Properties

Label 8015.2.a.l.1.39
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 1.39
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.858241 q^{2} -3.15413 q^{3} -1.26342 q^{4} -1.00000 q^{5} -2.70700 q^{6} -1.00000 q^{7} -2.80080 q^{8} +6.94851 q^{9} +O(q^{10})\) \(q+0.858241 q^{2} -3.15413 q^{3} -1.26342 q^{4} -1.00000 q^{5} -2.70700 q^{6} -1.00000 q^{7} -2.80080 q^{8} +6.94851 q^{9} -0.858241 q^{10} -3.80724 q^{11} +3.98500 q^{12} +4.68905 q^{13} -0.858241 q^{14} +3.15413 q^{15} +0.123083 q^{16} -4.07383 q^{17} +5.96350 q^{18} +7.23547 q^{19} +1.26342 q^{20} +3.15413 q^{21} -3.26753 q^{22} -0.764001 q^{23} +8.83408 q^{24} +1.00000 q^{25} +4.02433 q^{26} -12.4541 q^{27} +1.26342 q^{28} -0.590526 q^{29} +2.70700 q^{30} -6.93316 q^{31} +5.70724 q^{32} +12.0085 q^{33} -3.49633 q^{34} +1.00000 q^{35} -8.77891 q^{36} -2.77423 q^{37} +6.20978 q^{38} -14.7898 q^{39} +2.80080 q^{40} -11.9508 q^{41} +2.70700 q^{42} +3.49226 q^{43} +4.81016 q^{44} -6.94851 q^{45} -0.655697 q^{46} +3.74422 q^{47} -0.388221 q^{48} +1.00000 q^{49} +0.858241 q^{50} +12.8494 q^{51} -5.92425 q^{52} +12.9071 q^{53} -10.6886 q^{54} +3.80724 q^{55} +2.80080 q^{56} -22.8216 q^{57} -0.506814 q^{58} -7.01171 q^{59} -3.98500 q^{60} +4.71799 q^{61} -5.95032 q^{62} -6.94851 q^{63} +4.65202 q^{64} -4.68905 q^{65} +10.3062 q^{66} -15.3211 q^{67} +5.14697 q^{68} +2.40976 q^{69} +0.858241 q^{70} -3.14562 q^{71} -19.4614 q^{72} -13.3099 q^{73} -2.38096 q^{74} -3.15413 q^{75} -9.14146 q^{76} +3.80724 q^{77} -12.6932 q^{78} -14.5011 q^{79} -0.123083 q^{80} +18.4363 q^{81} -10.2567 q^{82} -11.8838 q^{83} -3.98500 q^{84} +4.07383 q^{85} +2.99720 q^{86} +1.86259 q^{87} +10.6633 q^{88} +4.25748 q^{89} -5.96350 q^{90} -4.68905 q^{91} +0.965256 q^{92} +21.8681 q^{93} +3.21344 q^{94} -7.23547 q^{95} -18.0014 q^{96} +13.3856 q^{97} +0.858241 q^{98} -26.4547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.858241 0.606868 0.303434 0.952852i \(-0.401867\pi\)
0.303434 + 0.952852i \(0.401867\pi\)
\(3\) −3.15413 −1.82104 −0.910518 0.413470i \(-0.864317\pi\)
−0.910518 + 0.413470i \(0.864317\pi\)
\(4\) −1.26342 −0.631711
\(5\) −1.00000 −0.447214
\(6\) −2.70700 −1.10513
\(7\) −1.00000 −0.377964
\(8\) −2.80080 −0.990233
\(9\) 6.94851 2.31617
\(10\) −0.858241 −0.271400
\(11\) −3.80724 −1.14793 −0.573963 0.818881i \(-0.694595\pi\)
−0.573963 + 0.818881i \(0.694595\pi\)
\(12\) 3.98500 1.15037
\(13\) 4.68905 1.30051 0.650254 0.759717i \(-0.274663\pi\)
0.650254 + 0.759717i \(0.274663\pi\)
\(14\) −0.858241 −0.229374
\(15\) 3.15413 0.814392
\(16\) 0.123083 0.0307708
\(17\) −4.07383 −0.988049 −0.494025 0.869448i \(-0.664475\pi\)
−0.494025 + 0.869448i \(0.664475\pi\)
\(18\) 5.96350 1.40561
\(19\) 7.23547 1.65993 0.829966 0.557815i \(-0.188360\pi\)
0.829966 + 0.557815i \(0.188360\pi\)
\(20\) 1.26342 0.282510
\(21\) 3.15413 0.688287
\(22\) −3.26753 −0.696640
\(23\) −0.764001 −0.159305 −0.0796526 0.996823i \(-0.525381\pi\)
−0.0796526 + 0.996823i \(0.525381\pi\)
\(24\) 8.83408 1.80325
\(25\) 1.00000 0.200000
\(26\) 4.02433 0.789236
\(27\) −12.4541 −2.39679
\(28\) 1.26342 0.238764
\(29\) −0.590526 −0.109658 −0.0548290 0.998496i \(-0.517461\pi\)
−0.0548290 + 0.998496i \(0.517461\pi\)
\(30\) 2.70700 0.494228
\(31\) −6.93316 −1.24523 −0.622617 0.782527i \(-0.713930\pi\)
−0.622617 + 0.782527i \(0.713930\pi\)
\(32\) 5.70724 1.00891
\(33\) 12.0085 2.09042
\(34\) −3.49633 −0.599615
\(35\) 1.00000 0.169031
\(36\) −8.77891 −1.46315
\(37\) −2.77423 −0.456080 −0.228040 0.973652i \(-0.573232\pi\)
−0.228040 + 0.973652i \(0.573232\pi\)
\(38\) 6.20978 1.00736
\(39\) −14.7898 −2.36827
\(40\) 2.80080 0.442846
\(41\) −11.9508 −1.86640 −0.933202 0.359351i \(-0.882998\pi\)
−0.933202 + 0.359351i \(0.882998\pi\)
\(42\) 2.70700 0.417699
\(43\) 3.49226 0.532565 0.266283 0.963895i \(-0.414205\pi\)
0.266283 + 0.963895i \(0.414205\pi\)
\(44\) 4.81016 0.725159
\(45\) −6.94851 −1.03582
\(46\) −0.655697 −0.0966772
\(47\) 3.74422 0.546151 0.273076 0.961993i \(-0.411959\pi\)
0.273076 + 0.961993i \(0.411959\pi\)
\(48\) −0.388221 −0.0560348
\(49\) 1.00000 0.142857
\(50\) 0.858241 0.121374
\(51\) 12.8494 1.79927
\(52\) −5.92425 −0.821546
\(53\) 12.9071 1.77292 0.886462 0.462801i \(-0.153155\pi\)
0.886462 + 0.462801i \(0.153155\pi\)
\(54\) −10.6886 −1.45454
\(55\) 3.80724 0.513368
\(56\) 2.80080 0.374273
\(57\) −22.8216 −3.02279
\(58\) −0.506814 −0.0665479
\(59\) −7.01171 −0.912848 −0.456424 0.889763i \(-0.650870\pi\)
−0.456424 + 0.889763i \(0.650870\pi\)
\(60\) −3.98500 −0.514461
\(61\) 4.71799 0.604077 0.302039 0.953296i \(-0.402333\pi\)
0.302039 + 0.953296i \(0.402333\pi\)
\(62\) −5.95032 −0.755692
\(63\) −6.94851 −0.875430
\(64\) 4.65202 0.581502
\(65\) −4.68905 −0.581605
\(66\) 10.3062 1.26861
\(67\) −15.3211 −1.87177 −0.935887 0.352301i \(-0.885399\pi\)
−0.935887 + 0.352301i \(0.885399\pi\)
\(68\) 5.14697 0.624162
\(69\) 2.40976 0.290100
\(70\) 0.858241 0.102579
\(71\) −3.14562 −0.373316 −0.186658 0.982425i \(-0.559766\pi\)
−0.186658 + 0.982425i \(0.559766\pi\)
\(72\) −19.4614 −2.29355
