Properties

Label 8015.2.a.l.1.48
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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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 1.48
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.80465 q^{2} -1.89741 q^{3} +1.25677 q^{4} -1.00000 q^{5} -3.42417 q^{6} -1.00000 q^{7} -1.34127 q^{8} +0.600181 q^{9} +O(q^{10})\) \(q+1.80465 q^{2} -1.89741 q^{3} +1.25677 q^{4} -1.00000 q^{5} -3.42417 q^{6} -1.00000 q^{7} -1.34127 q^{8} +0.600181 q^{9} -1.80465 q^{10} -1.17911 q^{11} -2.38461 q^{12} -4.31155 q^{13} -1.80465 q^{14} +1.89741 q^{15} -4.93407 q^{16} -6.27501 q^{17} +1.08312 q^{18} -8.34549 q^{19} -1.25677 q^{20} +1.89741 q^{21} -2.12787 q^{22} -2.43958 q^{23} +2.54495 q^{24} +1.00000 q^{25} -7.78085 q^{26} +4.55345 q^{27} -1.25677 q^{28} -8.45454 q^{29} +3.42417 q^{30} +6.67107 q^{31} -6.22174 q^{32} +2.23725 q^{33} -11.3242 q^{34} +1.00000 q^{35} +0.754289 q^{36} -8.35200 q^{37} -15.0607 q^{38} +8.18079 q^{39} +1.34127 q^{40} +3.15447 q^{41} +3.42417 q^{42} -4.66888 q^{43} -1.48186 q^{44} -0.600181 q^{45} -4.40259 q^{46} +10.7388 q^{47} +9.36197 q^{48} +1.00000 q^{49} +1.80465 q^{50} +11.9063 q^{51} -5.41863 q^{52} +5.67308 q^{53} +8.21740 q^{54} +1.17911 q^{55} +1.34127 q^{56} +15.8348 q^{57} -15.2575 q^{58} +7.57294 q^{59} +2.38461 q^{60} -6.87376 q^{61} +12.0390 q^{62} -0.600181 q^{63} -1.35993 q^{64} +4.31155 q^{65} +4.03746 q^{66} -9.26226 q^{67} -7.88624 q^{68} +4.62889 q^{69} +1.80465 q^{70} -4.02518 q^{71} -0.805006 q^{72} -8.17594 q^{73} -15.0725 q^{74} -1.89741 q^{75} -10.4884 q^{76} +1.17911 q^{77} +14.7635 q^{78} -15.0772 q^{79} +4.93407 q^{80} -10.4403 q^{81} +5.69272 q^{82} +16.8700 q^{83} +2.38461 q^{84} +6.27501 q^{85} -8.42571 q^{86} +16.0418 q^{87} +1.58150 q^{88} -3.42934 q^{89} -1.08312 q^{90} +4.31155 q^{91} -3.06599 q^{92} -12.6578 q^{93} +19.3798 q^{94} +8.34549 q^{95} +11.8052 q^{96} -7.01775 q^{97} +1.80465 q^{98} -0.707676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.80465 1.27608 0.638041 0.770002i \(-0.279745\pi\)
0.638041 + 0.770002i \(0.279745\pi\)
\(3\) −1.89741 −1.09547 −0.547736 0.836651i \(-0.684510\pi\)
−0.547736 + 0.836651i \(0.684510\pi\)
\(4\) 1.25677 0.628385
\(5\) −1.00000 −0.447214
\(6\) −3.42417 −1.39791
\(7\) −1.00000 −0.377964
\(8\) −1.34127 −0.474211
\(9\) 0.600181 0.200060
\(10\) −1.80465 −0.570681
\(11\) −1.17911 −0.355514 −0.177757 0.984074i \(-0.556884\pi\)
−0.177757 + 0.984074i \(0.556884\pi\)
\(12\) −2.38461 −0.688379
\(13\) −4.31155 −1.19581 −0.597904 0.801568i \(-0.704000\pi\)
−0.597904 + 0.801568i \(0.704000\pi\)
\(14\) −1.80465 −0.482314
\(15\) 1.89741 0.489910
\(16\) −4.93407 −1.23352
\(17\) −6.27501 −1.52191 −0.760956 0.648803i \(-0.775270\pi\)
−0.760956 + 0.648803i \(0.775270\pi\)
\(18\) 1.08312 0.255293
\(19\) −8.34549 −1.91459 −0.957293 0.289120i \(-0.906637\pi\)
−0.957293 + 0.289120i \(0.906637\pi\)
\(20\) −1.25677 −0.281022
\(21\) 1.89741 0.414050
\(22\) −2.12787 −0.453664
\(23\) −2.43958 −0.508687 −0.254343 0.967114i \(-0.581859\pi\)
−0.254343 + 0.967114i \(0.581859\pi\)
\(24\) 2.54495 0.519485
\(25\) 1.00000 0.200000
\(26\) −7.78085 −1.52595
\(27\) 4.55345 0.876312
\(28\) −1.25677 −0.237507
\(29\) −8.45454 −1.56997 −0.784984 0.619516i \(-0.787329\pi\)
−0.784984 + 0.619516i \(0.787329\pi\)
\(30\) 3.42417 0.625166
\(31\) 6.67107 1.19816 0.599080 0.800689i \(-0.295533\pi\)
0.599080 + 0.800689i \(0.295533\pi\)
\(32\) −6.22174 −1.09986
\(33\) 2.23725 0.389455
\(34\) −11.3242 −1.94208
\(35\) 1.00000 0.169031
\(36\) 0.754289 0.125715
\(37\) −8.35200 −1.37306 −0.686530 0.727101i \(-0.740867\pi\)
−0.686530 + 0.727101i \(0.740867\pi\)
\(38\) −15.0607 −2.44317
\(39\) 8.18079 1.30998
\(40\) 1.34127 0.212074
\(41\) 3.15447 0.492645 0.246322 0.969188i \(-0.420778\pi\)
0.246322 + 0.969188i \(0.420778\pi\)
\(42\) 3.42417 0.528361
\(43\) −4.66888 −0.711998 −0.355999 0.934486i \(-0.615859\pi\)
−0.355999 + 0.934486i \(0.615859\pi\)
\(44\) −1.48186 −0.223399
\(45\) −0.600181 −0.0894697
\(46\) −4.40259 −0.649126
\(47\) 10.7388 1.56642 0.783208 0.621760i \(-0.213582\pi\)
0.783208 + 0.621760i \(0.213582\pi\)
\(48\) 9.36197 1.35128
\(49\) 1.00000 0.142857
\(50\) 1.80465 0.255216
\(51\) 11.9063 1.66721
\(52\) −5.41863 −0.751428
\(53\) 5.67308 0.779258 0.389629 0.920972i \(-0.372603\pi\)
0.389629 + 0.920972i \(0.372603\pi\)
\(54\) 8.21740 1.11825
\(55\) 1.17911 0.158991
\(56\) 1.34127 0.179235
\(57\) 15.8348 2.09738
\(58\) −15.2575 −2.00341
\(59\) 7.57294 0.985913 0.492957 0.870054i \(-0.335916\pi\)
0.492957 + 0.870054i \(0.335916\pi\)
\(60\) 2.38461 0.307852
\(61\) −6.87376 −0.880095 −0.440047 0.897975i \(-0.645038\pi\)
−0.440047 + 0.897975i \(0.645038\pi\)
\(62\) 12.0390 1.52895
\(63\) −0.600181 −0.0756157
\(64\) −1.35993 −0.169992
\(65\) 4.31155 0.534782
\(66\) 4.03746 0.496977
\(67\) −9.26226 −1.13157 −0.565783 0.824554i \(-0.691426\pi\)
−0.565783 + 0.824554i \(0.691426\pi\)
\(68\) −7.88624 −0.956347
\(69\) 4.62889 0.557252
\(70\) 1.80465 0.215697
\(71\) −4.02518 −0.477701 −0.238850 0.971056i \(-0.576771\pi\)
