Properties

Label 8016.2.a.bg.1.9
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
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 1.9
Root \(1.68837\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+1.68837 q^{5}\) \(-0.722089 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+1.68837 q^{5}\) \(-0.722089 q^{7}\) \(+1.00000 q^{9}\) \(-4.92380 q^{11}\) \(-5.15606 q^{13}\) \(-1.68837 q^{15}\) \(+4.50170 q^{17}\) \(-3.23024 q^{19}\) \(+0.722089 q^{21}\) \(-9.11854 q^{23}\) \(-2.14939 q^{25}\) \(-1.00000 q^{27}\) \(+1.58248 q^{29}\) \(+2.13513 q^{31}\) \(+4.92380 q^{33}\) \(-1.21916 q^{35}\) \(-8.13571 q^{37}\) \(+5.15606 q^{39}\) \(+5.37711 q^{41}\) \(+4.74675 q^{43}\) \(+1.68837 q^{45}\) \(+3.74876 q^{47}\) \(-6.47859 q^{49}\) \(-4.50170 q^{51}\) \(+1.47444 q^{53}\) \(-8.31323 q^{55}\) \(+3.23024 q^{57}\) \(-3.12417 q^{59}\) \(+9.12058 q^{61}\) \(-0.722089 q^{63}\) \(-8.70535 q^{65}\) \(-11.6505 q^{67}\) \(+9.11854 q^{69}\) \(+13.6974 q^{71}\) \(-2.51026 q^{73}\) \(+2.14939 q^{75}\) \(+3.55542 q^{77}\) \(+12.4674 q^{79}\) \(+1.00000 q^{81}\) \(+2.96218 q^{83}\) \(+7.60056 q^{85}\) \(-1.58248 q^{87}\) \(+7.54127 q^{89}\) \(+3.72313 q^{91}\) \(-2.13513 q^{93}\) \(-5.45386 q^{95}\) \(+15.3021 q^{97}\) \(-4.92380 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.68837 0.755064 0.377532 0.925997i \(-0.376773\pi\)
0.377532 + 0.925997i \(0.376773\pi\)
\(6\) 0 0
\(7\) −0.722089 −0.272924 −0.136462 0.990645i \(-0.543573\pi\)
−0.136462 + 0.990645i \(0.543573\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.92380 −1.48458 −0.742291 0.670077i \(-0.766261\pi\)
−0.742291 + 0.670077i \(0.766261\pi\)
\(12\) 0 0
\(13\) −5.15606 −1.43003 −0.715017 0.699108i \(-0.753581\pi\)
−0.715017 + 0.699108i \(0.753581\pi\)
\(14\) 0 0
\(15\) −1.68837 −0.435936
\(16\) 0 0
\(17\) 4.50170 1.09182 0.545911 0.837843i \(-0.316184\pi\)
0.545911 + 0.837843i \(0.316184\pi\)
\(18\) 0 0
\(19\) −3.23024 −0.741069 −0.370535 0.928819i \(-0.620825\pi\)
−0.370535 + 0.928819i \(0.620825\pi\)
\(20\) 0 0
\(21\) 0.722089 0.157573
\(22\) 0 0
\(23\) −9.11854 −1.90135 −0.950673 0.310194i \(-0.899606\pi\)
−0.950673 + 0.310194i \(0.899606\pi\)
\(24\) 0 0
\(25\) −2.14939 −0.429878
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.58248 0.293859 0.146930 0.989147i \(-0.453061\pi\)
0.146930 + 0.989147i \(0.453061\pi\)
\(30\) 0 0
\(31\) 2.13513 0.383480 0.191740 0.981446i \(-0.438587\pi\)
0.191740 + 0.981446i \(0.438587\pi\)
\(32\) 0 0
\(33\) 4.92380 0.857124
\(34\) 0 0
\(35\) −1.21916 −0.206075
\(36\) 0 0
\(37\) −8.13571 −1.33750 −0.668751 0.743486i \(-0.733171\pi\)
−0.668751 + 0.743486i \(0.733171\pi\)
\(38\) 0 0
\(39\) 5.15606 0.825630
\(40\) 0 0
\(41\) 5.37711 0.839763 0.419882 0.907579i \(-0.362072\pi\)
0.419882 + 0.907579i \(0.362072\pi\)
\(42\) 0 0
\(43\) 4.74675 0.723872 0.361936 0.932203i \(-0.382116\pi\)
