Properties

Label 619.2.a.b.1.10
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.938541 q^{2} +2.04590 q^{3} -1.11914 q^{4} +3.68832 q^{5} -1.92016 q^{6} -2.71706 q^{7} +2.92744 q^{8} +1.18571 q^{9} +O(q^{10})\) \(q-0.938541 q^{2} +2.04590 q^{3} -1.11914 q^{4} +3.68832 q^{5} -1.92016 q^{6} -2.71706 q^{7} +2.92744 q^{8} +1.18571 q^{9} -3.46164 q^{10} -2.41470 q^{11} -2.28965 q^{12} +5.06418 q^{13} +2.55007 q^{14} +7.54594 q^{15} -0.509241 q^{16} +2.79712 q^{17} -1.11283 q^{18} +4.67066 q^{19} -4.12775 q^{20} -5.55882 q^{21} +2.26630 q^{22} +2.15658 q^{23} +5.98925 q^{24} +8.60372 q^{25} -4.75294 q^{26} -3.71186 q^{27} +3.04077 q^{28} +0.405665 q^{29} -7.08217 q^{30} -2.87253 q^{31} -5.37694 q^{32} -4.94024 q^{33} -2.62521 q^{34} -10.0214 q^{35} -1.32697 q^{36} +4.37362 q^{37} -4.38361 q^{38} +10.3608 q^{39} +10.7973 q^{40} -2.91057 q^{41} +5.21718 q^{42} +4.39958 q^{43} +2.70239 q^{44} +4.37326 q^{45} -2.02404 q^{46} -4.68612 q^{47} -1.04186 q^{48} +0.382395 q^{49} -8.07494 q^{50} +5.72263 q^{51} -5.66753 q^{52} +5.90078 q^{53} +3.48374 q^{54} -8.90619 q^{55} -7.95402 q^{56} +9.55571 q^{57} -0.380734 q^{58} +2.92099 q^{59} -8.44497 q^{60} -8.81228 q^{61} +2.69599 q^{62} -3.22163 q^{63} +6.06496 q^{64} +18.6783 q^{65} +4.63661 q^{66} +6.63389 q^{67} -3.13037 q^{68} +4.41214 q^{69} +9.40547 q^{70} +1.75461 q^{71} +3.47108 q^{72} +11.6980 q^{73} -4.10482 q^{74} +17.6023 q^{75} -5.22713 q^{76} +6.56088 q^{77} -9.72404 q^{78} -17.0954 q^{79} -1.87824 q^{80} -11.1512 q^{81} +2.73169 q^{82} -9.17823 q^{83} +6.22111 q^{84} +10.3167 q^{85} -4.12919 q^{86} +0.829951 q^{87} -7.06889 q^{88} -10.6864 q^{89} -4.10449 q^{90} -13.7597 q^{91} -2.41352 q^{92} -5.87692 q^{93} +4.39811 q^{94} +17.2269 q^{95} -11.0007 q^{96} -6.48573 q^{97} -0.358893 q^{98} -2.86312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.938541 −0.663649 −0.331824 0.943341i \(-0.607664\pi\)
−0.331824 + 0.943341i \(0.607664\pi\)
\(3\) 2.04590 1.18120 0.590600 0.806964i \(-0.298891\pi\)
0.590600 + 0.806964i \(0.298891\pi\)
\(4\) −1.11914 −0.559571
\(5\) 3.68832 1.64947 0.824734 0.565521i \(-0.191325\pi\)
0.824734 + 0.565521i \(0.191325\pi\)
\(6\) −1.92016 −0.783902
\(7\) −2.71706 −1.02695 −0.513475 0.858104i \(-0.671642\pi\)
−0.513475 + 0.858104i \(0.671642\pi\)
\(8\) 2.92744 1.03501
\(9\) 1.18571 0.395235
\(10\) −3.46164 −1.09467
\(11\) −2.41470 −0.728060 −0.364030 0.931387i \(-0.618599\pi\)
−0.364030 + 0.931387i \(0.618599\pi\)
\(12\) −2.28965 −0.660965
\(13\) 5.06418 1.40455 0.702275 0.711905i \(-0.252168\pi\)
0.702275 + 0.711905i \(0.252168\pi\)
\(14\) 2.55007 0.681534
\(15\) 7.54594 1.94835
\(16\) −0.509241 −0.127310
\(17\) 2.79712 0.678401 0.339201 0.940714i \(-0.389843\pi\)
0.339201 + 0.940714i \(0.389843\pi\)
\(18\) −1.11283 −0.262297
\(19\) 4.67066 1.07152 0.535762 0.844369i \(-0.320024\pi\)
0.535762 + 0.844369i \(0.320024\pi\)
\(20\) −4.12775 −0.922994
\(21\) −5.55882 −1.21303
\(22\) 2.26630 0.483176
\(23\) 2.15658 0.449678 0.224839 0.974396i \(-0.427814\pi\)
0.224839 + 0.974396i \(0.427814\pi\)
\(24\) 5.98925 1.22255
\(25\) 8.60372 1.72074
\(26\) −4.75294 −0.932128
\(27\) −3.71186 −0.714349
\(28\) 3.04077 0.574651
\(29\) 0.405665 0.0753302 0.0376651 0.999290i \(-0.488008\pi\)
0.0376651 + 0.999290i \(0.488008\pi\)
\(30\) −7.08217 −1.29302
\(31\) −2.87253 −0.515922 −0.257961 0.966155i \(-0.583051\pi\)
−0.257961 + 0.966155i \(0.583051\pi\)
\(32\) −5.37694 −0.950518
\(33\) −4.94024 −0.859985
\(34\) −2.62521 −0.450220
\(35\) −10.0214 −1.69392
\(36\) −1.32697 −0.221162
\(37\) 4.37362 0.719019 0.359509 0.933141i \(-0.382944\pi\)
0.359509 + 0.933141i \(0.382944\pi\)
\(38\) −4.38361 −0.711115
\(39\) 10.3608 1.65906
\(40\) 10.7973 1.70721
\(41\) −2.91057 −0.454555 −0.227278 0.973830i \(-0.572982\pi\)
−0.227278 + 0.973830i \(0.572982\pi\)
\(42\) 5.21718 0.805029
\(43\) 4.39958 0.670930 0.335465 0.942053i \(-0.391107\pi\)
0.335465 + 0.942053i \(0.391107\pi\)
\(44\) 2.70239 0.407401
\(45\) 4.37326 0.651928
\(46\) −2.02404 −0.298428
\(47\) −4.68612 −0.683540 −0.341770 0.939784i \(-0.611026\pi\)
−0.341770 + 0.939784i \(0.611026\pi\)
\(48\) −1.04186 −0.150379
\(49\) 0.382395 0.0546278
\(50\) −8.07494 −1.14197
\(51\) 5.72263 0.801328
\(52\) −5.66753 −0.785945
\(53\) 5.90078 0.810534 0.405267 0.914198i \(-0.367178\pi\)
0.405267 + 0.914198i \(0.367178\pi\)
\(54\) 3.48374 0.474076
\(55\) −8.90619 −1.20091
\(56\) −7.95402 −1.06290
\(57\) 9.55571 1.26568
\(58\) −0.380734 −0.0499928
\(59\) 2.92099 0.380280 0.190140 0.981757i \(-0.439106\pi\)
0.190140 + 0.981757i \(0.439106\pi\)
\(60\) −8.44497 −1.09024
\(61\) −8.81228 −1.12830 −0.564148 0.825673i \(-0.690795\pi\)
−0.564148 + 0.825673i \(0.690795\pi\)
\(62\) 2.69599 0.342391
\(63\) −3.22163 −0.405887
\(64\) 6.06496 0.758120
\(65\) 18.6783 2.31676
\(66\) 4.63661 0.570728
\(67\) 6.63389 0.810459 0.405230 0.914215i \(-0.367192\pi\)
0.405230 + 0.914215i \(0.367192\pi\)
\(68\) −3.13037 −0.379613
\(69\) 4.41214 0.531160
\(70\) 9.40547 1.12417
\(71\) 1.75461 0.208234 0.104117 0.994565i \(-0.466798\pi\)
