Properties

Label 8015.2.a.l.1.37
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.37
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.609593 q^{2} +2.28126 q^{3} -1.62840 q^{4} -1.00000 q^{5} +1.39064 q^{6} -1.00000 q^{7} -2.21184 q^{8} +2.20414 q^{9} +O(q^{10})\) \(q+0.609593 q^{2} +2.28126 q^{3} -1.62840 q^{4} -1.00000 q^{5} +1.39064 q^{6} -1.00000 q^{7} -2.21184 q^{8} +2.20414 q^{9} -0.609593 q^{10} +3.79775 q^{11} -3.71480 q^{12} +6.31536 q^{13} -0.609593 q^{14} -2.28126 q^{15} +1.90847 q^{16} +2.30733 q^{17} +1.34363 q^{18} -2.08034 q^{19} +1.62840 q^{20} -2.28126 q^{21} +2.31508 q^{22} +0.263969 q^{23} -5.04579 q^{24} +1.00000 q^{25} +3.84980 q^{26} -1.81556 q^{27} +1.62840 q^{28} +5.74574 q^{29} -1.39064 q^{30} -4.16265 q^{31} +5.58708 q^{32} +8.66366 q^{33} +1.40653 q^{34} +1.00000 q^{35} -3.58922 q^{36} +1.78740 q^{37} -1.26816 q^{38} +14.4070 q^{39} +2.21184 q^{40} -11.8375 q^{41} -1.39064 q^{42} +3.06067 q^{43} -6.18425 q^{44} -2.20414 q^{45} +0.160914 q^{46} +3.53800 q^{47} +4.35371 q^{48} +1.00000 q^{49} +0.609593 q^{50} +5.26362 q^{51} -10.2839 q^{52} -10.1754 q^{53} -1.10675 q^{54} -3.79775 q^{55} +2.21184 q^{56} -4.74579 q^{57} +3.50256 q^{58} +6.39001 q^{59} +3.71480 q^{60} +0.234512 q^{61} -2.53752 q^{62} -2.20414 q^{63} -0.411098 q^{64} -6.31536 q^{65} +5.28130 q^{66} -13.7050 q^{67} -3.75725 q^{68} +0.602182 q^{69} +0.609593 q^{70} -1.07440 q^{71} -4.87522 q^{72} +13.5549 q^{73} +1.08958 q^{74} +2.28126 q^{75} +3.38762 q^{76} -3.79775 q^{77} +8.78238 q^{78} -0.238780 q^{79} -1.90847 q^{80} -10.7542 q^{81} -7.21607 q^{82} +0.663084 q^{83} +3.71480 q^{84} -2.30733 q^{85} +1.86576 q^{86} +13.1075 q^{87} -8.40004 q^{88} +16.2882 q^{89} -1.34363 q^{90} -6.31536 q^{91} -0.429846 q^{92} -9.49609 q^{93} +2.15674 q^{94} +2.08034 q^{95} +12.7456 q^{96} +0.859629 q^{97} +0.609593 q^{98} +8.37079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.609593 0.431047 0.215524 0.976499i \(-0.430854\pi\)
0.215524 + 0.976499i \(0.430854\pi\)
\(3\) 2.28126 1.31709 0.658543 0.752543i \(-0.271173\pi\)
0.658543 + 0.752543i \(0.271173\pi\)
\(4\) −1.62840 −0.814198
\(5\) −1.00000 −0.447214
\(6\) 1.39064 0.567726
\(7\) −1.00000 −0.377964
\(8\) −2.21184 −0.782005
\(9\) 2.20414 0.734714
\(10\) −0.609593 −0.192770
\(11\) 3.79775 1.14507 0.572533 0.819882i \(-0.305961\pi\)
0.572533 + 0.819882i \(0.305961\pi\)
\(12\) −3.71480 −1.07237
\(13\) 6.31536 1.75157 0.875783 0.482706i \(-0.160346\pi\)
0.875783 + 0.482706i \(0.160346\pi\)
\(14\) −0.609593 −0.162920
\(15\) −2.28126 −0.589019
\(16\) 1.90847 0.477117
\(17\) 2.30733 0.559610 0.279805 0.960057i \(-0.409730\pi\)
0.279805 + 0.960057i \(0.409730\pi\)
\(18\) 1.34363 0.316697
\(19\) −2.08034 −0.477262 −0.238631 0.971110i \(-0.576699\pi\)
−0.238631 + 0.971110i \(0.576699\pi\)
\(20\) 1.62840 0.364121
\(21\) −2.28126 −0.497812
\(22\) 2.31508 0.493577
\(23\) 0.263969 0.0550414 0.0275207 0.999621i \(-0.491239\pi\)
0.0275207 + 0.999621i \(0.491239\pi\)
\(24\) −5.04579 −1.02997
\(25\) 1.00000 0.200000
\(26\) 3.84980 0.755007
\(27\) −1.81556 −0.349404
\(28\) 1.62840 0.307738
\(29\) 5.74574 1.06696 0.533479 0.845813i \(-0.320884\pi\)
0.533479 + 0.845813i \(0.320884\pi\)
\(30\) −1.39064 −0.253895
\(31\) −4.16265 −0.747635 −0.373817 0.927502i \(-0.621951\pi\)
−0.373817 + 0.927502i \(0.621951\pi\)
\(32\) 5.58708 0.987665
\(33\) 8.66366 1.50815
\(34\) 1.40653 0.241218
\(35\) 1.00000 0.169031
\(36\) −3.58922 −0.598203
\(37\) 1.78740 0.293846 0.146923 0.989148i \(-0.453063\pi\)
0.146923 + 0.989148i \(0.453063\pi\)
\(38\) −1.26816 −0.205723
\(39\) 14.4070 2.30696
\(40\) 2.21184 0.349723
\(41\) −11.8375 −1.84871 −0.924356 0.381531i \(-0.875397\pi\)
−0.924356 + 0.381531i \(0.875397\pi\)
\(42\) −1.39064 −0.214580
\(43\) 3.06067 0.466748 0.233374 0.972387i \(-0.425023\pi\)
0.233374 + 0.972387i \(0.425023\pi\)
\(44\) −6.18425 −0.932311
\(45\) −2.20414 −0.328574
\(46\) 0.160914 0.0237254
\(47\) 3.53800 0.516071 0.258035 0.966135i \(-0.416925\pi\)
0.258035 + 0.966135i \(0.416925\pi\)
\(48\) 4.35371 0.628405
\(49\) 1.00000 0.142857
\(50\) 0.609593 0.0862094
\(51\) 5.26362 0.737054
\(52\) −10.2839 −1.42612
\(53\) −10.1754 −1.39769 −0.698847 0.715271i \(-0.746303\pi\)
−0.698847 + 0.715271i \(0.746303\pi\)
\(54\) −1.10675 −0.150610
\(55\) −3.79775 −0.512089
\(56\) 2.21184 0.295570
\(57\) −4.74579 −0.628595
\(58\) 3.50256 0.459909
\(59\) 6.39001 0.831908 0.415954 0.909386i \(-0.363448\pi\)
0.415954 + 0.909386i \(0.363448\pi\)
\(60\) 3.71480 0.479578
\(61\) 0.234512 0.0300262 0.0150131 0.999887i \(-0.495221\pi\)
0.0150131 + 0.999887i \(0.495221\pi\)
\(62\) −2.53752 −0.322266
\(63\) −2.20414 −0.277696
\(64\) −0.411098 −0.0513873
\(65\) −6.31536 −0.783324
\(66\) 5.28130 0.650084
\(67\) −13.7050 −1.67433 −0.837164 0.546953i \(-0.815788\pi\)
−0.837164 + 0.546953i \(0.815788\pi\)
\(68\) −3.75725 −0.455633
\(69\) 0.602182 0.0724942
\(70\) 0.609593 0.0728603
\(71\) −1.07440 −0.127508 −0.0637541 0.997966i \(-0.520307\pi\)
−0.0637541 + 0.997966i \(0.520307\pi\)
\(72\) −4.87522 −0.574550
\(73\) 13.5549 1.58648 0.793241 0.608907i \(-0.208392\pi\)