−0.238850 + 0.971056i \(0.576771\pi\)
\(72\) −0.805006 −0.0948708
\(73\) −8.17594 −0.956921 −0.478460 0.878109i \(-0.658805\pi\)
−0.478460 + 0.878109i \(0.658805\pi\)
\(74\) −15.0725 −1.75214
\(75\) −1.89741 −0.219095
\(76\) −10.4884 −1.20310
\(77\) 1.17911 0.134372
\(78\) 14.7635 1.67164
\(79\) −15.0772 −1.69632 −0.848161 0.529739i \(-0.822290\pi\)
−0.848161 + 0.529739i \(0.822290\pi\)
\(80\) 4.93407 0.551646
\(81\) −10.4403 −1.16004
\(82\) 5.69272 0.628655
\(83\) 16.8700 1.85172 0.925859 0.377869i \(-0.123343\pi\)
0.925859 + 0.377869i \(0.123343\pi\)
\(84\) 2.38461 0.260183
\(85\) 6.27501 0.680620
\(86\) −8.42571 −0.908567
\(87\) 16.0418 1.71986
\(88\) 1.58150 0.168588
\(89\) −3.42934 −0.363510 −0.181755 0.983344i \(-0.558178\pi\)
−0.181755 + 0.983344i \(0.558178\pi\)
\(90\) −1.08312 −0.114171
\(91\) 4.31155 0.451973
\(92\) −3.06599 −0.319651
\(93\) −12.6578 −1.31255
\(94\) 19.3798 1.99887
\(95\) 8.34549 0.856229
\(96\) 11.8052 1.20486
\(97\) −7.01775 −0.712545 −0.356272 0.934382i \(-0.615952\pi\)
−0.356272 + 0.934382i \(0.615952\pi\)
\(98\) 1.80465 0.182297
\(99\) −0.707676 −0.0711242
\(100\) 1.25677 0.125677
\(101\) 9.71131 0.966312 0.483156 0.875534i \(-0.339490\pi\)
0.483156 + 0.875534i \(0.339490\pi\)
\(102\) 21.4867 2.12750
\(103\) 14.7691 1.45524 0.727620 0.685981i \(-0.240627\pi\)
0.727620 + 0.685981i \(0.240627\pi\)
\(104\) 5.78296 0.567066
\(105\) −1.89741 −0.185169
\(106\) 10.2379 0.994397
\(107\) −3.85087 −0.372278 −0.186139 0.982523i \(-0.559597\pi\)
−0.186139 + 0.982523i \(0.559597\pi\)
\(108\) 5.72264 0.550661
\(109\) −16.2827 −1.55960 −0.779801 0.626027i \(-0.784680\pi\)
−0.779801 + 0.626027i \(0.784680\pi\)
\(110\) 2.12787 0.202885
\(111\) 15.8472 1.50415
\(112\) 4.93407 0.466226
\(113\) 3.99030 0.375376 0.187688 0.982229i \(-0.439901\pi\)
0.187688 + 0.982229i \(0.439901\pi\)
\(114\) 28.5764 2.67642
\(115\) 2.43958 0.227492
\(116\) −10.6254 −0.986545
\(117\) −2.58771 −0.239234
\(118\) 13.6665 1.25811
\(119\) 6.27501 0.575229
\(120\) −2.54495 −0.232321
\(121\) −9.60971 −0.873610
\(122\) −12.4047 −1.12307
\(123\) −5.98533 −0.539679
\(124\) 8.38400 0.752906
\(125\) −1.00000 −0.0894427
\(126\) −1.08312 −0.0964918
\(127\) −11.0601 −0.981425 −0.490713 0.871322i \(-0.663263\pi\)
−0.490713 + 0.871322i \(0.663263\pi\)
\(128\) 9.98927 0.882935
\(129\) 8.85880 0.779974
\(130\) 7.78085 0.682425
\(131\) 4.37968 0.382654 0.191327 0.981526i \(-0.438721\pi\)
0.191327 + 0.981526i \(0.438721\pi\)
\(132\) 2.81171 0.244728
\(133\) 8.34549 0.723645
\(134\) −16.7152 −1.44397
\(135\) −4.55345 −0.391899
\(136\) 8.41649 0.721708
\(137\) 20.5760 1.75793 0.878965 0.476887i \(-0.158235\pi\)
0.878965 + 0.476887i \(0.158235\pi\)
\(138\) 8.35353 0.711100
\(139\) −19.6350 −1.66542 −0.832708 0.553712i \(-0.813211\pi\)
−0.832708 + 0.553712i \(0.813211\pi\)
\(140\) 1.25677 0.106216
\(141\) −20.3760 −1.71596
\(142\) −7.26405 −0.609585
\(143\) 5.08377 0.425126
\(144\) −2.96133 −0.246778
\(145\) 8.45454 0.702111
\(146\) −14.7547 −1.22111
\(147\) −1.89741 −0.156496
\(148\) −10.4965 −0.862811
\(149\) −16.1204 −1.32064 −0.660318 0.750986i \(-0.729579\pi\)
−0.660318 + 0.750986i \(0.729579\pi\)
\(150\) −3.42417 −0.279583
\(151\) −2.89920 −0.235933 −0.117967 0.993018i \(-0.537638\pi\)
−0.117967 + 0.993018i \(0.537638\pi\)
\(152\) 11.1936 0.907918
\(153\) −3.76614 −0.304474
\(154\) 2.12787 0.171469
\(155\) −6.67107 −0.535833
\(156\) 10.2814 0.823169
\(157\) −17.8860 −1.42746 −0.713728 0.700423i \(-0.752995\pi\)
−0.713728 + 0.700423i \(0.752995\pi\)
\(158\) −27.2092 −2.16465
\(159\) −10.7642 −0.853656
\(160\) 6.22174 0.491871
\(161\) 2.43958 0.192266
\(162\) −18.8412 −1.48030
\(163\) 19.0007 1.48825 0.744123 0.668042i \(-0.232867\pi\)
0.744123 + 0.668042i \(0.232867\pi\)
\(164\) 3.96444 0.309571
\(165\) −2.23725 −0.174170
\(166\) 30.4444 2.36294
\(167\) −23.3364 −1.80582 −0.902912 0.429824i \(-0.858575\pi\)
−0.902912 + 0.429824i \(0.858575\pi\)
\(168\) −2.54495 −0.196347
\(169\) 5.58945 0.429958
\(170\) 11.3242 0.868527
\(171\) −5.00880 −0.383033
\(172\) −5.86771 −0.447409
\(173\) −7.56837 −0.575412 −0.287706 0.957719i \(-0.592893\pi\)
−0.287706 + 0.957719i \(0.592893\pi\)
\(174\) 28.9498 2.19468
\(175\) −1.00000 −0.0755929
\(176\) 5.81779 0.438532
\(177\) −14.3690 −1.08004
\(178\) −6.18877 −0.463868
\(179\) −7.60210 −0.568208 −0.284104 0.958793i \(-0.591696\pi\)
−0.284104 + 0.958793i \(0.591696\pi\)
\(180\) −0.754289 −0.0562214
\(181\) −10.1245 −0.752552 −0.376276 0.926508i \(-0.622796\pi\)
−0.376276 + 0.926508i \(0.622796\pi\)
\(182\) 7.78085 0.576755
\(183\) 13.0424 0.964120
\(184\) 3.27213 0.241225
\(185\) 8.35200 0.614051
\(186\) −22.8429 −1.67492
\(187\) 7.39889 0.541061
\(188\) 13.4962 0.984312
\(189\) −4.55345 −0.331215
\(190\) 15.0607 1.09262
\(191\) 11.5722 0.837337 0.418669 0.908139i \(-0.362497\pi\)
0.418669 + 0.908139i \(0.362497\pi\)
\(192\) 2.58036 0.186221
\(193\) 10.4144 0.749642 0.374821 0.927097i \(-0.377704\pi\)
0.374821 + 0.927097i \(0.377704\pi\)
\(194\) −12.6646 −0.909265