0.104117 + 0.994565i \(0.466798\pi\)
\(72\) 3.47108 0.409071
\(73\) 11.6980 1.36914 0.684571 0.728946i \(-0.259990\pi\)
0.684571 + 0.728946i \(0.259990\pi\)
\(74\) −4.10482 −0.477176
\(75\) 17.6023 2.03254
\(76\) −5.22713 −0.599593
\(77\) 6.56088 0.747681
\(78\) −9.72404 −1.10103
\(79\) −17.0954 −1.92338 −0.961690 0.274141i \(-0.911607\pi\)
−0.961690 + 0.274141i \(0.911607\pi\)
\(80\) −1.87824 −0.209994
\(81\) −11.1512 −1.23902
\(82\) 2.73169 0.301665
\(83\) −9.17823 −1.00744 −0.503721 0.863867i \(-0.668036\pi\)
−0.503721 + 0.863867i \(0.668036\pi\)
\(84\) 6.22111 0.678779
\(85\) 10.3167 1.11900
\(86\) −4.12919 −0.445262
\(87\) 0.829951 0.0889801
\(88\) −7.06889 −0.753547
\(89\) −10.6864 −1.13276 −0.566378 0.824146i \(-0.691656\pi\)
−0.566378 + 0.824146i \(0.691656\pi\)
\(90\) −4.10449 −0.432651
\(91\) −13.7597 −1.44240
\(92\) −2.41352 −0.251627
\(93\) −5.87692 −0.609408
\(94\) 4.39811 0.453630
\(95\) 17.2269 1.76744
\(96\) −11.0007 −1.12275
\(97\) −6.48573 −0.658526 −0.329263 0.944238i \(-0.606800\pi\)
−0.329263 + 0.944238i \(0.606800\pi\)
\(98\) −0.358893 −0.0362537
\(99\) −2.86312 −0.287755
\(100\) −9.62877 −0.962877
\(101\) 13.6998 1.36318 0.681590 0.731734i \(-0.261289\pi\)
0.681590 + 0.731734i \(0.261289\pi\)
\(102\) −5.37092 −0.531800
\(103\) −19.4892 −1.92032 −0.960162 0.279444i \(-0.909850\pi\)
−0.960162 + 0.279444i \(0.909850\pi\)
\(104\) 14.8251 1.45372
\(105\) −20.5027 −2.00086
\(106\) −5.53812 −0.537910
\(107\) 4.56732 0.441540 0.220770 0.975326i \(-0.429143\pi\)
0.220770 + 0.975326i \(0.429143\pi\)
\(108\) 4.15410 0.399729
\(109\) 7.39066 0.707897 0.353949 0.935265i \(-0.384839\pi\)
0.353949 + 0.935265i \(0.384839\pi\)
\(110\) 8.35883 0.796983
\(111\) 8.94799 0.849305
\(112\) 1.38364 0.130741
\(113\) 18.9441 1.78211 0.891056 0.453894i \(-0.149965\pi\)
0.891056 + 0.453894i \(0.149965\pi\)
\(114\) −8.96842 −0.839970
\(115\) 7.95416 0.741729
\(116\) −0.453997 −0.0421526
\(117\) 6.00463 0.555128
\(118\) −2.74147 −0.252373
\(119\) −7.59993 −0.696685
\(120\) 22.0903 2.01656
\(121\) −5.16922 −0.469929
\(122\) 8.27068 0.748793
\(123\) −5.95474 −0.536921
\(124\) 3.21477 0.288695
\(125\) 13.2917 1.18884
\(126\) 3.02363 0.269366
\(127\) 3.05033 0.270673 0.135337 0.990800i \(-0.456788\pi\)
0.135337 + 0.990800i \(0.456788\pi\)
\(128\) 5.06167 0.447393
\(129\) 9.00110 0.792503
\(130\) −17.5304 −1.53752
\(131\) −12.7959 −1.11798 −0.558990 0.829174i \(-0.688811\pi\)
−0.558990 + 0.829174i \(0.688811\pi\)
\(132\) 5.52882 0.481222
\(133\) −12.6905 −1.10040
\(134\) −6.22618 −0.537860
\(135\) −13.6906 −1.17829
\(136\) 8.18840 0.702150
\(137\) −17.3319 −1.48076 −0.740380 0.672188i \(-0.765354\pi\)
−0.740380 + 0.672188i \(0.765354\pi\)
\(138\) −4.14098 −0.352503
\(139\) −12.8884 −1.09318 −0.546590 0.837401i \(-0.684074\pi\)
−0.546590 + 0.837401i \(0.684074\pi\)
\(140\) 11.2153 0.947869
\(141\) −9.58732 −0.807398
\(142\) −1.64677 −0.138194
\(143\) −12.2285 −1.02260
\(144\) −0.603809 −0.0503174
\(145\) 1.49622 0.124255
\(146\) −10.9790 −0.908629
\(147\) 0.782341 0.0645264
\(148\) −4.89470 −0.402342
\(149\) −18.6003 −1.52380 −0.761898 0.647697i \(-0.775732\pi\)
−0.761898 + 0.647697i \(0.775732\pi\)
\(150\) −16.5205 −1.34889
\(151\) 13.3926 1.08987 0.544936 0.838478i \(-0.316554\pi\)
0.544936 + 0.838478i \(0.316554\pi\)
\(152\) 13.6731 1.10903
\(153\) 3.31656 0.268128
\(154\) −6.15765 −0.496198
\(155\) −10.5948 −0.850997
\(156\) −11.5952 −0.928359
\(157\) −5.06098 −0.403910 −0.201955 0.979395i \(-0.564730\pi\)
−0.201955 + 0.979395i \(0.564730\pi\)
\(158\) 16.0447 1.27645
\(159\) 12.0724 0.957404
\(160\) −19.8319 −1.56785
\(161\) −5.85955 −0.461797
\(162\) 10.4659 0.822277
\(163\) −10.1216 −0.792782 −0.396391 0.918082i \(-0.629738\pi\)
−0.396391 + 0.918082i \(0.629738\pi\)
\(164\) 3.25734 0.254356
\(165\) −18.2212 −1.41852
\(166\) 8.61414 0.668587
\(167\) 11.3630 0.879299 0.439649 0.898169i \(-0.355103\pi\)
0.439649 + 0.898169i \(0.355103\pi\)
\(168\) −16.2731 −1.25550
\(169\) 12.6459 0.972763
\(170\) −9.68262 −0.742623
\(171\) 5.53803 0.423504
\(172\) −4.92375 −0.375433
\(173\) −18.1125 −1.37707 −0.688533 0.725205i \(-0.741745\pi\)
−0.688533 + 0.725205i \(0.741745\pi\)
\(174\) −0.778943 −0.0590515
\(175\) −23.3768 −1.76712
\(176\) 1.22966 0.0926894
\(177\) 5.97605 0.449188
\(178\) 10.0296 0.751751
\(179\) 9.43259 0.705025 0.352513 0.935807i \(-0.385327\pi\)
0.352513 + 0.935807i \(0.385327\pi\)
\(180\) −4.89430 −0.364800
\(181\) −24.5527 −1.82499 −0.912495 0.409089i \(-0.865847\pi\)
−0.912495 + 0.409089i \(0.865847\pi\)
\(182\) 12.9140 0.957250
\(183\) −18.0290 −1.33275
\(184\) 6.31326 0.465420
\(185\) 16.1313 1.18600
\(186\) 5.51573 0.404433
\(187\) −6.75421 −0.493916
\(188\) 5.24443 0.382489
\(189\) 10.0853 0.733601
\(190\) −16.1682 −1.17296
\(191\) −17.5270 −1.26821 −0.634106 0.773246i \(-0.718632\pi\)
−0.634106 + 0.773246i \(0.718632\pi\)
\(192\) 12.4083 0.895492
\(193\) −22.6101 −1.62751 −0.813756 0.581206i \(-0.802581\pi\)
−0.813756 + 0.581206i \(0.802581\pi\)
\(194\) 6.08712 0.437030
