Properties

Label 4010.2.a.k.1.12
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-0.560392\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.40727 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.40727 q^{6} -2.31473 q^{7} -1.00000 q^{8} -1.01959 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.40727 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.40727 q^{6} -2.31473 q^{7} -1.00000 q^{8} -1.01959 q^{9} +1.00000 q^{10} +3.47910 q^{11} +1.40727 q^{12} -0.582324 q^{13} +2.31473 q^{14} -1.40727 q^{15} +1.00000 q^{16} -0.139348 q^{17} +1.01959 q^{18} +1.62864 q^{19} -1.00000 q^{20} -3.25745 q^{21} -3.47910 q^{22} +3.15142 q^{23} -1.40727 q^{24} +1.00000 q^{25} +0.582324 q^{26} -5.65665 q^{27} -2.31473 q^{28} -0.911191 q^{29} +1.40727 q^{30} +2.01676 q^{31} -1.00000 q^{32} +4.89604 q^{33} +0.139348 q^{34} +2.31473 q^{35} -1.01959 q^{36} -9.08644 q^{37} -1.62864 q^{38} -0.819488 q^{39} +1.00000 q^{40} -10.4730 q^{41} +3.25745 q^{42} +11.6852 q^{43} +3.47910 q^{44} +1.01959 q^{45} -3.15142 q^{46} -0.278443 q^{47} +1.40727 q^{48} -1.64204 q^{49} -1.00000 q^{50} -0.196101 q^{51} -0.582324 q^{52} -4.00326 q^{53} +5.65665 q^{54} -3.47910 q^{55} +2.31473 q^{56} +2.29194 q^{57} +0.911191 q^{58} -2.63264 q^{59} -1.40727 q^{60} +6.69819 q^{61} -2.01676 q^{62} +2.36007 q^{63} +1.00000 q^{64} +0.582324 q^{65} -4.89604 q^{66} -3.55128 q^{67} -0.139348 q^{68} +4.43490 q^{69} -2.31473 q^{70} +11.1295 q^{71} +1.01959 q^{72} -13.7611 q^{73} +9.08644 q^{74} +1.40727 q^{75} +1.62864 q^{76} -8.05317 q^{77} +0.819488 q^{78} +4.01383 q^{79} -1.00000 q^{80} -4.90168 q^{81} +10.4730 q^{82} -1.94410 q^{83} -3.25745 q^{84} +0.139348 q^{85} -11.6852 q^{86} -1.28229 q^{87} -3.47910 q^{88} -5.16178 q^{89} -1.01959 q^{90} +1.34792 q^{91} +3.15142 q^{92} +2.83813 q^{93} +0.278443 q^{94} -1.62864 q^{95} -1.40727 q^{96} -3.28753 q^{97} +1.64204 q^{98} -3.54725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.40727 0.812488 0.406244 0.913765i \(-0.366838\pi\)
0.406244 + 0.913765i \(0.366838\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.40727 −0.574516
\(7\) −2.31473 −0.874884 −0.437442 0.899247i \(-0.644116\pi\)
−0.437442 + 0.899247i \(0.644116\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.01959 −0.339863
\(10\) 1.00000 0.316228
\(11\) 3.47910 1.04899 0.524494 0.851414i \(-0.324254\pi\)
0.524494 + 0.851414i \(0.324254\pi\)
\(12\) 1.40727 0.406244
\(13\) −0.582324 −0.161508 −0.0807538 0.996734i \(-0.525733\pi\)
−0.0807538 + 0.996734i \(0.525733\pi\)
\(14\) 2.31473 0.618637
\(15\) −1.40727 −0.363356
\(16\) 1.00000 0.250000
\(17\) −0.139348 −0.0337969 −0.0168984 0.999857i \(-0.505379\pi\)
−0.0168984 + 0.999857i \(0.505379\pi\)
\(18\) 1.01959 0.240319
\(19\) 1.62864 0.373635 0.186818 0.982395i \(-0.440183\pi\)
0.186818 + 0.982395i \(0.440183\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.25745 −0.710833
\(22\) −3.47910 −0.741747
\(23\) 3.15142 0.657116 0.328558 0.944484i \(-0.393437\pi\)
0.328558 + 0.944484i \(0.393437\pi\)
\(24\) −1.40727 −0.287258
\(25\) 1.00000 0.200000
\(26\) 0.582324 0.114203
\(27\) −5.65665 −1.08862
\(28\) −2.31473 −0.437442
\(29\) −0.911191 −0.169204 −0.0846020 0.996415i \(-0.526962\pi\)
−0.0846020 + 0.996415i \(0.526962\pi\)
\(30\) 1.40727 0.256931
\(31\) 2.01676 0.362221 0.181110 0.983463i \(-0.442031\pi\)
0.181110 + 0.983463i \(0.442031\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.89604 0.852291
\(34\) 0.139348 0.0238980
\(35\) 2.31473 0.391260
\(36\) −1.01959 −0.169931
\(37\) −9.08644 −1.49380 −0.746901 0.664935i \(-0.768459\pi\)
−0.746901 + 0.664935i \(0.768459\pi\)
\(38\) −1.62864 −0.264200
\(39\) −0.819488 −0.131223
\(40\) 1.00000 0.158114
\(41\) −10.4730 −1.63561 −0.817804 0.575496i \(-0.804809\pi\)
−0.817804 + 0.575496i \(0.804809\pi\)
\(42\) 3.25745 0.502635
\(43\) 11.6852 1.78197 0.890987 0.454029i \(-0.150014\pi\)
0.890987 + 0.454029i \(0.150014\pi\)
\(44\) 3.47910 0.524494
\(45\) 1.01959 0.151991
\(46\) −3.15142 −0.464651
\(47\) −0.278443 −0.0406150 −0.0203075 0.999794i \(-0.506465\pi\)
−0.0203075 + 0.999794i \(0.506465\pi\)
\(48\) 1.40727 0.203122
\(49\) −1.64204 −0.234577
\(50\) −1.00000 −0.141421
\(51\) −0.196101 −0.0274596
\(52\) −0.582324 −0.0807538
\(53\) −4.00326 −0.549890 −0.274945 0.961460i \(-0.588660\pi\)
−0.274945 + 0.961460i \(0.588660\pi\)
\(54\) 5.65665 0.769773
\(55\) −3.47910 −0.469122
\(56\) 2.31473 0.309318
\(57\) 2.29194 0.303574
\(58\) 0.911191 0.119645
\(59\) −2.63264 −0.342740 −0.171370 0.985207i \(-0.554819\pi\)
−0.171370 + 0.985207i \(0.554819\pi\)
\(60\) −1.40727 −0.181678
\(61\) 6.69819 0.857615 0.428808 0.903396i \(-0.358934\pi\)
0.428808 + 0.903396i \(0.358934\pi\)
\(62\) −2.01676 −0.256129
\(63\) 2.36007 0.297340
\(64\) 1.00000 0.125000
\(65\) 0.582324 0.0722284
\(66\) −4.89604 −0.602661
\(67\) −3.55128 −0.433858 −0.216929 0.976187i \(-0.569604\pi\)
−0.216929 + 0.976187i \(0.569604\pi\)
\(68\) −0.139348 −0.0168984
\(69\) 4.43490 0.533899
\(70\) −2.31473 −0.276663
\(71\) 11.1295 1.32083 0.660415 0.750901i \(-0.270381\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(72\) 1.01959 0.120160