\(73\) −13.3099 −1.55781 −0.778906 0.627141i \(-0.784225\pi\)
−0.778906 + 0.627141i \(0.784225\pi\)
\(74\) −2.38096 −0.276780
\(75\) −3.15413 −0.364207
\(76\) −9.14146 −1.04860
\(77\) 3.80724 0.433876
\(78\) −12.6932 −1.43723
\(79\) −14.5011 −1.63150 −0.815750 0.578404i \(-0.803676\pi\)
−0.815750 + 0.578404i \(0.803676\pi\)
\(80\) −0.123083 −0.0137611
\(81\) 18.4363 2.04848
\(82\) −10.2567 −1.13266
\(83\) −11.8838 −1.30442 −0.652210 0.758039i \(-0.726158\pi\)
−0.652210 + 0.758039i \(0.726158\pi\)
\(84\) −3.98500 −0.434799
\(85\) 4.07383 0.441869
\(86\) 2.99720 0.323197
\(87\) 1.86259 0.199691
\(88\) 10.6633 1.13672
\(89\) 4.25748 0.451292 0.225646 0.974209i \(-0.427551\pi\)
0.225646 + 0.974209i \(0.427551\pi\)
\(90\) −5.96350 −0.628608
\(91\) −4.68905 −0.491546
\(92\) 0.965256 0.100635
\(93\) 21.8681 2.26761
\(94\) 3.21344 0.331442
\(95\) −7.23547 −0.742344
\(96\) −18.0014 −1.83726
\(97\) 13.3856 1.35910 0.679551 0.733628i \(-0.262175\pi\)
0.679551 + 0.733628i \(0.262175\pi\)
\(98\) 0.858241 0.0866954
\(99\) −26.4547 −2.65879
\(100\) −1.26342 −0.126342
\(101\) 5.84607 0.581705 0.290853 0.956768i \(-0.406061\pi\)
0.290853 + 0.956768i \(0.406061\pi\)
\(102\) 11.0279 1.09192
\(103\) 3.79996 0.374421 0.187211 0.982320i \(-0.440055\pi\)
0.187211 + 0.982320i \(0.440055\pi\)
\(104\) −13.1331 −1.28781
\(105\) −3.15413 −0.307811
\(106\) 11.0774 1.07593
\(107\) −1.41474 −0.136768 −0.0683839 0.997659i \(-0.521784\pi\)
−0.0683839 + 0.997659i \(0.521784\pi\)
\(108\) 15.7348 1.51408
\(109\) −15.0737 −1.44380 −0.721898 0.691999i \(-0.756730\pi\)
−0.721898 + 0.691999i \(0.756730\pi\)
\(110\) 3.26753 0.311547
\(111\) 8.75027 0.830539
\(112\) −0.123083 −0.0116303
\(113\) −17.9528 −1.68886 −0.844428 0.535669i \(-0.820060\pi\)
−0.844428 + 0.535669i \(0.820060\pi\)
\(114\) −19.5864 −1.83444
\(115\) 0.764001 0.0712434
\(116\) 0.746085 0.0692722
\(117\) 32.5819 3.01220
\(118\) −6.01774 −0.553978
\(119\) 4.07383 0.373447
\(120\) −8.83408 −0.806438
\(121\) 3.49509 0.317736
\(122\) 4.04917 0.366595
\(123\) 37.6944 3.39879
\(124\) 8.75952 0.786628
\(125\) −1.00000 −0.0894427
\(126\) −5.96350 −0.531270
\(127\) −9.17177 −0.813863 −0.406932 0.913459i \(-0.633401\pi\)
−0.406932 + 0.913459i \(0.633401\pi\)
\(128\) −7.42193 −0.656012
\(129\) −11.0150 −0.969820
\(130\) −4.02433 −0.352957
\(131\) 0.0451058 0.00394091 0.00197045 0.999998i \(-0.499373\pi\)
0.00197045 + 0.999998i \(0.499373\pi\)
\(132\) −15.1718 −1.32054
\(133\) −7.23547 −0.627395
\(134\) −13.1492 −1.13592
\(135\) 12.4541 1.07188
\(136\) 11.4100 0.978399
\(137\) 21.8675 1.86827 0.934134 0.356924i \(-0.116174\pi\)
0.934134 + 0.356924i \(0.116174\pi\)
\(138\) 2.06815 0.176053
\(139\) 9.99513 0.847776 0.423888 0.905715i \(-0.360665\pi\)
0.423888 + 0.905715i \(0.360665\pi\)
\(140\) −1.26342 −0.106779
\(141\) −11.8098 −0.994561
\(142\) −2.69969 −0.226553
\(143\) −17.8523 −1.49289
\(144\) 0.855247 0.0712705
\(145\) 0.590526 0.0490405
\(146\) −11.4231 −0.945386
\(147\) −3.15413 −0.260148
\(148\) 3.50502 0.288111
\(149\) 2.71779 0.222650 0.111325 0.993784i \(-0.464491\pi\)
0.111325 + 0.993784i \(0.464491\pi\)
\(150\) −2.70700 −0.221026
\(151\) −16.8195 −1.36875 −0.684375 0.729130i \(-0.739925\pi\)
−0.684375 + 0.729130i \(0.739925\pi\)
\(152\) −20.2651 −1.64372
\(153\) −28.3071 −2.28849
\(154\) 3.26753 0.263305
\(155\) 6.93316 0.556885
\(156\) 18.6858 1.49606
\(157\) −10.7254 −0.855978 −0.427989 0.903784i \(-0.640778\pi\)
−0.427989 + 0.903784i \(0.640778\pi\)
\(158\) −12.4454 −0.990105
\(159\) −40.7106 −3.22856
\(160\) −5.70724 −0.451197
\(161\) 0.764001 0.0602117
\(162\) 15.8228 1.24315
\(163\) −4.04557 −0.316873 −0.158437 0.987369i \(-0.550645\pi\)
−0.158437 + 0.987369i \(0.550645\pi\)
\(164\) 15.0989 1.17903
\(165\) −12.0085 −0.934862
\(166\) −10.1992 −0.791610
\(167\) 18.8132 1.45581 0.727904 0.685680i \(-0.240495\pi\)
0.727904 + 0.685680i \(0.240495\pi\)
\(168\) −8.83408 −0.681564
\(169\) 8.98716 0.691320
\(170\) 3.49633 0.268156
\(171\) 50.2758 3.84468
\(172\) −4.41221 −0.336427
\(173\) −0.854004 −0.0649287 −0.0324643 0.999473i \(-0.510336\pi\)
−0.0324643 + 0.999473i \(0.510336\pi\)
\(174\) 1.59855 0.121186
\(175\) −1.00000 −0.0755929
\(176\) −0.468608 −0.0353227
\(177\) 22.1158 1.66233
\(178\) 3.65394 0.273874
\(179\) −16.9353 −1.26580 −0.632901 0.774232i \(-0.718136\pi\)
−0.632901 + 0.774232i \(0.718136\pi\)
\(180\) 8.77891 0.654341
\(181\) 11.4585 0.851703 0.425852 0.904793i \(-0.359975\pi\)
0.425852 + 0.904793i \(0.359975\pi\)
\(182\) −4.02433 −0.298303
\(183\) −14.8811 −1.10005
\(184\) 2.13982 0.157749
\(185\) 2.77423 0.203965
\(186\) 18.7681 1.37614
\(187\) 15.5101 1.13421
\(188\) −4.73054 −0.345010
\(189\) 12.4541 0.905903
\(190\) −6.20978 −0.450505
\(191\) −25.4170 −1.83911 −0.919553 0.392966i \(-0.871449\pi\)
−0.919553 + 0.392966i \(0.871449\pi\)
\(192\) −14.6731 −1.05894
\(193\) 23.0146 1.65663 0.828313 0.560266i \(-0.189301\pi\)
0.828313 + 0.560266i \(0.189301\pi\)
\(194\) 11.4881 0.824795
\(195\) 14.7898 1.05912
\(196\) −1.26342 −0.0902445