0.793241 + 0.608907i \(0.208392\pi\)
\(74\) 1.08958 0.126662
\(75\) 2.28126 0.263417
\(76\) 3.38762 0.388586
\(77\) −3.79775 −0.432794
\(78\) 8.78238 0.994409
\(79\) −0.238780 −0.0268648 −0.0134324 0.999910i \(-0.504276\pi\)
−0.0134324 + 0.999910i \(0.504276\pi\)
\(80\) −1.90847 −0.213373
\(81\) −10.7542 −1.19491
\(82\) −7.21607 −0.796882
\(83\) 0.663084 0.0727830 0.0363915 0.999338i \(-0.488414\pi\)
0.0363915 + 0.999338i \(0.488414\pi\)
\(84\) 3.71480 0.405317
\(85\) −2.30733 −0.250265
\(86\) 1.86576 0.201191
\(87\) 13.1075 1.40527
\(88\) −8.40004 −0.895447
\(89\) 16.2882 1.72655 0.863276 0.504733i \(-0.168409\pi\)
0.863276 + 0.504733i \(0.168409\pi\)
\(90\) −1.34363 −0.141631
\(91\) −6.31536 −0.662029
\(92\) −0.429846 −0.0448146
\(93\) −9.49609 −0.984699
\(94\) 2.15674 0.222451
\(95\) 2.08034 0.213438
\(96\) 12.7456 1.30084
\(97\) 0.859629 0.0872821 0.0436411 0.999047i \(-0.486104\pi\)
0.0436411 + 0.999047i \(0.486104\pi\)
\(98\) 0.609593 0.0615782
\(99\) 8.37079 0.841296
\(100\) −1.62840 −0.162840
\(101\) 0.661812 0.0658528 0.0329264 0.999458i \(-0.489517\pi\)
0.0329264 + 0.999458i \(0.489517\pi\)
\(102\) 3.20866 0.317705
\(103\) −1.19785 −0.118027 −0.0590136 0.998257i \(-0.518796\pi\)
−0.0590136 + 0.998257i \(0.518796\pi\)
\(104\) −13.9686 −1.36973
\(105\) 2.28126 0.222628
\(106\) −6.20283 −0.602472
\(107\) 9.72768 0.940410 0.470205 0.882557i \(-0.344180\pi\)
0.470205 + 0.882557i \(0.344180\pi\)
\(108\) 2.95644 0.284484
\(109\) 17.7364 1.69884 0.849421 0.527716i \(-0.176951\pi\)
0.849421 + 0.527716i \(0.176951\pi\)
\(110\) −2.31508 −0.220734
\(111\) 4.07751 0.387021
\(112\) −1.90847 −0.180333
\(113\) 12.3006 1.15714 0.578571 0.815632i \(-0.303611\pi\)
0.578571 + 0.815632i \(0.303611\pi\)
\(114\) −2.89300 −0.270954
\(115\) −0.263969 −0.0246152
\(116\) −9.35635 −0.868715
\(117\) 13.9200 1.28690
\(118\) 3.89530 0.358592
\(119\) −2.30733 −0.211513
\(120\) 5.04579 0.460615
\(121\) 3.42293 0.311176
\(122\) 0.142957 0.0129427
\(123\) −27.0045 −2.43491
\(124\) 6.77845 0.608723
\(125\) −1.00000 −0.0894427
\(126\) −1.34363 −0.119700
\(127\) 19.4000 1.72147 0.860737 0.509050i \(-0.170003\pi\)
0.860737 + 0.509050i \(0.170003\pi\)
\(128\) −11.4248 −1.00982
\(129\) 6.98219 0.614747
\(130\) −3.84980 −0.337649
\(131\) 19.4521 1.69954 0.849771 0.527152i \(-0.176740\pi\)
0.849771 + 0.527152i \(0.176740\pi\)
\(132\) −14.1079 −1.22793
\(133\) 2.08034 0.180388
\(134\) −8.35444 −0.721714
\(135\) 1.81556 0.156258
\(136\) −5.10345 −0.437618
\(137\) 1.65064 0.141023 0.0705117 0.997511i \(-0.477537\pi\)
0.0705117 + 0.997511i \(0.477537\pi\)
\(138\) 0.367086 0.0312484
\(139\) 19.0852 1.61879 0.809393 0.587267i \(-0.199796\pi\)
0.809393 + 0.587267i \(0.199796\pi\)
\(140\) −1.62840 −0.137625
\(141\) 8.07110 0.679709
\(142\) −0.654948 −0.0549620
\(143\) 23.9842 2.00566
\(144\) 4.20654 0.350545
\(145\) −5.74574 −0.477158
\(146\) 8.26298 0.683849
\(147\) 2.28126 0.188155
\(148\) −2.91059 −0.239249
\(149\) −2.28925 −0.187543 −0.0937713 0.995594i \(-0.529892\pi\)
−0.0937713 + 0.995594i \(0.529892\pi\)
\(150\) 1.39064 0.113545
\(151\) −3.43002 −0.279131 −0.139566 0.990213i \(-0.544571\pi\)
−0.139566 + 0.990213i \(0.544571\pi\)
\(152\) 4.60138 0.373222
\(153\) 5.08569 0.411153
\(154\) −2.31508 −0.186555
\(155\) 4.16265 0.334352
\(156\) −23.4603 −1.87832
\(157\) 4.74723 0.378870 0.189435 0.981893i \(-0.439334\pi\)
0.189435 + 0.981893i \(0.439334\pi\)
\(158\) −0.145558 −0.0115800
\(159\) −23.2126 −1.84088
\(160\) −5.58708 −0.441697
\(161\) −0.263969 −0.0208037
\(162\) −6.55567 −0.515062
\(163\) −3.02512 −0.236946 −0.118473 0.992957i \(-0.537800\pi\)
−0.118473 + 0.992957i \(0.537800\pi\)
\(164\) 19.2762 1.50522
\(165\) −8.66366 −0.674465
\(166\) 0.404211 0.0313729
\(167\) 8.65634 0.669848 0.334924 0.942245i \(-0.391289\pi\)
0.334924 + 0.942245i \(0.391289\pi\)
\(168\) 5.04579 0.389291
\(169\) 26.8837 2.06798
\(170\) −1.40653 −0.107876
\(171\) −4.58536 −0.350652
\(172\) −4.98399 −0.380026
\(173\) −13.1499 −0.999768 −0.499884 0.866092i \(-0.666624\pi\)
−0.499884 + 0.866092i \(0.666624\pi\)
\(174\) 7.99025 0.605740
\(175\) −1.00000 −0.0755929
\(176\) 7.24790 0.546331
\(177\) 14.5773 1.09569
\(178\) 9.92920 0.744225
\(179\) 11.6213 0.868619 0.434310 0.900764i \(-0.356992\pi\)
0.434310 + 0.900764i \(0.356992\pi\)
\(180\) 3.58922 0.267525
\(181\) 7.67898 0.570774 0.285387 0.958412i \(-0.407878\pi\)
0.285387 + 0.958412i \(0.407878\pi\)
\(182\) −3.84980 −0.285366
\(183\) 0.534983 0.0395471
\(184\) −0.583859 −0.0430426
\(185\) −1.78740 −0.131412
\(186\) −5.78875 −0.424452
\(187\) 8.76267 0.640790
\(188\) −5.76127 −0.420184
\(189\) 1.81556 0.132062
\(190\) 1.26816 0.0920019
\(191\) −11.6654 −0.844075 −0.422038 0.906578i \(-0.638685\pi\)
−0.422038 + 0.906578i \(0.638685\pi\)
\(192\) −0.937822 −0.0676815
\(193\) −7.62481 −0.548846 −0.274423 0.961609i \(-0.588487\pi\)
−0.274423 + 0.961609i \(0.588487\pi\)
\(194\) 0.524024 0.0376227
\(195\) −14.4070 −1.03170
\(196\) −1.62840 −0.116314
\(197\) 1.98744 0.141600 0.0707998 0.997491i \(-0.477445\pi\)