\(73\) −13.7611 −1.61062 −0.805308 0.592857i \(-0.798000\pi\)
−0.805308 + 0.592857i \(0.798000\pi\)
\(74\) 9.08644 1.05628
\(75\) 1.40727 0.162498
\(76\) 1.62864 0.186818
\(77\) −8.05317 −0.917744
\(78\) 0.819488 0.0927888
\(79\) 4.01383 0.451591 0.225796 0.974175i \(-0.427502\pi\)
0.225796 + 0.974175i \(0.427502\pi\)
\(80\) −1.00000 −0.111803
\(81\) −4.90168 −0.544631
\(82\) 10.4730 1.15655
\(83\) −1.94410 −0.213393 −0.106696 0.994292i \(-0.534027\pi\)
−0.106696 + 0.994292i \(0.534027\pi\)
\(84\) −3.25745 −0.355417
\(85\) 0.139348 0.0151144
\(86\) −11.6852 −1.26005
\(87\) −1.28229 −0.137476
\(88\) −3.47910 −0.370874
\(89\) −5.16178 −0.547148 −0.273574 0.961851i \(-0.588206\pi\)
−0.273574 + 0.961851i \(0.588206\pi\)
\(90\) −1.01959 −0.107474
\(91\) 1.34792 0.141301
\(92\) 3.15142 0.328558
\(93\) 2.83813 0.294300
\(94\) 0.278443 0.0287192
\(95\) −1.62864 −0.167095
\(96\) −1.40727 −0.143629
\(97\) −3.28753 −0.333798 −0.166899 0.985974i \(-0.553375\pi\)
−0.166899 + 0.985974i \(0.553375\pi\)
\(98\) 1.64204 0.165871
\(99\) −3.54725 −0.356512
\(100\) 1.00000 0.100000
\(101\) 9.53218 0.948488 0.474244 0.880394i \(-0.342722\pi\)
0.474244 + 0.880394i \(0.342722\pi\)
\(102\) 0.196101 0.0194168
\(103\) −7.77644 −0.766235 −0.383118 0.923700i \(-0.625150\pi\)
−0.383118 + 0.923700i \(0.625150\pi\)
\(104\) 0.582324 0.0571016
\(105\) 3.25745 0.317894
\(106\) 4.00326 0.388831
\(107\) −10.6438 −1.02897 −0.514487 0.857498i \(-0.672018\pi\)
−0.514487 + 0.857498i \(0.672018\pi\)
\(108\) −5.65665 −0.544311
\(109\) 3.07843 0.294861 0.147430 0.989072i \(-0.452900\pi\)
0.147430 + 0.989072i \(0.452900\pi\)
\(110\) 3.47910 0.331719
\(111\) −12.7871 −1.21370
\(112\) −2.31473 −0.218721
\(113\) −11.0361 −1.03819 −0.519097 0.854715i \(-0.673732\pi\)
−0.519097 + 0.854715i \(0.673732\pi\)
\(114\) −2.29194 −0.214660
\(115\) −3.15142 −0.293871
\(116\) −0.911191 −0.0846020
\(117\) 0.593731 0.0548904
\(118\) 2.63264 0.242354
\(119\) 0.322553 0.0295684
\(120\) 1.40727 0.128466
\(121\) 1.10415 0.100378
\(122\) −6.69819 −0.606426
\(123\) −14.7384 −1.32891
\(124\) 2.01676 0.181110
\(125\) −1.00000 −0.0894427
\(126\) −2.36007 −0.210251
\(127\) −2.27475 −0.201851 −0.100926 0.994894i \(-0.532180\pi\)
−0.100926 + 0.994894i \(0.532180\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 16.4442 1.44783
\(130\) −0.582324 −0.0510732
\(131\) 5.08920 0.444645 0.222323 0.974973i \(-0.428636\pi\)
0.222323 + 0.974973i \(0.428636\pi\)
\(132\) 4.89604 0.426146
\(133\) −3.76985 −0.326888
\(134\) 3.55128 0.306784
\(135\) 5.65665 0.486847
\(136\) 0.139348 0.0119490
\(137\) −3.92866 −0.335648 −0.167824 0.985817i \(-0.553674\pi\)
−0.167824 + 0.985817i \(0.553674\pi\)
\(138\) −4.43490 −0.377524
\(139\) −17.1248 −1.45251 −0.726255 0.687426i \(-0.758741\pi\)
−0.726255 + 0.687426i \(0.758741\pi\)
\(140\) 2.31473 0.195630
\(141\) −0.391844 −0.0329992
\(142\) −11.1295 −0.933967
\(143\) −2.02597 −0.169420
\(144\) −1.01959 −0.0849657
\(145\) 0.911191 0.0756703
\(146\) 13.7611 1.13888
\(147\) −2.31080 −0.190591
\(148\) −9.08644 −0.746901
\(149\) −17.2232 −1.41098 −0.705488 0.708722i \(-0.749272\pi\)
−0.705488 + 0.708722i \(0.749272\pi\)
\(150\) −1.40727 −0.114903
\(151\) −12.1174 −0.986097 −0.493048 0.870002i \(-0.664117\pi\)
−0.493048 + 0.870002i \(0.664117\pi\)
\(152\) −1.62864 −0.132100
\(153\) 0.142078 0.0114863
\(154\) 8.05317 0.648943
\(155\) −2.01676 −0.161990
\(156\) −0.819488 −0.0656116
\(157\) −1.41886 −0.113237 −0.0566187 0.998396i \(-0.518032\pi\)
−0.0566187 + 0.998396i \(0.518032\pi\)
\(158\) −4.01383 −0.319323
\(159\) −5.63368 −0.446780
\(160\) 1.00000 0.0790569
\(161\) −7.29467 −0.574900
\(162\) 4.90168 0.385112
\(163\) 12.3056 0.963846 0.481923 0.876213i \(-0.339938\pi\)
0.481923 + 0.876213i \(0.339938\pi\)
\(164\) −10.4730 −0.817804
\(165\) −4.89604 −0.381156
\(166\) 1.94410 0.150891
\(167\) −14.7121 −1.13846 −0.569228 0.822180i \(-0.692758\pi\)
−0.569228 + 0.822180i \(0.692758\pi\)
\(168\) 3.25745 0.251318
\(169\) −12.6609 −0.973915
\(170\) −0.139348 −0.0106875
\(171\) −1.66054 −0.126985
\(172\) 11.6852 0.890987
\(173\) 4.30633 0.327404 0.163702 0.986510i \(-0.447656\pi\)
0.163702 + 0.986510i \(0.447656\pi\)
\(174\) 1.28229 0.0972104
\(175\) −2.31473 −0.174977
\(176\) 3.47910 0.262247
\(177\) −3.70483 −0.278472
\(178\) 5.16178 0.386892
\(179\) −0.127338 −0.00951766 −0.00475883 0.999989i \(-0.501515\pi\)
−0.00475883 + 0.999989i \(0.501515\pi\)
\(180\) 1.01959 0.0759956
\(181\) −20.3487 −1.51251 −0.756254 0.654278i \(-0.772973\pi\)
−0.756254 + 0.654278i \(0.772973\pi\)
\(182\) −1.34792 −0.0999146
\(183\) 9.42617 0.696802
\(184\) −3.15142 −0.232326
\(185\) 9.08644 0.668049
\(186\) −2.83813 −0.208102
\(187\) −0.484806 −0.0354525
\(188\) −0.278443 −0.0203075
\(189\) 13.0936 0.952419
\(190\) 1.62864 0.118154
\(191\) −5.25976 −0.380583 −0.190291 0.981728i \(-0.560943\pi\)
−0.190291 + 0.981728i \(0.560943\pi\)
\(192\) 1.40727 0.101561
\(193\) −25.9563 −1.86837 −0.934187 0.356784i \(-0.883873\pi\)
−0.934187 + 0.356784i \(0.883873\pi\)
\(194\) 3.28753 0.236031
\(195\) 0.819488 0.0586848