0.361936 + 0.932203i \(0.382116\pi\)
\(44\) 0 0
\(45\) 1.68837 0.251688
\(46\) 0 0
\(47\) 3.74876 0.546812 0.273406 0.961899i \(-0.411850\pi\)
0.273406 + 0.961899i \(0.411850\pi\)
\(48\) 0 0
\(49\) −6.47859 −0.925513
\(50\) 0 0
\(51\) −4.50170 −0.630364
\(52\) 0 0
\(53\) 1.47444 0.202530 0.101265 0.994859i \(-0.467711\pi\)
0.101265 + 0.994859i \(0.467711\pi\)
\(54\) 0 0
\(55\) −8.31323 −1.12096
\(56\) 0 0
\(57\) 3.23024 0.427856
\(58\) 0 0
\(59\) −3.12417 −0.406733 −0.203366 0.979103i \(-0.565188\pi\)
−0.203366 + 0.979103i \(0.565188\pi\)
\(60\) 0 0
\(61\) 9.12058 1.16777 0.583886 0.811836i \(-0.301532\pi\)
0.583886 + 0.811836i \(0.301532\pi\)
\(62\) 0 0
\(63\) −0.722089 −0.0909747
\(64\) 0 0
\(65\) −8.70535 −1.07977
\(66\) 0 0
\(67\) −11.6505 −1.42333 −0.711667 0.702517i \(-0.752059\pi\)
−0.711667 + 0.702517i \(0.752059\pi\)
\(68\) 0 0
\(69\) 9.11854 1.09774
\(70\) 0 0
\(71\) 13.6974 1.62559 0.812793 0.582552i \(-0.197946\pi\)
0.812793 + 0.582552i \(0.197946\pi\)
\(72\) 0 0
\(73\) −2.51026 −0.293804 −0.146902 0.989151i \(-0.546930\pi\)
−0.146902 + 0.989151i \(0.546930\pi\)
\(74\) 0 0
\(75\) 2.14939 0.248190
\(76\) 0 0
\(77\) 3.55542 0.405178
\(78\) 0 0
\(79\) 12.4674 1.40269 0.701344 0.712823i \(-0.252584\pi\)
0.701344 + 0.712823i \(0.252584\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.96218 0.325141 0.162571 0.986697i \(-0.448021\pi\)
0.162571 + 0.986697i \(0.448021\pi\)
\(84\) 0 0
\(85\) 7.60056 0.824396
\(86\) 0 0
\(87\) −1.58248 −0.169660
\(88\) 0 0
\(89\) 7.54127 0.799373 0.399687 0.916652i \(-0.369119\pi\)
0.399687 + 0.916652i \(0.369119\pi\)
\(90\) 0 0
\(91\) 3.72313 0.390290
\(92\) 0 0
\(93\) −2.13513 −0.221402
\(94\) 0 0
\(95\) −5.45386 −0.559555
\(96\) 0 0
\(97\) 15.3021 1.55369 0.776847 0.629689i \(-0.216818\pi\)
0.776847 + 0.629689i \(0.216818\pi\)
\(98\) 0 0
\(99\) −4.92380 −0.494861
\(100\) 0 0
\(101\) −2.99072 −0.297588 −0.148794 0.988868i \(-0.547539\pi\)
−0.148794 + 0.988868i \(0.547539\pi\)
\(102\) 0 0
\(103\) −6.09205 −0.600268 −0.300134 0.953897i \(-0.597031\pi\)
−0.300134 + 0.953897i \(0.597031\pi\)
\(104\) 0 0
\(105\) 1.21916 0.118977
\(106\) 0 0
\(107\) −12.2446 −1.18373 −0.591865 0.806037i \(-0.701608\pi\)
−0.591865 + 0.806037i \(0.701608\pi\)
\(108\) 0 0
\(109\) 17.7801 1.70303 0.851514 0.524332i \(-0.175685\pi\)
0.851514 + 0.524332i \(0.175685\pi\)
\(110\) 0 0
\(111\) 8.13571 0.772207
\(112\) 0 0
\(113\) 14.4321 1.35766 0.678829 0.734296i \(-0.262488\pi\)
0.678829 + 0.734296i \(0.262488\pi\)
\(114\) 0 0
\(115\) −15.3955 −1.43564
\(116\) 0 0
\(117\) −5.15606 −0.476678
\(118\) 0 0
\(119\) −3.25063 −0.297985
\(120\) 0 0
\(121\) 13.2439 1.20399
\(122\) 0 0
\(123\) −5.37711 −0.484838
\(124\) 0 0
\(125\) −12.0709 −1.07965
\(126\) 0 0
\(127\) 12.6883 1.12591 0.562954 0.826488i \(-0.309665\pi\)
0.562954 + 0.826488i \(0.309665\pi\)
\(128\) 0 0
\(129\) −4.74675 −0.417928
\(130\) 0 0