0.0707998 + 0.997491i \(0.477445\pi\)
\(198\) 5.10277 0.362638
\(199\) −20.2140 −1.43293 −0.716466 0.697622i \(-0.754241\pi\)
−0.716466 + 0.697622i \(0.754241\pi\)
\(200\) −2.21184 −0.156401
\(201\) −31.2646 −2.20523
\(202\) 0.403436 0.0283856
\(203\) −5.74574 −0.403272
\(204\) −8.57126 −0.600108
\(205\) 11.8375 0.826769
\(206\) −0.730198 −0.0508753
\(207\) 0.581826 0.0404397
\(208\) 12.0527 0.835702
\(209\) −7.90061 −0.546497
\(210\) 1.39064 0.0959632
\(211\) 0.669141 0.0460656 0.0230328 0.999735i \(-0.492668\pi\)
0.0230328 + 0.999735i \(0.492668\pi\)
\(212\) 16.5695 1.13800
\(213\) −2.45099 −0.167939
\(214\) 5.92992 0.405361
\(215\) −3.06067 −0.208736
\(216\) 4.01573 0.273236
\(217\) 4.16265 0.282579
\(218\) 10.8120 0.732281
\(219\) 30.9223 2.08953
\(220\) 6.18425 0.416942
\(221\) 14.5716 0.980193
\(222\) 2.48562 0.166824
\(223\) 8.37637 0.560923 0.280461 0.959865i \(-0.409513\pi\)
0.280461 + 0.959865i \(0.409513\pi\)
\(224\) −5.58708 −0.373302
\(225\) 2.20414 0.146943
\(226\) 7.49834 0.498782
\(227\) −3.34665 −0.222125 −0.111062 0.993813i \(-0.535425\pi\)
−0.111062 + 0.993813i \(0.535425\pi\)
\(228\) 7.72803 0.511801
\(229\) 1.00000 0.0660819
\(230\) −0.160914 −0.0106103
\(231\) −8.66366 −0.570027
\(232\) −12.7087 −0.834366
\(233\) −14.0456 −0.920158 −0.460079 0.887878i \(-0.652179\pi\)
−0.460079 + 0.887878i \(0.652179\pi\)
\(234\) 8.48550 0.554715
\(235\) −3.53800 −0.230794
\(236\) −10.4055 −0.677338
\(237\) −0.544719 −0.0353833
\(238\) −1.40653 −0.0911719
\(239\) 25.2062 1.63045 0.815225 0.579144i \(-0.196613\pi\)
0.815225 + 0.579144i \(0.196613\pi\)
\(240\) −4.35371 −0.281031
\(241\) 6.11985 0.394214 0.197107 0.980382i \(-0.436845\pi\)
0.197107 + 0.980382i \(0.436845\pi\)
\(242\) 2.08659 0.134131
\(243\) −19.0864 −1.22439
\(244\) −0.381879 −0.0244473
\(245\) −1.00000 −0.0638877
\(246\) −16.4617 −1.04956
\(247\) −13.1381 −0.835956
\(248\) 9.20714 0.584654
\(249\) 1.51267 0.0958614
\(250\) −0.609593 −0.0385540
\(251\) −20.6471 −1.30323 −0.651617 0.758548i \(-0.725909\pi\)
−0.651617 + 0.758548i \(0.725909\pi\)
\(252\) 3.58922 0.226100
\(253\) 1.00249 0.0630260
\(254\) 11.8261 0.742036
\(255\) −5.26362 −0.329621
\(256\) −6.14225 −0.383891
\(257\) −1.24330 −0.0775547 −0.0387773 0.999248i \(-0.512346\pi\)
−0.0387773 + 0.999248i \(0.512346\pi\)
\(258\) 4.25629 0.264985
\(259\) −1.78740 −0.111063
\(260\) 10.2839 0.637781
\(261\) 12.6644 0.783909
\(262\) 11.8579 0.732583
\(263\) 17.0619 1.05208 0.526042 0.850459i \(-0.323676\pi\)
0.526042 + 0.850459i \(0.323676\pi\)
\(264\) −19.1627 −1.17938
\(265\) 10.1754 0.625068
\(266\) 1.26816 0.0777558
\(267\) 37.1577 2.27402
\(268\) 22.3171 1.36323
\(269\) 14.6943 0.895927 0.447963 0.894052i \(-0.352150\pi\)
0.447963 + 0.894052i \(0.352150\pi\)
\(270\) 1.10675 0.0673546
\(271\) −29.4092 −1.78648 −0.893242 0.449576i \(-0.851575\pi\)
−0.893242 + 0.449576i \(0.851575\pi\)
\(272\) 4.40347 0.267000
\(273\) −14.4070 −0.871949
\(274\) 1.00622 0.0607877
\(275\) 3.79775 0.229013
\(276\) −0.980591 −0.0590247
\(277\) 5.58984 0.335861 0.167930 0.985799i \(-0.446292\pi\)
0.167930 + 0.985799i \(0.446292\pi\)
\(278\) 11.6342 0.697773
\(279\) −9.17508 −0.549298
\(280\) −2.21184 −0.132183
\(281\) 11.8748 0.708389 0.354195 0.935172i \(-0.384755\pi\)
0.354195 + 0.935172i \(0.384755\pi\)
\(282\) 4.92008 0.292987
\(283\) 23.0995 1.37312 0.686561 0.727072i \(-0.259119\pi\)
0.686561 + 0.727072i \(0.259119\pi\)
\(284\) 1.74955 0.103817
\(285\) 4.74579 0.281116
\(286\) 14.6206 0.864533
\(287\) 11.8375 0.698748
\(288\) 12.3147 0.725652
\(289\) −11.6762 −0.686837
\(290\) −3.50256 −0.205678
\(291\) 1.96104 0.114958
\(292\) −22.0728 −1.29171
\(293\) −4.47880 −0.261654 −0.130827 0.991405i \(-0.541763\pi\)
−0.130827 + 0.991405i \(0.541763\pi\)
\(294\) 1.39064 0.0811037
\(295\) −6.39001 −0.372041
\(296\) −3.95344 −0.229789
\(297\) −6.89503 −0.400090
\(298\) −1.39551 −0.0808397
\(299\) 1.66706 0.0964085
\(300\) −3.71480 −0.214474
\(301\) −3.06067 −0.176414
\(302\) −2.09091 −0.120319
\(303\) 1.50976 0.0867337
\(304\) −3.97026 −0.227710
\(305\) −0.234512 −0.0134281
\(306\) 3.10020 0.177226
\(307\) −11.0768 −0.632187 −0.316094 0.948728i \(-0.602371\pi\)
−0.316094 + 0.948728i \(0.602371\pi\)
\(308\) 6.18425 0.352380
\(309\) −2.73260 −0.155452
\(310\) 2.53752 0.144122
\(311\) −13.7160 −0.777762 −0.388881 0.921288i \(-0.627138\pi\)
−0.388881 + 0.921288i \(0.627138\pi\)
\(312\) −31.8660 −1.80406
\(313\) 19.9914 1.12998 0.564989 0.825098i \(-0.308880\pi\)
0.564989 + 0.825098i \(0.308880\pi\)
\(314\) 2.89388 0.163311
\(315\) 2.20414 0.124189
\(316\) 0.388828 0.0218733
\(317\) 21.3063 1.19668 0.598341 0.801242i \(-0.295827\pi\)
0.598341 + 0.801242i \(0.295827\pi\)
\(318\) −14.1503 −0.793507
\(319\) 21.8209 1.22174
\(320\) 0.411098 0.0229811
\(321\) 22.1914 1.23860
\(322\) −0.160914 −0.00896737
\(323\) −4.80003 −0.267081
\(324\) 17.5121 0.972893
\(325\) 6.31536 0.350313
\(326\) −1.84409 −0.102135
\(327\) 40.4614 2.23752
\(328\) 26.1828 1.44570
\(329\) −3.53800 −0.195056
\(330\) −5.28130 −0.290726
\(331\) −0.788224 −0.0433247 −0.0216624 0.999765i \(-0.506896\pi\)