\(196\) −1.64204 −0.117289
\(197\) 1.98558 0.141467 0.0707334 0.997495i \(-0.477466\pi\)
0.0707334 + 0.997495i \(0.477466\pi\)
\(198\) 3.54725 0.252092
\(199\) 18.6861 1.32462 0.662311 0.749229i \(-0.269576\pi\)
0.662311 + 0.749229i \(0.269576\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.99762 −0.352505
\(202\) −9.53218 −0.670682
\(203\) 2.10916 0.148034
\(204\) −0.196101 −0.0137298
\(205\) 10.4730 0.731466
\(206\) 7.77644 0.541810
\(207\) −3.21315 −0.223329
\(208\) −0.582324 −0.0403769
\(209\) 5.66620 0.391939
\(210\) −3.25745 −0.224785
\(211\) −17.0537 −1.17403 −0.587014 0.809577i \(-0.699697\pi\)
−0.587014 + 0.809577i \(0.699697\pi\)
\(212\) −4.00326 −0.274945
\(213\) 15.6622 1.07316
\(214\) 10.6438 0.727594
\(215\) −11.6852 −0.796923
\(216\) 5.65665 0.384886
\(217\) −4.66825 −0.316901
\(218\) −3.07843 −0.208498
\(219\) −19.3656 −1.30861
\(220\) −3.47910 −0.234561
\(221\) 0.0811457 0.00545845
\(222\) 12.7871 0.858213
\(223\) 9.44253 0.632318 0.316159 0.948706i \(-0.397607\pi\)
0.316159 + 0.948706i \(0.397607\pi\)
\(224\) 2.31473 0.154659
\(225\) −1.01959 −0.0679725
\(226\) 11.0361 0.734114
\(227\) −28.2941 −1.87795 −0.938974 0.343988i \(-0.888222\pi\)
−0.938974 + 0.343988i \(0.888222\pi\)
\(228\) 2.29194 0.151787
\(229\) −14.5510 −0.961559 −0.480780 0.876841i \(-0.659646\pi\)
−0.480780 + 0.876841i \(0.659646\pi\)
\(230\) 3.15142 0.207798
\(231\) −11.3330 −0.745656
\(232\) 0.911191 0.0598226
\(233\) 5.80631 0.380384 0.190192 0.981747i \(-0.439089\pi\)
0.190192 + 0.981747i \(0.439089\pi\)
\(234\) −0.593731 −0.0388134
\(235\) 0.278443 0.0181636
\(236\) −2.63264 −0.171370
\(237\) 5.64855 0.366913
\(238\) −0.322553 −0.0209080
\(239\) 21.6434 1.40000 0.699998 0.714145i \(-0.253184\pi\)
0.699998 + 0.714145i \(0.253184\pi\)
\(240\) −1.40727 −0.0908390
\(241\) −7.24006 −0.466373 −0.233187 0.972432i \(-0.574915\pi\)
−0.233187 + 0.972432i \(0.574915\pi\)
\(242\) −1.10415 −0.0709777
\(243\) 10.0720 0.646117
\(244\) 6.69819 0.428808
\(245\) 1.64204 0.104906
\(246\) 14.7384 0.939684
\(247\) −0.948396 −0.0603450
\(248\) −2.01676 −0.128064
\(249\) −2.73588 −0.173379
\(250\) 1.00000 0.0632456
\(251\) 15.1467 0.956051 0.478025 0.878346i \(-0.341353\pi\)
0.478025 + 0.878346i \(0.341353\pi\)
\(252\) 2.36007 0.148670
\(253\) 10.9641 0.689307
\(254\) 2.27475 0.142730
\(255\) 0.196101 0.0122803
\(256\) 1.00000 0.0625000
\(257\) 26.3434 1.64325 0.821627 0.570026i \(-0.193067\pi\)
0.821627 + 0.570026i \(0.193067\pi\)
\(258\) −16.4442 −1.02377
\(259\) 21.0326 1.30690
\(260\) 0.582324 0.0361142
\(261\) 0.929039 0.0575061
\(262\) −5.08920 −0.314412
\(263\) −20.9665 −1.29285 −0.646424 0.762978i \(-0.723736\pi\)
−0.646424 + 0.762978i \(0.723736\pi\)
\(264\) −4.89604 −0.301330
\(265\) 4.00326 0.245918
\(266\) 3.76985 0.231145
\(267\) −7.26403 −0.444551
\(268\) −3.55128 −0.216929
\(269\) 7.00564 0.427142 0.213571 0.976928i \(-0.431491\pi\)
0.213571 + 0.976928i \(0.431491\pi\)
\(270\) −5.65665 −0.344253
\(271\) 18.4642 1.12162 0.560809 0.827945i \(-0.310490\pi\)
0.560809 + 0.827945i \(0.310490\pi\)
\(272\) −0.139348 −0.00844922
\(273\) 1.89689 0.114805
\(274\) 3.92866 0.237339
\(275\) 3.47910 0.209798
\(276\) 4.43490 0.266949
\(277\) −32.0109 −1.92335 −0.961674 0.274195i \(-0.911588\pi\)
−0.961674 + 0.274195i \(0.911588\pi\)
\(278\) 17.1248 1.02708
\(279\) −2.05626 −0.123105
\(280\) −2.31473 −0.138331
\(281\) −11.3622 −0.677811 −0.338905 0.940820i \(-0.610057\pi\)
−0.338905 + 0.940820i \(0.610057\pi\)
\(282\) 0.391844 0.0233340
\(283\) 21.2582 1.26367 0.631834 0.775104i \(-0.282302\pi\)
0.631834 + 0.775104i \(0.282302\pi\)
\(284\) 11.1295 0.660415
\(285\) −2.29194 −0.135763
\(286\) 2.02597 0.119798
\(287\) 24.2421 1.43097
\(288\) 1.01959 0.0600798
\(289\) −16.9806 −0.998858
\(290\) −0.911191 −0.0535070
\(291\) −4.62644 −0.271207
\(292\) −13.7611 −0.805308
\(293\) 20.4238 1.19317 0.596586 0.802549i \(-0.296523\pi\)
0.596586 + 0.802549i \(0.296523\pi\)
\(294\) 2.31080 0.134769
\(295\) 2.63264 0.153278
\(296\) 9.08644 0.528139
\(297\) −19.6801 −1.14195
\(298\) 17.2232 0.997711
\(299\) −1.83515 −0.106129
\(300\) 1.40727 0.0812488
\(301\) −27.0480 −1.55902
\(302\) 12.1174 0.697276
\(303\) 13.4144 0.770635
\(304\) 1.62864 0.0934089
\(305\) −6.69819 −0.383537
\(306\) −0.142078 −0.00812203
\(307\) −20.7595 −1.18481 −0.592405 0.805640i \(-0.701821\pi\)
−0.592405 + 0.805640i \(0.701821\pi\)
\(308\) −8.05317 −0.458872
\(309\) −10.9436 −0.622557
\(310\) 2.01676 0.114544
\(311\) 20.4833 1.16150 0.580752 0.814080i \(-0.302759\pi\)
0.580752 + 0.814080i \(0.302759\pi\)
\(312\) 0.819488 0.0463944
\(313\) 19.4038 1.09677 0.548383 0.836227i \(-0.315244\pi\)
0.548383 + 0.836227i \(0.315244\pi\)
\(314\) 1.41886 0.0800709
\(315\) −2.36007 −0.132975
\(316\) 4.01383 0.225796
\(317\) 13.3472 0.749652 0.374826 0.927095i \(-0.377702\pi\)
0.374826 + 0.927095i \(0.377702\pi\)
\(318\) 5.63368 0.315921
\(319\) −3.17013 −0.177493
\(320\) −1.00000 −0.0559017
\(321\) −14.9787 −0.836029
\(322\) 7.29467 0.406516
\(323\) −0.226948 −0.0126277
\(324\) −4.90168 −0.272315
\(325\) −0.582324 −0.0323015
\(326\) −12.3056 −0.681542