\(195\) 38.2140 2.73656
\(196\) −0.427954 −0.0305681
\(197\) 17.7717 1.26618 0.633091 0.774078i \(-0.281786\pi\)
0.633091 + 0.774078i \(0.281786\pi\)
\(198\) 2.68716 0.190968
\(199\) −10.2870 −0.729228 −0.364614 0.931159i \(-0.618799\pi\)
−0.364614 + 0.931159i \(0.618799\pi\)
\(200\) 25.1869 1.78098
\(201\) 13.5723 0.957315
\(202\) −12.8578 −0.904672
\(203\) −1.10222 −0.0773604
\(204\) −6.40443 −0.448400
\(205\) −10.7351 −0.749774
\(206\) 18.2914 1.27442
\(207\) 2.55707 0.177729
\(208\) −2.57889 −0.178814
\(209\) −11.2783 −0.780133
\(210\) 19.2427 1.32787
\(211\) 15.1797 1.04502 0.522508 0.852634i \(-0.324996\pi\)
0.522508 + 0.852634i \(0.324996\pi\)
\(212\) −6.60381 −0.453551
\(213\) 3.58976 0.245966
\(214\) −4.28662 −0.293027
\(215\) 16.2271 1.10668
\(216\) −10.8663 −0.739356
\(217\) 7.80484 0.529827
\(218\) −6.93644 −0.469795
\(219\) 23.9328 1.61723
\(220\) 9.96729 0.671994
\(221\) 14.1651 0.952849
\(222\) −8.39805 −0.563640
\(223\) −18.6218 −1.24701 −0.623505 0.781820i \(-0.714292\pi\)
−0.623505 + 0.781820i \(0.714292\pi\)
\(224\) 14.6094 0.976135
\(225\) 10.2015 0.680098
\(226\) −17.7798 −1.18270
\(227\) −24.7238 −1.64098 −0.820488 0.571664i \(-0.806298\pi\)
−0.820488 + 0.571664i \(0.806298\pi\)
\(228\) −10.6942 −0.708240
\(229\) 4.39930 0.290714 0.145357 0.989379i \(-0.453567\pi\)
0.145357 + 0.989379i \(0.453567\pi\)
\(230\) −7.46530 −0.492247
\(231\) 13.4229 0.883162
\(232\) 1.18756 0.0779673
\(233\) 23.3827 1.53185 0.765926 0.642929i \(-0.222281\pi\)
0.765926 + 0.642929i \(0.222281\pi\)
\(234\) −5.63559 −0.368410
\(235\) −17.2839 −1.12748
\(236\) −3.26900 −0.212794
\(237\) −34.9754 −2.27190
\(238\) 7.13285 0.462354
\(239\) 19.1315 1.23752 0.618758 0.785582i \(-0.287636\pi\)
0.618758 + 0.785582i \(0.287636\pi\)
\(240\) −3.84270 −0.248045
\(241\) 10.0131 0.644998 0.322499 0.946570i \(-0.395477\pi\)
0.322499 + 0.946570i \(0.395477\pi\)
\(242\) 4.85152 0.311868
\(243\) −11.6787 −0.749188
\(244\) 9.86219 0.631362
\(245\) 1.41040 0.0901068
\(246\) 5.58877 0.356327
\(247\) 23.6531 1.50501
\(248\) −8.40918 −0.533983
\(249\) −18.7777 −1.18999
\(250\) −12.4748 −0.788974
\(251\) 1.41992 0.0896248 0.0448124 0.998995i \(-0.485731\pi\)
0.0448124 + 0.998995i \(0.485731\pi\)
\(252\) 3.60546 0.227122
\(253\) −5.20749 −0.327392
\(254\) −2.86286 −0.179632
\(255\) 21.1069 1.32176
\(256\) −16.8805 −1.05503
\(257\) 24.5756 1.53298 0.766492 0.642254i \(-0.222000\pi\)
0.766492 + 0.642254i \(0.222000\pi\)
\(258\) −8.44790 −0.525943
\(259\) −11.8834 −0.738397
\(260\) −20.9037 −1.29639
\(261\) 0.481000 0.0297731
\(262\) 12.0094 0.741946
\(263\) 28.8924 1.78158 0.890789 0.454416i \(-0.150152\pi\)
0.890789 + 0.454416i \(0.150152\pi\)
\(264\) −14.4622 −0.890090
\(265\) 21.7640 1.33695
\(266\) 11.9105 0.730280
\(267\) −21.8633 −1.33801
\(268\) −7.42426 −0.453509
\(269\) −17.2295 −1.05050 −0.525250 0.850948i \(-0.676028\pi\)
−0.525250 + 0.850948i \(0.676028\pi\)
\(270\) 12.8491 0.781974
\(271\) 19.4823 1.18347 0.591734 0.806133i \(-0.298444\pi\)
0.591734 + 0.806133i \(0.298444\pi\)
\(272\) −1.42441 −0.0863673
\(273\) −28.1509 −1.70377
\(274\) 16.2667 0.982704
\(275\) −20.7754 −1.25280
\(276\) −4.93781 −0.297221
\(277\) 11.3433 0.681554 0.340777 0.940144i \(-0.389310\pi\)
0.340777 + 0.940144i \(0.389310\pi\)
\(278\) 12.0963 0.725487
\(279\) −3.40598 −0.203911
\(280\) −29.3370 −1.75322
\(281\) −19.3347 −1.15341 −0.576705 0.816952i \(-0.695662\pi\)
−0.576705 + 0.816952i \(0.695662\pi\)
\(282\) 8.99809 0.535829
\(283\) 10.2100 0.606923 0.303462 0.952844i \(-0.401858\pi\)
0.303462 + 0.952844i \(0.401858\pi\)
\(284\) −1.96366 −0.116522
\(285\) 35.2445 2.08771
\(286\) 11.4769 0.678645
\(287\) 7.90819 0.466806
\(288\) −6.37547 −0.375678
\(289\) −9.17612 −0.539772
\(290\) −1.40427 −0.0824615
\(291\) −13.2692 −0.777852
\(292\) −13.0917 −0.766132
\(293\) 12.0608 0.704600 0.352300 0.935887i \(-0.385400\pi\)
0.352300 + 0.935887i \(0.385400\pi\)
\(294\) −0.734259 −0.0428229
\(295\) 10.7736 0.627260
\(296\) 12.8035 0.744189
\(297\) 8.96304 0.520088
\(298\) 17.4571 1.01126
\(299\) 10.9213 0.631595
\(300\) −19.6995 −1.13735
\(301\) −11.9539 −0.689012
\(302\) −12.5695 −0.723292
\(303\) 28.0284 1.61019
\(304\) −2.37849 −0.136416
\(305\) −32.5025 −1.86109
\(306\) −3.11273 −0.177943
\(307\) −0.550676 −0.0314288 −0.0157144 0.999877i \(-0.505002\pi\)
−0.0157144 + 0.999877i \(0.505002\pi\)
\(308\) −7.34255 −0.418381
\(309\) −39.8729 −2.26829
\(310\) 9.94368 0.564763
\(311\) 19.9296 1.13010 0.565051 0.825056i \(-0.308857\pi\)
0.565051 + 0.825056i \(0.308857\pi\)
\(312\) 30.3306 1.71713
\(313\) −21.7539 −1.22961 −0.614803 0.788681i \(-0.710764\pi\)
−0.614803 + 0.788681i \(0.710764\pi\)
\(314\) 4.74994 0.268055
\(315\) −11.8824 −0.669498
\(316\) 19.1321 1.07627
\(317\) −16.7111 −0.938588 −0.469294 0.883042i \(-0.655492\pi\)
−0.469294 + 0.883042i \(0.655492\pi\)
\(318\) −11.3304 −0.635380
\(319\) −0.979561 −0.0548449
\(320\) 22.3695 1.25049
\(321\) 9.34428 0.521547
\(322\) 5.49942 0.306471
\(323\) 13.0644 0.726923
\(324\) 12.4798 0.693322
\(325\) 43.5708 2.41687