\(131\) 13.7297 1.19957 0.599786 0.800160i \(-0.295252\pi\)
0.599786 + 0.800160i \(0.295252\pi\)
\(132\) 0 0
\(133\) 2.33252 0.202256
\(134\) 0 0
\(135\) −1.68837 −0.145312
\(136\) 0 0
\(137\) −15.1614 −1.29533 −0.647664 0.761926i \(-0.724254\pi\)
−0.647664 + 0.761926i \(0.724254\pi\)
\(138\) 0 0
\(139\) 9.47213 0.803415 0.401708 0.915768i \(-0.368417\pi\)
0.401708 + 0.915768i \(0.368417\pi\)
\(140\) 0 0
\(141\) −3.74876 −0.315702
\(142\) 0 0
\(143\) 25.3874 2.12300
\(144\) 0 0
\(145\) 2.67182 0.221883
\(146\) 0 0
\(147\) 6.47859 0.534345
\(148\) 0 0
\(149\) 15.3592 1.25828 0.629139 0.777293i \(-0.283408\pi\)
0.629139 + 0.777293i \(0.283408\pi\)
\(150\) 0 0
\(151\) 12.8576 1.04634 0.523170 0.852228i \(-0.324749\pi\)
0.523170 + 0.852228i \(0.324749\pi\)
\(152\) 0 0
\(153\) 4.50170 0.363941
\(154\) 0 0
\(155\) 3.60489 0.289552
\(156\) 0 0
\(157\) −4.41216 −0.352129 −0.176064 0.984379i \(-0.556337\pi\)
−0.176064 + 0.984379i \(0.556337\pi\)
\(158\) 0 0
\(159\) −1.47444 −0.116931
\(160\) 0 0
\(161\) 6.58439 0.518923
\(162\) 0 0
\(163\) 8.45760 0.662450 0.331225 0.943552i \(-0.392538\pi\)
0.331225 + 0.943552i \(0.392538\pi\)
\(164\) 0 0
\(165\) 8.31323 0.647184
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 13.5849 1.04499
\(170\) 0 0
\(171\) −3.23024 −0.247023
\(172\) 0 0
\(173\) −4.24683 −0.322880 −0.161440 0.986882i \(-0.551614\pi\)
−0.161440 + 0.986882i \(0.551614\pi\)
\(174\) 0 0
\(175\) 1.55205 0.117324
\(176\) 0 0
\(177\) 3.12417 0.234827
\(178\) 0 0
\(179\) −0.599313 −0.0447948 −0.0223974 0.999749i \(-0.507130\pi\)
−0.0223974 + 0.999749i \(0.507130\pi\)
\(180\) 0 0
\(181\) −24.3349 −1.80880 −0.904400 0.426686i \(-0.859681\pi\)
−0.904400 + 0.426686i \(0.859681\pi\)
\(182\) 0 0
\(183\) −9.12058 −0.674213
\(184\) 0 0
\(185\) −13.7361 −1.00990
\(186\) 0 0
\(187\) −22.1655 −1.62090
\(188\) 0 0
\(189\) 0.722089 0.0525242
\(190\) 0 0
\(191\) −13.3821 −0.968294 −0.484147 0.874987i \(-0.660870\pi\)
−0.484147 + 0.874987i \(0.660870\pi\)
\(192\) 0 0
\(193\) −11.8898 −0.855847 −0.427924 0.903815i \(-0.640755\pi\)
−0.427924 + 0.903815i \(0.640755\pi\)
\(194\) 0 0
\(195\) 8.70535 0.623403
\(196\) 0 0
\(197\) 18.9713 1.35165 0.675823 0.737064i \(-0.263788\pi\)
0.675823 + 0.737064i \(0.263788\pi\)
\(198\) 0 0
\(199\) −20.3938 −1.44568 −0.722838 0.691017i \(-0.757163\pi\)
−0.722838 + 0.691017i \(0.757163\pi\)
\(200\) 0 0
\(201\) 11.6505 0.821762
\(202\) 0 0
\(203\) −1.14269 −0.0802013
\(204\) 0 0
\(205\) 9.07857 0.634075
\(206\) 0 0
\(207\) −9.11854 −0.633782
\(208\) 0 0
\(209\) 15.9051 1.10018
\(210\) 0 0
\(211\) −2.39036 −0.164559 −0.0822797 0.996609i \(-0.526220\pi\)
−0.0822797 + 0.996609i \(0.526220\pi\)
\(212\) 0 0
\(213\) −13.6974 −0.938533
\(214\) 0 0
\(215\) 8.01429 0.546570
\(216\) 0 0
\(217\) −1.54175 −0.104661
\(218\) 0 0
\(219\) 2.51026 0.169628
\(220\) 0 0
\(221\) −23.2110 −1.56134