\(197\) −5.89035 −0.419670 −0.209835 0.977737i \(-0.567293\pi\)
−0.209835 + 0.977737i \(0.567293\pi\)
\(198\) −22.7045 −1.61354
\(199\) 6.85706 0.486084 0.243042 0.970016i \(-0.421855\pi\)
0.243042 + 0.970016i \(0.421855\pi\)
\(200\) −2.80080 −0.198047
\(201\) 48.3248 3.40857
\(202\) 5.01733 0.353018
\(203\) 0.590526 0.0414468
\(204\) −16.2342 −1.13662
\(205\) 11.9508 0.834682
\(206\) 3.26128 0.227224
\(207\) −5.30867 −0.368978
\(208\) 0.577144 0.0400177
\(209\) −27.5472 −1.90548
\(210\) −2.70700 −0.186801
\(211\) 19.6455 1.35245 0.676225 0.736695i \(-0.263615\pi\)
0.676225 + 0.736695i \(0.263615\pi\)
\(212\) −16.3071 −1.11998
\(213\) 9.92167 0.679821
\(214\) −1.21419 −0.0830000
\(215\) −3.49226 −0.238170
\(216\) 34.8815 2.37338
\(217\) 6.93316 0.470654
\(218\) −12.9368 −0.876194
\(219\) 41.9813 2.83683
\(220\) −4.81016 −0.324301
\(221\) −19.1024 −1.28497
\(222\) 7.50984 0.504027
\(223\) −10.0369 −0.672124 −0.336062 0.941840i \(-0.609095\pi\)
−0.336062 + 0.941840i \(0.609095\pi\)
\(224\) −5.70724 −0.381331
\(225\) 6.94851 0.463234
\(226\) −15.4078 −1.02491
\(227\) 28.7335 1.90711 0.953556 0.301216i \(-0.0973924\pi\)
0.953556 + 0.301216i \(0.0973924\pi\)
\(228\) 28.8333 1.90953
\(229\) 1.00000 0.0660819
\(230\) 0.655697 0.0432354
\(231\) −12.0085 −0.790103
\(232\) 1.65395 0.108587
\(233\) 10.2643 0.672436 0.336218 0.941784i \(-0.390852\pi\)
0.336218 + 0.941784i \(0.390852\pi\)
\(234\) 27.9631 1.82801
\(235\) −3.74422 −0.244246
\(236\) 8.85876 0.576656
\(237\) 45.7383 2.97102
\(238\) 3.49633 0.226633
\(239\) 12.1795 0.787826 0.393913 0.919148i \(-0.371121\pi\)
0.393913 + 0.919148i \(0.371121\pi\)
\(240\) 0.388221 0.0250595
\(241\) −21.3677 −1.37641 −0.688207 0.725514i \(-0.741602\pi\)
−0.688207 + 0.725514i \(0.741602\pi\)
\(242\) 2.99963 0.192824
\(243\) −20.7881 −1.33355
\(244\) −5.96082 −0.381602
\(245\) −1.00000 −0.0638877
\(246\) 32.3509 2.06262
\(247\) 33.9275 2.15875
\(248\) 19.4184 1.23307
\(249\) 37.4831 2.37539
\(250\) −0.858241 −0.0542799
\(251\) −6.07591 −0.383508 −0.191754 0.981443i \(-0.561418\pi\)
−0.191754 + 0.981443i \(0.561418\pi\)
\(252\) 8.77891 0.553019
\(253\) 2.90874 0.182871
\(254\) −7.87159 −0.493907
\(255\) −12.8494 −0.804659
\(256\) −15.6738 −0.979615
\(257\) −2.62208 −0.163561 −0.0817804 0.996650i \(-0.526061\pi\)
−0.0817804 + 0.996650i \(0.526061\pi\)
\(258\) −9.45355 −0.588553
\(259\) 2.77423 0.172382
\(260\) 5.92425 0.367406
\(261\) −4.10328 −0.253987
\(262\) 0.0387116 0.00239161
\(263\) 5.81447 0.358536 0.179268 0.983800i \(-0.442627\pi\)
0.179268 + 0.983800i \(0.442627\pi\)
\(264\) −33.6335 −2.07000
\(265\) −12.9071 −0.792876
\(266\) −6.20978 −0.380746
\(267\) −13.4286 −0.821818
\(268\) 19.3571 1.18242
\(269\) −20.6446 −1.25872 −0.629362 0.777112i \(-0.716684\pi\)
−0.629362 + 0.777112i \(0.716684\pi\)
\(270\) 10.6886 0.650489
\(271\) 26.0918 1.58497 0.792483 0.609894i \(-0.208788\pi\)
0.792483 + 0.609894i \(0.208788\pi\)
\(272\) −0.501421 −0.0304031
\(273\) 14.7898 0.895122
\(274\) 18.7676 1.13379
\(275\) −3.80724 −0.229585
\(276\) −3.04454 −0.183260
\(277\) −5.67594 −0.341034 −0.170517 0.985355i \(-0.554544\pi\)
−0.170517 + 0.985355i \(0.554544\pi\)
\(278\) 8.57823 0.514488
\(279\) −48.1752 −2.88417
\(280\) −2.80080 −0.167380
\(281\) 0.770969 0.0459922 0.0229961 0.999736i \(-0.492679\pi\)
0.0229961 + 0.999736i \(0.492679\pi\)
\(282\) −10.1356 −0.603567
\(283\) 9.63994 0.573035 0.286518 0.958075i \(-0.407502\pi\)
0.286518 + 0.958075i \(0.407502\pi\)
\(284\) 3.97424 0.235828
\(285\) 22.8216 1.35183
\(286\) −15.3216 −0.905985
\(287\) 11.9508 0.705435
\(288\) 39.6568 2.33680
\(289\) −0.403906 −0.0237592
\(290\) 0.506814 0.0297611
\(291\) −42.2199 −2.47497
\(292\) 16.8161 0.984087
\(293\) 16.2750 0.950797 0.475399 0.879771i \(-0.342304\pi\)
0.475399 + 0.879771i \(0.342304\pi\)
\(294\) −2.70700 −0.157875
\(295\) 7.01171 0.408238
\(296\) 7.77007 0.451626
\(297\) 47.4158 2.75134
\(298\) 2.33251 0.135119
\(299\) −3.58244 −0.207178
\(300\) 3.98500 0.230074
\(301\) −3.49226 −0.201291
\(302\) −14.4352 −0.830651
\(303\) −18.4392 −1.05931
\(304\) 0.890566 0.0510775
\(305\) −4.71799 −0.270152
\(306\) −24.2943 −1.38881
\(307\) −0.339195 −0.0193589 −0.00967944 0.999953i \(-0.503081\pi\)
−0.00967944 + 0.999953i \(0.503081\pi\)
\(308\) −4.81016 −0.274084
\(309\) −11.9855 −0.681834
\(310\) 5.95032 0.337956
\(311\) −9.36543 −0.531065 −0.265533 0.964102i \(-0.585548\pi\)
−0.265533 + 0.964102i \(0.585548\pi\)
\(312\) 41.4234 2.34514
\(313\) 11.5134 0.650775 0.325388 0.945581i \(-0.394505\pi\)
0.325388 + 0.945581i \(0.394505\pi\)
\(314\) −9.20496 −0.519466
\(315\) 6.94851 0.391504
\(316\) 18.3210 1.03064
\(317\) −4.38299 −0.246173 −0.123087 0.992396i \(-0.539279\pi\)
−0.123087 + 0.992396i \(0.539279\pi\)
\(318\) −34.9395 −1.95931
\(319\) 2.24828 0.125879
\(320\) −4.65202 −0.260056
\(321\) 4.46226 0.249059
\(322\) 0.655697 0.0365405
\(323\) −29.4761 −1.64009
\(324\) −23.2928 −1.29405
\(325\) 4.68905 0.260102
\(326\) −3.47207 −0.192300
\(327\) 47.5443 2.62920
\(328\) 33.4719 1.84818
\(329\) −3.74422 −0.206426