\(326\) 9.49950 0.526129
\(327\) 15.1206 0.836169
\(328\) −8.52054 −0.470468
\(329\) 12.7324 0.701962
\(330\) 17.1013 0.941397
\(331\) −8.57405 −0.471273 −0.235636 0.971841i \(-0.575717\pi\)
−0.235636 + 0.971841i \(0.575717\pi\)
\(332\) 10.2717 0.563734
\(333\) 5.18583 0.284181
\(334\) −10.6647 −0.583545
\(335\) 24.4679 1.33683
\(336\) 2.83078 0.154432
\(337\) 6.53912 0.356209 0.178104 0.984012i \(-0.443004\pi\)
0.178104 + 0.984012i \(0.443004\pi\)
\(338\) −11.8687 −0.645572
\(339\) 38.7577 2.10503
\(340\) −11.5458 −0.626160
\(341\) 6.93631 0.375622
\(342\) −5.19767 −0.281058
\(343\) 17.9804 0.970851
\(344\) 12.8795 0.694417
\(345\) 16.2734 0.876131
\(346\) 16.9993 0.913888
\(347\) −13.6009 −0.730136 −0.365068 0.930981i \(-0.618954\pi\)
−0.365068 + 0.930981i \(0.618954\pi\)
\(348\) −0.928832 −0.0497906
\(349\) −8.81304 −0.471751 −0.235876 0.971783i \(-0.575796\pi\)
−0.235876 + 0.971783i \(0.575796\pi\)
\(350\) 21.9401 1.17275
\(351\) −18.7975 −1.00334
\(352\) 12.9837 0.692034
\(353\) −10.1022 −0.537688 −0.268844 0.963184i \(-0.586642\pi\)
−0.268844 + 0.963184i \(0.586642\pi\)
\(354\) −5.60877 −0.298103
\(355\) 6.47157 0.343475
\(356\) 11.9596 0.633857
\(357\) −15.5487 −0.822924
\(358\) −8.85287 −0.467889
\(359\) 21.5410 1.13689 0.568445 0.822721i \(-0.307545\pi\)
0.568445 + 0.822721i \(0.307545\pi\)
\(360\) 12.8025 0.674750
\(361\) 2.81510 0.148163
\(362\) 23.0437 1.21115
\(363\) −10.5757 −0.555081
\(364\) 15.3990 0.807127
\(365\) 43.1458 2.25836
\(366\) 16.9210 0.884474
\(367\) 7.76452 0.405305 0.202652 0.979251i \(-0.435044\pi\)
0.202652 + 0.979251i \(0.435044\pi\)
\(368\) −1.09822 −0.0572486
\(369\) −3.45108 −0.179656
\(370\) −15.1399 −0.787086
\(371\) −16.0328 −0.832379
\(372\) 6.57710 0.341007
\(373\) 29.4708 1.52594 0.762970 0.646434i \(-0.223740\pi\)
0.762970 + 0.646434i \(0.223740\pi\)
\(374\) 6.33910 0.327787
\(375\) 27.1934 1.40426
\(376\) −13.7183 −0.707469
\(377\) 2.05436 0.105805
\(378\) −9.46551 −0.486853
\(379\) 8.31615 0.427172 0.213586 0.976924i \(-0.431486\pi\)
0.213586 + 0.976924i \(0.431486\pi\)
\(380\) −19.2793 −0.989009
\(381\) 6.24068 0.319720
\(382\) 16.4498 0.841647
\(383\) 5.60989 0.286652 0.143326 0.989676i \(-0.454220\pi\)
0.143326 + 0.989676i \(0.454220\pi\)
\(384\) 10.3557 0.528460
\(385\) 24.1986 1.23328
\(386\) 21.2205 1.08010
\(387\) 5.21661 0.265175
\(388\) 7.25845 0.368492
\(389\) −0.563342 −0.0285626 −0.0142813 0.999898i \(-0.504546\pi\)
−0.0142813 + 0.999898i \(0.504546\pi\)
\(390\) −35.8654 −1.81611
\(391\) 6.03221 0.305062
\(392\) 1.11944 0.0565402
\(393\) −26.1791 −1.32056
\(394\) −16.6795 −0.840299
\(395\) −63.0532 −3.17255
\(396\) 3.20424 0.161019
\(397\) −7.43322 −0.373063 −0.186531 0.982449i \(-0.559725\pi\)
−0.186531 + 0.982449i \(0.559725\pi\)
\(398\) 9.65480 0.483951
\(399\) −25.9634 −1.29980
\(400\) −4.38136 −0.219068
\(401\) 15.9423 0.796119 0.398059 0.917360i \(-0.369684\pi\)
0.398059 + 0.917360i \(0.369684\pi\)
\(402\) −12.7381 −0.635321
\(403\) −14.5470 −0.724639
\(404\) −15.3320 −0.762795
\(405\) −41.1293 −2.04373
\(406\) 1.03447 0.0513401
\(407\) −10.5610 −0.523488
\(408\) 16.7527 0.829380
\(409\) −28.5003 −1.40925 −0.704624 0.709581i \(-0.748884\pi\)
−0.704624 + 0.709581i \(0.748884\pi\)
\(410\) 10.0754 0.497587
\(411\) −35.4592 −1.74908
\(412\) 21.8111 1.07456
\(413\) −7.93649 −0.390529
\(414\) −2.39991 −0.117949
\(415\) −33.8522 −1.66174
\(416\) −27.2298 −1.33505
\(417\) −26.3684 −1.29126
\(418\) 10.5851 0.517734
\(419\) 4.52331 0.220978 0.110489 0.993877i \(-0.464758\pi\)
0.110489 + 0.993877i \(0.464758\pi\)
\(420\) 22.9455 1.11962
\(421\) 16.3341 0.796074 0.398037 0.917369i \(-0.369692\pi\)
0.398037 + 0.917369i \(0.369692\pi\)
\(422\) −14.2468 −0.693523
\(423\) −5.55635 −0.270159
\(424\) 17.2742 0.838909
\(425\) 24.0656 1.16735
\(426\) −3.36913 −0.163235
\(427\) 23.9435 1.15871
\(428\) −5.11148 −0.247073
\(429\) −25.0182 −1.20789
\(430\) −15.2298 −0.734445
\(431\) −3.98556 −0.191978 −0.0959889 0.995382i \(-0.530601\pi\)
−0.0959889 + 0.995382i \(0.530601\pi\)
\(432\) 1.89023 0.0909438
\(433\) 26.3837 1.26792 0.633959 0.773366i \(-0.281429\pi\)
0.633959 + 0.773366i \(0.281429\pi\)
\(434\) −7.32516 −0.351619
\(435\) 3.06113 0.146770
\(436\) −8.27120 −0.396118
\(437\) 10.0727 0.481840
\(438\) −22.4620 −1.07327
\(439\) 32.3911 1.54595 0.772973 0.634439i \(-0.218769\pi\)
0.772973 + 0.634439i \(0.218769\pi\)
\(440\) −26.0724 −1.24295
\(441\) 0.453408 0.0215908
\(442\) −13.2945 −0.632357
\(443\) −2.29328 −0.108957 −0.0544785 0.998515i \(-0.517350\pi\)
−0.0544785 + 0.998515i \(0.517350\pi\)
\(444\) −10.0141 −0.475246
\(445\) −39.4149 −1.86844
\(446\) 17.4773 0.827576
\(447\) −38.0543 −1.79991
\(448\) −16.4788 −0.778552
\(449\) 19.5422 0.922254 0.461127 0.887334i \(-0.347445\pi\)
0.461127 + 0.887334i \(0.347445\pi\)
\(450\) −9.57450 −0.451346
\(451\) 7.02817 0.330943
\(452\) −21.2011 −0.997217
\(453\) 27.3998 1.28736
\(454\) 23.2043 1.08903
\(455\) −50.7501 −2.37920
\(456\) 27.9738 1.30999
\(457\) −4.68139 −0.218986 −0.109493 0.993988i \(-0.534923\pi\)