\(222\) 0 0
\(223\) −16.4864 −1.10401 −0.552006 0.833840i \(-0.686137\pi\)
−0.552006 + 0.833840i \(0.686137\pi\)
\(224\) 0 0
\(225\) −2.14939 −0.143293
\(226\) 0 0
\(227\) −5.37540 −0.356778 −0.178389 0.983960i \(-0.557089\pi\)
−0.178389 + 0.983960i \(0.557089\pi\)
\(228\) 0 0
\(229\) −7.85562 −0.519114 −0.259557 0.965728i \(-0.583577\pi\)
−0.259557 + 0.965728i \(0.583577\pi\)
\(230\) 0 0
\(231\) −3.55542 −0.233930
\(232\) 0 0
\(233\) 5.08638 0.333220 0.166610 0.986023i \(-0.446718\pi\)
0.166610 + 0.986023i \(0.446718\pi\)
\(234\) 0 0
\(235\) 6.32930 0.412878
\(236\) 0 0
\(237\) −12.4674 −0.809842
\(238\) 0 0
\(239\) 12.8450 0.830877 0.415438 0.909621i \(-0.363628\pi\)
0.415438 + 0.909621i \(0.363628\pi\)
\(240\) 0 0
\(241\) 5.56580 0.358524 0.179262 0.983801i \(-0.442629\pi\)
0.179262 + 0.983801i \(0.442629\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −10.9383 −0.698821
\(246\) 0 0
\(247\) 16.6553 1.05975
\(248\) 0 0
\(249\) −2.96218 −0.187720
\(250\) 0 0
\(251\) 13.4878 0.851343 0.425671 0.904878i \(-0.360038\pi\)
0.425671 + 0.904878i \(0.360038\pi\)
\(252\) 0 0
\(253\) 44.8979 2.82271
\(254\) 0 0
\(255\) −7.60056 −0.475965
\(256\) 0 0
\(257\) 15.0902 0.941299 0.470650 0.882320i \(-0.344020\pi\)
0.470650 + 0.882320i \(0.344020\pi\)
\(258\) 0 0
\(259\) 5.87470 0.365036
\(260\) 0 0
\(261\) 1.58248 0.0979531
\(262\) 0 0
\(263\) −11.8686 −0.731847 −0.365924 0.930645i \(-0.619247\pi\)
−0.365924 + 0.930645i \(0.619247\pi\)
\(264\) 0 0
\(265\) 2.48941 0.152923
\(266\) 0 0
\(267\) −7.54127 −0.461518
\(268\) 0 0
\(269\) 0.857197 0.0522642 0.0261321 0.999658i \(-0.491681\pi\)
0.0261321 + 0.999658i \(0.491681\pi\)
\(270\) 0 0
\(271\) −16.9528 −1.02981 −0.514905 0.857247i \(-0.672173\pi\)
−0.514905 + 0.857247i \(0.672173\pi\)
\(272\) 0 0
\(273\) −3.72313 −0.225334
\(274\) 0 0
\(275\) 10.5832 0.638190
\(276\) 0 0
\(277\) 31.3840 1.88568 0.942840 0.333247i \(-0.108144\pi\)
0.942840 + 0.333247i \(0.108144\pi\)
\(278\) 0 0
\(279\) 2.13513 0.127827
\(280\) 0 0
\(281\) −8.26822 −0.493241 −0.246620 0.969112i \(-0.579320\pi\)
−0.246620 + 0.969112i \(0.579320\pi\)
\(282\) 0 0
\(283\) 6.24839 0.371428 0.185714 0.982604i \(-0.440540\pi\)
0.185714 + 0.982604i \(0.440540\pi\)
\(284\) 0 0
\(285\) 5.45386 0.323059
\(286\) 0 0
\(287\) −3.88275 −0.229192
\(288\) 0 0
\(289\) 3.26531 0.192077
\(290\) 0 0
\(291\) −15.3021 −0.897026
\(292\) 0 0
\(293\) −22.7074 −1.32658 −0.663289 0.748363i \(-0.730840\pi\)
−0.663289 + 0.748363i \(0.730840\pi\)
\(294\) 0 0
\(295\) −5.27478 −0.307109
\(296\) 0 0
\(297\) 4.92380 0.285708
\(298\) 0 0
\(299\) 47.0157 2.71899
\(300\) 0 0
\(301\) −3.42757 −0.197562
\(302\) 0 0
\(303\) 2.99072 0.171813
\(304\) 0 0
\(305\) 15.3990 0.881742
\(306\) 0 0
\(307\) 9.71355 0.554381 0.277191 0.960815i \(-0.410597\pi\)
0.277191 + 0.960815i \(0.410597\pi\)
\(308\) 0 0
\(309\) 6.09205 0.346565
\(310\) 0 0