−0.0216624 + 0.999765i \(0.506896\pi\)
\(332\) −1.07976 −0.0592598
\(333\) 3.93968 0.215893
\(334\) 5.27684 0.288736
\(335\) 13.7050 0.748782
\(336\) −4.35371 −0.237515
\(337\) 0.0861554 0.00469318 0.00234659 0.999997i \(-0.499253\pi\)
0.00234659 + 0.999997i \(0.499253\pi\)
\(338\) 16.3881 0.891397
\(339\) 28.0608 1.52405
\(340\) 3.75725 0.203765
\(341\) −15.8087 −0.856091
\(342\) −2.79520 −0.151147
\(343\) −1.00000 −0.0539949
\(344\) −6.76973 −0.364999
\(345\) −0.602182 −0.0324204
\(346\) −8.01608 −0.430947
\(347\) −34.3437 −1.84367 −0.921834 0.387585i \(-0.873309\pi\)
−0.921834 + 0.387585i \(0.873309\pi\)
\(348\) −21.3443 −1.14417
\(349\) 16.6826 0.893001 0.446501 0.894783i \(-0.352670\pi\)
0.446501 + 0.894783i \(0.352670\pi\)
\(350\) −0.609593 −0.0325841
\(351\) −11.4659 −0.612004
\(352\) 21.2183 1.13094
\(353\) 14.7560 0.785381 0.392690 0.919671i \(-0.371544\pi\)
0.392690 + 0.919671i \(0.371544\pi\)
\(354\) 8.88619 0.472296
\(355\) 1.07440 0.0570234
\(356\) −26.5237 −1.40576
\(357\) −5.26362 −0.278580
\(358\) 7.08428 0.374416
\(359\) 16.6736 0.879998 0.439999 0.897998i \(-0.354979\pi\)
0.439999 + 0.897998i \(0.354979\pi\)
\(360\) 4.87522 0.256947
\(361\) −14.6722 −0.772221
\(362\) 4.68105 0.246031
\(363\) 7.80859 0.409845
\(364\) 10.2839 0.539023
\(365\) −13.5549 −0.709497
\(366\) 0.326122 0.0170467
\(367\) 7.63042 0.398305 0.199152 0.979969i \(-0.436181\pi\)
0.199152 + 0.979969i \(0.436181\pi\)
\(368\) 0.503777 0.0262612
\(369\) −26.0916 −1.35828
\(370\) −1.08958 −0.0566448
\(371\) 10.1754 0.528279
\(372\) 15.4634 0.801740
\(373\) 27.0632 1.40128 0.700640 0.713515i \(-0.252898\pi\)
0.700640 + 0.713515i \(0.252898\pi\)
\(374\) 5.34166 0.276211
\(375\) −2.28126 −0.117804
\(376\) −7.82551 −0.403570
\(377\) 36.2864 1.86885
\(378\) 1.10675 0.0569250
\(379\) 9.09630 0.467245 0.233623 0.972327i \(-0.424942\pi\)
0.233623 + 0.972327i \(0.424942\pi\)
\(380\) −3.38762 −0.173781
\(381\) 44.2565 2.26733
\(382\) −7.11111 −0.363836
\(383\) −8.50193 −0.434429 −0.217214 0.976124i \(-0.569697\pi\)
−0.217214 + 0.976124i \(0.569697\pi\)
\(384\) −26.0628 −1.33001
\(385\) 3.79775 0.193551
\(386\) −4.64803 −0.236578
\(387\) 6.74616 0.342927
\(388\) −1.39982 −0.0710650
\(389\) −34.3231 −1.74025 −0.870125 0.492831i \(-0.835962\pi\)
−0.870125 + 0.492831i \(0.835962\pi\)
\(390\) −8.78238 −0.444713
\(391\) 0.609064 0.0308017
\(392\) −2.21184 −0.111715
\(393\) 44.3754 2.23844
\(394\) 1.21153 0.0610361
\(395\) 0.238780 0.0120143
\(396\) −13.6310 −0.684982
\(397\) −32.9950 −1.65597 −0.827986 0.560748i \(-0.810514\pi\)
−0.827986 + 0.560748i \(0.810514\pi\)
\(398\) −12.3223 −0.617661
\(399\) 4.74579 0.237587
\(400\) 1.90847 0.0954235
\(401\) 20.4563 1.02154 0.510769 0.859718i \(-0.329361\pi\)
0.510769 + 0.859718i \(0.329361\pi\)
\(402\) −19.0586 −0.950559
\(403\) −26.2886 −1.30953
\(404\) −1.07769 −0.0536172
\(405\) 10.7542 0.534380
\(406\) −3.50256 −0.173829
\(407\) 6.78809 0.336473
\(408\) −11.6423 −0.576380
\(409\) −6.65977 −0.329304 −0.164652 0.986352i \(-0.552650\pi\)
−0.164652 + 0.986352i \(0.552650\pi\)
\(410\) 7.21607 0.356376
\(411\) 3.76553 0.185740
\(412\) 1.95057 0.0960976
\(413\) −6.39001 −0.314432
\(414\) 0.354677 0.0174314
\(415\) −0.663084 −0.0325495
\(416\) 35.2844 1.72996
\(417\) 43.5383 2.13208
\(418\) −4.81616 −0.235566
\(419\) 1.90366 0.0930001 0.0465000 0.998918i \(-0.485193\pi\)
0.0465000 + 0.998918i \(0.485193\pi\)
\(420\) −3.71480 −0.181263
\(421\) −3.01582 −0.146982 −0.0734911 0.997296i \(-0.523414\pi\)
−0.0734911 + 0.997296i \(0.523414\pi\)
\(422\) 0.407904 0.0198564
\(423\) 7.79826 0.379165
\(424\) 22.5063 1.09300
\(425\) 2.30733 0.111922
\(426\) −1.49411 −0.0723897
\(427\) −0.234512 −0.0113488
\(428\) −15.8405 −0.765681
\(429\) 54.7141 2.64162
\(430\) −1.86576 −0.0899751
\(431\) −4.68990 −0.225905 −0.112952 0.993600i \(-0.536031\pi\)
−0.112952 + 0.993600i \(0.536031\pi\)
\(432\) −3.46493 −0.166707
\(433\) 22.3918 1.07608 0.538040 0.842919i \(-0.319165\pi\)
0.538040 + 0.842919i \(0.319165\pi\)
\(434\) 2.53752 0.121805
\(435\) −13.1075 −0.628458
\(436\) −28.8819 −1.38319
\(437\) −0.549145 −0.0262692
\(438\) 18.8500 0.900687
\(439\) −36.5093 −1.74249 −0.871247 0.490844i \(-0.836688\pi\)
−0.871247 + 0.490844i \(0.836688\pi\)
\(440\) 8.40004 0.400456
\(441\) 2.20414 0.104959
\(442\) 8.88275 0.422509
\(443\) −32.1161 −1.52588 −0.762940 0.646470i \(-0.776245\pi\)
−0.762940 + 0.646470i \(0.776245\pi\)
\(444\) −6.63981 −0.315111
\(445\) −16.2882 −0.772137
\(446\) 5.10617 0.241784
\(447\) −5.22237 −0.247010
\(448\) 0.411098 0.0194226
\(449\) 16.3807 0.773054 0.386527 0.922278i \(-0.373675\pi\)
0.386527 + 0.922278i \(0.373675\pi\)
\(450\) 1.34363 0.0633393
\(451\) −44.9560 −2.11690
\(452\) −20.0302 −0.942142
\(453\) −7.82476 −0.367639
\(454\) −2.04009 −0.0957463
\(455\) 6.31536 0.296069
\(456\) 10.4970 0.491565
\(457\) −21.5899 −1.00993 −0.504967 0.863139i \(-0.668495\pi\)
−0.504967 + 0.863139i \(0.668495\pi\)
\(458\) 0.609593 0.0284844
\(459\) −4.18909 −0.195530
\(460\) 0.429846 0.0200417
\(461\) −4.31949 −0.201179 −0.100589 0.994928i \(-0.532073\pi\)