−0.109493 + 0.993988i \(0.534923\pi\)
\(458\) −4.12892 −0.192932
\(459\) −10.3825 −0.484615
\(460\) −8.90183 −0.415050
\(461\) 8.93426 0.416110 0.208055 0.978117i \(-0.433287\pi\)
0.208055 + 0.978117i \(0.433287\pi\)
\(462\) −12.5979 −0.586109
\(463\) −30.6401 −1.42397 −0.711983 0.702197i \(-0.752203\pi\)
−0.711983 + 0.702197i \(0.752203\pi\)
\(464\) −0.206581 −0.00959030
\(465\) −21.6760 −1.00520
\(466\) −21.9456 −1.01661
\(467\) −26.9036 −1.24495 −0.622475 0.782640i \(-0.713873\pi\)
−0.622475 + 0.782640i \(0.713873\pi\)
\(468\) −6.72002 −0.310633
\(469\) −18.0247 −0.832301
\(470\) 16.2216 0.748249
\(471\) −10.3543 −0.477099
\(472\) 8.55103 0.393593
\(473\) −10.6237 −0.488477
\(474\) 32.8258 1.50774
\(475\) 40.1851 1.84382
\(476\) 8.50540 0.389844
\(477\) 6.99659 0.320352
\(478\) −17.9557 −0.821276
\(479\) 33.0101 1.50827 0.754135 0.656719i \(-0.228056\pi\)
0.754135 + 0.656719i \(0.228056\pi\)
\(480\) −40.5740 −1.85194
\(481\) 22.1488 1.00990
\(482\) −9.39766 −0.428052
\(483\) −11.9880 −0.545475
\(484\) 5.78509 0.262959
\(485\) −23.9215 −1.08622
\(486\) 10.9609 0.497197
\(487\) −22.0103 −0.997383 −0.498691 0.866780i \(-0.666186\pi\)
−0.498691 + 0.866780i \(0.666186\pi\)
\(488\) −25.7974 −1.16779
\(489\) −20.7077 −0.936435
\(490\) −1.32371 −0.0597993
\(491\) −23.2875 −1.05095 −0.525474 0.850809i \(-0.676112\pi\)
−0.525474 + 0.850809i \(0.676112\pi\)
\(492\) 6.66420 0.300445
\(493\) 1.13469 0.0511041
\(494\) −22.1994 −0.998797
\(495\) −10.5601 −0.474642
\(496\) 1.46281 0.0656822
\(497\) −4.76737 −0.213846
\(498\) 17.6237 0.789735
\(499\) 20.0711 0.898507 0.449254 0.893404i \(-0.351690\pi\)
0.449254 + 0.893404i \(0.351690\pi\)
\(500\) −14.8753 −0.665242
\(501\) 23.2476 1.03863
\(502\) −1.33266 −0.0594794
\(503\) 10.8823 0.485218 0.242609 0.970124i \(-0.421997\pi\)
0.242609 + 0.970124i \(0.421997\pi\)
\(504\) −9.43113 −0.420096
\(505\) 50.5292 2.24852
\(506\) 4.88745 0.217273
\(507\) 25.8723 1.14903
\(508\) −3.41375 −0.151461
\(509\) 3.58455 0.158883 0.0794413 0.996840i \(-0.474686\pi\)
0.0794413 + 0.996840i \(0.474686\pi\)
\(510\) −19.8097 −0.877187
\(511\) −31.7840 −1.40604
\(512\) 5.71970 0.252777
\(513\) −17.3369 −0.765441
\(514\) −23.0652 −1.01736
\(515\) −71.8823 −3.16751
\(516\) −10.0735 −0.443461
\(517\) 11.3156 0.497658
\(518\) 11.1530 0.490036
\(519\) −37.0563 −1.62659
\(520\) 54.6797 2.39786
\(521\) 5.42122 0.237508 0.118754 0.992924i \(-0.462110\pi\)
0.118754 + 0.992924i \(0.462110\pi\)
\(522\) −0.451438 −0.0197589
\(523\) −42.6840 −1.86644 −0.933220 0.359306i \(-0.883013\pi\)
−0.933220 + 0.359306i \(0.883013\pi\)
\(524\) 14.3204 0.625589
\(525\) −47.8266 −2.08732
\(526\) −27.1167 −1.18234
\(527\) −8.03482 −0.350002
\(528\) 2.51577 0.109485
\(529\) −18.3492 −0.797790
\(530\) −20.4264 −0.887265
\(531\) 3.46343 0.150300
\(532\) 14.2024 0.615753
\(533\) −14.7397 −0.638446
\(534\) 20.5196 0.887969
\(535\) 16.8458 0.728305
\(536\) 19.4203 0.838831
\(537\) 19.2981 0.832776
\(538\) 16.1706 0.697163
\(539\) −0.923369 −0.0397723
\(540\) 15.3217 0.659339
\(541\) −12.2836 −0.528113 −0.264057 0.964507i \(-0.585061\pi\)
−0.264057 + 0.964507i \(0.585061\pi\)
\(542\) −18.2850 −0.785407
\(543\) −50.2324 −2.15568
\(544\) −15.0399 −0.644832
\(545\) 27.2591 1.16765
\(546\) 26.4208 1.13070
\(547\) −19.4082 −0.829836 −0.414918 0.909859i \(-0.636190\pi\)
−0.414918 + 0.909859i \(0.636190\pi\)
\(548\) 19.3968 0.828590
\(549\) −10.4488 −0.445943
\(550\) 19.4986 0.831422
\(551\) 1.89473 0.0807181
\(552\) 12.9163 0.549754
\(553\) 46.4491 1.97522
\(554\) −10.6462 −0.452312
\(555\) 33.0031 1.40090
\(556\) 14.4239 0.611711
\(557\) −12.9922 −0.550498 −0.275249 0.961373i \(-0.588760\pi\)
−0.275249 + 0.961373i \(0.588760\pi\)
\(558\) 3.19665 0.135325
\(559\) 22.2803 0.942355
\(560\) 5.10329 0.215653
\(561\) −13.8184 −0.583415
\(562\) 18.1464 0.765459
\(563\) −32.6802 −1.37731 −0.688653 0.725091i \(-0.741798\pi\)
−0.688653 + 0.725091i \(0.741798\pi\)
\(564\) 10.7296 0.451796
\(565\) 69.8720 2.93954
\(566\) −9.58253 −0.402784
\(567\) 30.2985 1.27242
\(568\) 5.13652 0.215524
\(569\) 28.2125 1.18273 0.591365 0.806404i \(-0.298589\pi\)
0.591365 + 0.806404i \(0.298589\pi\)
\(570\) −33.0784 −1.38550
\(571\) 6.12528 0.256335 0.128168 0.991753i \(-0.459090\pi\)
0.128168 + 0.991753i \(0.459090\pi\)
\(572\) 13.6854 0.572215
\(573\) −35.8586 −1.49801
\(574\) −7.42216 −0.309795
\(575\) 18.5546 0.773780
\(576\) 7.19125 0.299636
\(577\) 6.27920 0.261406 0.130703 0.991422i \(-0.458277\pi\)
0.130703 + 0.991422i \(0.458277\pi\)
\(578\) 8.61217 0.358219
\(579\) −46.2580 −1.92242
\(580\) −1.67449 −0.0695293
\(581\) 24.9378 1.03459
\(582\) 12.4536 0.516220
\(583\) −14.2486 −0.590117
\(584\) 34.2451 1.41707
\(585\) 22.1470 0.915665
\(586\) −11.3196 −0.467606
\(587\) 11.0713 0.456961 0.228481 0.973548i \(-0.426624\pi\)
0.228481 + 0.973548i \(0.426624\pi\)
\(588\) −0.875551 −0.0361071
\(589\) −13.4166 −0.552823
\(590\) −10.1114 −0.416280
\(591\) 36.3591 1.49561
\(592\) −2.22722 −0.0915384
\(593\) 5.98380 0.245725 0.122863 0.992424i \(-0.460793\pi\)