\(311\) 30.6568 1.73839 0.869193 0.494474i \(-0.164639\pi\)
0.869193 + 0.494474i \(0.164639\pi\)
\(312\) 0 0
\(313\) 3.88725 0.219720 0.109860 0.993947i \(-0.464960\pi\)
0.109860 + 0.993947i \(0.464960\pi\)
\(314\) 0 0
\(315\) −1.21916 −0.0686917
\(316\) 0 0
\(317\) −18.2051 −1.02250 −0.511250 0.859432i \(-0.670817\pi\)
−0.511250 + 0.859432i \(0.670817\pi\)
\(318\) 0 0
\(319\) −7.79183 −0.436259
\(320\) 0 0
\(321\) 12.2446 0.683427
\(322\) 0 0
\(323\) −14.5416 −0.809116
\(324\) 0 0
\(325\) 11.0824 0.614740
\(326\) 0 0
\(327\) −17.7801 −0.983243
\(328\) 0 0
\(329\) −2.70694 −0.149238
\(330\) 0 0
\(331\) −24.8334 −1.36497 −0.682483 0.730902i \(-0.739100\pi\)
−0.682483 + 0.730902i \(0.739100\pi\)
\(332\) 0 0
\(333\) −8.13571 −0.445834
\(334\) 0 0
\(335\) −19.6704 −1.07471
\(336\) 0 0
\(337\) −1.67704 −0.0913543 −0.0456771 0.998956i \(-0.514545\pi\)
−0.0456771 + 0.998956i \(0.514545\pi\)
\(338\) 0 0
\(339\) −14.4321 −0.783845
\(340\) 0 0
\(341\) −10.5129 −0.569308
\(342\) 0 0
\(343\) 9.73274 0.525519
\(344\) 0 0
\(345\) 15.3955 0.828866
\(346\) 0 0
\(347\) −13.4895 −0.724152 −0.362076 0.932149i \(-0.617932\pi\)
−0.362076 + 0.932149i \(0.617932\pi\)
\(348\) 0 0
\(349\) 6.01732 0.322099 0.161050 0.986946i \(-0.448512\pi\)
0.161050 + 0.986946i \(0.448512\pi\)
\(350\) 0 0
\(351\) 5.15606 0.275210
\(352\) 0 0
\(353\) 22.0017 1.17103 0.585515 0.810661i \(-0.300892\pi\)
0.585515 + 0.810661i \(0.300892\pi\)
\(354\) 0 0
\(355\) 23.1264 1.22742
\(356\) 0 0
\(357\) 3.25063 0.172041
\(358\) 0 0
\(359\) −20.7777 −1.09661 −0.548303 0.836280i \(-0.684726\pi\)
−0.548303 + 0.836280i \(0.684726\pi\)
\(360\) 0 0
\(361\) −8.56552 −0.450817
\(362\) 0 0
\(363\) −13.2439 −0.695122
\(364\) 0 0
\(365\) −4.23826 −0.221841
\(366\) 0 0
\(367\) 30.9260 1.61432 0.807162 0.590330i \(-0.201002\pi\)
0.807162 + 0.590330i \(0.201002\pi\)
\(368\) 0 0
\(369\) 5.37711 0.279921
\(370\) 0 0
\(371\) −1.06468 −0.0552753
\(372\) 0 0
\(373\) −1.24001 −0.0642053 −0.0321027 0.999485i \(-0.510220\pi\)
−0.0321027 + 0.999485i \(0.510220\pi\)
\(374\) 0 0
\(375\) 12.0709 0.623336
\(376\) 0 0
\(377\) −8.15936 −0.420229
\(378\) 0 0
\(379\) 36.1456 1.85667 0.928337 0.371739i \(-0.121238\pi\)
0.928337 + 0.371739i \(0.121238\pi\)
\(380\) 0 0
\(381\) −12.6883 −0.650044
\(382\) 0 0
\(383\) −14.4479 −0.738253 −0.369127 0.929379i \(-0.620343\pi\)
−0.369127 + 0.929379i \(0.620343\pi\)
\(384\) 0 0
\(385\) 6.00289 0.305936
\(386\) 0 0
\(387\) 4.74675 0.241291
\(388\) 0 0
\(389\) −8.58955 −0.435508 −0.217754 0.976004i \(-0.569873\pi\)
−0.217754 + 0.976004i \(0.569873\pi\)
\(390\) 0 0
\(391\) −41.0489 −2.07593
\(392\) 0 0
\(393\) −13.7297 −0.692573
\(394\) 0 0
\(395\) 21.0496 1.05912
\(396\) 0 0
\(397\) 27.3990 1.37512 0.687558 0.726129i \(-0.258683\pi\)
0.687558 + 0.726129i \(0.258683\pi\)
\(398\) 0 0
\(399\) −2.33252 −0.116772
\(400\) 0 0