\(195\) −8.18079 −0.585839
\(196\) 1.25677 0.0897693
\(197\) 4.42420 0.315211 0.157606 0.987502i \(-0.449623\pi\)
0.157606 + 0.987502i \(0.449623\pi\)
\(198\) −1.27711 −0.0907603
\(199\) 14.6784 1.04052 0.520261 0.854008i \(-0.325835\pi\)
0.520261 + 0.854008i \(0.325835\pi\)
\(200\) −1.34127 −0.0948422
\(201\) 17.5743 1.23960
\(202\) 17.5255 1.23309
\(203\) 8.45454 0.593392
\(204\) 14.9635 1.04765
\(205\) −3.15447 −0.220318
\(206\) 26.6530 1.85700
\(207\) −1.46419 −0.101768
\(208\) 21.2735 1.47505
\(209\) 9.84021 0.680661
\(210\) −3.42417 −0.236290
\(211\) −0.982999 −0.0676724 −0.0338362 0.999427i \(-0.510772\pi\)
−0.0338362 + 0.999427i \(0.510772\pi\)
\(212\) 7.12976 0.489674
\(213\) 7.63743 0.523308
\(214\) −6.94948 −0.475057
\(215\) 4.66888 0.318415
\(216\) −6.10741 −0.415557
\(217\) −6.67107 −0.452862
\(218\) −29.3847 −1.99018
\(219\) 15.5131 1.04828
\(220\) 1.48186 0.0999073
\(221\) 27.0550 1.81992
\(222\) 28.5987 1.91942
\(223\) −15.4909 −1.03734 −0.518672 0.854973i \(-0.673574\pi\)
−0.518672 + 0.854973i \(0.673574\pi\)
\(224\) 6.22174 0.415707
\(225\) 0.600181 0.0400121
\(226\) 7.20110 0.479010
\(227\) −5.75599 −0.382038 −0.191019 0.981586i \(-0.561179\pi\)
−0.191019 + 0.981586i \(0.561179\pi\)
\(228\) 19.9008 1.31796
\(229\) 1.00000 0.0660819
\(230\) 4.40259 0.290298
\(231\) −2.23725 −0.147200
\(232\) 11.3398 0.744496
\(233\) 12.6523 0.828880 0.414440 0.910077i \(-0.363977\pi\)
0.414440 + 0.910077i \(0.363977\pi\)
\(234\) −4.66992 −0.305282
\(235\) −10.7388 −0.700522
\(236\) 9.51745 0.619533
\(237\) 28.6078 1.85827
\(238\) 11.3242 0.734039
\(239\) −18.6702 −1.20768 −0.603838 0.797107i \(-0.706363\pi\)
−0.603838 + 0.797107i \(0.706363\pi\)
\(240\) −9.36197 −0.604313
\(241\) 27.0449 1.74211 0.871057 0.491182i \(-0.163435\pi\)
0.871057 + 0.491182i \(0.163435\pi\)
\(242\) −17.3422 −1.11480
\(243\) 6.14927 0.394476
\(244\) −8.63873 −0.553038
\(245\) −1.00000 −0.0638877
\(246\) −10.8014 −0.688675
\(247\) 35.9820 2.28948
\(248\) −8.94772 −0.568181
\(249\) −32.0093 −2.02851
\(250\) −1.80465 −0.114136
\(251\) 4.81484 0.303910 0.151955 0.988387i \(-0.451443\pi\)
0.151955 + 0.988387i \(0.451443\pi\)
\(252\) −0.754289 −0.0475158
\(253\) 2.87652 0.180845
\(254\) −19.9596 −1.25238
\(255\) −11.9063 −0.745601
\(256\) 20.7470 1.29669
\(257\) −10.4107 −0.649400 −0.324700 0.945817i \(-0.605263\pi\)
−0.324700 + 0.945817i \(0.605263\pi\)
\(258\) 15.9871 0.995310
\(259\) 8.35200 0.518968
\(260\) 5.41863 0.336049
\(261\) −5.07425 −0.314088
\(262\) 7.90379 0.488298
\(263\) −20.1531 −1.24269 −0.621346 0.783536i \(-0.713414\pi\)
−0.621346 + 0.783536i \(0.713414\pi\)
\(264\) −3.00076 −0.184684
\(265\) −5.67308 −0.348495
\(266\) 15.0607 0.923431
\(267\) 6.50689 0.398215
\(268\) −11.6405 −0.711059
\(269\) −15.7211 −0.958535 −0.479268 0.877669i \(-0.659098\pi\)
−0.479268 + 0.877669i \(0.659098\pi\)
\(270\) −8.21740 −0.500095
\(271\) 17.4652 1.06093 0.530466 0.847706i \(-0.322017\pi\)
0.530466 + 0.847706i \(0.322017\pi\)
\(272\) 30.9613 1.87731
\(273\) −8.18079 −0.495124
\(274\) 37.1326 2.24326
\(275\) −1.17911 −0.0711027
\(276\) 5.81745 0.350169
\(277\) 19.0232 1.14299 0.571497 0.820604i \(-0.306363\pi\)
0.571497 + 0.820604i \(0.306363\pi\)
\(278\) −35.4343 −2.12521
\(279\) 4.00385 0.239704
\(280\) −1.34127 −0.0801563
\(281\) −2.46876 −0.147274 −0.0736368 0.997285i \(-0.523461\pi\)
−0.0736368 + 0.997285i \(0.523461\pi\)
\(282\) −36.7715 −2.18971
\(283\) −21.5984 −1.28389 −0.641945 0.766751i \(-0.721872\pi\)
−0.641945 + 0.766751i \(0.721872\pi\)
\(284\) −5.05872 −0.300180
\(285\) −15.8348 −0.937975
\(286\) 9.17444 0.542496
\(287\) −3.15447 −0.186202
\(288\) −3.73417 −0.220038
\(289\) 22.3757 1.31622
\(290\) 15.2575 0.895951
\(291\) 13.3156 0.780573
\(292\) −10.2753 −0.601315
\(293\) 21.4460 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(294\) −3.42417 −0.199702
\(295\) −7.57294 −0.440914
\(296\) 11.2023 0.651121
\(297\) −5.36900 −0.311541
\(298\) −29.0918 −1.68524
\(299\) 10.5183 0.608292
\(300\) −2.38461 −0.137676
\(301\) 4.66888 0.269110
\(302\) −5.23204 −0.301070
\(303\) −18.4264 −1.05857
\(304\) 41.1772 2.36167
\(305\) 6.87376 0.393590
\(306\) −6.79657 −0.388534
\(307\) 1.74161 0.0993991 0.0496996 0.998764i \(-0.484174\pi\)
0.0496996 + 0.998764i \(0.484174\pi\)
\(308\) 1.48186 0.0844370
\(309\) −28.0230 −1.59417
\(310\) −12.0390 −0.683767
\(311\) −26.0742 −1.47853 −0.739266 0.673414i \(-0.764827\pi\)
−0.739266 + 0.673414i \(0.764827\pi\)
\(312\) −10.9727 −0.621205
\(313\) 18.8528 1.06562 0.532811 0.846234i \(-0.321136\pi\)
0.532811 + 0.846234i \(0.321136\pi\)
\(314\) −32.2779 −1.82155
\(315\) 0.600181 0.0338164
\(316\) −18.9486 −1.06594
\(317\) −4.29458 −0.241208 −0.120604 0.992701i \(-0.538483\pi\)
−0.120604 + 0.992701i \(0.538483\pi\)
\(318\) −19.4256 −1.08933
\(319\) 9.96879 0.558145
\(320\) 1.35993 0.0760225
\(321\) 7.30670 0.407820
\(322\) 4.40259 0.245347
\(323\) 52.3680 2.91383
\(324\) −13.1211 −0.728949
\(325\) −4.31155 −0.239162
\(326\) 34.2896 1.89912
\(327\) 30.8951 1.70850
\(328\) −4.23100 −0.233618