−0.100589 + 0.994928i \(0.532073\pi\)
\(462\) −5.28130 −0.245708
\(463\) 8.35380 0.388234 0.194117 0.980978i \(-0.437816\pi\)
0.194117 + 0.980978i \(0.437816\pi\)
\(464\) 10.9656 0.509064
\(465\) 9.49609 0.440371
\(466\) −8.56210 −0.396632
\(467\) −22.4340 −1.03812 −0.519060 0.854738i \(-0.673718\pi\)
−0.519060 + 0.854738i \(0.673718\pi\)
\(468\) −22.6672 −1.04779
\(469\) 13.7050 0.632836
\(470\) −2.15674 −0.0994830
\(471\) 10.8297 0.499004
\(472\) −14.1337 −0.650556
\(473\) 11.6237 0.534458
\(474\) −0.332057 −0.0152519
\(475\) −2.08034 −0.0954525
\(476\) 3.75725 0.172213
\(477\) −22.4280 −1.02691
\(478\) 15.3655 0.702801
\(479\) 12.9007 0.589446 0.294723 0.955583i \(-0.404773\pi\)
0.294723 + 0.955583i \(0.404773\pi\)
\(480\) −12.7456 −0.581753
\(481\) 11.2880 0.514691
\(482\) 3.73062 0.169925
\(483\) −0.602182 −0.0274002
\(484\) −5.57389 −0.253359
\(485\) −0.859629 −0.0390338
\(486\) −11.6349 −0.527771
\(487\) −16.5679 −0.750762 −0.375381 0.926871i \(-0.622488\pi\)
−0.375381 + 0.926871i \(0.622488\pi\)
\(488\) −0.518705 −0.0234807
\(489\) −6.90108 −0.312078
\(490\) −0.609593 −0.0275386
\(491\) 23.4466 1.05813 0.529065 0.848582i \(-0.322543\pi\)
0.529065 + 0.848582i \(0.322543\pi\)
\(492\) 43.9740 1.98250
\(493\) 13.2573 0.597080
\(494\) −8.00888 −0.360336
\(495\) −8.37079 −0.376239
\(496\) −7.94430 −0.356709
\(497\) 1.07440 0.0481936
\(498\) 0.922111 0.0413208
\(499\) −13.0359 −0.583566 −0.291783 0.956485i \(-0.594248\pi\)
−0.291783 + 0.956485i \(0.594248\pi\)
\(500\) 1.62840 0.0728241
\(501\) 19.7474 0.882247
\(502\) −12.5863 −0.561755
\(503\) −15.9848 −0.712727 −0.356364 0.934347i \(-0.615984\pi\)
−0.356364 + 0.934347i \(0.615984\pi\)
\(504\) 4.87522 0.217160
\(505\) −0.661812 −0.0294503
\(506\) 0.611110 0.0271672
\(507\) 61.3288 2.72371
\(508\) −31.5909 −1.40162
\(509\) −31.3783 −1.39082 −0.695409 0.718614i \(-0.744777\pi\)
−0.695409 + 0.718614i \(0.744777\pi\)
\(510\) −3.20866 −0.142082
\(511\) −13.5549 −0.599634
\(512\) 19.1052 0.844340
\(513\) 3.77697 0.166757
\(514\) −0.757904 −0.0334297
\(515\) 1.19785 0.0527834
\(516\) −11.3698 −0.500526
\(517\) 13.4365 0.590935
\(518\) −1.08958 −0.0478736
\(519\) −29.9983 −1.31678
\(520\) 13.9686 0.612563
\(521\) 11.2520 0.492960 0.246480 0.969148i \(-0.420726\pi\)
0.246480 + 0.969148i \(0.420726\pi\)
\(522\) 7.72015 0.337902
\(523\) −18.4116 −0.805083 −0.402541 0.915402i \(-0.631873\pi\)
−0.402541 + 0.915402i \(0.631873\pi\)
\(524\) −31.6758 −1.38376
\(525\) −2.28126 −0.0995623
\(526\) 10.4008 0.453498
\(527\) −9.60461 −0.418384
\(528\) 16.5343 0.719564
\(529\) −22.9303 −0.996970
\(530\) 6.20283 0.269434
\(531\) 14.0845 0.611215
\(532\) −3.38762 −0.146872
\(533\) −74.7583 −3.23814
\(534\) 22.6511 0.980208
\(535\) −9.72768 −0.420564
\(536\) 30.3132 1.30933
\(537\) 26.5113 1.14405
\(538\) 8.95753 0.386187
\(539\) 3.79775 0.163581
\(540\) −2.95644 −0.127225
\(541\) 14.4700 0.622114 0.311057 0.950391i \(-0.399317\pi\)
0.311057 + 0.950391i \(0.399317\pi\)
\(542\) −17.9277 −0.770059
\(543\) 17.5177 0.751758
\(544\) 12.8912 0.552707
\(545\) −17.7364 −0.759745
\(546\) −8.78238 −0.375851
\(547\) 12.6106 0.539190 0.269595 0.962974i \(-0.413110\pi\)
0.269595 + 0.962974i \(0.413110\pi\)
\(548\) −2.68789 −0.114821
\(549\) 0.516899 0.0220607
\(550\) 2.31508 0.0987155
\(551\) −11.9531 −0.509219
\(552\) −1.33193 −0.0566908
\(553\) 0.238780 0.0101540
\(554\) 3.40753 0.144772
\(555\) −4.07751 −0.173081
\(556\) −31.0783 −1.31801
\(557\) −10.3207 −0.437303 −0.218651 0.975803i \(-0.570166\pi\)
−0.218651 + 0.975803i \(0.570166\pi\)
\(558\) −5.59306 −0.236773
\(559\) 19.3292 0.817540
\(560\) 1.90847 0.0806476
\(561\) 19.9899 0.843975
\(562\) 7.23877 0.305349
\(563\) −42.2694 −1.78144 −0.890720 0.454552i \(-0.849800\pi\)
−0.890720 + 0.454552i \(0.849800\pi\)
\(564\) −13.1430 −0.553418
\(565\) −12.3006 −0.517489
\(566\) 14.0813 0.591881
\(567\) 10.7542 0.451633
\(568\) 2.37641 0.0997120
\(569\) 9.06146 0.379876 0.189938 0.981796i \(-0.439171\pi\)
0.189938 + 0.981796i \(0.439171\pi\)
\(570\) 2.89300 0.121174
\(571\) 14.3577 0.600852 0.300426 0.953805i \(-0.402871\pi\)
0.300426 + 0.953805i \(0.402871\pi\)
\(572\) −39.0557 −1.63300
\(573\) −26.6117 −1.11172
\(574\) 7.21607 0.301193
\(575\) 0.263969 0.0110083
\(576\) −0.906120 −0.0377550
\(577\) −31.1895 −1.29844 −0.649219 0.760602i \(-0.724904\pi\)
−0.649219 + 0.760602i \(0.724904\pi\)
\(578\) −7.11774 −0.296059
\(579\) −17.3942 −0.722877
\(580\) 9.35635 0.388501
\(581\) −0.663084 −0.0275094
\(582\) 1.19543 0.0495523
\(583\) −38.6435 −1.60045
\(584\) −29.9814 −1.24064
\(585\) −13.9200 −0.575519
\(586\) −2.73024 −0.112785
\(587\) 4.50524 0.185951 0.0929755 0.995668i \(-0.470362\pi\)
0.0929755 + 0.995668i \(0.470362\pi\)
\(588\) −3.71480 −0.153196
\(589\) 8.65973 0.356818
\(590\) −3.89530 −0.160367
\(591\) 4.53388 0.186499
\(592\) 3.41119 0.140199
\(593\) 39.1481 1.60762 0.803810 0.594886i \(-0.202803\pi\)
0.803810 + 0.594886i \(0.202803\pi\)
\(594\) −4.20316 −0.172458
\(595\) 2.30733 0.0945913
\(596\) 3.72781 0.152697
\(597\) −46.1133 −1.88729