\(401\) 3.71562 0.185549 0.0927747 0.995687i \(-0.470426\pi\)
0.0927747 + 0.995687i \(0.470426\pi\)
\(402\) 0 0
\(403\) −11.0088 −0.548389
\(404\) 0 0
\(405\) 1.68837 0.0838960
\(406\) 0 0
\(407\) 40.0586 1.98563
\(408\) 0 0
\(409\) −31.4154 −1.55339 −0.776695 0.629877i \(-0.783105\pi\)
−0.776695 + 0.629877i \(0.783105\pi\)
\(410\) 0 0
\(411\) 15.1614 0.747858
\(412\) 0 0
\(413\) 2.25593 0.111007
\(414\) 0 0
\(415\) 5.00126 0.245502
\(416\) 0 0
\(417\) −9.47213 −0.463852
\(418\) 0 0
\(419\) −30.3030 −1.48040 −0.740200 0.672387i \(-0.765269\pi\)
−0.740200 + 0.672387i \(0.765269\pi\)
\(420\) 0 0
\(421\) −31.7995 −1.54981 −0.774907 0.632075i \(-0.782203\pi\)
−0.774907 + 0.632075i \(0.782203\pi\)
\(422\) 0 0
\(423\) 3.74876 0.182271
\(424\) 0 0
\(425\) −9.67592 −0.469351
\(426\) 0 0
\(427\) −6.58587 −0.318713
\(428\) 0 0
\(429\) −25.3874 −1.22572
\(430\) 0 0
\(431\) 19.1018 0.920101 0.460051 0.887893i \(-0.347831\pi\)
0.460051 + 0.887893i \(0.347831\pi\)
\(432\) 0 0
\(433\) −2.19475 −0.105473 −0.0527365 0.998608i \(-0.516794\pi\)
−0.0527365 + 0.998608i \(0.516794\pi\)
\(434\) 0 0
\(435\) −2.67182 −0.128104
\(436\) 0 0
\(437\) 29.4551 1.40903
\(438\) 0 0
\(439\) 23.8050 1.13615 0.568074 0.822977i \(-0.307689\pi\)
0.568074 + 0.822977i \(0.307689\pi\)
\(440\) 0 0
\(441\) −6.47859 −0.308504
\(442\) 0 0
\(443\) −24.1042 −1.14522 −0.572612 0.819826i \(-0.694070\pi\)
−0.572612 + 0.819826i \(0.694070\pi\)
\(444\) 0 0
\(445\) 12.7325 0.603578
\(446\) 0 0
\(447\) −15.3592 −0.726467
\(448\) 0 0
\(449\) −5.66111 −0.267164 −0.133582 0.991038i \(-0.542648\pi\)
−0.133582 + 0.991038i \(0.542648\pi\)
\(450\) 0 0
\(451\) −26.4758 −1.24670
\(452\) 0 0
\(453\) −12.8576 −0.604105
\(454\) 0 0
\(455\) 6.28604 0.294694
\(456\) 0 0
\(457\) 15.1307 0.707786 0.353893 0.935286i \(-0.384858\pi\)
0.353893 + 0.935286i \(0.384858\pi\)
\(458\) 0 0
\(459\) −4.50170 −0.210121
\(460\) 0 0
\(461\) −3.92069 −0.182605 −0.0913023 0.995823i \(-0.529103\pi\)
−0.0913023 + 0.995823i \(0.529103\pi\)
\(462\) 0 0
\(463\) 32.3205 1.50206 0.751030 0.660268i \(-0.229557\pi\)
0.751030 + 0.660268i \(0.229557\pi\)
\(464\) 0 0
\(465\) −3.60489 −0.167173
\(466\) 0 0
\(467\) −27.8059 −1.28670 −0.643352 0.765570i \(-0.722457\pi\)
−0.643352 + 0.765570i \(0.722457\pi\)
\(468\) 0 0
\(469\) 8.41269 0.388462
\(470\) 0 0
\(471\) 4.41216 0.203302
\(472\) 0 0
\(473\) −23.3721 −1.07465
\(474\) 0 0
\(475\) 6.94306 0.318570
\(476\) 0 0
\(477\) 1.47444 0.0675100
\(478\) 0 0
\(479\) 1.80360 0.0824086 0.0412043 0.999151i \(-0.486881\pi\)
0.0412043 + 0.999151i \(0.486881\pi\)
\(480\) 0 0
\(481\) 41.9482 1.91267
\(482\) 0 0
\(483\) −6.58439 −0.299600
\(484\) 0 0
\(485\) 25.8357 1.17314
\(486\) 0 0
\(487\) 37.5627 1.70213 0.851064 0.525062i \(-0.175958\pi\)
0.851064 + 0.525062i \(0.175958\pi\)
\(488\) 0 0
\(489\) −8.45760 −0.382466
\(490\) 0 0
\(491\) 19.5565 0.882570 0.441285 0.897367i \(-0.354523\pi\)