\(329\) −10.7388 −0.592049
\(330\) −4.03746 −0.222255
\(331\) −33.1987 −1.82477 −0.912384 0.409336i \(-0.865760\pi\)
−0.912384 + 0.409336i \(0.865760\pi\)
\(332\) 21.2017 1.16359
\(333\) −5.01271 −0.274695
\(334\) −42.1141 −2.30438
\(335\) 9.26226 0.506051
\(336\) −9.36197 −0.510738
\(337\) −32.6322 −1.77759 −0.888796 0.458304i \(-0.848457\pi\)
−0.888796 + 0.458304i \(0.848457\pi\)
\(338\) 10.0870 0.548661
\(339\) −7.57125 −0.411214
\(340\) 7.88624 0.427691
\(341\) −7.86589 −0.425962
\(342\) −9.03915 −0.488781
\(343\) −1.00000 −0.0539949
\(344\) 6.26224 0.337637
\(345\) −4.62889 −0.249211
\(346\) −13.6583 −0.734273
\(347\) −5.77989 −0.310281 −0.155140 0.987892i \(-0.549583\pi\)
−0.155140 + 0.987892i \(0.549583\pi\)
\(348\) 20.1608 1.08073
\(349\) −9.46667 −0.506739 −0.253370 0.967370i \(-0.581539\pi\)
−0.253370 + 0.967370i \(0.581539\pi\)
\(350\) −1.80465 −0.0964627
\(351\) −19.6324 −1.04790
\(352\) 7.33608 0.391014
\(353\) −26.0073 −1.38423 −0.692113 0.721789i \(-0.743320\pi\)
−0.692113 + 0.721789i \(0.743320\pi\)
\(354\) −25.9311 −1.37822
\(355\) 4.02518 0.213634
\(356\) −4.30990 −0.228424
\(357\) −11.9063 −0.630147
\(358\) −13.7192 −0.725080
\(359\) −8.74886 −0.461747 −0.230874 0.972984i \(-0.574158\pi\)
−0.230874 + 0.972984i \(0.574158\pi\)
\(360\) 0.805006 0.0424275
\(361\) 50.6471 2.66564
\(362\) −18.2713 −0.960318
\(363\) 18.2336 0.957016
\(364\) 5.41863 0.284013
\(365\) 8.17594 0.427948
\(366\) 23.5369 1.23030
\(367\) 19.6223 1.02428 0.512138 0.858903i \(-0.328854\pi\)
0.512138 + 0.858903i \(0.328854\pi\)
\(368\) 12.0370 0.627474
\(369\) 1.89325 0.0985587
\(370\) 15.0725 0.783580
\(371\) −5.67308 −0.294532
\(372\) −15.9079 −0.824787
\(373\) 29.5822 1.53171 0.765853 0.643015i \(-0.222317\pi\)
0.765853 + 0.643015i \(0.222317\pi\)
\(374\) 13.3524 0.690438
\(375\) 1.89741 0.0979821
\(376\) −14.4036 −0.742811
\(377\) 36.4522 1.87738
\(378\) −8.21740 −0.422657
\(379\) −4.34627 −0.223253 −0.111626 0.993750i \(-0.535606\pi\)
−0.111626 + 0.993750i \(0.535606\pi\)
\(380\) 10.4884 0.538041
\(381\) 20.9856 1.07512
\(382\) 20.8838 1.06851
\(383\) −5.07998 −0.259575 −0.129787 0.991542i \(-0.541430\pi\)
−0.129787 + 0.991542i \(0.541430\pi\)
\(384\) −18.9538 −0.967231
\(385\) −1.17911 −0.0600928
\(386\) 18.7943 0.956605
\(387\) −2.80217 −0.142442
\(388\) −8.81970 −0.447752
\(389\) −22.0334 −1.11714 −0.558568 0.829459i \(-0.688649\pi\)
−0.558568 + 0.829459i \(0.688649\pi\)
\(390\) −14.7635 −0.747578
\(391\) 15.3084 0.774177
\(392\) −1.34127 −0.0677444
\(393\) −8.31006 −0.419187
\(394\) 7.98414 0.402235
\(395\) 15.0772 0.758618
\(396\) −0.889387 −0.0446934
\(397\) 2.42155 0.121534 0.0607670 0.998152i \(-0.480645\pi\)
0.0607670 + 0.998152i \(0.480645\pi\)
\(398\) 26.4893 1.32779
\(399\) −15.8348 −0.792734
\(400\) −4.93407 −0.246703
\(401\) 38.0656 1.90090 0.950452 0.310872i \(-0.100621\pi\)
0.950452 + 0.310872i \(0.100621\pi\)
\(402\) 31.7156 1.58183
\(403\) −28.7626 −1.43277
\(404\) 12.2049 0.607216
\(405\) 10.4403 0.518784
\(406\) 15.2575 0.757217
\(407\) 9.84789 0.488142
\(408\) −15.9696 −0.790611
\(409\) 3.51772 0.173940 0.0869701 0.996211i \(-0.472282\pi\)
0.0869701 + 0.996211i \(0.472282\pi\)
\(410\) −5.69272 −0.281143
\(411\) −39.0413 −1.92576
\(412\) 18.5613 0.914451
\(413\) −7.57294 −0.372640
\(414\) −2.64235 −0.129864
\(415\) −16.8700 −0.828113
\(416\) 26.8253 1.31522
\(417\) 37.2557 1.82442
\(418\) 17.7581 0.868579
\(419\) 3.41851 0.167005 0.0835025 0.996508i \(-0.473389\pi\)
0.0835025 + 0.996508i \(0.473389\pi\)
\(420\) −2.38461 −0.116357
\(421\) 9.10984 0.443986 0.221993 0.975048i \(-0.428744\pi\)
0.221993 + 0.975048i \(0.428744\pi\)
\(422\) −1.77397 −0.0863556
\(423\) 6.44522 0.313377
\(424\) −7.60915 −0.369533
\(425\) −6.27501 −0.304382
\(426\) 13.7829 0.667784
\(427\) 6.87376 0.332644
\(428\) −4.83966 −0.233934
\(429\) −9.64602 −0.465714
\(430\) 8.42571 0.406324
\(431\) −11.4372 −0.550909 −0.275454 0.961314i \(-0.588828\pi\)
−0.275454 + 0.961314i \(0.588828\pi\)
\(432\) −22.4670 −1.08095
\(433\) 21.1673 1.01724 0.508618 0.860992i \(-0.330157\pi\)
0.508618 + 0.860992i \(0.330157\pi\)
\(434\) −12.0390 −0.577889
\(435\) −16.0418 −0.769144
\(436\) −20.4636 −0.980031
\(437\) 20.3594 0.973924
\(438\) 27.9958 1.33769
\(439\) 34.1256 1.62873 0.814363 0.580355i \(-0.197086\pi\)
0.814363 + 0.580355i \(0.197086\pi\)
\(440\) −1.58150 −0.0753951
\(441\) 0.600181 0.0285800
\(442\) 48.8249 2.32236
\(443\) −11.4697 −0.544940 −0.272470 0.962164i \(-0.587841\pi\)
−0.272470 + 0.962164i \(0.587841\pi\)
\(444\) 19.9163 0.945186
\(445\) 3.42934 0.162566
\(446\) −27.9556 −1.32374
\(447\) 30.5871 1.44672
\(448\) 1.35993 0.0642508
\(449\) −24.4493 −1.15383 −0.576917 0.816803i \(-0.695744\pi\)
−0.576917 + 0.816803i \(0.695744\pi\)
\(450\) 1.08312 0.0510587
\(451\) −3.71945 −0.175142
\(452\) 5.01489 0.235880
\(453\) 5.50098 0.258458
\(454\) −10.3876 −0.487512
\(455\) −4.31155 −0.202129
\(456\) −21.2388 −0.994599
\(457\) 0.719906 0.0336758 0.0168379 0.999858i \(-0.494640\pi\)
0.0168379 + 0.999858i \(0.494640\pi\)
\(458\) 1.80465 0.0843259