\(330\) −10.3062 −0.567338
\(331\) −13.3632 −0.734507 −0.367253 0.930121i \(-0.619702\pi\)
−0.367253 + 0.930121i \(0.619702\pi\)
\(332\) 15.0143 0.824017
\(333\) −19.2768 −1.05636
\(334\) 16.1462 0.883482
\(335\) 15.3211 0.837083
\(336\) 0.388221 0.0211792
\(337\) 32.6187 1.77685 0.888427 0.459017i \(-0.151798\pi\)
0.888427 + 0.459017i \(0.151798\pi\)
\(338\) 7.71314 0.419540
\(339\) 56.6254 3.07547
\(340\) −5.14697 −0.279134
\(341\) 26.3962 1.42944
\(342\) 43.1487 2.33321
\(343\) −1.00000 −0.0539949
\(344\) −9.78114 −0.527364
\(345\) −2.40976 −0.129737
\(346\) −0.732941 −0.0394031
\(347\) 6.22228 0.334030 0.167015 0.985954i \(-0.446587\pi\)
0.167015 + 0.985954i \(0.446587\pi\)
\(348\) −2.35324 −0.126147
\(349\) 0.696412 0.0372781 0.0186390 0.999826i \(-0.494067\pi\)
0.0186390 + 0.999826i \(0.494067\pi\)
\(350\) −0.858241 −0.0458749
\(351\) −58.3979 −3.11705
\(352\) −21.7288 −1.15815
\(353\) −30.8486 −1.64191 −0.820954 0.570995i \(-0.806558\pi\)
−0.820954 + 0.570995i \(0.806558\pi\)
\(354\) 18.9807 1.00881
\(355\) 3.14562 0.166952
\(356\) −5.37899 −0.285086
\(357\) −12.8494 −0.680061
\(358\) −14.5346 −0.768175
\(359\) −35.9257 −1.89609 −0.948043 0.318141i \(-0.896941\pi\)
−0.948043 + 0.318141i \(0.896941\pi\)
\(360\) 19.4614 1.02571
\(361\) 33.3521 1.75537
\(362\) 9.83415 0.516871
\(363\) −11.0240 −0.578608
\(364\) 5.92425 0.310515
\(365\) 13.3099 0.696675
\(366\) −12.7716 −0.667583
\(367\) 35.7607 1.86669 0.933347 0.358976i \(-0.116874\pi\)
0.933347 + 0.358976i \(0.116874\pi\)
\(368\) −0.0940358 −0.00490196
\(369\) −83.0404 −4.32291
\(370\) 2.38096 0.123780
\(371\) −12.9071 −0.670103
\(372\) −27.6286 −1.43248
\(373\) 12.8413 0.664900 0.332450 0.943121i \(-0.392125\pi\)
0.332450 + 0.943121i \(0.392125\pi\)
\(374\) 13.3114 0.688314
\(375\) 3.15413 0.162878
\(376\) −10.4868 −0.540817
\(377\) −2.76901 −0.142611
\(378\) 10.6886 0.549763
\(379\) 25.6885 1.31953 0.659764 0.751473i \(-0.270656\pi\)
0.659764 + 0.751473i \(0.270656\pi\)
\(380\) 9.14146 0.468947
\(381\) 28.9289 1.48207
\(382\) −21.8139 −1.11609
\(383\) 33.9607 1.73531 0.867655 0.497167i \(-0.165626\pi\)
0.867655 + 0.497167i \(0.165626\pi\)
\(384\) 23.4097 1.19462
\(385\) −3.80724 −0.194035
\(386\) 19.7521 1.00535
\(387\) 24.2660 1.23351
\(388\) −16.9117 −0.858560
\(389\) −17.0767 −0.865823 −0.432911 0.901436i \(-0.642514\pi\)
−0.432911 + 0.901436i \(0.642514\pi\)
\(390\) 12.6932 0.642748
\(391\) 3.11241 0.157401
\(392\) −2.80080 −0.141462
\(393\) −0.142269 −0.00717653
\(394\) −5.05533 −0.254684
\(395\) 14.5011 0.729629
\(396\) 33.4234 1.67959
\(397\) −32.3989 −1.62606 −0.813028 0.582225i \(-0.802182\pi\)
−0.813028 + 0.582225i \(0.802182\pi\)
\(398\) 5.88500 0.294989
\(399\) 22.8216 1.14251
\(400\) 0.123083 0.00615417
\(401\) −14.5152 −0.724853 −0.362427 0.932012i \(-0.618052\pi\)
−0.362427 + 0.932012i \(0.618052\pi\)
\(402\) 41.4743 2.06855
\(403\) −32.5099 −1.61943
\(404\) −7.38606 −0.367470
\(405\) −18.4363 −0.916106
\(406\) 0.506814 0.0251527
\(407\) 10.5622 0.523547
\(408\) −35.9886 −1.78170
\(409\) 0.122161 0.00604047 0.00302023 0.999995i \(-0.499039\pi\)
0.00302023 + 0.999995i \(0.499039\pi\)
\(410\) 10.2567 0.506541
\(411\) −68.9729 −3.40218
\(412\) −4.80096 −0.236526
\(413\) 7.01171 0.345024
\(414\) −4.55612 −0.223921
\(415\) 11.8838 0.583354
\(416\) 26.7615 1.31209
\(417\) −31.5259 −1.54383
\(418\) −23.6421 −1.15637
\(419\) −18.8288 −0.919849 −0.459925 0.887958i \(-0.652124\pi\)
−0.459925 + 0.887958i \(0.652124\pi\)
\(420\) 3.98500 0.194448
\(421\) 32.2030 1.56948 0.784739 0.619826i \(-0.212797\pi\)
0.784739 + 0.619826i \(0.212797\pi\)
\(422\) 16.8606 0.820759
\(423\) 26.0168 1.26498
\(424\) −36.1502 −1.75561
\(425\) −4.07383 −0.197610
\(426\) 8.51518 0.412562
\(427\) −4.71799 −0.228320
\(428\) 1.78741 0.0863978
\(429\) 56.3085 2.71860
\(430\) −2.99720 −0.144538
\(431\) −20.2546 −0.975629 −0.487815 0.872947i \(-0.662206\pi\)
−0.487815 + 0.872947i \(0.662206\pi\)
\(432\) −1.53289 −0.0737514
\(433\) 9.84939 0.473331 0.236666 0.971591i \(-0.423945\pi\)
0.236666 + 0.971591i \(0.423945\pi\)
\(434\) 5.95032 0.285625
\(435\) −1.86259 −0.0893046
\(436\) 19.0444 0.912063
\(437\) −5.52791 −0.264436
\(438\) 36.0300 1.72158
\(439\) 4.62921 0.220940 0.110470 0.993879i \(-0.464764\pi\)
0.110470 + 0.993879i \(0.464764\pi\)
\(440\) −10.6633 −0.508354
\(441\) 6.94851 0.330882
\(442\) −16.3944 −0.779804
\(443\) −25.3536 −1.20459 −0.602294 0.798275i \(-0.705746\pi\)
−0.602294 + 0.798275i \(0.705746\pi\)
\(444\) −11.0553 −0.524661
\(445\) −4.25748 −0.201824
\(446\) −8.61412 −0.407890
\(447\) −8.57224 −0.405453
\(448\) −4.65202 −0.219787
\(449\) −20.7081 −0.977277 −0.488638 0.872486i \(-0.662506\pi\)
−0.488638 + 0.872486i \(0.662506\pi\)
\(450\) 5.96350 0.281122
\(451\) 45.4997 2.14250
\(452\) 22.6820 1.06687
\(453\) 53.0508 2.49254
\(454\) 24.6603 1.15736
\(455\) 4.68905 0.219826
\(456\) 63.9188 2.99327
\(457\) 25.0559 1.17207 0.586034 0.810287i \(-0.300689\pi\)
0.586034 + 0.810287i \(0.300689\pi\)
\(458\) 0.858241 0.0401030
\(459\) 50.7359 2.36815
\(460\) −0.965256 −0.0450053