0.441285 + 0.897367i \(0.354523\pi\)
\(492\) 0 0
\(493\) 7.12386 0.320842
\(494\) 0 0
\(495\) −8.31323 −0.373652
\(496\) 0 0
\(497\) −9.89077 −0.443661
\(498\) 0 0
\(499\) 10.2225 0.457623 0.228812 0.973471i \(-0.426516\pi\)
0.228812 + 0.973471i \(0.426516\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −11.2594 −0.502034 −0.251017 0.967983i \(-0.580765\pi\)
−0.251017 + 0.967983i \(0.580765\pi\)
\(504\) 0 0
\(505\) −5.04946 −0.224698
\(506\) 0 0
\(507\) −13.5849 −0.603328
\(508\) 0 0
\(509\) −7.84518 −0.347731 −0.173866 0.984769i \(-0.555626\pi\)
−0.173866 + 0.984769i \(0.555626\pi\)
\(510\) 0 0
\(511\) 1.81263 0.0801861
\(512\) 0 0
\(513\) 3.23024 0.142619
\(514\) 0 0
\(515\) −10.2857 −0.453241
\(516\) 0 0
\(517\) −18.4581 −0.811788
\(518\) 0 0
\(519\) 4.24683 0.186415
\(520\) 0 0
\(521\) −28.2656 −1.23834 −0.619168 0.785258i \(-0.712530\pi\)
−0.619168 + 0.785258i \(0.712530\pi\)
\(522\) 0 0
\(523\) −3.43781 −0.150325 −0.0751624 0.997171i \(-0.523948\pi\)
−0.0751624 + 0.997171i \(0.523948\pi\)
\(524\) 0 0
\(525\) −1.55205 −0.0677371
\(526\) 0 0
\(527\) 9.61170 0.418692
\(528\) 0 0
\(529\) 60.1477 2.61512
\(530\) 0 0
\(531\) −3.12417 −0.135578
\(532\) 0 0
\(533\) −27.7247 −1.20089
\(534\) 0 0
\(535\) −20.6735 −0.893792
\(536\) 0 0
\(537\) 0.599313 0.0258623
\(538\) 0 0
\(539\) 31.8993 1.37400
\(540\) 0 0
\(541\) 23.8036 1.02340 0.511699 0.859165i \(-0.329016\pi\)
0.511699 + 0.859165i \(0.329016\pi\)
\(542\) 0 0
\(543\) 24.3349 1.04431
\(544\) 0 0
\(545\) 30.0195 1.28589
\(546\) 0 0
\(547\) 12.5205 0.535337 0.267669 0.963511i \(-0.413747\pi\)
0.267669 + 0.963511i \(0.413747\pi\)
\(548\) 0 0
\(549\) 9.12058 0.389257
\(550\) 0 0
\(551\) −5.11180 −0.217770
\(552\) 0 0
\(553\) −9.00255 −0.382827
\(554\) 0 0
\(555\) 13.7361 0.583066
\(556\) 0 0
\(557\) 29.1939 1.23699 0.618493 0.785790i \(-0.287743\pi\)
0.618493 + 0.785790i \(0.287743\pi\)
\(558\) 0 0
\(559\) −24.4745 −1.03516
\(560\) 0 0
\(561\) 22.1655 0.935828
\(562\) 0 0
\(563\) 38.1606 1.60828 0.804139 0.594441i \(-0.202627\pi\)
0.804139 + 0.594441i \(0.202627\pi\)
\(564\) 0 0
\(565\) 24.3668 1.02512
\(566\) 0 0
\(567\) −0.722089 −0.0303249
\(568\) 0 0
\(569\) 20.6265 0.864709 0.432354 0.901704i \(-0.357683\pi\)
0.432354 + 0.901704i \(0.357683\pi\)
\(570\) 0 0
\(571\) 24.5539 1.02755 0.513774 0.857925i \(-0.328247\pi\)
0.513774 + 0.857925i \(0.328247\pi\)
\(572\) 0 0
\(573\) 13.3821 0.559045
\(574\) 0 0
\(575\) 19.5993 0.817348
\(576\) 0 0
\(577\) −36.6540 −1.52593 −0.762963 0.646443i \(-0.776256\pi\)
−0.762963 + 0.646443i \(0.776256\pi\)
\(578\) 0 0
\(579\) 11.8898 0.494124
\(580\) 0 0
\(581\) −2.13896 −0.0887388
\(582\) 0 0
\(583\) −7.25986 −0.300673
\(584\) 0 0
\(585\) −8.70535 −0.359922
\(586\) 0 0
\(587\) 12.0092 0.495671 0.247836 0.968802i \(-0.420281\pi\)
0.247836 + 0.968802i \(0.420281\pi\)
\(588\) 0 0
\(589\) −6.89698 −0.284185