0.122863 + 0.992424i \(0.460793\pi\)
\(594\) −8.41218 −0.345156
\(595\) −28.0310 −1.14916
\(596\) 20.8164 0.852671
\(597\) −21.0462 −0.861365
\(598\) −10.2501 −0.419157
\(599\) −17.4424 −0.712679 −0.356339 0.934357i \(-0.615975\pi\)
−0.356339 + 0.934357i \(0.615975\pi\)
\(600\) 51.5298 2.10370
\(601\) 44.5375 1.81672 0.908362 0.418185i \(-0.137334\pi\)
0.908362 + 0.418185i \(0.137334\pi\)
\(602\) 11.2192 0.457262
\(603\) 7.86584 0.320322
\(604\) −14.9882 −0.609860
\(605\) −19.0657 −0.775133
\(606\) −26.3058 −1.06860
\(607\) 16.9812 0.689244 0.344622 0.938742i \(-0.388007\pi\)
0.344622 + 0.938742i \(0.388007\pi\)
\(608\) −25.1139 −1.01850
\(609\) −2.25502 −0.0913781
\(610\) 30.5049 1.23511
\(611\) −23.7313 −0.960067
\(612\) −3.71170 −0.150037
\(613\) 39.8340 1.60888 0.804439 0.594035i \(-0.202466\pi\)
0.804439 + 0.594035i \(0.202466\pi\)
\(614\) 0.516832 0.0208577
\(615\) −21.9630 −0.885634
\(616\) 19.2066 0.773855
\(617\) 8.08667 0.325557 0.162779 0.986663i \(-0.447954\pi\)
0.162779 + 0.986663i \(0.447954\pi\)
\(618\) 37.4223 1.50535
\(619\) 1.00000 0.0401934
\(620\) 11.8571 0.476193
\(621\) −8.00493 −0.321227
\(622\) −18.7047 −0.749990
\(623\) 29.0355 1.16328
\(624\) −5.27614 −0.211215
\(625\) 6.00537 0.240215
\(626\) 20.4170 0.816026
\(627\) −23.0742 −0.921494
\(628\) 5.66395 0.226016
\(629\) 12.2335 0.487783
\(630\) 11.1521 0.444311
\(631\) 13.6691 0.544158 0.272079 0.962275i \(-0.412289\pi\)
0.272079 + 0.962275i \(0.412289\pi\)
\(632\) −50.0457 −1.99071
\(633\) 31.0562 1.23437
\(634\) 15.6840 0.622893
\(635\) 11.2506 0.446467
\(636\) −13.5107 −0.535735
\(637\) 1.93652 0.0767276
\(638\) 0.919358 0.0363977
\(639\) 2.08045 0.0823014
\(640\) 18.6691 0.737959
\(641\) 26.9643 1.06503 0.532513 0.846422i \(-0.321248\pi\)
0.532513 + 0.846422i \(0.321248\pi\)
\(642\) −8.76999 −0.346124
\(643\) −36.6704 −1.44614 −0.723069 0.690775i \(-0.757269\pi\)
−0.723069 + 0.690775i \(0.757269\pi\)
\(644\) 6.55766 0.258408
\(645\) 33.1990 1.30721
\(646\) −12.2615 −0.482421
\(647\) −10.7513 −0.422676 −0.211338 0.977413i \(-0.567782\pi\)
−0.211338 + 0.977413i \(0.567782\pi\)
\(648\) −32.6445 −1.28240
\(649\) −7.05332 −0.276867
\(650\) −40.8929 −1.60395
\(651\) 15.9679 0.625832
\(652\) 11.3275 0.443618
\(653\) −29.5031 −1.15455 −0.577273 0.816552i \(-0.695883\pi\)
−0.577273 + 0.816552i \(0.695883\pi\)
\(654\) −14.1913 −0.554922
\(655\) −47.1953 −1.84407
\(656\) 1.48218 0.0578695
\(657\) 13.8703 0.541133
\(658\) −11.9499 −0.465856
\(659\) 33.1605 1.29175 0.645874 0.763444i \(-0.276493\pi\)
0.645874 + 0.763444i \(0.276493\pi\)
\(660\) 20.3921 0.793760
\(661\) −9.47927 −0.368701 −0.184350 0.982861i \(-0.559018\pi\)
−0.184350 + 0.982861i \(0.559018\pi\)
\(662\) 8.04710 0.312759
\(663\) 28.9804 1.12551
\(664\) −26.8687 −1.04271
\(665\) −46.8065 −1.81508
\(666\) −4.86711 −0.188597
\(667\) 0.874850 0.0338743
\(668\) −12.7169 −0.492030
\(669\) −38.0984 −1.47297
\(670\) −22.9642 −0.887183
\(671\) 21.2790 0.821467
\(672\) 29.8895 1.15301
\(673\) −35.0763 −1.35209 −0.676046 0.736859i \(-0.736308\pi\)
−0.676046 + 0.736859i \(0.736308\pi\)
\(674\) −6.13723 −0.236397
\(675\) −31.9358 −1.22921
\(676\) −14.1526 −0.544329
\(677\) 45.3854 1.74430 0.872152 0.489235i \(-0.162724\pi\)
0.872152 + 0.489235i \(0.162724\pi\)
\(678\) −36.3757 −1.39700
\(679\) 17.6221 0.676274
\(680\) 30.2015 1.15817
\(681\) −50.5824 −1.93832
\(682\) −6.51001 −0.249281
\(683\) 38.5031 1.47328 0.736640 0.676285i \(-0.236411\pi\)
0.736640 + 0.676285i \(0.236411\pi\)
\(684\) −6.19784 −0.236980
\(685\) −63.9255 −2.44247
\(686\) −16.8753 −0.644304
\(687\) 9.00052 0.343391
\(688\) −2.24045 −0.0854162
\(689\) 29.8826 1.13844
\(690\) −15.2733 −0.581443
\(691\) 45.9369 1.74752 0.873761 0.486356i \(-0.161674\pi\)
0.873761 + 0.486356i \(0.161674\pi\)
\(692\) 20.2704 0.770566
\(693\) 7.77927 0.295510
\(694\) 12.7650 0.484554
\(695\) −47.5365 −1.80316
\(696\) 2.42963 0.0920950
\(697\) −8.14122 −0.308371
\(698\) 8.27140 0.313077
\(699\) 47.8387 1.80942
\(700\) 26.1619 0.988828
\(701\) 45.3751 1.71380 0.856898 0.515486i \(-0.172389\pi\)
0.856898 + 0.515486i \(0.172389\pi\)
\(702\) 17.6423 0.665864
\(703\) 20.4277 0.770446
\(704\) −14.6451 −0.551956
\(705\) −35.3611 −1.33178
\(706\) 9.48137 0.356836
\(707\) −37.2231 −1.39992
\(708\) −6.68805 −0.251352
\(709\) 46.4351 1.74391 0.871954 0.489589i \(-0.162853\pi\)
0.871954 + 0.489589i \(0.162853\pi\)
\(710\) −6.07383 −0.227947
\(711\) −20.2701 −0.760187
\(712\) −31.2838 −1.17241
\(713\) −6.19485 −0.231999
\(714\) 14.5931 0.546133
\(715\) −45.1026 −1.68674
\(716\) −10.5564 −0.394511
\(717\) 39.1412 1.46176
\(718\) −20.2171 −0.754495
\(719\) 27.1580 1.01282 0.506410 0.862293i \(-0.330972\pi\)
0.506410 + 0.862293i \(0.330972\pi\)
\(720\) −2.22704 −0.0829970
\(721\) 52.9532 1.97208
\(722\) −2.64208 −0.0983281
\(723\) 20.4857 0.761872
\(724\) 27.4780 1.02121
\(725\) 3.49023 0.129624
\(726\) 9.92573 0.368378
\(727\) −5.60126 −0.207739 −0.103870 0.994591i \(-0.533122\pi\)
−0.103870 + 0.994591i \(0.533122\pi\)