\(327\) 4.33219 0.239571
\(328\) 10.4730 0.578275
\(329\) 0.644519 0.0355335
\(330\) 4.89604 0.269518
\(331\) −15.3821 −0.845477 −0.422738 0.906252i \(-0.638931\pi\)
−0.422738 + 0.906252i \(0.638931\pi\)
\(332\) −1.94410 −0.106696
\(333\) 9.26443 0.507687
\(334\) 14.7121 0.805010
\(335\) 3.55128 0.194027
\(336\) −3.25745 −0.177708
\(337\) 6.72138 0.366137 0.183068 0.983100i \(-0.441397\pi\)
0.183068 + 0.983100i \(0.441397\pi\)
\(338\) 12.6609 0.688662
\(339\) −15.5309 −0.843520
\(340\) 0.139348 0.00755721
\(341\) 7.01652 0.379966
\(342\) 1.66054 0.0897918
\(343\) 20.0040 1.08011
\(344\) −11.6852 −0.630023
\(345\) −4.43490 −0.238767
\(346\) −4.30633 −0.231510
\(347\) −17.7250 −0.951527 −0.475763 0.879573i \(-0.657828\pi\)
−0.475763 + 0.879573i \(0.657828\pi\)
\(348\) −1.28229 −0.0687381
\(349\) 32.0292 1.71448 0.857242 0.514913i \(-0.172176\pi\)
0.857242 + 0.514913i \(0.172176\pi\)
\(350\) 2.31473 0.123727
\(351\) 3.29400 0.175821
\(352\) −3.47910 −0.185437
\(353\) −19.3684 −1.03087 −0.515437 0.856928i \(-0.672370\pi\)
−0.515437 + 0.856928i \(0.672370\pi\)
\(354\) 3.70483 0.196910
\(355\) −11.1295 −0.590693
\(356\) −5.16178 −0.273574
\(357\) 0.453919 0.0240239
\(358\) 0.127338 0.00673000
\(359\) 27.2501 1.43821 0.719103 0.694904i \(-0.244553\pi\)
0.719103 + 0.694904i \(0.244553\pi\)
\(360\) −1.01959 −0.0537370
\(361\) −16.3475 −0.860397
\(362\) 20.3487 1.06951
\(363\) 1.55384 0.0815557
\(364\) 1.34792 0.0706503
\(365\) 13.7611 0.720289
\(366\) −9.42617 −0.492714
\(367\) −11.7183 −0.611689 −0.305845 0.952081i \(-0.598939\pi\)
−0.305845 + 0.952081i \(0.598939\pi\)
\(368\) 3.15142 0.164279
\(369\) 10.6781 0.555882
\(370\) −9.08644 −0.472382
\(371\) 9.26646 0.481091
\(372\) 2.83813 0.147150
\(373\) −9.29599 −0.481328 −0.240664 0.970608i \(-0.577365\pi\)
−0.240664 + 0.970608i \(0.577365\pi\)
\(374\) 0.484806 0.0250687
\(375\) −1.40727 −0.0726712
\(376\) 0.278443 0.0143596
\(377\) 0.530609 0.0273277
\(378\) −13.0936 −0.673462
\(379\) 10.2709 0.527582 0.263791 0.964580i \(-0.415027\pi\)
0.263791 + 0.964580i \(0.415027\pi\)
\(380\) −1.62864 −0.0835474
\(381\) −3.20119 −0.164002
\(382\) 5.25976 0.269112
\(383\) −30.2413 −1.54526 −0.772630 0.634857i \(-0.781059\pi\)
−0.772630 + 0.634857i \(0.781059\pi\)
\(384\) −1.40727 −0.0718145
\(385\) 8.05317 0.410428
\(386\) 25.9563 1.32114
\(387\) −11.9141 −0.605626
\(388\) −3.28753 −0.166899
\(389\) 24.9976 1.26743 0.633714 0.773567i \(-0.281529\pi\)
0.633714 + 0.773567i \(0.281529\pi\)
\(390\) −0.819488 −0.0414964
\(391\) −0.439144 −0.0222085
\(392\) 1.64204 0.0829356
\(393\) 7.16188 0.361269
\(394\) −1.98558 −0.100032
\(395\) −4.01383 −0.201958
\(396\) −3.54725 −0.178256
\(397\) −5.29439 −0.265718 −0.132859 0.991135i \(-0.542416\pi\)
−0.132859 + 0.991135i \(0.542416\pi\)
\(398\) −18.6861 −0.936649
\(399\) −5.30521 −0.265593
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 4.99762 0.249259
\(403\) −1.17441 −0.0585015
\(404\) 9.53218 0.474244
\(405\) 4.90168 0.243566
\(406\) −2.10916 −0.104676
\(407\) −31.6127 −1.56698
\(408\) 0.196101 0.00970842
\(409\) −9.22127 −0.455962 −0.227981 0.973666i \(-0.573212\pi\)
−0.227981 + 0.973666i \(0.573212\pi\)
\(410\) −10.4730 −0.517225
\(411\) −5.52869 −0.272710
\(412\) −7.77644 −0.383118
\(413\) 6.09383 0.299858
\(414\) 3.21315 0.157918
\(415\) 1.94410 0.0954322
\(416\) 0.582324 0.0285508
\(417\) −24.0993 −1.18015
\(418\) −5.66620 −0.277143
\(419\) −4.10376 −0.200482 −0.100241 0.994963i \(-0.531961\pi\)
−0.100241 + 0.994963i \(0.531961\pi\)
\(420\) 3.25745 0.158947
\(421\) 10.7992 0.526321 0.263161 0.964752i \(-0.415235\pi\)
0.263161 + 0.964752i \(0.415235\pi\)
\(422\) 17.0537 0.830163
\(423\) 0.283897 0.0138035
\(424\) 4.00326 0.194416
\(425\) −0.139348 −0.00675937
\(426\) −15.6622 −0.758838
\(427\) −15.5045 −0.750314
\(428\) −10.6438 −0.514487
\(429\) −2.85108 −0.137652
\(430\) 11.6852 0.563510
\(431\) 5.24419 0.252604 0.126302 0.991992i \(-0.459689\pi\)
0.126302 + 0.991992i \(0.459689\pi\)
\(432\) −5.65665 −0.272156
\(433\) −29.1625 −1.40146 −0.700729 0.713427i \(-0.747142\pi\)
−0.700729 + 0.713427i \(0.747142\pi\)
\(434\) 4.66825 0.224083
\(435\) 1.28229 0.0614812
\(436\) 3.07843 0.147430
\(437\) 5.13252 0.245522
\(438\) 19.3656 0.925325
\(439\) −30.0804 −1.43566 −0.717830 0.696219i \(-0.754864\pi\)
−0.717830 + 0.696219i \(0.754864\pi\)
\(440\) 3.47910 0.165860
\(441\) 1.67421 0.0797241
\(442\) −0.0811457 −0.00385971
\(443\) 2.12105 0.100774 0.0503872 0.998730i \(-0.483954\pi\)
0.0503872 + 0.998730i \(0.483954\pi\)
\(444\) −12.7871 −0.606848
\(445\) 5.16178 0.244692
\(446\) −9.44253 −0.447117
\(447\) −24.2377 −1.14640
\(448\) −2.31473 −0.109361
\(449\) −4.81533 −0.227250 −0.113625 0.993524i \(-0.536246\pi\)
−0.113625 + 0.993524i \(0.536246\pi\)
\(450\) 1.01959 0.0480638
\(451\) −36.4367 −1.71574
\(452\) −11.0361 −0.519097
\(453\) −17.0524 −0.801192
\(454\) 28.2941 1.32791
\(455\) −1.34792 −0.0631915
\(456\) −2.29194 −0.107330
\(457\) −8.69990 −0.406964 −0.203482 0.979079i \(-0.565226\pi\)
−0.203482 + 0.979079i \(0.565226\pi\)
\(458\) 14.5510 0.679925
\(459\) 0.788243 0.0367920