\(459\) −28.5729 −1.33367
\(460\) 3.06599 0.142952
\(461\) −22.2097 −1.03441 −0.517204 0.855862i \(-0.673027\pi\)
−0.517204 + 0.855862i \(0.673027\pi\)
\(462\) −4.03746 −0.187840
\(463\) 34.0802 1.58384 0.791920 0.610625i \(-0.209082\pi\)
0.791920 + 0.610625i \(0.209082\pi\)
\(464\) 41.7153 1.93658
\(465\) 12.6578 0.586991
\(466\) 22.8330 1.05772
\(467\) 25.2207 1.16707 0.583537 0.812086i \(-0.301668\pi\)
0.583537 + 0.812086i \(0.301668\pi\)
\(468\) −3.25216 −0.150331
\(469\) 9.26226 0.427692
\(470\) −19.3798 −0.893924
\(471\) 33.9371 1.56374
\(472\) −10.1574 −0.467531
\(473\) 5.50510 0.253125
\(474\) 51.6271 2.37131
\(475\) −8.34549 −0.382917
\(476\) 7.88624 0.361465
\(477\) 3.40488 0.155899
\(478\) −33.6932 −1.54109
\(479\) −7.82653 −0.357603 −0.178802 0.983885i \(-0.557222\pi\)
−0.178802 + 0.983885i \(0.557222\pi\)
\(480\) −11.8052 −0.538832
\(481\) 36.0101 1.64192
\(482\) 48.8066 2.22308
\(483\) −4.62889 −0.210622
\(484\) −12.0772 −0.548964
\(485\) 7.01775 0.318660
\(486\) 11.0973 0.503384
\(487\) 20.0572 0.908879 0.454440 0.890778i \(-0.349840\pi\)
0.454440 + 0.890778i \(0.349840\pi\)
\(488\) 9.21958 0.417351
\(489\) −36.0521 −1.63033
\(490\) −1.80465 −0.0815259
\(491\) −18.2503 −0.823624 −0.411812 0.911269i \(-0.635104\pi\)
−0.411812 + 0.911269i \(0.635104\pi\)
\(492\) −7.52218 −0.339126
\(493\) 53.0523 2.38935
\(494\) 64.9349 2.92156
\(495\) 0.707676 0.0318077
\(496\) −32.9155 −1.47795
\(497\) 4.02518 0.180554
\(498\) −57.7656 −2.58854
\(499\) −9.98776 −0.447113 −0.223557 0.974691i \(-0.571767\pi\)
−0.223557 + 0.974691i \(0.571767\pi\)
\(500\) −1.25677 −0.0562045
\(501\) 44.2788 1.97823
\(502\) 8.68911 0.387814
\(503\) −19.0253 −0.848294 −0.424147 0.905593i \(-0.639426\pi\)
−0.424147 + 0.905593i \(0.639426\pi\)
\(504\) 0.805006 0.0358578
\(505\) −9.71131 −0.432148
\(506\) 5.19111 0.230773
\(507\) −10.6055 −0.471007
\(508\) −13.9000 −0.616713
\(509\) −25.5640 −1.13310 −0.566552 0.824026i \(-0.691723\pi\)
−0.566552 + 0.824026i \(0.691723\pi\)
\(510\) −21.4867 −0.951447
\(511\) 8.17594 0.361682
\(512\) 17.4626 0.771746
\(513\) −38.0008 −1.67777
\(514\) −18.7876 −0.828687
\(515\) −14.7691 −0.650803
\(516\) 11.1335 0.490124
\(517\) −12.6622 −0.556882
\(518\) 15.0725 0.662246
\(519\) 14.3603 0.630348
\(520\) −5.78296 −0.253599
\(521\) −4.60081 −0.201565 −0.100783 0.994908i \(-0.532135\pi\)
−0.100783 + 0.994908i \(0.532135\pi\)
\(522\) −9.15726 −0.400802
\(523\) −24.7295 −1.08135 −0.540673 0.841233i \(-0.681830\pi\)
−0.540673 + 0.841233i \(0.681830\pi\)
\(524\) 5.50425 0.240454
\(525\) 1.89741 0.0828099
\(526\) −36.3693 −1.58578
\(527\) −41.8610 −1.82349
\(528\) −11.0388 −0.480400
\(529\) −17.0485 −0.741238
\(530\) −10.2379 −0.444708
\(531\) 4.54514 0.197242
\(532\) 10.4884 0.454728
\(533\) −13.6006 −0.589109
\(534\) 11.7427 0.508155
\(535\) 3.85087 0.166488
\(536\) 12.4232 0.536601
\(537\) 14.4243 0.622456
\(538\) −28.3712 −1.22317
\(539\) −1.17911 −0.0507877
\(540\) −5.72264 −0.246263
\(541\) −8.17373 −0.351416 −0.175708 0.984442i \(-0.556221\pi\)
−0.175708 + 0.984442i \(0.556221\pi\)
\(542\) 31.5185 1.35384
\(543\) 19.2105 0.824400
\(544\) 39.0414 1.67389
\(545\) 16.2827 0.697475
\(546\) −14.7635 −0.631819
\(547\) −16.3200 −0.697794 −0.348897 0.937161i \(-0.613444\pi\)
−0.348897 + 0.937161i \(0.613444\pi\)
\(548\) 25.8594 1.10466
\(549\) −4.12550 −0.176072
\(550\) −2.12787 −0.0907329
\(551\) 70.5572 3.00584
\(552\) −6.20859 −0.264255
\(553\) 15.0772 0.641149
\(554\) 34.3303 1.45855
\(555\) −15.8472 −0.672677
\(556\) −24.6766 −1.04652
\(557\) −19.5320 −0.827596 −0.413798 0.910369i \(-0.635798\pi\)
−0.413798 + 0.910369i \(0.635798\pi\)
\(558\) 7.22556 0.305882
\(559\) 20.1301 0.851413
\(560\) −4.93407 −0.208502
\(561\) −14.0388 −0.592717
\(562\) −4.45525 −0.187933
\(563\) 14.4725 0.609942 0.304971 0.952362i \(-0.401353\pi\)
0.304971 + 0.952362i \(0.401353\pi\)
\(564\) −25.6079 −1.07829
\(565\) −3.99030 −0.167873
\(566\) −38.9775 −1.63835
\(567\) 10.4403 0.438452
\(568\) 5.39886 0.226531
\(569\) 21.2094 0.889144 0.444572 0.895743i \(-0.353356\pi\)
0.444572 + 0.895743i \(0.353356\pi\)
\(570\) −28.5764 −1.19693
\(571\) −23.9805 −1.00355 −0.501776 0.864998i \(-0.667320\pi\)
−0.501776 + 0.864998i \(0.667320\pi\)
\(572\) 6.38913 0.267143
\(573\) −21.9573 −0.917280
\(574\) −5.69272 −0.237609
\(575\) −2.43958 −0.101737
\(576\) −0.816206 −0.0340086
\(577\) −18.4212 −0.766883 −0.383442 0.923565i \(-0.625261\pi\)
−0.383442 + 0.923565i \(0.625261\pi\)
\(578\) 40.3804 1.67960
\(579\) −19.7604 −0.821213
\(580\) 10.6254 0.441196
\(581\) −16.8700 −0.699884
\(582\) 24.0300 0.996075
\(583\) −6.68916 −0.277037
\(584\) 10.9662 0.453783
\(585\) 2.58771 0.106989
\(586\) 38.7026 1.59879
\(587\) −11.6032 −0.478914 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(588\) −2.38461 −0.0983398
\(589\) −55.6733 −2.29398
\(590\) −13.6665 −0.562642
\(591\) −8.39454 −0.345305
\(592\) 41.2094 1.69369
\(593\) 6.19360 0.254341 0.127170 0.991881i \(-0.459410\pi\)
0.127170 + 0.991881i \(0.459410\pi\)
\(594\) −9.68917 −0.397552