\(461\) 40.5976 1.89082 0.945410 0.325883i \(-0.105662\pi\)
0.945410 + 0.325883i \(0.105662\pi\)
\(462\) −10.3062 −0.479488
\(463\) −12.2642 −0.569966 −0.284983 0.958533i \(-0.591988\pi\)
−0.284983 + 0.958533i \(0.591988\pi\)
\(464\) −0.0726840 −0.00337427
\(465\) −21.8681 −1.01411
\(466\) 8.80924 0.408080
\(467\) −40.0594 −1.85373 −0.926863 0.375399i \(-0.877506\pi\)
−0.926863 + 0.375399i \(0.877506\pi\)
\(468\) −41.1647 −1.90284
\(469\) 15.3211 0.707464
\(470\) −3.21344 −0.148225
\(471\) 33.8292 1.55877
\(472\) 19.6384 0.903932
\(473\) −13.2959 −0.611346
\(474\) 39.2545 1.80302
\(475\) 7.23547 0.331986
\(476\) −5.14697 −0.235911
\(477\) 89.6851 4.10640
\(478\) 10.4529 0.478106
\(479\) 38.7728 1.77158 0.885788 0.464090i \(-0.153618\pi\)
0.885788 + 0.464090i \(0.153618\pi\)
\(480\) 18.0014 0.821646
\(481\) −13.0085 −0.593136
\(482\) −18.3386 −0.835302
\(483\) −2.40976 −0.109648
\(484\) −4.41578 −0.200717
\(485\) −13.3856 −0.607809
\(486\) −17.8412 −0.809291
\(487\) 8.02262 0.363540 0.181770 0.983341i \(-0.441817\pi\)
0.181770 + 0.983341i \(0.441817\pi\)
\(488\) −13.2142 −0.598177
\(489\) 12.7602 0.577038
\(490\) −0.858241 −0.0387714
\(491\) −19.9634 −0.900937 −0.450469 0.892792i \(-0.648743\pi\)
−0.450469 + 0.892792i \(0.648743\pi\)
\(492\) −47.6240 −2.14705
\(493\) 2.40570 0.108347
\(494\) 29.1179 1.31008
\(495\) 26.4547 1.18905
\(496\) −0.853357 −0.0383169
\(497\) 3.14562 0.141100
\(498\) 32.1695 1.44155
\(499\) 10.0366 0.449300 0.224650 0.974439i \(-0.427876\pi\)
0.224650 + 0.974439i \(0.427876\pi\)
\(500\) 1.26342 0.0565020
\(501\) −59.3391 −2.65108
\(502\) −5.21459 −0.232739
\(503\) −8.19455 −0.365377 −0.182688 0.983171i \(-0.558480\pi\)
−0.182688 + 0.983171i \(0.558480\pi\)
\(504\) 19.4614 0.866880
\(505\) −5.84607 −0.260147
\(506\) 2.49640 0.110978
\(507\) −28.3466 −1.25892
\(508\) 11.5878 0.514127
\(509\) 15.5259 0.688172 0.344086 0.938938i \(-0.388189\pi\)
0.344086 + 0.938938i \(0.388189\pi\)
\(510\) −11.0279 −0.488322
\(511\) 13.3099 0.588797
\(512\) 1.39193 0.0615152
\(513\) −90.1113 −3.97851
\(514\) −2.25038 −0.0992598
\(515\) −3.79996 −0.167446
\(516\) 13.9167 0.612646
\(517\) −14.2552 −0.626942
\(518\) 2.38096 0.104613
\(519\) 2.69364 0.118237
\(520\) 13.1331 0.575924
\(521\) 19.8743 0.870711 0.435355 0.900259i \(-0.356623\pi\)
0.435355 + 0.900259i \(0.356623\pi\)
\(522\) −3.52160 −0.154136
\(523\) −22.1053 −0.966598 −0.483299 0.875455i \(-0.660562\pi\)
−0.483299 + 0.875455i \(0.660562\pi\)
\(524\) −0.0569876 −0.00248952
\(525\) 3.15413 0.137657
\(526\) 4.99022 0.217584
\(527\) 28.2445 1.23035
\(528\) 1.47805 0.0643239
\(529\) −22.4163 −0.974622
\(530\) −11.0774 −0.481171
\(531\) −48.7210 −2.11431
\(532\) 9.14146 0.396333
\(533\) −56.0380 −2.42727
\(534\) −11.5250 −0.498735
\(535\) 1.41474 0.0611644
\(536\) 42.9115 1.85349
\(537\) 53.4160 2.30507
\(538\) −17.7180 −0.763879
\(539\) −3.80724 −0.163990
\(540\) −15.7348 −0.677118
\(541\) 16.5788 0.712779 0.356389 0.934337i \(-0.384008\pi\)
0.356389 + 0.934337i \(0.384008\pi\)
\(542\) 22.3931 0.961865
\(543\) −36.1415 −1.55098
\(544\) −23.2503 −0.996850
\(545\) 15.0737 0.645685
\(546\) 12.6932 0.543221
\(547\) −41.0499 −1.75517 −0.877583 0.479424i \(-0.840845\pi\)
−0.877583 + 0.479424i \(0.840845\pi\)
\(548\) −27.6279 −1.18021
\(549\) 32.7830 1.39915
\(550\) −3.26753 −0.139328
\(551\) −4.27274 −0.182025
\(552\) −6.74925 −0.287267
\(553\) 14.5011 0.616649
\(554\) −4.87132 −0.206963
\(555\) −8.75027 −0.371428
\(556\) −12.6281 −0.535550
\(557\) −14.8735 −0.630212 −0.315106 0.949056i \(-0.602040\pi\)
−0.315106 + 0.949056i \(0.602040\pi\)
\(558\) −41.3459 −1.75031
\(559\) 16.3754 0.692605
\(560\) 0.123083 0.00520122
\(561\) −48.9207 −2.06543
\(562\) 0.661677 0.0279112
\(563\) 25.9023 1.09165 0.545825 0.837899i \(-0.316216\pi\)
0.545825 + 0.837899i \(0.316216\pi\)
\(564\) 14.9207 0.628275
\(565\) 17.9528 0.755280
\(566\) 8.27339 0.347757
\(567\) −18.4363 −0.774251
\(568\) 8.81025 0.369670
\(569\) −23.9155 −1.00259 −0.501296 0.865276i \(-0.667143\pi\)
−0.501296 + 0.865276i \(0.667143\pi\)
\(570\) 19.5864 0.820385
\(571\) 14.5900 0.610572 0.305286 0.952261i \(-0.401248\pi\)
0.305286 + 0.952261i \(0.401248\pi\)
\(572\) 22.5551 0.943074
\(573\) 80.1683 3.34908
\(574\) 10.2567 0.428106
\(575\) −0.764001 −0.0318610
\(576\) 32.3246 1.34686
\(577\) 25.6298 1.06698 0.533491 0.845806i \(-0.320880\pi\)
0.533491 + 0.845806i \(0.320880\pi\)
\(578\) −0.346649 −0.0144187
\(579\) −72.5909 −3.01677
\(580\) −0.746085 −0.0309795
\(581\) 11.8838 0.493024
\(582\) −36.2348 −1.50198
\(583\) −49.1404 −2.03519
\(584\) 37.2785 1.54260
\(585\) −32.5819 −1.34710
\(586\) 13.9679 0.577008
\(587\) −40.9084 −1.68847 −0.844236 0.535972i \(-0.819945\pi\)
−0.844236 + 0.535972i \(0.819945\pi\)
\(588\) 3.98500 0.164338
\(589\) −50.1647 −2.06700
\(590\) 6.01774 0.247746
\(591\) 18.5789 0.764234
\(592\) −0.341461 −0.0140340
\(593\) −9.06565 −0.372282 −0.186141 0.982523i \(-0.559598\pi\)
−0.186141 + 0.982523i \(0.559598\pi\)
\(594\) 40.6942 1.66970
\(595\) −4.07383 −0.167011