\(460\) −3.15142 −0.146936
\(461\) 19.0132 0.885532 0.442766 0.896637i \(-0.353997\pi\)
0.442766 + 0.896637i \(0.353997\pi\)
\(462\) 11.3330 0.527259
\(463\) −27.2544 −1.26662 −0.633311 0.773898i \(-0.718304\pi\)
−0.633311 + 0.773898i \(0.718304\pi\)
\(464\) −0.911191 −0.0423010
\(465\) −2.83813 −0.131615
\(466\) −5.80631 −0.268972
\(467\) 17.2210 0.796893 0.398447 0.917192i \(-0.369549\pi\)
0.398447 + 0.917192i \(0.369549\pi\)
\(468\) 0.593731 0.0274452
\(469\) 8.22025 0.379576
\(470\) −0.278443 −0.0128436
\(471\) −1.99672 −0.0920040
\(472\) 2.63264 0.121177
\(473\) 40.6540 1.86927
\(474\) −5.64855 −0.259446
\(475\) 1.62864 0.0747271
\(476\) 0.322553 0.0147842
\(477\) 4.08168 0.186887
\(478\) −21.6434 −0.989947
\(479\) 37.8840 1.73096 0.865482 0.500940i \(-0.167012\pi\)
0.865482 + 0.500940i \(0.167012\pi\)
\(480\) 1.40727 0.0642328
\(481\) 5.29126 0.241260
\(482\) 7.24006 0.329776
\(483\) −10.2656 −0.467100
\(484\) 1.10415 0.0501888
\(485\) 3.28753 0.149279
\(486\) −10.0720 −0.456873
\(487\) 14.9895 0.679241 0.339621 0.940563i \(-0.389701\pi\)
0.339621 + 0.940563i \(0.389701\pi\)
\(488\) −6.69819 −0.303213
\(489\) 17.3173 0.783114
\(490\) −1.64204 −0.0741799
\(491\) 16.8228 0.759203 0.379601 0.925150i \(-0.376061\pi\)
0.379601 + 0.925150i \(0.376061\pi\)
\(492\) −14.7384 −0.664457
\(493\) 0.126973 0.00571856
\(494\) 0.948396 0.0426704
\(495\) 3.54725 0.159437
\(496\) 2.01676 0.0905552
\(497\) −25.7618 −1.15557
\(498\) 2.73588 0.122598
\(499\) 5.83436 0.261182 0.130591 0.991436i \(-0.458313\pi\)
0.130591 + 0.991436i \(0.458313\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −20.7039 −0.924983
\(502\) −15.1467 −0.676030
\(503\) 30.0823 1.34130 0.670651 0.741773i \(-0.266015\pi\)
0.670651 + 0.741773i \(0.266015\pi\)
\(504\) −2.36007 −0.105126
\(505\) −9.53218 −0.424177
\(506\) −10.9641 −0.487414
\(507\) −17.8173 −0.791295
\(508\) −2.27475 −0.100926
\(509\) −3.74020 −0.165781 −0.0828906 0.996559i \(-0.526415\pi\)
−0.0828906 + 0.996559i \(0.526415\pi\)
\(510\) −0.196101 −0.00868348
\(511\) 31.8532 1.40910
\(512\) −1.00000 −0.0441942
\(513\) −9.21264 −0.406748
\(514\) −26.3434 −1.16196
\(515\) 7.77644 0.342671
\(516\) 16.4442 0.723917
\(517\) −0.968730 −0.0426047
\(518\) −21.0326 −0.924121
\(519\) 6.06018 0.266012
\(520\) −0.582324 −0.0255366
\(521\) −9.55314 −0.418531 −0.209265 0.977859i \(-0.567107\pi\)
−0.209265 + 0.977859i \(0.567107\pi\)
\(522\) −0.929039 −0.0406629
\(523\) −18.6976 −0.817589 −0.408795 0.912626i \(-0.634051\pi\)
−0.408795 + 0.912626i \(0.634051\pi\)
\(524\) 5.08920 0.222323
\(525\) −3.25745 −0.142167
\(526\) 20.9665 0.914182
\(527\) −0.281032 −0.0122419
\(528\) 4.89604 0.213073
\(529\) −13.0686 −0.568199
\(530\) −4.00326 −0.173891
\(531\) 2.68420 0.116485
\(532\) −3.76985 −0.163444
\(533\) 6.09869 0.264163
\(534\) 7.26403 0.314345
\(535\) 10.6438 0.460171
\(536\) 3.55128 0.153392
\(537\) −0.179198 −0.00773299
\(538\) −7.00564 −0.302035
\(539\) −5.71283 −0.246069
\(540\) 5.65665 0.243423
\(541\) −17.8749 −0.768500 −0.384250 0.923229i \(-0.625540\pi\)
−0.384250 + 0.923229i \(0.625540\pi\)
\(542\) −18.4642 −0.793103
\(543\) −28.6362 −1.22890
\(544\) 0.139348 0.00597450
\(545\) −3.07843 −0.131866
\(546\) −1.89689 −0.0811794
\(547\) −12.0523 −0.515317 −0.257659 0.966236i \(-0.582951\pi\)
−0.257659 + 0.966236i \(0.582951\pi\)
\(548\) −3.92866 −0.167824
\(549\) −6.82939 −0.291471
\(550\) −3.47910 −0.148349
\(551\) −1.48400 −0.0632206
\(552\) −4.43490 −0.188762
\(553\) −9.29092 −0.395090
\(554\) 32.0109 1.36001
\(555\) 12.7871 0.542782
\(556\) −17.1248 −0.726255
\(557\) −30.6283 −1.29776 −0.648882 0.760889i \(-0.724763\pi\)
−0.648882 + 0.760889i \(0.724763\pi\)
\(558\) 2.05626 0.0870486
\(559\) −6.80457 −0.287802
\(560\) 2.31473 0.0978150
\(561\) −0.682254 −0.0288048
\(562\) 11.3622 0.479285
\(563\) 3.75483 0.158247 0.0791236 0.996865i \(-0.474788\pi\)
0.0791236 + 0.996865i \(0.474788\pi\)
\(564\) −0.391844 −0.0164996
\(565\) 11.0361 0.464294
\(566\) −21.2582 −0.893548
\(567\) 11.3460 0.476489
\(568\) −11.1295 −0.466984
\(569\) −0.517257 −0.0216845 −0.0108423 0.999941i \(-0.503451\pi\)
−0.0108423 + 0.999941i \(0.503451\pi\)
\(570\) 2.29194 0.0959987
\(571\) −1.99557 −0.0835120 −0.0417560 0.999128i \(-0.513295\pi\)
−0.0417560 + 0.999128i \(0.513295\pi\)
\(572\) −2.02597 −0.0847099
\(573\) −7.40190 −0.309219
\(574\) −24.2421 −1.01185
\(575\) 3.15142 0.131423
\(576\) −1.01959 −0.0424828
\(577\) −1.09999 −0.0457934 −0.0228967 0.999738i \(-0.507289\pi\)
−0.0228967 + 0.999738i \(0.507289\pi\)
\(578\) 16.9806 0.706299
\(579\) −36.5275 −1.51803
\(580\) 0.911191 0.0378352
\(581\) 4.50006 0.186694
\(582\) 4.62644 0.191772
\(583\) −13.9278 −0.576829
\(584\) 13.7611 0.569439
\(585\) −0.593731 −0.0245477
\(586\) −20.4238 −0.843700
\(587\) 43.8254 1.80887 0.904433 0.426616i \(-0.140294\pi\)
0.904433 + 0.426616i \(0.140294\pi\)
\(588\) −2.31080 −0.0952957
\(589\) 3.28458 0.135339
\(590\) −2.63264 −0.108384
\(591\) 2.79425 0.114940
\(592\) −9.08644 −0.373451
\(593\) −6.60596 −0.271274 −0.135637 0.990759i \(-0.543308\pi\)
−0.135637 + 0.990759i \(0.543308\pi\)