\(728\) −40.2806 −1.49290
\(729\) 9.56024 0.354083
\(730\) −40.4941 −1.49875
\(731\) 12.3062 0.455160
\(732\) 20.1770 0.745765
\(733\) 11.3772 0.420225 0.210113 0.977677i \(-0.432617\pi\)
0.210113 + 0.977677i \(0.432617\pi\)
\(734\) −7.28732 −0.268980
\(735\) 2.88553 0.106434
\(736\) −11.5958 −0.427427
\(737\) −16.0189 −0.590063
\(738\) 3.23898 0.119229
\(739\) 17.4817 0.643076 0.321538 0.946897i \(-0.395800\pi\)
0.321538 + 0.946897i \(0.395800\pi\)
\(740\) −18.0532 −0.663650
\(741\) 48.3918 1.77772
\(742\) 15.0474 0.552407
\(743\) 0.403961 0.0148199 0.00740994 0.999973i \(-0.497641\pi\)
0.00740994 + 0.999973i \(0.497641\pi\)
\(744\) −17.2043 −0.630741
\(745\) −68.6039 −2.51345
\(746\) −27.6596 −1.01269
\(747\) −10.8827 −0.398176
\(748\) 7.55891 0.276381
\(749\) −12.4097 −0.453439
\(750\) −25.5221 −0.931937
\(751\) −32.7479 −1.19499 −0.597494 0.801874i \(-0.703837\pi\)
−0.597494 + 0.801874i \(0.703837\pi\)
\(752\) 2.38636 0.0870216
\(753\) 2.90502 0.105865
\(754\) −1.92810 −0.0702174
\(755\) 49.3961 1.79771
\(756\) −11.2869 −0.410501
\(757\) −26.3257 −0.956823 −0.478411 0.878136i \(-0.658787\pi\)
−0.478411 + 0.878136i \(0.658787\pi\)
\(758\) −7.80505 −0.283492
\(759\) −10.6540 −0.386716
\(760\) 50.4308 1.82932
\(761\) −22.9125 −0.830578 −0.415289 0.909689i \(-0.636320\pi\)
−0.415289 + 0.909689i \(0.636320\pi\)
\(762\) −5.85713 −0.212181
\(763\) −20.0809 −0.726976
\(764\) 19.6152 0.709654
\(765\) 12.2325 0.442268
\(766\) −5.26511 −0.190236
\(767\) 14.7924 0.534123
\(768\) −34.5358 −1.24620
\(769\) 9.94215 0.358523 0.179262 0.983801i \(-0.442629\pi\)
0.179262 + 0.983801i \(0.442629\pi\)
\(770\) −22.7114 −0.818462
\(771\) 50.2792 1.81076
\(772\) 25.3039 0.910708
\(773\) −33.5600 −1.20707 −0.603535 0.797337i \(-0.706242\pi\)
−0.603535 + 0.797337i \(0.706242\pi\)
\(774\) −4.89600 −0.175983
\(775\) −24.7145 −0.887770
\(776\) −18.9866 −0.681579
\(777\) −24.3122 −0.872195
\(778\) 0.528719 0.0189555
\(779\) −13.5943 −0.487067
\(780\) −42.7668 −1.53130
\(781\) −4.23686 −0.151607
\(782\) −5.66148 −0.202454
\(783\) −1.50578 −0.0538120
\(784\) −0.194731 −0.00695468
\(785\) −18.6665 −0.666237
\(786\) 24.5701 0.876387
\(787\) −22.0758 −0.786916 −0.393458 0.919343i \(-0.628721\pi\)
−0.393458 + 0.919343i \(0.628721\pi\)
\(788\) −19.8890 −0.708518
\(789\) 59.1109 2.10440
\(790\) 59.1780 2.10546
\(791\) −51.4722 −1.83014
\(792\) −8.38163 −0.297828
\(793\) −44.6270 −1.58475
\(794\) 6.97638 0.247582
\(795\) 44.5269 1.57921
\(796\) 11.5126 0.408055
\(797\) 10.0663 0.356567 0.178283 0.983979i \(-0.442946\pi\)
0.178283 + 0.983979i \(0.442946\pi\)
\(798\) 24.3677 0.862608
\(799\) −13.1076 −0.463714
\(800\) −46.2617 −1.63560
\(801\) −12.6709 −0.447705
\(802\) −14.9625 −0.528343
\(803\) −28.2471 −0.996817
\(804\) −15.1893 −0.535685
\(805\) −21.6119 −0.761719
\(806\) 13.6530 0.480906
\(807\) −35.2498 −1.24085
\(808\) 40.1053 1.41090
\(809\) 28.9342 1.01727 0.508635 0.860982i \(-0.330150\pi\)
0.508635 + 0.860982i \(0.330150\pi\)
\(810\) 38.6015 1.35632
\(811\) −43.6513 −1.53280 −0.766402 0.642362i \(-0.777955\pi\)
−0.766402 + 0.642362i \(0.777955\pi\)
\(812\) 1.23354 0.0432886
\(813\) 39.8589 1.39791
\(814\) 9.91191 0.347412
\(815\) −37.3316 −1.30767
\(816\) −2.91419 −0.102017
\(817\) 20.5490 0.718917
\(818\) 26.7487 0.935246
\(819\) −16.3149 −0.570089
\(820\) 12.0141 0.419552
\(821\) 23.3643 0.815420 0.407710 0.913112i \(-0.366328\pi\)
0.407710 + 0.913112i \(0.366328\pi\)
\(822\) 33.2799 1.16077
\(823\) −12.8335 −0.447346 −0.223673 0.974664i \(-0.571805\pi\)
−0.223673 + 0.974664i \(0.571805\pi\)
\(824\) −57.0534 −1.98755
\(825\) −42.5044 −1.47981
\(826\) 7.44872 0.259174
\(827\) 39.1758 1.36227 0.681137 0.732156i \(-0.261486\pi\)
0.681137 + 0.732156i \(0.261486\pi\)
\(828\) −2.86172 −0.0994517
\(829\) −1.61275 −0.0560133 −0.0280066 0.999608i \(-0.508916\pi\)
−0.0280066 + 0.999608i \(0.508916\pi\)
\(830\) 31.7717 1.10281
\(831\) 23.2073 0.805052
\(832\) 30.7140 1.06482
\(833\) 1.06960 0.0370596
\(834\) 24.7478 0.856945
\(835\) 41.9106 1.45037
\(836\) 12.6220 0.436540
\(837\) 10.6625 0.368549
\(838\) −4.24531 −0.146652
\(839\) 36.9833 1.27680 0.638402 0.769703i \(-0.279596\pi\)
0.638402 + 0.769703i \(0.279596\pi\)
\(840\) −60.0205 −2.07091
\(841\) −28.8354 −0.994325
\(842\) −15.3302 −0.528313
\(843\) −39.5568 −1.36241
\(844\) −16.9883 −0.584760
\(845\) 46.6422 1.60454
\(846\) 5.21486 0.179291
\(847\) 14.0451 0.482594
\(848\) −3.00492 −0.103189
\(849\) 20.8887 0.716898
\(850\) −22.5866 −0.774713
\(851\) 9.43206 0.323327
\(852\) −4.01744 −0.137635
\(853\) 34.2323 1.17209 0.586046 0.810278i \(-0.300684\pi\)
0.586046 + 0.810278i \(0.300684\pi\)
\(854\) −22.4719 −0.768973
\(855\) 20.4260 0.698556
\(856\) 13.3706 0.456996
\(857\) −15.6699 −0.535275 −0.267637 0.963520i \(-0.586243\pi\)
−0.267637 + 0.963520i \(0.586243\pi\)
\(858\) 23.4806 0.801616
\(859\) −52.0826 −1.77703 −0.888517 0.458844i \(-0.848264\pi\)
−0.888517 + 0.458844i \(0.848264\pi\)
\(860\) −18.1604 −0.619264
\(861\) 16.1794 0.551392
\(862\) 3.74061 0.127406