\(596\) −3.43371 −0.140650
\(597\) −21.6280 −0.885176
\(598\) −3.07459 −0.125729
\(599\) 13.2235 0.540300 0.270150 0.962818i \(-0.412927\pi\)
0.270150 + 0.962818i \(0.412927\pi\)
\(600\) 8.83408 0.360650
\(601\) 38.3644 1.56492 0.782458 0.622704i \(-0.213966\pi\)
0.782458 + 0.622704i \(0.213966\pi\)
\(602\) −2.99720 −0.122157
\(603\) −106.459 −4.33535
\(604\) 21.2501 0.864656
\(605\) −3.49509 −0.142096
\(606\) −15.8253 −0.642859
\(607\) 15.1679 0.615646 0.307823 0.951444i \(-0.400400\pi\)
0.307823 + 0.951444i \(0.400400\pi\)
\(608\) 41.2946 1.67472
\(609\) −1.86259 −0.0754761
\(610\) −4.04917 −0.163946
\(611\) 17.5568 0.710274
\(612\) 35.7638 1.44567
\(613\) 20.8571 0.842412 0.421206 0.906965i \(-0.361607\pi\)
0.421206 + 0.906965i \(0.361607\pi\)
\(614\) −0.291111 −0.0117483
\(615\) −37.6944 −1.51998
\(616\) −10.6633 −0.429638
\(617\) −0.696274 −0.0280309 −0.0140155 0.999902i \(-0.504461\pi\)
−0.0140155 + 0.999902i \(0.504461\pi\)
\(618\) −10.2865 −0.413783
\(619\) −4.20837 −0.169149 −0.0845743 0.996417i \(-0.526953\pi\)
−0.0845743 + 0.996417i \(0.526953\pi\)
\(620\) −8.75952 −0.351791
\(621\) 9.51495 0.381822
\(622\) −8.03780 −0.322286
\(623\) −4.25748 −0.170572
\(624\) −1.82038 −0.0728737
\(625\) 1.00000 0.0400000
\(626\) 9.88126 0.394935
\(627\) 86.8873 3.46995
\(628\) 13.5507 0.540731
\(629\) 11.3017 0.450630
\(630\) 5.96350 0.237591
\(631\) −7.57622 −0.301605 −0.150802 0.988564i \(-0.548186\pi\)
−0.150802 + 0.988564i \(0.548186\pi\)
\(632\) 40.6147 1.61557
\(633\) −61.9643 −2.46286
\(634\) −3.76166 −0.149395
\(635\) 9.17177 0.363971
\(636\) 51.4347 2.03952
\(637\) 4.68905 0.185787
\(638\) 1.92956 0.0763921
\(639\) −21.8573 −0.864663
\(640\) 7.42193 0.293377
\(641\) −18.5034 −0.730842 −0.365421 0.930842i \(-0.619075\pi\)
−0.365421 + 0.930842i \(0.619075\pi\)
\(642\) 3.82969 0.151146
\(643\) −27.0357 −1.06619 −0.533093 0.846057i \(-0.678970\pi\)
−0.533093 + 0.846057i \(0.678970\pi\)
\(644\) −0.965256 −0.0380364
\(645\) 11.0150 0.433717
\(646\) −25.2976 −0.995320
\(647\) 34.7167 1.36485 0.682427 0.730954i \(-0.260925\pi\)
0.682427 + 0.730954i \(0.260925\pi\)
\(648\) −51.6364 −2.02847
\(649\) 26.6953 1.04788
\(650\) 4.02433 0.157847
\(651\) −21.8681 −0.857077
\(652\) 5.11126 0.200172
\(653\) 29.4351 1.15188 0.575941 0.817491i \(-0.304636\pi\)
0.575941 + 0.817491i \(0.304636\pi\)
\(654\) 40.8044 1.59558
\(655\) −0.0451058 −0.00176243
\(656\) −1.47095 −0.0574309
\(657\) −92.4843 −3.60816
\(658\) −3.21344 −0.125273
\(659\) −19.9080 −0.775506 −0.387753 0.921763i \(-0.626749\pi\)
−0.387753 + 0.921763i \(0.626749\pi\)
\(660\) 15.1718 0.590563
\(661\) 36.2107 1.40843 0.704217 0.709985i \(-0.251298\pi\)
0.704217 + 0.709985i \(0.251298\pi\)
\(662\) −11.4688 −0.445748
\(663\) 60.2513 2.33997
\(664\) 33.2842 1.29168
\(665\) 7.23547 0.280580
\(666\) −16.5441 −0.641071
\(667\) 0.451163 0.0174691
\(668\) −23.7690 −0.919650
\(669\) 31.6578 1.22396
\(670\) 13.1492 0.507999
\(671\) −17.9625 −0.693436
\(672\) 18.0014 0.694417
\(673\) 23.8379 0.918885 0.459443 0.888207i \(-0.348049\pi\)
0.459443 + 0.888207i \(0.348049\pi\)
\(674\) 27.9947 1.07832
\(675\) −12.4541 −0.479359
\(676\) −11.3546 −0.436715
\(677\) 28.3256 1.08864 0.544321 0.838877i \(-0.316787\pi\)
0.544321 + 0.838877i \(0.316787\pi\)
\(678\) 48.5982 1.86640
\(679\) −13.3856 −0.513692
\(680\) −11.4100 −0.437553
\(681\) −90.6292 −3.47292
\(682\) 22.6543 0.867479
\(683\) −51.5505 −1.97252 −0.986262 0.165189i \(-0.947176\pi\)
−0.986262 + 0.165189i \(0.947176\pi\)
\(684\) −63.5196 −2.42873
\(685\) −21.8675 −0.835514
\(686\) −0.858241 −0.0327678
\(687\) −3.15413 −0.120337
\(688\) 0.429840 0.0163875
\(689\) 60.5219 2.30570
\(690\) −2.06815 −0.0787331
\(691\) 39.8340 1.51536 0.757679 0.652628i \(-0.226334\pi\)
0.757679 + 0.652628i \(0.226334\pi\)
\(692\) 1.07897 0.0410162
\(693\) 26.4547 1.00493
\(694\) 5.34022 0.202712
\(695\) −9.99513 −0.379137
\(696\) −5.21676 −0.197741
\(697\) 48.6856 1.84410
\(698\) 0.597689 0.0226229
\(699\) −32.3749 −1.22453
\(700\) 1.26342 0.0477529
\(701\) 14.8070 0.559252 0.279626 0.960109i \(-0.409790\pi\)
0.279626 + 0.960109i \(0.409790\pi\)
\(702\) −50.1194 −1.89164
\(703\) −20.0729 −0.757062
\(704\) −17.7114 −0.667522
\(705\) 11.8098 0.444781
\(706\) −26.4756 −0.996421
\(707\) −5.84607 −0.219864
\(708\) −27.9417 −1.05011
\(709\) 38.6138 1.45017 0.725087 0.688658i \(-0.241800\pi\)
0.725087 + 0.688658i \(0.241800\pi\)
\(710\) 2.69969 0.101318
\(711\) −100.761 −3.77883
\(712\) −11.9243 −0.446884
\(713\) 5.29694 0.198372
\(714\) −11.0279 −0.412707
\(715\) 17.8523 0.667640
\(716\) 21.3964 0.799622
\(717\) −38.4157 −1.43466
\(718\) −30.8329 −1.15067
\(719\) −18.2248 −0.679672 −0.339836 0.940485i \(-0.610372\pi\)
−0.339836 + 0.940485i \(0.610372\pi\)
\(720\) −0.855247 −0.0318732
\(721\) −3.79996 −0.141518
\(722\) 28.6241 1.06528
\(723\) 67.3964 2.50650
\(724\) −14.4769 −0.538031
\(725\) −0.590526 −0.0219316
\(726\) −9.46122 −0.351139
\(727\) 14.7747 0.547965 0.273983 0.961735i \(-0.411659\pi\)
0.273983 + 0.961735i \(0.411659\pi\)