\(594\) 19.6801 0.807483
\(595\) −0.322553 −0.0132234
\(596\) −17.2232 −0.705488
\(597\) 26.2964 1.07624
\(598\) 1.83515 0.0750447
\(599\) −21.6376 −0.884087 −0.442044 0.896994i \(-0.645746\pi\)
−0.442044 + 0.896994i \(0.645746\pi\)
\(600\) −1.40727 −0.0574516
\(601\) 21.8802 0.892512 0.446256 0.894905i \(-0.352757\pi\)
0.446256 + 0.894905i \(0.352757\pi\)
\(602\) 27.0480 1.10239
\(603\) 3.62085 0.147452
\(604\) −12.1174 −0.493048
\(605\) −1.10415 −0.0448902
\(606\) −13.4144 −0.544921
\(607\) 10.1609 0.412419 0.206210 0.978508i \(-0.433887\pi\)
0.206210 + 0.978508i \(0.433887\pi\)
\(608\) −1.62864 −0.0660500
\(609\) 2.96816 0.120276
\(610\) 6.69819 0.271202
\(611\) 0.162144 0.00655964
\(612\) 0.142078 0.00574315
\(613\) −7.86797 −0.317784 −0.158892 0.987296i \(-0.550792\pi\)
−0.158892 + 0.987296i \(0.550792\pi\)
\(614\) 20.7595 0.837787
\(615\) 14.7384 0.594308
\(616\) 8.05317 0.324471
\(617\) −16.2628 −0.654715 −0.327358 0.944900i \(-0.606158\pi\)
−0.327358 + 0.944900i \(0.606158\pi\)
\(618\) 10.9436 0.440215
\(619\) −17.9336 −0.720814 −0.360407 0.932795i \(-0.617362\pi\)
−0.360407 + 0.932795i \(0.617362\pi\)
\(620\) −2.01676 −0.0809951
\(621\) −17.8265 −0.715351
\(622\) −20.4833 −0.821307
\(623\) 11.9481 0.478691
\(624\) −0.819488 −0.0328058
\(625\) 1.00000 0.0400000
\(626\) −19.4038 −0.775531
\(627\) 7.97388 0.318446
\(628\) −1.41886 −0.0566187
\(629\) 1.26618 0.0504858
\(630\) 2.36007 0.0940273
\(631\) −18.5889 −0.740013 −0.370006 0.929029i \(-0.620645\pi\)
−0.370006 + 0.929029i \(0.620645\pi\)
\(632\) −4.01383 −0.159662
\(633\) −23.9992 −0.953884
\(634\) −13.3472 −0.530084
\(635\) 2.27475 0.0902706
\(636\) −5.63368 −0.223390
\(637\) 0.956201 0.0378861
\(638\) 3.17013 0.125507
\(639\) −11.3475 −0.448900
\(640\) 1.00000 0.0395285
\(641\) −12.9876 −0.512981 −0.256490 0.966547i \(-0.582566\pi\)
−0.256490 + 0.966547i \(0.582566\pi\)
\(642\) 14.9787 0.591162
\(643\) 45.4288 1.79154 0.895769 0.444520i \(-0.146626\pi\)
0.895769 + 0.444520i \(0.146626\pi\)
\(644\) −7.29467 −0.287450
\(645\) −16.4442 −0.647491
\(646\) 0.226948 0.00892914
\(647\) −44.9252 −1.76619 −0.883097 0.469191i \(-0.844546\pi\)
−0.883097 + 0.469191i \(0.844546\pi\)
\(648\) 4.90168 0.192556
\(649\) −9.15921 −0.359530
\(650\) 0.582324 0.0228406
\(651\) −6.56949 −0.257479
\(652\) 12.3056 0.481923
\(653\) 6.82076 0.266917 0.133459 0.991054i \(-0.457392\pi\)
0.133459 + 0.991054i \(0.457392\pi\)
\(654\) −4.33219 −0.169402
\(655\) −5.08920 −0.198851
\(656\) −10.4730 −0.408902
\(657\) 14.0307 0.547388
\(658\) −0.644519 −0.0251259
\(659\) 29.0943 1.13335 0.566676 0.823941i \(-0.308229\pi\)
0.566676 + 0.823941i \(0.308229\pi\)
\(660\) −4.89604 −0.190578
\(661\) 13.2971 0.517195 0.258598 0.965985i \(-0.416740\pi\)
0.258598 + 0.965985i \(0.416740\pi\)
\(662\) 15.3821 0.597842
\(663\) 0.114194 0.00443493
\(664\) 1.94410 0.0754457
\(665\) 3.76985 0.146189
\(666\) −9.26443 −0.358989
\(667\) −2.87154 −0.111187
\(668\) −14.7121 −0.569228
\(669\) 13.2882 0.513751
\(670\) −3.55128 −0.137198
\(671\) 23.3037 0.899629
\(672\) 3.25745 0.125659
\(673\) 42.0441 1.62068 0.810341 0.585958i \(-0.199282\pi\)
0.810341 + 0.585958i \(0.199282\pi\)
\(674\) −6.72138 −0.258898
\(675\) −5.65665 −0.217725
\(676\) −12.6609 −0.486958
\(677\) 34.3850 1.32152 0.660761 0.750597i \(-0.270234\pi\)
0.660761 + 0.750597i \(0.270234\pi\)
\(678\) 15.5309 0.596459
\(679\) 7.60973 0.292035
\(680\) −0.139348 −0.00534375
\(681\) −39.8175 −1.52581
\(682\) −7.01652 −0.268676
\(683\) −23.0199 −0.880834 −0.440417 0.897793i \(-0.645169\pi\)
−0.440417 + 0.897793i \(0.645169\pi\)
\(684\) −1.66054 −0.0634924
\(685\) 3.92866 0.150106
\(686\) −20.0040 −0.763755
\(687\) −20.4772 −0.781256
\(688\) 11.6852 0.445494
\(689\) 2.33120 0.0888115
\(690\) 4.43490 0.168834
\(691\) −40.1220 −1.52631 −0.763157 0.646213i \(-0.776352\pi\)
−0.763157 + 0.646213i \(0.776352\pi\)
\(692\) 4.30633 0.163702
\(693\) 8.21091 0.311907
\(694\) 17.7250 0.672831
\(695\) 17.1248 0.649582
\(696\) 1.28229 0.0486052
\(697\) 1.45939 0.0552785
\(698\) −32.0292 −1.21232
\(699\) 8.17106 0.309058
\(700\) −2.31473 −0.0874884
\(701\) 31.6800 1.19654 0.598269 0.801295i \(-0.295855\pi\)
0.598269 + 0.801295i \(0.295855\pi\)
\(702\) −3.29400 −0.124324
\(703\) −14.7985 −0.558137
\(704\) 3.47910 0.131124
\(705\) 0.391844 0.0147577
\(706\) 19.3684 0.728938
\(707\) −22.0644 −0.829817
\(708\) −3.70483 −0.139236
\(709\) −2.44345 −0.0917656 −0.0458828 0.998947i \(-0.514610\pi\)
−0.0458828 + 0.998947i \(0.514610\pi\)
\(710\) 11.1295 0.417683
\(711\) −4.09245 −0.153479
\(712\) 5.16178 0.193446
\(713\) 6.35565 0.238021
\(714\) −0.453919 −0.0169875
\(715\) 2.02597 0.0757668
\(716\) −0.127338 −0.00475883
\(717\) 30.4582 1.13748
\(718\) −27.2501 −1.01697
\(719\) −6.45604 −0.240770 −0.120385 0.992727i \(-0.538413\pi\)
−0.120385 + 0.992727i \(0.538413\pi\)
\(720\) 1.01959 0.0379978
\(721\) 18.0003 0.670367
\(722\) 16.3475 0.608392
\(723\) −10.1887 −0.378923
\(724\) −20.3487 −0.756254
\(725\) −0.911191 −0.0338408
\(726\) −1.55384 −0.0576686
\(727\) −27.4239 −1.01710 −0.508549 0.861033i \(-0.669818\pi\)
