 0.987934i \(0.549497\pi\)
\(882\) −28.1096 −0.946501
\(883\) 56.0149 1.88505 0.942526 0.334133i \(-0.108444\pi\)
0.942526 + 0.334133i \(0.108444\pi\)
\(884\) −8.70757 −0.292867
\(885\) 37.7448 1.26878
\(886\) 5.72311 0.192272
\(887\) −18.4238 −0.618610 −0.309305 0.950963i \(-0.600096\pi\)
−0.309305 + 0.950963i \(0.600096\pi\)
\(888\) 25.1953 0.845499
\(889\) 91.5915 3.07188
\(890\) −0.300278 −0.0100654
\(891\) 24.2512 0.812445
\(892\) −30.6121 −1.02497
\(893\) −33.8474 −1.13266
\(894\) 11.5718 0.387018
\(895\) −19.1713 −0.640827
\(896\) −30.8866 −1.03185
\(897\) −9.37119 −0.312895
\(898\) −1.85684 −0.0619634
\(899\) 0.624710 0.0208353
\(900\) −14.6198 −0.487325
\(901\) −18.7274 −0.623901
\(902\) −0.349504 −0.0116372
\(903\) −32.6913 −1.08790
\(904\) 4.82092 0.160342
\(905\) −8.14103 −0.270617
\(906\) 12.3245 0.409455
\(907\) 34.6290 1.14984 0.574918 0.818211i \(-0.305034\pi\)
0.574918 + 0.818211i \(0.305034\pi\)
\(908\) −34.5862 −1.14778
\(909\) −92.4107 −3.06507
\(910\) 1.84131 0.0610388
\(911\) 39.7520 1.31704 0.658521 0.752562i \(-0.271182\pi\)
0.658521 + 0.752562i \(0.271182\pi\)
\(912\) 46.3820 1.53586
\(913\) −15.6546 −0.518091
\(914\) 5.79444 0.191663
\(915\) 16.0838 0.531715
\(916\) −3.62859 −0.119892
\(917\) −25.3657 −0.837649
\(918\) 7.04365 0.232475
\(919\) 1.88632 0.0622240 0.0311120 0.999516i \(-0.490095\pi\)
0.0311120 + 0.999516i \(0.490095\pi\)
\(920\) 1.26208 0.0416095
\(921\) −19.4897 −0.642206
\(922\) 0.163296 0.00537787
\(923\) 14.2633 0.469484
\(924\) −32.2568 −1.06117
\(925\) −9.86168 −0.324250
\(926\) −3.16654 −0.104059
\(927\) 78.4122 2.57539
\(928\) 1.55480 0.0510387
\(929\) 58.5796 1.92193 0.960967 0.276665i \(-0.0892291\pi\)
0.960967 + 0.276665i \(0.0892291\pi\)
\(930\) −0.604141 −0.0198106
\(931\) −72.0117 −2.36009
\(932\) −34.6873 −1.13622
\(933\) 106.719 3.49382
\(934\) −2.30222 −0.0753309
\(935\) 2.44895 0.0800891
\(936\) 10.6879 0.349346
\(937\) 40.7269 1.33049 0.665244 0.746626i \(-0.268327\pi\)
0.665244 + 0.746626i \(0.268327\pi\)
\(938\) −13.3496 −0.435879
\(939\) 24.0007 0.783232
\(940\) −17.4068 −0.567748
\(941\) 8.81728 0.287435 0.143717 0.989619i \(-0.454094\pi\)
0.143717 + 0.989619i \(0.454094\pi\)
\(942\) −6.37824 −0.207814
\(943\) 2.79885 0.0911430
\(944\) −43.9176 −1.42940
\(945\) 73.3648 2.38656
\(946\) 0.396308 0.0128851
\(947\) 7.72028 0.250875 0.125438 0.992102i \(-0.459966\pi\)
0.125438 + 0.992102i \(0.459966\pi\)
\(948\) −23.4179 −0.760577
\(949\) 1.81391 0.0588821
\(950\) 0.760375 0.0246698
\(951\) 57.0841 1.85108
\(952\) −9.84479 −0.319072
\(953\) −43.5999 −1.41234 −0.706170 0.708042i \(-0.749579\pi\)
−0.706170 + 0.708042i \(0.749579\pi\)
\(954\) 11.3778 0.368370
\(955\) 3.40543 0.110197
\(956\) 26.0815 0.843537
\(957\) 2.15735 0.0697373
\(958\) 5.31961 0.171869
\(959\) 43.0253 1.38936
\(960\) 22.8337 0.736954
\(961\) −30.1230 −0.971711
\(962\) 3.56852 0.115054
\(963\) −2.26118 −0.0728657
\(964\) −33.8659 −1.09075
\(965\) −13.0471 −0.420000
\(966\) −5.24431 −0.168733
\(967\) 17.4798 0.562114 0.281057 0.959691i \(-0.409315\pi\)
0.281057 + 0.959691i \(0.409315\pi\)
\(968\) 0.790020 0.0253922
\(969\) 30.1868 0.969739
\(970\) 0.442982 0.0142233
\(971\) 44.3467 1.42315 0.711577 0.702609i \(-0.247981\pi\)
0.711577 + 0.702609i \(0.247981\pi\)
\(972\) 68.9467 2.21147
\(973\) −99.1679 −3.17918
\(974\) −6.14212 −0.196806
\(975\) −5.86606 −0.187864
\(976\) −18.7142 −0.599027
\(977\) 23.2598 0.744147 0.372074 0.928203i \(-0.378647\pi\)
0.372074 + 0.928203i \(0.378647\pi\)
\(978\) 3.89132 0.124431
\(979\) 1.50523 0.0481074
\(980\) −37.0337 −1.18300
\(981\) 121.800 3.88877
\(982\) 7.11442 0.227030
\(983\) 29.9241 0.954431 0.477216 0.878786i \(-0.341646\pi\)
0.477216 + 0.878786i \(0.341646\pi\)
\(984\) −4.47610 −0.142693
\(985\) −21.8240 −0.695372
\(986\) 0.325905 0.0103789
\(987\) 146.129 4.65135
\(988\) 13.5527 0.431168
\(989\) −3.17366 −0.100917
\(990\) −1.48785 −0.0472870
\(991\) 47.1723 1.49848 0.749239 0.662300i \(-0.230420\pi\)
0.749239 + 0.662300i \(0.230420\pi\)
\(992\) 2.18258 0.0692971
\(993\) −114.493 −3.63334
\(994\) 7.98206 0.253175
\(995\) 13.8430 0.438852
\(996\) −99.2369 −3.14444
\(997\) 35.5594 1.12618 0.563089 0.826396i \(-0.309613\pi\)
0.563089 + 0.826396i \(0.309613\pi\)
\(998\) 6.93147 0.219412
\(999\) 142.184 4.49849
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 \(a_p\))