\(728\) 13.1331 0.486745
\(729\) 10.2593 0.379974
\(730\) 11.4231 0.422789
\(731\) −14.2269 −0.526200
\(732\) 18.8012 0.694912
\(733\) 12.2286 0.451673 0.225837 0.974165i \(-0.427488\pi\)
0.225837 + 0.974165i \(0.427488\pi\)
\(734\) 30.6913 1.13284
\(735\) 3.15413 0.116342
\(736\) −4.36034 −0.160724
\(737\) 58.3313 2.14866
\(738\) −71.2687 −2.62344
\(739\) −27.8081 −1.02294 −0.511469 0.859302i \(-0.670899\pi\)
−0.511469 + 0.859302i \(0.670899\pi\)
\(740\) −3.50502 −0.128847
\(741\) −107.012 −3.93117
\(742\) −11.0774 −0.406664
\(743\) −7.94065 −0.291314 −0.145657 0.989335i \(-0.546530\pi\)
−0.145657 + 0.989335i \(0.546530\pi\)
\(744\) −61.2482 −2.24547
\(745\) −2.71779 −0.0995719
\(746\) 11.0210 0.403506
\(747\) −82.5749 −3.02126
\(748\) −19.5958 −0.716492
\(749\) 1.41474 0.0516934
\(750\) 2.70700 0.0988456
\(751\) 8.25956 0.301396 0.150698 0.988580i \(-0.451848\pi\)
0.150698 + 0.988580i \(0.451848\pi\)
\(752\) 0.460852 0.0168055
\(753\) 19.1642 0.698382
\(754\) −2.37647 −0.0865461
\(755\) 16.8195 0.612124
\(756\) −15.7348 −0.572269
\(757\) 25.6148 0.930986 0.465493 0.885052i \(-0.345877\pi\)
0.465493 + 0.885052i \(0.345877\pi\)
\(758\) 22.0469 0.800779
\(759\) −9.17452 −0.333014
\(760\) 20.2651 0.735093
\(761\) 35.4025 1.28334 0.641669 0.766981i \(-0.278242\pi\)
0.641669 + 0.766981i \(0.278242\pi\)
\(762\) 24.8280 0.899423
\(763\) 15.0737 0.545704
\(764\) 32.1124 1.16178
\(765\) 28.3071 1.02344
\(766\) 29.1464 1.05310
\(767\) −32.8783 −1.18717
\(768\) 49.4373 1.78391
\(769\) 43.7943 1.57926 0.789631 0.613582i \(-0.210272\pi\)
0.789631 + 0.613582i \(0.210272\pi\)
\(770\) −3.26753 −0.117754
\(771\) 8.27037 0.297850
\(772\) −29.0772 −1.04651
\(773\) 15.4427 0.555437 0.277718 0.960663i \(-0.410422\pi\)
0.277718 + 0.960663i \(0.410422\pi\)
\(774\) 20.8261 0.748579
\(775\) −6.93316 −0.249047
\(776\) −37.4904 −1.34583
\(777\) −8.75027 −0.313914
\(778\) −14.6559 −0.525440
\(779\) −86.4698 −3.09810
\(780\) −18.6858 −0.669060
\(781\) 11.9761 0.428539
\(782\) 2.67120 0.0955218
\(783\) 7.35448 0.262828
\(784\) 0.123083 0.00439584
\(785\) 10.7254 0.382805
\(786\) −0.122101 −0.00435521
\(787\) 4.07908 0.145404 0.0727018 0.997354i \(-0.476838\pi\)
0.0727018 + 0.997354i \(0.476838\pi\)
\(788\) 7.44200 0.265110
\(789\) −18.3396 −0.652906
\(790\) 12.4454 0.442789
\(791\) 17.9528 0.638328
\(792\) 74.0943 2.63283
\(793\) 22.1229 0.785607
\(794\) −27.8061 −0.986801
\(795\) 40.7106 1.44386
\(796\) −8.66336 −0.307065
\(797\) −14.6474 −0.518838 −0.259419 0.965765i \(-0.583531\pi\)
−0.259419 + 0.965765i \(0.583531\pi\)
\(798\) 19.5864 0.693352
\(799\) −15.2533 −0.539624
\(800\) 5.70724 0.201781
\(801\) 29.5831 1.04527
\(802\) −12.4575 −0.439890
\(803\) 50.6742 1.78825
\(804\) −61.0546 −2.15323
\(805\) −0.764001 −0.0269275
\(806\) −27.9013 −0.982783
\(807\) 65.1157 2.29218
\(808\) −16.3737 −0.576024
\(809\) 23.1089 0.812466 0.406233 0.913769i \(-0.366842\pi\)
0.406233 + 0.913769i \(0.366842\pi\)
\(810\) −15.8228 −0.555956
\(811\) −10.7872 −0.378791 −0.189395 0.981901i \(-0.560653\pi\)
−0.189395 + 0.981901i \(0.560653\pi\)
\(812\) −0.746085 −0.0261824
\(813\) −82.2969 −2.88628
\(814\) 9.06488 0.317724
\(815\) 4.04557 0.141710
\(816\) 1.58154 0.0553651
\(817\) 25.2682 0.884021
\(818\) 0.104843 0.00366577
\(819\) −32.5819 −1.13850
\(820\) −15.0989 −0.527278
\(821\) −40.2600 −1.40508 −0.702541 0.711643i \(-0.747951\pi\)
−0.702541 + 0.711643i \(0.747951\pi\)
\(822\) −59.1953 −2.06467
\(823\) 14.3262 0.499381 0.249690 0.968326i \(-0.419671\pi\)
0.249690 + 0.968326i \(0.419671\pi\)
\(824\) −10.6429 −0.370764
\(825\) 12.0085 0.418083
\(826\) 6.01774 0.209384
\(827\) −24.6400 −0.856818 −0.428409 0.903585i \(-0.640926\pi\)
−0.428409 + 0.903585i \(0.640926\pi\)
\(828\) 6.70709 0.233088
\(829\) −38.6902 −1.34376 −0.671882 0.740658i \(-0.734514\pi\)
−0.671882 + 0.740658i \(0.734514\pi\)
\(830\) 10.1992 0.354019
\(831\) 17.9026 0.621035
\(832\) 21.8135 0.756248
\(833\) −4.07383 −0.141150
\(834\) −27.0568 −0.936901
\(835\) −18.8132 −0.651057
\(836\) 34.8038 1.20371
\(837\) 86.3464 2.98457
\(838\) −16.1597 −0.558227
\(839\) −7.89509 −0.272569 −0.136284 0.990670i \(-0.543516\pi\)
−0.136284 + 0.990670i \(0.543516\pi\)
\(840\) 8.83408 0.304805
\(841\) −28.6513 −0.987975
\(842\) 27.6379 0.952466
\(843\) −2.43173 −0.0837534
\(844\) −24.8206 −0.854359
\(845\) −8.98716 −0.309168
\(846\) 22.3287 0.767675
\(847\) −3.49509 −0.120093
\(848\) 1.58865 0.0545544
\(849\) −30.4056 −1.04352
\(850\) −3.49633 −0.119923
\(851\) 2.11951 0.0726560
\(852\) −12.5353 −0.429451
\(853\) −20.8660 −0.714439 −0.357219 0.934021i \(-0.616275\pi\)
−0.357219 + 0.934021i \(0.616275\pi\)
\(854\) −4.04917 −0.138560
\(855\) −50.2758 −1.71939
\(856\) 3.96240 0.135432
\(857\) −5.77917 −0.197413 −0.0987064 0.995117i \(-0.531470\pi\)
−0.0987064 + 0.995117i \(0.531470\pi\)
\(858\) 48.3263 1.64983
\(859\) −27.0660 −0.923479 −0.461740 0.887015i \(-0.652775\pi\)
−0.461740 + 0.887015i \(0.652775\pi\)
\(860\) 4.41221 0.150455
\(861\) −37.6944 −1.28462
\(862\) −17.3833 −0.592078