−0.508549 + 0.861033i \(0.669818\pi\)
\(728\) −1.34792 −0.0499573
\(729\) 28.8790 1.06959
\(730\) −13.7611 −0.509321
\(731\) −1.62831 −0.0602251
\(732\) 9.42617 0.348401
\(733\) −22.7244 −0.839346 −0.419673 0.907675i \(-0.637855\pi\)
−0.419673 + 0.907675i \(0.637855\pi\)
\(734\) 11.7183 0.432530
\(735\) 2.31080 0.0852351
\(736\) −3.15142 −0.116163
\(737\) −12.3553 −0.455113
\(738\) −10.6781 −0.393068
\(739\) −10.8263 −0.398250 −0.199125 0.979974i \(-0.563810\pi\)
−0.199125 + 0.979974i \(0.563810\pi\)
\(740\) 9.08644 0.334024
\(741\) −1.33465 −0.0490296
\(742\) −9.26646 −0.340182
\(743\) 28.6781 1.05210 0.526050 0.850454i \(-0.323673\pi\)
0.526050 + 0.850454i \(0.323673\pi\)
\(744\) −2.83813 −0.104051
\(745\) 17.2232 0.631008
\(746\) 9.29599 0.340350
\(747\) 1.98218 0.0725242
\(748\) −0.484806 −0.0177263
\(749\) 24.6375 0.900233
\(750\) 1.40727 0.0513863
\(751\) 25.4867 0.930022 0.465011 0.885305i \(-0.346050\pi\)
0.465011 + 0.885305i \(0.346050\pi\)
\(752\) −0.278443 −0.0101538
\(753\) 21.3155 0.776780
\(754\) −0.530609 −0.0193236
\(755\) 12.1174 0.440996
\(756\) 13.0936 0.476210
\(757\) −16.2588 −0.590935 −0.295467 0.955353i \(-0.595475\pi\)
−0.295467 + 0.955353i \(0.595475\pi\)
\(758\) −10.2709 −0.373057
\(759\) 15.4295 0.560054
\(760\) 1.62864 0.0590770
\(761\) 41.5505 1.50621 0.753103 0.657903i \(-0.228556\pi\)
0.753103 + 0.657903i \(0.228556\pi\)
\(762\) 3.20119 0.115967
\(763\) −7.12573 −0.257969
\(764\) −5.25976 −0.190291
\(765\) −0.142078 −0.00513683
\(766\) 30.2413 1.09266
\(767\) 1.53305 0.0553551
\(768\) 1.40727 0.0507805
\(769\) 17.6390 0.636080 0.318040 0.948077i \(-0.396975\pi\)
0.318040 + 0.948077i \(0.396975\pi\)
\(770\) −8.05317 −0.290216
\(771\) 37.0722 1.33512
\(772\) −25.9563 −0.934187
\(773\) 18.9896 0.683007 0.341504 0.939880i \(-0.389064\pi\)
0.341504 + 0.939880i \(0.389064\pi\)
\(774\) 11.9141 0.428242
\(775\) 2.01676 0.0724442
\(776\) 3.28753 0.118015
\(777\) 29.5986 1.06184
\(778\) −24.9976 −0.896207
\(779\) −17.0567 −0.611121
\(780\) 0.819488 0.0293424
\(781\) 38.7207 1.38554
\(782\) 0.439144 0.0157038
\(783\) 5.15429 0.184199
\(784\) −1.64204 −0.0586444
\(785\) 1.41886 0.0506413
\(786\) −7.16188 −0.255456
\(787\) 20.7331 0.739057 0.369528 0.929219i \(-0.379519\pi\)
0.369528 + 0.929219i \(0.379519\pi\)
\(788\) 1.98558 0.0707334
\(789\) −29.5055 −1.05042
\(790\) 4.01383 0.142806
\(791\) 25.5457 0.908299
\(792\) 3.54725 0.126046
\(793\) −3.90052 −0.138511
\(794\) 5.29439 0.187891
\(795\) 5.63368 0.199806
\(796\) 18.6861 0.662311
\(797\) 40.1774 1.42316 0.711578 0.702607i \(-0.247981\pi\)
0.711578 + 0.702607i \(0.247981\pi\)
\(798\) 5.30521 0.187802
\(799\) 0.0388004 0.00137266
\(800\) −1.00000 −0.0353553
\(801\) 5.26289 0.185955
\(802\) 1.00000 0.0353112
\(803\) −47.8763 −1.68952
\(804\) −4.99762 −0.176252
\(805\) 7.29467 0.257103
\(806\) 1.17441 0.0413668
\(807\) 9.85884 0.347048
\(808\) −9.53218 −0.335341
\(809\) 7.41283 0.260621 0.130311 0.991473i \(-0.458403\pi\)
0.130311 + 0.991473i \(0.458403\pi\)
\(810\) −4.90168 −0.172227
\(811\) 27.0990 0.951575 0.475788 0.879560i \(-0.342163\pi\)
0.475788 + 0.879560i \(0.342163\pi\)
\(812\) 2.10916 0.0740169
\(813\) 25.9841 0.911301
\(814\) 31.6127 1.10802
\(815\) −12.3056 −0.431045
\(816\) −0.196101 −0.00686489
\(817\) 19.0310 0.665809
\(818\) 9.22127 0.322414
\(819\) −1.37432 −0.0480228
\(820\) 10.4730 0.365733
\(821\) 1.85828 0.0648546 0.0324273 0.999474i \(-0.489676\pi\)
0.0324273 + 0.999474i \(0.489676\pi\)
\(822\) 5.52869 0.192835
\(823\) 7.92084 0.276103 0.138052 0.990425i \(-0.455916\pi\)
0.138052 + 0.990425i \(0.455916\pi\)
\(824\) 7.77644 0.270905
\(825\) 4.89604 0.170458
\(826\) −6.09383 −0.212032
\(827\) 48.5583 1.68854 0.844269 0.535920i \(-0.180035\pi\)
0.844269 + 0.535920i \(0.180035\pi\)
\(828\) −3.21315 −0.111665
\(829\) 22.5846 0.784397 0.392198 0.919881i \(-0.371715\pi\)
0.392198 + 0.919881i \(0.371715\pi\)
\(830\) −1.94410 −0.0674807
\(831\) −45.0480 −1.56270
\(832\) −0.582324 −0.0201885
\(833\) 0.228815 0.00792798
\(834\) 24.0993 0.834490
\(835\) 14.7121 0.509133
\(836\) 5.66620 0.195970
\(837\) −11.4081 −0.394322
\(838\) 4.10376 0.141762
\(839\) 6.52784 0.225366 0.112683 0.993631i \(-0.464056\pi\)
0.112683 + 0.993631i \(0.464056\pi\)
\(840\) −3.25745 −0.112393
\(841\) −28.1697 −0.971370
\(842\) −10.7992 −0.372165
\(843\) −15.9897 −0.550713
\(844\) −17.0537 −0.587014
\(845\) 12.6609 0.435548
\(846\) −0.283897 −0.00976057
\(847\) −2.55581 −0.0878188
\(848\) −4.00326 −0.137473
\(849\) 29.9160 1.02672
\(850\) 0.139348 0.00477960
\(851\) −28.6352 −0.981601
\(852\) 15.6622 0.536579
\(853\) −34.4213 −1.17856 −0.589282 0.807927i \(-0.700589\pi\)
−0.589282 + 0.807927i \(0.700589\pi\)
\(854\) 15.5045 0.530552
\(855\) 1.66054 0.0567893
\(856\) 10.6438 0.363797
\(857\) −26.6137 −0.909105 −0.454552 0.890720i \(-0.650201\pi\)
−0.454552 + 0.890720i \(0.650201\pi\)
\(858\) 2.85108 0.0973344
\(859\) 56.3500 1.92264 0.961318 0.275441i \(-0.0888240\pi\)
0.961318 + 0.275441i \(0.0888240\pi\)
\(860\) −11.6852 −0.398462
\(861\) 34.1153 1.16265
\(862\) −5.24419 −0.178618
\(863\) −30.1071 −1.02486 −0.512428 0.858730i \(-0.671254\pi\)