\(598\) 1.01623 0.0415566
\(599\) 0.838810 0.0342729 0.0171364 0.999853i \(-0.494545\pi\)
0.0171364 + 0.999853i \(0.494545\pi\)
\(600\) −5.04579 −0.205993
\(601\) 26.1208 1.06549 0.532745 0.846276i \(-0.321161\pi\)
0.532745 + 0.846276i \(0.321161\pi\)
\(602\) −1.86576 −0.0760429
\(603\) −30.2077 −1.23015
\(604\) 5.58543 0.227268
\(605\) −3.42293 −0.139162
\(606\) 0.920342 0.0373863
\(607\) 17.3205 0.703018 0.351509 0.936184i \(-0.385669\pi\)
0.351509 + 0.936184i \(0.385669\pi\)
\(608\) −11.6230 −0.471375
\(609\) −13.1075 −0.531144
\(610\) −0.142957 −0.00578816
\(611\) 22.3437 0.903931
\(612\) −8.28151 −0.334760
\(613\) 44.9456 1.81534 0.907668 0.419689i \(-0.137861\pi\)
0.907668 + 0.419689i \(0.137861\pi\)
\(614\) −6.75234 −0.272502
\(615\) 27.0045 1.08893
\(616\) 8.40004 0.338447
\(617\) −47.8359 −1.92580 −0.962901 0.269857i \(-0.913024\pi\)
−0.962901 + 0.269857i \(0.913024\pi\)
\(618\) −1.66577 −0.0670071
\(619\) −6.13786 −0.246701 −0.123351 0.992363i \(-0.539364\pi\)
−0.123351 + 0.992363i \(0.539364\pi\)
\(620\) −6.77845 −0.272229
\(621\) −0.479251 −0.0192317
\(622\) −8.36117 −0.335252
\(623\) −16.2882 −0.652575
\(624\) 27.4953 1.10069
\(625\) 1.00000 0.0400000
\(626\) 12.1866 0.487074
\(627\) −18.0233 −0.719783
\(628\) −7.73037 −0.308475
\(629\) 4.12411 0.164439
\(630\) 1.34363 0.0535315
\(631\) −7.33730 −0.292093 −0.146047 0.989278i \(-0.546655\pi\)
−0.146047 + 0.989278i \(0.546655\pi\)
\(632\) 0.528144 0.0210084
\(633\) 1.52648 0.0606723
\(634\) 12.9882 0.515826
\(635\) −19.4000 −0.769866
\(636\) 37.7994 1.49884
\(637\) 6.31536 0.250224
\(638\) 13.3019 0.526626
\(639\) −2.36814 −0.0936821
\(640\) 11.4248 0.451603
\(641\) 25.3709 1.00209 0.501046 0.865421i \(-0.332949\pi\)
0.501046 + 0.865421i \(0.332949\pi\)
\(642\) 13.5277 0.533895
\(643\) −5.66988 −0.223598 −0.111799 0.993731i \(-0.535661\pi\)
−0.111799 + 0.993731i \(0.535661\pi\)
\(644\) 0.429846 0.0169383
\(645\) −6.98219 −0.274923
\(646\) −2.92606 −0.115124
\(647\) 9.55879 0.375795 0.187897 0.982189i \(-0.439833\pi\)
0.187897 + 0.982189i \(0.439833\pi\)
\(648\) 23.7866 0.934425
\(649\) 24.2677 0.952590
\(650\) 3.84980 0.151001
\(651\) 9.49609 0.372181
\(652\) 4.92609 0.192921
\(653\) −32.2310 −1.26130 −0.630648 0.776069i \(-0.717211\pi\)
−0.630648 + 0.776069i \(0.717211\pi\)
\(654\) 24.6650 0.964477
\(655\) −19.4521 −0.760058
\(656\) −22.5916 −0.882053
\(657\) 29.8770 1.16561
\(658\) −2.15674 −0.0840785
\(659\) −6.43221 −0.250563 −0.125282 0.992121i \(-0.539983\pi\)
−0.125282 + 0.992121i \(0.539983\pi\)
\(660\) 14.1079 0.549148
\(661\) 20.2028 0.785799 0.392900 0.919581i \(-0.371472\pi\)
0.392900 + 0.919581i \(0.371472\pi\)
\(662\) −0.480496 −0.0186750
\(663\) 33.2416 1.29100
\(664\) −1.46664 −0.0569166
\(665\) −2.08034 −0.0806721
\(666\) 2.40160 0.0930600
\(667\) 1.51670 0.0587268
\(668\) −14.0960 −0.545389
\(669\) 19.1087 0.738784
\(670\) 8.35444 0.322760
\(671\) 0.890620 0.0343820
\(672\) −12.7456 −0.491671
\(673\) −40.2837 −1.55282 −0.776411 0.630227i \(-0.782962\pi\)
−0.776411 + 0.630227i \(0.782962\pi\)
\(674\) 0.0525197 0.00202298
\(675\) −1.81556 −0.0698808
\(676\) −43.7774 −1.68375
\(677\) 6.17098 0.237170 0.118585 0.992944i \(-0.462164\pi\)
0.118585 + 0.992944i \(0.462164\pi\)
\(678\) 17.1057 0.656939
\(679\) −0.859629 −0.0329895
\(680\) 5.10345 0.195709
\(681\) −7.63457 −0.292557
\(682\) −9.63689 −0.369015
\(683\) 19.4027 0.742424 0.371212 0.928548i \(-0.378942\pi\)
0.371212 + 0.928548i \(0.378942\pi\)
\(684\) 7.46679 0.285500
\(685\) −1.65064 −0.0630676
\(686\) −0.609593 −0.0232744
\(687\) 2.28126 0.0870355
\(688\) 5.84120 0.222694
\(689\) −64.2611 −2.44815
\(690\) −0.367086 −0.0139747
\(691\) 23.2145 0.883123 0.441561 0.897231i \(-0.354425\pi\)
0.441561 + 0.897231i \(0.354425\pi\)
\(692\) 21.4133 0.814010
\(693\) −8.37079 −0.317980
\(694\) −20.9357 −0.794708
\(695\) −19.0852 −0.723943
\(696\) −28.9918 −1.09893
\(697\) −27.3131 −1.03456
\(698\) 10.1696 0.384926
\(699\) −32.0417 −1.21193
\(700\) 1.62840 0.0615476
\(701\) −0.359130 −0.0135642 −0.00678208 0.999977i \(-0.502159\pi\)
−0.00678208 + 0.999977i \(0.502159\pi\)
\(702\) −6.98952 −0.263802
\(703\) −3.71839 −0.140242
\(704\) −1.56125 −0.0588418
\(705\) −8.07110 −0.303975
\(706\) 8.99512 0.338536
\(707\) −0.661812 −0.0248900
\(708\) −23.7376 −0.892113
\(709\) 41.8277 1.57087 0.785435 0.618944i \(-0.212439\pi\)
0.785435 + 0.618944i \(0.212439\pi\)
\(710\) 0.654948 0.0245798
\(711\) −0.526305 −0.0197380
\(712\) −36.0271 −1.35017
\(713\) −1.09881 −0.0411508
\(714\) −3.20866 −0.120081
\(715\) −23.9842 −0.896957
\(716\) −18.9241 −0.707228
\(717\) 57.5018 2.14744
\(718\) 10.1641 0.379321
\(719\) −11.5715 −0.431545 −0.215772 0.976444i \(-0.569227\pi\)
−0.215772 + 0.976444i \(0.569227\pi\)
\(720\) −4.20654 −0.156769
\(721\) 1.19785 0.0446101
\(722\) −8.94406 −0.332863
\(723\) 13.9610 0.519214
\(724\) −12.5044 −0.464723
\(725\) 5.74574 0.213392
\(726\) 4.76006 0.176662
\(727\) −41.5692 −1.54172 −0.770859 0.637006i \(-0.780173\pi\)
−0.770859 + 0.637006i \(0.780173\pi\)
\(728\) 13.9686 0.517710
\(729\) −11.2785 −0.417722