\(863\) 32.7795 1.11583 0.557913 0.829899i \(-0.311602\pi\)
0.557913 + 0.829899i \(0.311602\pi\)
\(864\) −71.0786 −2.41814
\(865\) 0.854004 0.0290370
\(866\) 8.45314 0.287250
\(867\) 1.27397 0.0432663
\(868\) −8.75952 −0.297317
\(869\) 55.2092 1.87284
\(870\) −1.59855 −0.0541961
\(871\) −71.8415 −2.43426
\(872\) 42.2184 1.42970
\(873\) 93.0100 3.14791
\(874\) −4.74427 −0.160477
\(875\) 1.00000 0.0338062
\(876\) −53.0401 −1.79206
\(877\) −31.8055 −1.07400 −0.536998 0.843583i \(-0.680442\pi\)
−0.536998 + 0.843583i \(0.680442\pi\)
\(878\) 3.97298 0.134081
\(879\) −51.3335 −1.73144
\(880\) 0.468608 0.0157968
\(881\) 21.4210 0.721692 0.360846 0.932625i \(-0.382488\pi\)
0.360846 + 0.932625i \(0.382488\pi\)
\(882\) 5.96350 0.200801
\(883\) 12.1792 0.409862 0.204931 0.978776i \(-0.434303\pi\)
0.204931 + 0.978776i \(0.434303\pi\)
\(884\) 24.1344 0.811727
\(885\) −22.1158 −0.743416
\(886\) −21.7595 −0.731025
\(887\) 41.1229 1.38077 0.690386 0.723441i \(-0.257441\pi\)
0.690386 + 0.723441i \(0.257441\pi\)
\(888\) −24.5078 −0.822427
\(889\) 9.17177 0.307611
\(890\) −3.65394 −0.122480
\(891\) −70.1914 −2.35150
\(892\) 12.6809 0.424588
\(893\) 27.0912 0.906573
\(894\) −7.35704 −0.246056
\(895\) 16.9353 0.566084
\(896\) 7.42193 0.247949
\(897\) 11.2995 0.377278
\(898\) −17.7726 −0.593078
\(899\) 4.09422 0.136550
\(900\) −8.77891 −0.292630
\(901\) −52.5813 −1.75174
\(902\) 39.0497 1.30021
\(903\) 11.0150 0.366558
\(904\) 50.2822 1.67236
\(905\) −11.4585 −0.380893
\(906\) 45.5304 1.51264
\(907\) 17.3948 0.577586 0.288793 0.957391i \(-0.406746\pi\)
0.288793 + 0.957391i \(0.406746\pi\)
\(908\) −36.3026 −1.20474
\(909\) 40.6215 1.34733
\(910\) 4.02433 0.133405
\(911\) −18.4553 −0.611451 −0.305726 0.952120i \(-0.598899\pi\)
−0.305726 + 0.952120i \(0.598899\pi\)
\(912\) −2.80896 −0.0930139
\(913\) 45.2446 1.49738
\(914\) 21.5040 0.711290
\(915\) 14.8811 0.491956
\(916\) −1.26342 −0.0417447
\(917\) −0.0451058 −0.00148952
\(918\) 43.5436 1.43715
\(919\) −23.1891 −0.764938 −0.382469 0.923968i \(-0.624926\pi\)
−0.382469 + 0.923968i \(0.624926\pi\)
\(920\) −2.13982 −0.0705476
\(921\) 1.06986 0.0352532
\(922\) 34.8425 1.14748
\(923\) −14.7499 −0.485500
\(924\) 15.1718 0.499117
\(925\) −2.77423 −0.0912161
\(926\) −10.5256 −0.345894
\(927\) 26.4041 0.867223
\(928\) −3.37028 −0.110635
\(929\) −22.6059 −0.741674 −0.370837 0.928698i \(-0.620929\pi\)
−0.370837 + 0.928698i \(0.620929\pi\)
\(930\) −18.7681 −0.615429
\(931\) 7.23547 0.237133
\(932\) −12.9681 −0.424786
\(933\) 29.5398 0.967088
\(934\) −34.3806 −1.12497
\(935\) −15.5101 −0.507233
\(936\) −91.2555 −2.98278
\(937\) −8.49316 −0.277459 −0.138730 0.990330i \(-0.544302\pi\)
−0.138730 + 0.990330i \(0.544302\pi\)
\(938\) 13.1492 0.429337
\(939\) −36.3147 −1.18509
\(940\) 4.73054 0.154293
\(941\) −37.0113 −1.20653 −0.603267 0.797539i \(-0.706135\pi\)
−0.603267 + 0.797539i \(0.706135\pi\)
\(942\) 29.0336 0.945966
\(943\) 9.13044 0.297328
\(944\) −0.863026 −0.0280891
\(945\) −12.4541 −0.405132
\(946\) −11.4111 −0.371006
\(947\) 16.5147 0.536655 0.268327 0.963328i \(-0.413529\pi\)
0.268327 + 0.963328i \(0.413529\pi\)
\(948\) −57.7868 −1.87683
\(949\) −62.4110 −2.02595
\(950\) 6.20978 0.201472
\(951\) 13.8245 0.448290
\(952\) −11.4100 −0.369800
\(953\) 19.4260 0.629271 0.314635 0.949213i \(-0.398118\pi\)
0.314635 + 0.949213i \(0.398118\pi\)
\(954\) 76.9714 2.49204
\(955\) 25.4170 0.822473
\(956\) −15.3879 −0.497679
\(957\) −7.09135 −0.229231
\(958\) 33.2764 1.07511
\(959\) −21.8675 −0.706139
\(960\) 14.6731 0.473571
\(961\) 17.0688 0.550605
\(962\) −11.1644 −0.359955
\(963\) −9.83032 −0.316778
\(964\) 26.9964 0.869497
\(965\) −23.0146 −0.740866
\(966\) −2.06815 −0.0665416
\(967\) 9.05670 0.291244 0.145622 0.989340i \(-0.453482\pi\)
0.145622 + 0.989340i \(0.453482\pi\)
\(968\) −9.78907 −0.314633
\(969\) 92.9713 2.98667
\(970\) −11.4881 −0.368860
\(971\) 15.1364 0.485751 0.242876 0.970057i \(-0.421909\pi\)
0.242876 + 0.970057i \(0.421909\pi\)
\(972\) 26.2641 0.842422
\(973\) −9.99513 −0.320429
\(974\) 6.88534 0.220620
\(975\) −14.7898 −0.473654
\(976\) 0.580707 0.0185880
\(977\) −24.0438 −0.769231 −0.384615 0.923077i \(-0.625666\pi\)
−0.384615 + 0.923077i \(0.625666\pi\)
\(978\) 10.9513 0.350186
\(979\) −16.2092 −0.518050
\(980\) 1.26342 0.0403586
\(981\) −104.740 −3.34408
\(982\) −17.1334 −0.546750
\(983\) −46.6467 −1.48780 −0.743900 0.668291i \(-0.767026\pi\)
−0.743900 + 0.668291i \(0.767026\pi\)
\(984\) −105.575 −3.36559
\(985\) 5.89035 0.187682
\(986\) 2.06467 0.0657526
\(987\) 11.8098 0.375909
\(988\) −42.8647 −1.36371
\(989\) −2.66809 −0.0848404
\(990\) 22.7045 0.721596
\(991\) −21.9043 −0.695814 −0.347907 0.937529i \(-0.613108\pi\)
−0.347907 + 0.937529i \(0.613108\pi\)
\(992\) −39.5692 −1.25632
\(993\) 42.1491 1.33756
\(994\) 2.69969 0.0856291
\(995\) −6.85706 −0.217383
\(996\) −47.3570 −1.50056
\(997\) 24.7170 0.782794 0.391397 0.920222i \(-0.371992\pi\)
0.391397 + 0.920222i \(0.371992\pi\)
\(998\) 8.61383 0.272666
\(999\) 34.5505 1.09313
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 \(a_p\))