\(863\) 48.0878 1.63693 0.818463 0.574559i \(-0.194826\pi\)
0.818463 + 0.574559i \(0.194826\pi\)
\(864\) 19.9585 0.679001
\(865\) −66.8046 −2.27143
\(866\) −24.7622 −0.841452
\(867\) −18.7734 −0.637579
\(868\) −8.73472 −0.296476
\(869\) 41.2802 1.40033
\(870\) −2.87299 −0.0974035
\(871\) 33.5952 1.13833
\(872\) 21.6357 0.732678
\(873\) −7.69017 −0.260273
\(874\) −9.45360 −0.319773
\(875\) −36.1142 −1.22088
\(876\) −26.7842 −0.904955
\(877\) −53.0077 −1.78994 −0.894971 0.446125i \(-0.852804\pi\)
−0.894971 + 0.446125i \(0.852804\pi\)
\(878\) −30.4004 −1.02596
\(879\) 24.6752 0.832273
\(880\) 4.53539 0.152888
\(881\) 16.0327 0.540156 0.270078 0.962838i \(-0.412950\pi\)
0.270078 + 0.962838i \(0.412950\pi\)
\(882\) −0.425542 −0.0143287
\(883\) 9.79720 0.329702 0.164851 0.986318i \(-0.447286\pi\)
0.164851 + 0.986318i \(0.447286\pi\)
\(884\) −15.8528 −0.533186
\(885\) 22.0416 0.740920
\(886\) 2.15234 0.0723092
\(887\) 18.9336 0.635727 0.317863 0.948137i \(-0.397035\pi\)
0.317863 + 0.948137i \(0.397035\pi\)
\(888\) 26.1947 0.879037
\(889\) −8.28793 −0.277968
\(890\) 36.9924 1.23999
\(891\) 26.9269 0.902084
\(892\) 20.8404 0.697790
\(893\) −21.8873 −0.732430
\(894\) 35.7155 1.19451
\(895\) 34.7904 1.16292
\(896\) −13.7528 −0.459450
\(897\) 22.3439 0.746041
\(898\) −18.3412 −0.612053
\(899\) −1.16529 −0.0388645
\(900\) −11.4169 −0.380563
\(901\) 16.5052 0.549867
\(902\) −6.59622 −0.219630
\(903\) −24.4565 −0.813861
\(904\) 55.4578 1.84450
\(905\) −90.5583 −3.01026
\(906\) −25.7159 −0.854353
\(907\) −4.06639 −0.135022 −0.0675111 0.997719i \(-0.521506\pi\)
−0.0675111 + 0.997719i \(0.521506\pi\)
\(908\) 27.6694 0.918242
\(909\) 16.2439 0.538777
\(910\) 47.6310 1.57895
\(911\) 9.87329 0.327117 0.163558 0.986534i \(-0.447703\pi\)
0.163558 + 0.986534i \(0.447703\pi\)
\(912\) −4.86615 −0.161134
\(913\) 22.1627 0.733477
\(914\) 4.39368 0.145330
\(915\) −66.4969 −2.19832
\(916\) −4.92344 −0.162675
\(917\) 34.7671 1.14811
\(918\) 9.74443 0.321614
\(919\) 5.98000 0.197262 0.0986311 0.995124i \(-0.468554\pi\)
0.0986311 + 0.995124i \(0.468554\pi\)
\(920\) 23.2853 0.767695
\(921\) −1.12663 −0.0371237
\(922\) −8.38517 −0.276151
\(923\) 8.88566 0.292475
\(924\) −15.0221 −0.494191
\(925\) 37.6294 1.23725
\(926\) 28.7570 0.945013
\(927\) −23.1084 −0.758980
\(928\) −2.18124 −0.0716027
\(929\) 2.88995 0.0948162 0.0474081 0.998876i \(-0.484904\pi\)
0.0474081 + 0.998876i \(0.484904\pi\)
\(930\) 20.3438 0.667099
\(931\) 1.78604 0.0585350
\(932\) −26.1685 −0.857179
\(933\) 40.7739 1.33488
\(934\) 25.2501 0.826209
\(935\) −24.9117 −0.814699
\(936\) 17.5782 0.574561
\(937\) 6.34674 0.207339 0.103670 0.994612i \(-0.466942\pi\)
0.103670 + 0.994612i \(0.466942\pi\)
\(938\) 16.9169 0.552356
\(939\) −44.5064 −1.45241
\(940\) 19.3431 0.630903
\(941\) 12.1993 0.397685 0.198843 0.980031i \(-0.436282\pi\)
0.198843 + 0.980031i \(0.436282\pi\)
\(942\) 9.71790 0.316626
\(943\) −6.27688 −0.204403
\(944\) −1.48749 −0.0484136
\(945\) 37.1980 1.21005
\(946\) 9.97075 0.324177
\(947\) −37.1970 −1.20874 −0.604370 0.796704i \(-0.706575\pi\)
−0.604370 + 0.796704i \(0.706575\pi\)
\(948\) 39.1424 1.27129
\(949\) 59.2406 1.92303
\(950\) −37.7153 −1.22365
\(951\) −34.1892 −1.10866
\(952\) −22.2484 −0.721073
\(953\) −56.1815 −1.81990 −0.909948 0.414722i \(-0.863879\pi\)
−0.909948 + 0.414722i \(0.863879\pi\)
\(954\) −6.56658 −0.212601
\(955\) −64.6454 −2.09187
\(956\) −21.4109 −0.692478
\(957\) −2.00408 −0.0647828
\(958\) −30.9813 −1.00096
\(959\) 47.0916 1.52067
\(960\) 45.7658 1.47708
\(961\) −22.7485 −0.733824
\(962\) −20.7875 −0.670217
\(963\) 5.41550 0.174512
\(964\) −11.2060 −0.360922
\(965\) −83.3934 −2.68453
\(966\) 11.2513 0.362004
\(967\) 32.7394 1.05283 0.526414 0.850229i \(-0.323536\pi\)
0.526414 + 0.850229i \(0.323536\pi\)
\(968\) −15.1326 −0.486380
\(969\) 26.7285 0.858642
\(970\) 22.4513 0.720867
\(971\) −34.8206 −1.11744 −0.558722 0.829355i \(-0.688708\pi\)
−0.558722 + 0.829355i \(0.688708\pi\)
\(972\) 13.0701 0.419223
\(973\) 35.0185 1.12264
\(974\) 20.6576 0.661912
\(975\) 89.1414 2.85481
\(976\) 4.48757 0.143644
\(977\) 21.5209 0.688515 0.344258 0.938875i \(-0.388131\pi\)
0.344258 + 0.938875i \(0.388131\pi\)
\(978\) 19.4350 0.621464
\(979\) 25.8044 0.824713
\(980\) −1.57843 −0.0504211
\(981\) 8.76315 0.279786
\(982\) 21.8562 0.697461
\(983\) 18.7063 0.596638 0.298319 0.954466i \(-0.403574\pi\)
0.298319 + 0.954466i \(0.403574\pi\)
\(984\) −17.4322 −0.555717
\(985\) 65.5478 2.08853
\(986\) −1.06496 −0.0339151
\(987\) 26.0493 0.829158
\(988\) −26.4711 −0.842159
\(989\) 9.48805 0.301702
\(990\) 9.91111 0.314996
\(991\) −45.2879 −1.43862 −0.719308 0.694691i \(-0.755541\pi\)
−0.719308 + 0.694691i \(0.755541\pi\)
\(992\) 15.4454 0.490393
\(993\) −17.5416 −0.556667
\(994\) 4.47438 0.141919
\(995\) −37.9419 −1.20284
\(996\) 21.0149 0.665884
\(997\) 43.1794 1.36751 0.683753 0.729713i \(-0.260346\pi\)
0.683753 + 0.729713i \(0.260346\pi\)
\(998\) −18.8376 −0.596293
\(999\) −16.2343 −0.513630
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 \(a_p\))