\(595\) −6.27501 −0.257250
\(596\) −20.2597 −0.829868
\(597\) −27.8509 −1.13986
\(598\) 18.9820 0.776230
\(599\) −12.5178 −0.511465 −0.255732 0.966748i \(-0.582317\pi\)
−0.255732 + 0.966748i \(0.582317\pi\)
\(600\) 2.54495 0.103897
\(601\) −43.7326 −1.78389 −0.891945 0.452144i \(-0.850659\pi\)
−0.891945 + 0.452144i \(0.850659\pi\)
\(602\) 8.42571 0.343406
\(603\) −5.55903 −0.226381
\(604\) −3.64362 −0.148257
\(605\) 9.60971 0.390690
\(606\) −33.2532 −1.35082
\(607\) 7.18883 0.291785 0.145893 0.989300i \(-0.453395\pi\)
0.145893 + 0.989300i \(0.453395\pi\)
\(608\) 51.9234 2.10577
\(609\) −16.0418 −0.650045
\(610\) 12.4047 0.502253
\(611\) −46.3009 −1.87313
\(612\) −4.73317 −0.191327
\(613\) −25.4911 −1.02958 −0.514788 0.857317i \(-0.672129\pi\)
−0.514788 + 0.857317i \(0.672129\pi\)
\(614\) 3.14301 0.126841
\(615\) 5.98533 0.241352
\(616\) −1.58150 −0.0637205
\(617\) 7.08595 0.285269 0.142635 0.989775i \(-0.454443\pi\)
0.142635 + 0.989775i \(0.454443\pi\)
\(618\) −50.5718 −2.03430
\(619\) −12.4599 −0.500806 −0.250403 0.968142i \(-0.580563\pi\)
−0.250403 + 0.968142i \(0.580563\pi\)
\(620\) −8.38400 −0.336710
\(621\) −11.1085 −0.445768
\(622\) −47.0548 −1.88673
\(623\) 3.42934 0.137394
\(624\) −40.3646 −1.61588
\(625\) 1.00000 0.0400000
\(626\) 34.0227 1.35982
\(627\) −18.6709 −0.745646
\(628\) −22.4785 −0.896991
\(629\) 52.4089 2.08968
\(630\) 1.08312 0.0431525
\(631\) −9.34565 −0.372044 −0.186022 0.982546i \(-0.559560\pi\)
−0.186022 + 0.982546i \(0.559560\pi\)
\(632\) 20.2227 0.804415
\(633\) 1.86516 0.0741333
\(634\) −7.75023 −0.307801
\(635\) 11.0601 0.438907
\(636\) −13.5281 −0.536425
\(637\) −4.31155 −0.170830
\(638\) 17.9902 0.712239
\(639\) −2.41584 −0.0955690
\(640\) −9.98927 −0.394860
\(641\) 33.8535 1.33713 0.668567 0.743652i \(-0.266908\pi\)
0.668567 + 0.743652i \(0.266908\pi\)
\(642\) 13.1860 0.520412
\(643\) −21.9663 −0.866268 −0.433134 0.901329i \(-0.642592\pi\)
−0.433134 + 0.901329i \(0.642592\pi\)
\(644\) 3.06599 0.120817
\(645\) −8.85880 −0.348815
\(646\) 94.5060 3.71829
\(647\) 45.9565 1.80674 0.903368 0.428867i \(-0.141087\pi\)
0.903368 + 0.428867i \(0.141087\pi\)
\(648\) 14.0033 0.550102
\(649\) −8.92930 −0.350506
\(650\) −7.78085 −0.305190
\(651\) 12.6578 0.496098
\(652\) 23.8795 0.935192
\(653\) 35.2509 1.37947 0.689736 0.724061i \(-0.257726\pi\)
0.689736 + 0.724061i \(0.257726\pi\)
\(654\) 55.7549 2.18019
\(655\) −4.37968 −0.171128
\(656\) −15.5644 −0.607686
\(657\) −4.90704 −0.191442
\(658\) −19.3798 −0.755503
\(659\) 30.1615 1.17493 0.587463 0.809251i \(-0.300127\pi\)
0.587463 + 0.809251i \(0.300127\pi\)
\(660\) −2.81171 −0.109446
\(661\) −23.8616 −0.928110 −0.464055 0.885806i \(-0.653606\pi\)
−0.464055 + 0.885806i \(0.653606\pi\)
\(662\) −59.9122 −2.32855
\(663\) −51.3345 −1.99367
\(664\) −22.6272 −0.878105
\(665\) −8.34549 −0.323624
\(666\) −9.04620 −0.350533
\(667\) 20.6255 0.798622
\(668\) −29.3285 −1.13475
\(669\) 29.3926 1.13638
\(670\) 16.7152 0.645763
\(671\) 8.10488 0.312886
\(672\) −11.8052 −0.455396
\(673\) −22.5098 −0.867688 −0.433844 0.900988i \(-0.642843\pi\)
−0.433844 + 0.900988i \(0.642843\pi\)
\(674\) −58.8898 −2.26835
\(675\) 4.55345 0.175262
\(676\) 7.02465 0.270179
\(677\) 29.4466 1.13172 0.565862 0.824500i \(-0.308543\pi\)
0.565862 + 0.824500i \(0.308543\pi\)
\(678\) −13.6635 −0.524742
\(679\) 7.01775 0.269317
\(680\) −8.41649 −0.322758
\(681\) 10.9215 0.418512
\(682\) −14.1952 −0.543562
\(683\) 22.6563 0.866919 0.433460 0.901173i \(-0.357293\pi\)
0.433460 + 0.901173i \(0.357293\pi\)
\(684\) −6.29491 −0.240692
\(685\) −20.5760 −0.786170
\(686\) −1.80465 −0.0689019
\(687\) −1.89741 −0.0723909
\(688\) 23.0366 0.878261
\(689\) −24.4598 −0.931843
\(690\) −8.35353 −0.318013
\(691\) 26.6414 1.01349 0.506744 0.862097i \(-0.330849\pi\)
0.506744 + 0.862097i \(0.330849\pi\)
\(692\) −9.51170 −0.361580
\(693\) 0.707676 0.0268824
\(694\) −10.4307 −0.395943
\(695\) 19.6350 0.744797
\(696\) −21.5164 −0.815575
\(697\) −19.7943 −0.749763
\(698\) −17.0841 −0.646641
\(699\) −24.0067 −0.908015
\(700\) −1.25677 −0.0475014
\(701\) −32.2092 −1.21652 −0.608262 0.793736i \(-0.708133\pi\)
−0.608262 + 0.793736i \(0.708133\pi\)
\(702\) −35.4297 −1.33721
\(703\) 69.7015 2.62884
\(704\) 1.60350 0.0604343
\(705\) 20.3760 0.767403
\(706\) −46.9341 −1.76639
\(707\) −9.71131 −0.365232
\(708\) −18.0585 −0.678682
\(709\) 19.4894 0.731938 0.365969 0.930627i \(-0.380738\pi\)
0.365969 + 0.930627i \(0.380738\pi\)
\(710\) 7.26405 0.272615
\(711\) −9.04907 −0.339367
\(712\) 4.59968 0.172380
\(713\) −16.2746 −0.609488
\(714\) −21.4867 −0.804120
\(715\) −5.08377 −0.190122
\(716\) −9.55410 −0.357053
\(717\) 35.4251 1.32298
\(718\) −15.7887 −0.589227
\(719\) −7.42710 −0.276984 −0.138492 0.990364i \(-0.544226\pi\)
−0.138492 + 0.990364i \(0.544226\pi\)
\(720\) 2.96133 0.110362
\(721\) −14.7691 −0.550029
\(722\) 91.4005 3.40157
\(723\) −51.3153 −1.90844
\(724\) −12.7242 −0.472892
\(725\) −8.45454 −0.313994
\(726\) 32.9053 1.22123
\(727\) −48.5065 −1.79901 −0.899503 0.436915i \(-0.856071\pi\)