\(730\) −8.26298 −0.305826
\(731\) 7.06198 0.261197
\(732\) −0.871165 −0.0321992
\(733\) 31.0415 1.14654 0.573271 0.819366i \(-0.305674\pi\)
0.573271 + 0.819366i \(0.305674\pi\)
\(734\) 4.65145 0.171688
\(735\) −2.28126 −0.0841455
\(736\) 1.47482 0.0543624
\(737\) −52.0481 −1.91721
\(738\) −15.9053 −0.585481
\(739\) −6.34693 −0.233476 −0.116738 0.993163i \(-0.537244\pi\)
−0.116738 + 0.993163i \(0.537244\pi\)
\(740\) 2.91059 0.106995
\(741\) −29.9714 −1.10103
\(742\) 6.20283 0.227713
\(743\) −3.10557 −0.113932 −0.0569662 0.998376i \(-0.518143\pi\)
−0.0569662 + 0.998376i \(0.518143\pi\)
\(744\) 21.0039 0.770039
\(745\) 2.28925 0.0838716
\(746\) 16.4975 0.604018
\(747\) 1.46153 0.0534747
\(748\) −14.2691 −0.521730
\(749\) −9.72768 −0.355442
\(750\) −1.39064 −0.0507789
\(751\) −26.9835 −0.984643 −0.492321 0.870413i \(-0.663852\pi\)
−0.492321 + 0.870413i \(0.663852\pi\)
\(752\) 6.75217 0.246226
\(753\) −47.1014 −1.71647
\(754\) 22.1199 0.805561
\(755\) 3.43002 0.124831
\(756\) −2.95644 −0.107525
\(757\) −28.5549 −1.03784 −0.518922 0.854821i \(-0.673667\pi\)
−0.518922 + 0.854821i \(0.673667\pi\)
\(758\) 5.54504 0.201405
\(759\) 2.28694 0.0830106
\(760\) −4.60138 −0.166910
\(761\) 32.6720 1.18436 0.592180 0.805806i \(-0.298267\pi\)
0.592180 + 0.805806i \(0.298267\pi\)
\(762\) 26.9784 0.977325
\(763\) −17.7364 −0.642102
\(764\) 18.9958 0.687245
\(765\) −5.08569 −0.183873
\(766\) −5.18272 −0.187259
\(767\) 40.3552 1.45714
\(768\) −14.0121 −0.505617
\(769\) 36.5131 1.31670 0.658348 0.752714i \(-0.271256\pi\)
0.658348 + 0.752714i \(0.271256\pi\)
\(770\) 2.31508 0.0834298
\(771\) −2.83628 −0.102146
\(772\) 12.4162 0.446869
\(773\) −20.2383 −0.727919 −0.363960 0.931415i \(-0.618575\pi\)
−0.363960 + 0.931415i \(0.618575\pi\)
\(774\) 4.11241 0.147818
\(775\) −4.16265 −0.149527
\(776\) −1.90137 −0.0682551
\(777\) −4.07751 −0.146280
\(778\) −20.9231 −0.750130
\(779\) 24.6261 0.882321
\(780\) 23.4603 0.840012
\(781\) −4.08032 −0.146005
\(782\) 0.371281 0.0132770
\(783\) −10.4317 −0.372799
\(784\) 1.90847 0.0681596
\(785\) −4.74723 −0.169436
\(786\) 27.0509 0.964874
\(787\) −0.668350 −0.0238241 −0.0119121 0.999929i \(-0.503792\pi\)
−0.0119121 + 0.999929i \(0.503792\pi\)
\(788\) −3.23635 −0.115290
\(789\) 38.9227 1.38568
\(790\) 0.145558 0.00517874
\(791\) −12.3006 −0.437358
\(792\) −18.5149 −0.657898
\(793\) 1.48103 0.0525929
\(794\) −20.1135 −0.713802
\(795\) 23.2126 0.823267
\(796\) 32.9164 1.16669
\(797\) −43.8557 −1.55345 −0.776724 0.629841i \(-0.783120\pi\)
−0.776724 + 0.629841i \(0.783120\pi\)
\(798\) 2.89300 0.102411
\(799\) 8.16334 0.288798
\(800\) 5.58708 0.197533
\(801\) 35.9016 1.26852
\(802\) 12.4700 0.440331
\(803\) 51.4782 1.81663
\(804\) 50.9111 1.79550
\(805\) 0.263969 0.00930369
\(806\) −16.0254 −0.564469
\(807\) 33.5215 1.18001
\(808\) −1.46383 −0.0514972
\(809\) 41.8880 1.47270 0.736352 0.676599i \(-0.236547\pi\)
0.736352 + 0.676599i \(0.236547\pi\)
\(810\) 6.55567 0.230343
\(811\) −20.0408 −0.703729 −0.351864 0.936051i \(-0.614452\pi\)
−0.351864 + 0.936051i \(0.614452\pi\)
\(812\) 9.35635 0.328344
\(813\) −67.0901 −2.35295
\(814\) 4.13797 0.145036
\(815\) 3.02512 0.105965
\(816\) 10.0455 0.351661
\(817\) −6.36724 −0.222761
\(818\) −4.05974 −0.141946
\(819\) −13.9200 −0.486403
\(820\) −19.2762 −0.673154
\(821\) −3.57754 −0.124857 −0.0624285 0.998049i \(-0.519885\pi\)
−0.0624285 + 0.998049i \(0.519885\pi\)
\(822\) 2.29544 0.0800626
\(823\) 27.1110 0.945029 0.472515 0.881323i \(-0.343346\pi\)
0.472515 + 0.881323i \(0.343346\pi\)
\(824\) 2.64945 0.0922978
\(825\) 8.66366 0.301630
\(826\) −3.89530 −0.135535
\(827\) −13.2119 −0.459424 −0.229712 0.973259i \(-0.573778\pi\)
−0.229712 + 0.973259i \(0.573778\pi\)
\(828\) −0.947443 −0.0329259
\(829\) −7.55284 −0.262321 −0.131161 0.991361i \(-0.541870\pi\)
−0.131161 + 0.991361i \(0.541870\pi\)
\(830\) −0.404211 −0.0140304
\(831\) 12.7519 0.442358
\(832\) −2.59623 −0.0900082
\(833\) 2.30733 0.0799443
\(834\) 26.5406 0.919027
\(835\) −8.65634 −0.299565
\(836\) 12.8653 0.444957
\(837\) 7.55753 0.261226
\(838\) 1.16046 0.0400874
\(839\) −21.4644 −0.741032 −0.370516 0.928826i \(-0.620819\pi\)
−0.370516 + 0.928826i \(0.620819\pi\)
\(840\) −5.04579 −0.174096
\(841\) 4.01358 0.138399
\(842\) −1.83842 −0.0633562
\(843\) 27.0894 0.933009
\(844\) −1.08963 −0.0375065
\(845\) −26.8837 −0.924829
\(846\) 4.75376 0.163438
\(847\) −3.42293 −0.117613
\(848\) −19.4194 −0.666864
\(849\) 52.6959 1.80852
\(850\) 1.40653 0.0482436
\(851\) 0.471817 0.0161737
\(852\) 3.99119 0.136736
\(853\) 52.3177 1.79133 0.895663 0.444734i \(-0.146702\pi\)
0.895663 + 0.444734i \(0.146702\pi\)
\(854\) −0.142957 −0.00489189
\(855\) 4.58536 0.156816
\(856\) −21.5161 −0.735405
\(857\) 5.25720 0.179583 0.0897913 0.995961i \(-0.471380\pi\)
0.0897913 + 0.995961i \(0.471380\pi\)
\(858\) 33.3533 1.13866
\(859\) −29.6058 −1.01014 −0.505068 0.863079i \(-0.668533\pi\)
−0.505068 + 0.863079i \(0.668533\pi\)
\(860\) 4.98399 0.169953
\(861\) 27.0045 0.920310
\(862\) −2.85893 −0.0973755
\(863\) −14.3280 −0.487731 −0.243866 0.969809i \(-0.578416\pi\)