−0.512428 + 0.858730i \(0.671254\pi\)
\(864\) 5.65665 0.192443
\(865\) −4.30633 −0.146420
\(866\) 29.1625 0.990981
\(867\) −23.8963 −0.811560
\(868\) −4.66825 −0.158451
\(869\) 13.9645 0.473714
\(870\) −1.28229 −0.0434738
\(871\) 2.06800 0.0700715
\(872\) −3.07843 −0.104249
\(873\) 3.35192 0.113445
\(874\) −5.13252 −0.173610
\(875\) 2.31473 0.0782520
\(876\) −19.3656 −0.654303
\(877\) −12.6241 −0.426286 −0.213143 0.977021i \(-0.568370\pi\)
−0.213143 + 0.977021i \(0.568370\pi\)
\(878\) 30.0804 1.01516
\(879\) 28.7419 0.969439
\(880\) −3.47910 −0.117281
\(881\) −41.3783 −1.39407 −0.697036 0.717036i \(-0.745498\pi\)
−0.697036 + 0.717036i \(0.745498\pi\)
\(882\) −1.67421 −0.0563734
\(883\) 32.1412 1.08164 0.540819 0.841139i \(-0.318114\pi\)
0.540819 + 0.841139i \(0.318114\pi\)
\(884\) 0.0811457 0.00272923
\(885\) 3.70483 0.124537
\(886\) −2.12105 −0.0712582
\(887\) −19.6729 −0.660552 −0.330276 0.943884i \(-0.607142\pi\)
−0.330276 + 0.943884i \(0.607142\pi\)
\(888\) 12.7871 0.429107
\(889\) 5.26542 0.176596
\(890\) −5.16178 −0.173023
\(891\) −17.0534 −0.571312
\(892\) 9.44253 0.316159
\(893\) −0.453483 −0.0151752
\(894\) 24.2377 0.810629
\(895\) 0.127338 0.00425643
\(896\) 2.31473 0.0773296
\(897\) −2.58255 −0.0862288
\(898\) 4.81533 0.160690
\(899\) −1.83765 −0.0612892
\(900\) −1.01959 −0.0339863
\(901\) 0.557847 0.0185846
\(902\) 36.4367 1.21321
\(903\) −38.0639 −1.26669
\(904\) 11.0361 0.367057
\(905\) 20.3487 0.676414
\(906\) 17.0524 0.566528
\(907\) 32.5781 1.08174 0.540869 0.841107i \(-0.318095\pi\)
0.540869 + 0.841107i \(0.318095\pi\)
\(908\) −28.2941 −0.938974
\(909\) −9.71890 −0.322355
\(910\) 1.34792 0.0446832
\(911\) −36.2667 −1.20157 −0.600785 0.799410i \(-0.705145\pi\)
−0.600785 + 0.799410i \(0.705145\pi\)
\(912\) 2.29194 0.0758936
\(913\) −6.76373 −0.223847
\(914\) 8.69990 0.287767
\(915\) −9.42617 −0.311620
\(916\) −14.5510 −0.480780
\(917\) −11.7801 −0.389013
\(918\) −0.788243 −0.0260159
\(919\) 41.2652 1.36121 0.680607 0.732649i \(-0.261716\pi\)
0.680607 + 0.732649i \(0.261716\pi\)
\(920\) 3.15142 0.103899
\(921\) −29.2143 −0.962644
\(922\) −19.0132 −0.626165
\(923\) −6.48098 −0.213324
\(924\) −11.3330 −0.372828
\(925\) −9.08644 −0.298760
\(926\) 27.2544 0.895637
\(927\) 7.92876 0.260415
\(928\) 0.911191 0.0299113
\(929\) 37.5042 1.23047 0.615236 0.788343i \(-0.289061\pi\)
0.615236 + 0.788343i \(0.289061\pi\)
\(930\) 2.83813 0.0930659
\(931\) −2.67429 −0.0876464
\(932\) 5.80631 0.190192
\(933\) 28.8256 0.943709
\(934\) −17.2210 −0.563488
\(935\) 0.484806 0.0158549
\(936\) −0.593731 −0.0194067
\(937\) 7.29612 0.238354 0.119177 0.992873i \(-0.461974\pi\)
0.119177 + 0.992873i \(0.461974\pi\)
\(938\) −8.22025 −0.268401
\(939\) 27.3064 0.891110
\(940\) 0.278443 0.00908180
\(941\) 28.6884 0.935214 0.467607 0.883936i \(-0.345116\pi\)
0.467607 + 0.883936i \(0.345116\pi\)
\(942\) 1.99672 0.0650567
\(943\) −33.0048 −1.07478
\(944\) −2.63264 −0.0856850
\(945\) −13.0936 −0.425935
\(946\) −40.6540 −1.32177
\(947\) 54.3429 1.76591 0.882953 0.469461i \(-0.155552\pi\)
0.882953 + 0.469461i \(0.155552\pi\)
\(948\) 5.64855 0.183456
\(949\) 8.01343 0.260127
\(950\) −1.62864 −0.0528400
\(951\) 18.7831 0.609084
\(952\) −0.322553 −0.0104540
\(953\) −13.0826 −0.423787 −0.211893 0.977293i \(-0.567963\pi\)
−0.211893 + 0.977293i \(0.567963\pi\)
\(954\) −4.08168 −0.132149
\(955\) 5.25976 0.170202
\(956\) 21.6434 0.699998
\(957\) −4.46123 −0.144211
\(958\) −37.8840 −1.22398
\(959\) 9.09377 0.293653
\(960\) −1.40727 −0.0454195
\(961\) −26.9327 −0.868796
\(962\) −5.29126 −0.170597
\(963\) 10.8523 0.349710
\(964\) −7.24006 −0.233187
\(965\) 25.9563 0.835562
\(966\) 10.2656 0.330289
\(967\) −16.5320 −0.531634 −0.265817 0.964024i \(-0.585642\pi\)
−0.265817 + 0.964024i \(0.585642\pi\)
\(968\) −1.10415 −0.0354888
\(969\) −0.319377 −0.0102599
\(970\) −3.28753 −0.105556
\(971\) −34.3647 −1.10281 −0.551407 0.834236i \(-0.685909\pi\)
−0.551407 + 0.834236i \(0.685909\pi\)
\(972\) 10.0720 0.323058
\(973\) 39.6393 1.27078
\(974\) −14.9895 −0.480296
\(975\) −0.819488 −0.0262446
\(976\) 6.69819 0.214404
\(977\) −7.12105 −0.227823 −0.113911 0.993491i \(-0.536338\pi\)
−0.113911 + 0.993491i \(0.536338\pi\)
\(978\) −17.3173 −0.553745
\(979\) −17.9584 −0.573952
\(980\) 1.64204 0.0524531
\(981\) −3.13873 −0.100212
\(982\) −16.8228 −0.536837
\(983\) −54.9430 −1.75241 −0.876205 0.481939i \(-0.839933\pi\)
−0.876205 + 0.481939i \(0.839933\pi\)
\(984\) 14.7384 0.469842
\(985\) −1.98558 −0.0632659
\(986\) −0.126973 −0.00404363
\(987\) 0.907012 0.0288705
\(988\) −0.948396 −0.0301725
\(989\) 36.8249 1.17096
\(990\) −3.54725 −0.112739
\(991\) −36.7894 −1.16865 −0.584327 0.811518i \(-0.698641\pi\)
−0.584327 + 0.811518i \(0.698641\pi\)
\(992\) −2.01676 −0.0640322
\(993\) −21.6468 −0.686940
\(994\) 25.7618 0.817113
\(995\) −18.6861 −0.592389
\(996\) −2.73588 −0.0866896
\(997\) 26.0627 0.825413 0.412706 0.910864i \(-0.364584\pi\)
0.412706 + 0.910864i \(0.364584\pi\)
\(998\) −5.83436 −0.184683
\(999\) 51.3988 1.62619
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 \(a_p\))