−0.899503 + 0.436915i \(0.856071\pi\)
\(728\) −5.78296 −0.214331
\(729\) 19.6533 0.727899
\(730\) 14.7547 0.546097
\(731\) 29.2972 1.08360
\(732\) 16.3913 0.605838
\(733\) 14.1021 0.520872 0.260436 0.965491i \(-0.416134\pi\)
0.260436 + 0.965491i \(0.416134\pi\)
\(734\) 35.4114 1.30706
\(735\) 1.89741 0.0699872
\(736\) 15.1784 0.559483
\(737\) 10.9212 0.402287
\(738\) 3.41666 0.125769
\(739\) −29.3210 −1.07859 −0.539296 0.842116i \(-0.681310\pi\)
−0.539296 + 0.842116i \(0.681310\pi\)
\(740\) 10.4965 0.385861
\(741\) −68.2727 −2.50806
\(742\) −10.2379 −0.375847
\(743\) −48.7566 −1.78871 −0.894353 0.447362i \(-0.852363\pi\)
−0.894353 + 0.447362i \(0.852363\pi\)
\(744\) 16.9775 0.622426
\(745\) 16.1204 0.590607
\(746\) 53.3855 1.95458
\(747\) 10.1250 0.370455
\(748\) 9.29871 0.339994
\(749\) 3.85087 0.140708
\(750\) 3.42417 0.125033
\(751\) −34.2348 −1.24925 −0.624623 0.780926i \(-0.714748\pi\)
−0.624623 + 0.780926i \(0.714748\pi\)
\(752\) −52.9860 −1.93220
\(753\) −9.13574 −0.332925
\(754\) 65.7835 2.39569
\(755\) 2.89920 0.105513
\(756\) −5.72264 −0.208130
\(757\) −26.8171 −0.974683 −0.487341 0.873212i \(-0.662033\pi\)
−0.487341 + 0.873212i \(0.662033\pi\)
\(758\) −7.84350 −0.284889
\(759\) −5.45794 −0.198111
\(760\) −11.1936 −0.406033
\(761\) −49.7758 −1.80437 −0.902186 0.431347i \(-0.858038\pi\)
−0.902186 + 0.431347i \(0.858038\pi\)
\(762\) 37.8717 1.37195
\(763\) 16.2827 0.589474
\(764\) 14.5436 0.526170
\(765\) 3.76614 0.136165
\(766\) −9.16760 −0.331239
\(767\) −32.6511 −1.17896
\(768\) −39.3657 −1.42049
\(769\) 11.6586 0.420419 0.210210 0.977656i \(-0.432585\pi\)
0.210210 + 0.977656i \(0.432585\pi\)
\(770\) −2.12787 −0.0766833
\(771\) 19.7534 0.711400
\(772\) 13.0885 0.471064
\(773\) −3.98512 −0.143335 −0.0716674 0.997429i \(-0.522832\pi\)
−0.0716674 + 0.997429i \(0.522832\pi\)
\(774\) −5.05695 −0.181768
\(775\) 6.67107 0.239632
\(776\) 9.41271 0.337897
\(777\) −15.8472 −0.568515
\(778\) −39.7626 −1.42556
\(779\) −26.3256 −0.943211
\(780\) −10.2814 −0.368132
\(781\) 4.74611 0.169829
\(782\) 27.6263 0.987913
\(783\) −38.4973 −1.37578
\(784\) −4.93407 −0.176217
\(785\) 17.8860 0.638377
\(786\) −14.9968 −0.534917
\(787\) 8.63861 0.307933 0.153967 0.988076i \(-0.450795\pi\)
0.153967 + 0.988076i \(0.450795\pi\)
\(788\) 5.56020 0.198074
\(789\) 38.2387 1.36133
\(790\) 27.2092 0.968059
\(791\) −3.99030 −0.141879
\(792\) 0.949186 0.0337279
\(793\) 29.6365 1.05242
\(794\) 4.37005 0.155087
\(795\) 10.7642 0.381767
\(796\) 18.4473 0.653848
\(797\) −26.4526 −0.937000 −0.468500 0.883463i \(-0.655205\pi\)
−0.468500 + 0.883463i \(0.655205\pi\)
\(798\) −28.5764 −1.01159
\(799\) −67.3860 −2.38395
\(800\) −6.22174 −0.219972
\(801\) −2.05823 −0.0727239
\(802\) 68.6951 2.42571
\(803\) 9.64029 0.340198
\(804\) 22.0869 0.778945
\(805\) −2.43958 −0.0859837
\(806\) −51.9066 −1.82833
\(807\) 29.8295 1.05005
\(808\) −13.0255 −0.458236
\(809\) 13.4552 0.473059 0.236530 0.971624i \(-0.423990\pi\)
0.236530 + 0.971624i \(0.423990\pi\)
\(810\) 18.8412 0.662011
\(811\) 13.0283 0.457485 0.228743 0.973487i \(-0.426539\pi\)
0.228743 + 0.973487i \(0.426539\pi\)
\(812\) 10.6254 0.372879
\(813\) −33.1386 −1.16222
\(814\) 17.7720 0.622909
\(815\) −19.0007 −0.665564
\(816\) −58.7464 −2.05654
\(817\) 38.9641 1.36318
\(818\) 6.34827 0.221962
\(819\) 2.58771 0.0904219
\(820\) −3.96444 −0.138444
\(821\) −12.1738 −0.424868 −0.212434 0.977175i \(-0.568139\pi\)
−0.212434 + 0.977175i \(0.568139\pi\)
\(822\) −70.4559 −2.45743
\(823\) −17.4314 −0.607622 −0.303811 0.952732i \(-0.598259\pi\)
−0.303811 + 0.952732i \(0.598259\pi\)
\(824\) −19.8093 −0.690091
\(825\) 2.23725 0.0778911
\(826\) −13.6665 −0.475519
\(827\) −9.93135 −0.345347 −0.172673 0.984979i \(-0.555241\pi\)
−0.172673 + 0.984979i \(0.555241\pi\)
\(828\) −1.84015 −0.0639495
\(829\) 22.5240 0.782289 0.391145 0.920329i \(-0.372079\pi\)
0.391145 + 0.920329i \(0.372079\pi\)
\(830\) −30.4444 −1.05674
\(831\) −36.0949 −1.25212
\(832\) 5.86342 0.203277
\(833\) −6.27501 −0.217416
\(834\) 67.2335 2.32811
\(835\) 23.3364 0.807589
\(836\) 12.3669 0.427717
\(837\) 30.3764 1.04996
\(838\) 6.16922 0.213112
\(839\) 16.4303 0.567238 0.283619 0.958937i \(-0.408465\pi\)
0.283619 + 0.958937i \(0.408465\pi\)
\(840\) 2.54495 0.0878090
\(841\) 42.4792 1.46480
\(842\) 16.4401 0.566563
\(843\) 4.68425 0.161334
\(844\) −1.23540 −0.0425243
\(845\) −5.58945 −0.192283
\(846\) 11.6314 0.399895
\(847\) 9.60971 0.330194
\(848\) −27.9914 −0.961228
\(849\) 40.9810 1.40647
\(850\) −11.3242 −0.388417
\(851\) 20.3753 0.698458
\(852\) 9.59850 0.328839
\(853\) 27.8299 0.952879 0.476439 0.879207i \(-0.341927\pi\)
0.476439 + 0.879207i \(0.341927\pi\)
\(854\) 12.4047 0.424482
\(855\) 5.00880 0.171297
\(856\) 5.16506 0.176538
\(857\) −53.5957 −1.83080 −0.915398 0.402551i \(-0.868124\pi\)
−0.915398 + 0.402551i \(0.868124\pi\)
\(858\) −17.4077 −0.594289
\(859\) −13.7286 −0.468413 −0.234206 0.972187i \(-0.575249\pi\)
−0.234206 + 0.972187i \(0.575249\pi\)
\(860\) 5.86771 0.200087
\(861\) 5.98533 0.203980
\(862\) −20.6401 −0.703005