−0.243866 + 0.969809i \(0.578416\pi\)
\(864\) −10.1436 −0.345094
\(865\) 13.1499 0.447110
\(866\) 13.6499 0.463841
\(867\) −26.6365 −0.904623
\(868\) −6.77845 −0.230076
\(869\) −0.906827 −0.0307620
\(870\) −7.99025 −0.270895
\(871\) −86.5517 −2.93269
\(872\) −39.2302 −1.32850
\(873\) 1.89475 0.0641274
\(874\) −0.334755 −0.0113233
\(875\) 1.00000 0.0338062
\(876\) −50.3537 −1.70129
\(877\) 13.9713 0.471776 0.235888 0.971780i \(-0.424200\pi\)
0.235888 + 0.971780i \(0.424200\pi\)
\(878\) −22.2558 −0.751097
\(879\) −10.2173 −0.344621
\(880\) −7.24790 −0.244327
\(881\) −7.31628 −0.246492 −0.123246 0.992376i \(-0.539330\pi\)
−0.123246 + 0.992376i \(0.539330\pi\)
\(882\) 1.34363 0.0452424
\(883\) −7.48992 −0.252056 −0.126028 0.992027i \(-0.540223\pi\)
−0.126028 + 0.992027i \(0.540223\pi\)
\(884\) −23.7284 −0.798072
\(885\) −14.5773 −0.490009
\(886\) −19.5777 −0.657726
\(887\) 7.56087 0.253869 0.126935 0.991911i \(-0.459486\pi\)
0.126935 + 0.991911i \(0.459486\pi\)
\(888\) −9.01882 −0.302652
\(889\) −19.4000 −0.650656
\(890\) −9.92920 −0.332827
\(891\) −40.8417 −1.36825
\(892\) −13.6400 −0.456703
\(893\) −7.36024 −0.246301
\(894\) −3.18352 −0.106473
\(895\) −11.6213 −0.388458
\(896\) 11.4248 0.381674
\(897\) 3.80299 0.126978
\(898\) 9.98557 0.333223
\(899\) −23.9175 −0.797695
\(900\) −3.58922 −0.119641
\(901\) −23.4779 −0.782163
\(902\) −27.4049 −0.912482
\(903\) −6.98219 −0.232353
\(904\) −27.2070 −0.904890
\(905\) −7.67898 −0.255258
\(906\) −4.76992 −0.158470
\(907\) 19.0567 0.632769 0.316384 0.948631i \(-0.397531\pi\)
0.316384 + 0.948631i \(0.397531\pi\)
\(908\) 5.44967 0.180854
\(909\) 1.45873 0.0483830
\(910\) 3.84980 0.127619
\(911\) −28.3228 −0.938376 −0.469188 0.883098i \(-0.655453\pi\)
−0.469188 + 0.883098i \(0.655453\pi\)
\(912\) −9.05720 −0.299914
\(913\) 2.51823 0.0833413
\(914\) −13.1611 −0.435329
\(915\) −0.534983 −0.0176860
\(916\) −1.62840 −0.0538037
\(917\) −19.4521 −0.642366
\(918\) −2.55364 −0.0842825
\(919\) −46.8679 −1.54603 −0.773014 0.634389i \(-0.781252\pi\)
−0.773014 + 0.634389i \(0.781252\pi\)
\(920\) 0.583859 0.0192492
\(921\) −25.2691 −0.832644
\(922\) −2.63313 −0.0867175
\(923\) −6.78524 −0.223339
\(924\) 14.1079 0.464115
\(925\) 1.78740 0.0587692
\(926\) 5.09241 0.167347
\(927\) −2.64022 −0.0867163
\(928\) 32.1019 1.05380
\(929\) −0.543077 −0.0178178 −0.00890889 0.999960i \(-0.502836\pi\)
−0.00890889 + 0.999960i \(0.502836\pi\)
\(930\) 5.78875 0.189820
\(931\) −2.08034 −0.0681803
\(932\) 22.8718 0.749192
\(933\) −31.2897 −1.02438
\(934\) −13.6756 −0.447479
\(935\) −8.76267 −0.286570
\(936\) −30.7888 −1.00636
\(937\) −40.3388 −1.31781 −0.658906 0.752225i \(-0.728981\pi\)
−0.658906 + 0.752225i \(0.728981\pi\)
\(938\) 8.35444 0.272782
\(939\) 45.6055 1.48828
\(940\) 5.76127 0.187912
\(941\) −25.9572 −0.846179 −0.423089 0.906088i \(-0.639054\pi\)
−0.423089 + 0.906088i \(0.639054\pi\)
\(942\) 6.60168 0.215094
\(943\) −3.12474 −0.101756
\(944\) 12.1951 0.396918
\(945\) −1.81556 −0.0590600
\(946\) 7.08571 0.230376
\(947\) −21.6527 −0.703618 −0.351809 0.936072i \(-0.614433\pi\)
−0.351809 + 0.936072i \(0.614433\pi\)
\(948\) 0.887019 0.0288090
\(949\) 85.6041 2.77883
\(950\) −1.26816 −0.0411445
\(951\) 48.6052 1.57613
\(952\) 5.10345 0.165404
\(953\) −45.8460 −1.48510 −0.742549 0.669792i \(-0.766383\pi\)
−0.742549 + 0.669792i \(0.766383\pi\)
\(954\) −13.6719 −0.442645
\(955\) 11.6654 0.377482
\(956\) −41.0456 −1.32751
\(957\) 49.7792 1.60913
\(958\) 7.86415 0.254079
\(959\) −1.65064 −0.0533018
\(960\) 0.937822 0.0302681
\(961\) −13.6723 −0.441043
\(962\) 6.88111 0.221856
\(963\) 21.4412 0.690933
\(964\) −9.96555 −0.320969
\(965\) 7.62481 0.245451
\(966\) −0.367086 −0.0118108
\(967\) 46.0290 1.48019 0.740097 0.672500i \(-0.234780\pi\)
0.740097 + 0.672500i \(0.234780\pi\)
\(968\) −7.57099 −0.243341
\(969\) −10.9501 −0.351768
\(970\) −0.524024 −0.0168254
\(971\) 16.3045 0.523237 0.261619 0.965171i \(-0.415744\pi\)
0.261619 + 0.965171i \(0.415744\pi\)
\(972\) 31.0802 0.996899
\(973\) −19.0852 −0.611844
\(974\) −10.0997 −0.323614
\(975\) 14.4070 0.461392
\(976\) 0.447560 0.0143260
\(977\) −19.3729 −0.619796 −0.309898 0.950770i \(-0.600295\pi\)
−0.309898 + 0.950770i \(0.600295\pi\)
\(978\) −4.20685 −0.134520
\(979\) 61.8588 1.97701
\(980\) 1.62840 0.0520172
\(981\) 39.0936 1.24816
\(982\) 14.2929 0.456103
\(983\) 30.7155 0.979672 0.489836 0.871815i \(-0.337057\pi\)
0.489836 + 0.871815i \(0.337057\pi\)
\(984\) 59.7297 1.90411
\(985\) −1.98744 −0.0633253
\(986\) 8.08157 0.257370
\(987\) −8.07110 −0.256906
\(988\) 21.3940 0.680634
\(989\) 0.807923 0.0256905
\(990\) −5.10277 −0.162177
\(991\) −15.5511 −0.493997 −0.246998 0.969016i \(-0.579444\pi\)
−0.246998 + 0.969016i \(0.579444\pi\)
\(992\) −23.2571 −0.738413
\(993\) −1.79814 −0.0570623
\(994\) 0.654948 0.0207737
\(995\) 20.2140 0.640826
\(996\) −2.46322 −0.0780502
\(997\) 28.5147 0.903071 0.451535 0.892253i \(-0.350876\pi\)
0.451535 + 0.892253i \(0.350876\pi\)
\(998\) −7.94657 −0.251544
\(999\) −3.24512 −0.102671
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 \(a_p\))