\(863\) −45.6596 −1.55427 −0.777135 0.629334i \(-0.783328\pi\)
−0.777135 + 0.629334i \(0.783328\pi\)
\(864\) −28.3304 −0.963819
\(865\) 7.56837 0.257332
\(866\) 38.1996 1.29808
\(867\) −42.4560 −1.44188
\(868\) −8.38400 −0.284572
\(869\) 17.7776 0.603065
\(870\) −28.9498 −0.981490
\(871\) 39.9347 1.35314
\(872\) 21.8396 0.739581
\(873\) −4.21192 −0.142552
\(874\) 36.7417 1.24281
\(875\) 1.00000 0.0338062
\(876\) 19.4964 0.658724
\(877\) 21.1754 0.715043 0.357522 0.933905i \(-0.383622\pi\)
0.357522 + 0.933905i \(0.383622\pi\)
\(878\) 61.5849 2.07839
\(879\) −40.6920 −1.37251
\(880\) −5.81779 −0.196118
\(881\) 18.3941 0.619712 0.309856 0.950783i \(-0.399719\pi\)
0.309856 + 0.950783i \(0.399719\pi\)
\(882\) 1.08312 0.0364705
\(883\) −12.2328 −0.411666 −0.205833 0.978587i \(-0.565990\pi\)
−0.205833 + 0.978587i \(0.565990\pi\)
\(884\) 34.0019 1.14361
\(885\) 14.3690 0.483009
\(886\) −20.6987 −0.695388
\(887\) −12.4677 −0.418624 −0.209312 0.977849i \(-0.567122\pi\)
−0.209312 + 0.977849i \(0.567122\pi\)
\(888\) −21.2554 −0.713285
\(889\) 11.0601 0.370944
\(890\) 6.18877 0.207448
\(891\) 12.3102 0.412409
\(892\) −19.4684 −0.651852
\(893\) −89.6205 −2.99904
\(894\) 55.1991 1.84613
\(895\) 7.60210 0.254110
\(896\) −9.98927 −0.333718
\(897\) −19.9577 −0.666367
\(898\) −44.1225 −1.47239
\(899\) −56.4008 −1.88107
\(900\) 0.754289 0.0251430
\(901\) −35.5986 −1.18596
\(902\) −6.71231 −0.223496
\(903\) −8.85880 −0.294802
\(904\) −5.35207 −0.178007
\(905\) 10.1245 0.336551
\(906\) 9.92735 0.329814
\(907\) 23.1146 0.767508 0.383754 0.923435i \(-0.374631\pi\)
0.383754 + 0.923435i \(0.374631\pi\)
\(908\) −7.23395 −0.240067
\(909\) 5.82855 0.193321
\(910\) −7.78085 −0.257933
\(911\) −6.66096 −0.220687 −0.110344 0.993893i \(-0.535195\pi\)
−0.110344 + 0.993893i \(0.535195\pi\)
\(912\) −78.1302 −2.58715
\(913\) −19.8914 −0.658311
\(914\) 1.29918 0.0429730
\(915\) −13.0424 −0.431167
\(916\) 1.25677 0.0415249
\(917\) −4.37968 −0.144630
\(918\) −51.5642 −1.70187
\(919\) −5.43880 −0.179409 −0.0897047 0.995968i \(-0.528592\pi\)
−0.0897047 + 0.995968i \(0.528592\pi\)
\(920\) −3.27213 −0.107879
\(921\) −3.30456 −0.108889
\(922\) −40.0807 −1.31999
\(923\) 17.3548 0.571239
\(924\) −2.81171 −0.0924985
\(925\) −8.35200 −0.274612
\(926\) 61.5028 2.02111
\(927\) 8.86411 0.291136
\(928\) 52.6019 1.72674
\(929\) −35.6530 −1.16974 −0.584869 0.811128i \(-0.698854\pi\)
−0.584869 + 0.811128i \(0.698854\pi\)
\(930\) 22.8429 0.749048
\(931\) −8.34549 −0.273512
\(932\) 15.9010 0.520856
\(933\) 49.4735 1.61969
\(934\) 45.5146 1.48928
\(935\) −7.39889 −0.241970
\(936\) 3.47082 0.113447
\(937\) −17.8279 −0.582413 −0.291207 0.956660i \(-0.594057\pi\)
−0.291207 + 0.956660i \(0.594057\pi\)
\(938\) 16.7152 0.545769
\(939\) −35.7716 −1.16736
\(940\) −13.4962 −0.440198
\(941\) 22.7426 0.741387 0.370693 0.928755i \(-0.379120\pi\)
0.370693 + 0.928755i \(0.379120\pi\)
\(942\) 61.2446 1.99546
\(943\) −7.69556 −0.250602
\(944\) −37.3654 −1.21614
\(945\) 4.55345 0.148124
\(946\) 9.93479 0.323008
\(947\) −50.8578 −1.65266 −0.826328 0.563190i \(-0.809574\pi\)
−0.826328 + 0.563190i \(0.809574\pi\)
\(948\) 35.9534 1.16771
\(949\) 35.2509 1.14429
\(950\) −15.0607 −0.488634
\(951\) 8.14861 0.264237
\(952\) −8.41649 −0.272780
\(953\) 32.4333 1.05062 0.525309 0.850911i \(-0.323950\pi\)
0.525309 + 0.850911i \(0.323950\pi\)
\(954\) 6.14462 0.198939
\(955\) −11.5722 −0.374469
\(956\) −23.4642 −0.758885
\(957\) −18.9149 −0.611433
\(958\) −14.1242 −0.456331
\(959\) −20.5760 −0.664435
\(960\) −2.58036 −0.0832806
\(961\) 13.5032 0.435586
\(962\) 64.9856 2.09522
\(963\) −2.31122 −0.0744780
\(964\) 33.9892 1.09472
\(965\) −10.4144 −0.335250
\(966\) −8.35353 −0.268770
\(967\) −35.0683 −1.12772 −0.563860 0.825870i \(-0.690684\pi\)
−0.563860 + 0.825870i \(0.690684\pi\)
\(968\) 12.8892 0.414276
\(969\) −99.3637 −3.19202
\(970\) 12.6646 0.406636
\(971\) −38.9943 −1.25139 −0.625694 0.780069i \(-0.715184\pi\)
−0.625694 + 0.780069i \(0.715184\pi\)
\(972\) 7.72822 0.247883
\(973\) 19.6350 0.629468
\(974\) 36.1963 1.15980
\(975\) 8.18079 0.261995
\(976\) 33.9156 1.08561
\(977\) −16.5406 −0.529181 −0.264591 0.964361i \(-0.585237\pi\)
−0.264591 + 0.964361i \(0.585237\pi\)
\(978\) −65.0616 −2.08044
\(979\) 4.04356 0.129233
\(980\) −1.25677 −0.0401460
\(981\) −9.77258 −0.312015
\(982\) −32.9354 −1.05101
\(983\) −2.93120 −0.0934907 −0.0467453 0.998907i \(-0.514885\pi\)
−0.0467453 + 0.998907i \(0.514885\pi\)
\(984\) 8.02795 0.255922
\(985\) −4.42420 −0.140967
\(986\) 95.7409 3.04901
\(987\) 20.3760 0.648574
\(988\) 45.2211 1.43867
\(989\) 11.3901 0.362184
\(990\) 1.27711 0.0405892
\(991\) 14.2363 0.452233 0.226116 0.974100i \(-0.427397\pi\)
0.226116 + 0.974100i \(0.427397\pi\)
\(992\) −41.5056 −1.31781
\(993\) 62.9918 1.99898
\(994\) 7.26405 0.230402
\(995\) −14.6784 −0.465335
\(996\) −40.2283 −1.27468
\(997\) 27.4134 0.868190 0.434095 0.900867i \(-0.357068\pi\)
0.434095 + 0.900867i \(0.357068\pi\)
\(998\) −18.0244 −0.570553
\(999\) −38.0304 −1.20323
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 \(a_p\))