\(590\) 0 0
\(591\) −18.9713 −0.780374
\(592\) 0 0
\(593\) −19.6797 −0.808150 −0.404075 0.914726i \(-0.632407\pi\)
−0.404075 + 0.914726i \(0.632407\pi\)
\(594\) 0 0
\(595\) −5.48828 −0.224997
\(596\) 0 0
\(597\) 20.3938 0.834662
\(598\) 0 0
\(599\) 6.13982 0.250866 0.125433 0.992102i \(-0.459968\pi\)
0.125433 + 0.992102i \(0.459968\pi\)
\(600\) 0 0
\(601\) −28.1181 −1.14696 −0.573482 0.819218i \(-0.694408\pi\)
−0.573482 + 0.819218i \(0.694408\pi\)
\(602\) 0 0
\(603\) −11.6505 −0.474445
\(604\) 0 0
\(605\) 22.3606 0.909087
\(606\) 0 0
\(607\) −13.8152 −0.560743 −0.280372 0.959892i \(-0.590458\pi\)
−0.280372 + 0.959892i \(0.590458\pi\)
\(608\) 0 0
\(609\) 1.14269 0.0463042
\(610\) 0 0
\(611\) −19.3288 −0.781960
\(612\) 0 0
\(613\) 17.5891 0.710416 0.355208 0.934787i \(-0.384410\pi\)
0.355208 + 0.934787i \(0.384410\pi\)
\(614\) 0 0
\(615\) −9.07857 −0.366083
\(616\) 0 0
\(617\) −7.71765 −0.310701 −0.155351 0.987859i \(-0.549651\pi\)
−0.155351 + 0.987859i \(0.549651\pi\)
\(618\) 0 0
\(619\) −25.1563 −1.01112 −0.505559 0.862792i \(-0.668714\pi\)
−0.505559 + 0.862792i \(0.668714\pi\)
\(620\) 0 0
\(621\) 9.11854 0.365914
\(622\) 0 0
\(623\) −5.44547 −0.218168
\(624\) 0 0
\(625\) −9.63315 −0.385326
\(626\) 0 0
\(627\) −15.9051 −0.635188
\(628\) 0 0
\(629\) −36.6245 −1.46032
\(630\) 0 0
\(631\) 32.0287 1.27504 0.637521 0.770433i \(-0.279960\pi\)
0.637521 + 0.770433i \(0.279960\pi\)
\(632\) 0 0
\(633\) 2.39036 0.0950084
\(634\) 0 0
\(635\) 21.4227 0.850133
\(636\) 0 0
\(637\) 33.4040 1.32351
\(638\) 0 0
\(639\) 13.6974 0.541862
\(640\) 0 0
\(641\) 35.3785 1.39737 0.698683 0.715431i \(-0.253770\pi\)
0.698683 + 0.715431i \(0.253770\pi\)
\(642\) 0 0
\(643\) 8.42726 0.332339 0.166169 0.986097i \(-0.446860\pi\)
0.166169 + 0.986097i \(0.446860\pi\)
\(644\) 0 0
\(645\) −8.01429 −0.315562
\(646\) 0 0
\(647\) −45.0291 −1.77028 −0.885138 0.465328i \(-0.845936\pi\)
−0.885138 + 0.465328i \(0.845936\pi\)
\(648\) 0 0
\(649\) 15.3828 0.603829
\(650\) 0 0
\(651\) 1.54175 0.0604260
\(652\) 0 0
\(653\) −44.0405 −1.72344 −0.861719 0.507386i \(-0.830612\pi\)
−0.861719 + 0.507386i \(0.830612\pi\)
\(654\) 0 0
\(655\) 23.1809 0.905754
\(656\) 0 0
\(657\) −2.51026 −0.0979346
\(658\) 0 0
\(659\) 49.6642 1.93464 0.967321 0.253555i \(-0.0815999\pi\)
0.967321 + 0.253555i \(0.0815999\pi\)
\(660\) 0 0
\(661\) 12.2095 0.474893 0.237446 0.971401i \(-0.423690\pi\)
0.237446 + 0.971401i \(0.423690\pi\)
\(662\) 0 0
\(663\) 23.2110 0.901442
\(664\) 0 0
\(665\) 3.93817 0.152716
\(666\) 0 0
\(667\) −14.4299 −0.558728
\(668\) 0 0
\(669\) 16.4864 0.637401
\(670\) 0 0
\(671\) −44.9080 −1.73365
\(672\) 0 0
\(673\) 30.6693 1.18221 0.591107 0.806593i \(-0.298691\pi\)
0.591107 + 0.806593i \(0.298691\pi\)
\(674\) 0 0
\(675\) 2.14939 0.0827301
\(676\) 0 0
\(677\) 15.8194 0.607988 0.303994 0.952674i \(-0.401680\pi\)
0.303994 + 0.952674i \(0.401680\pi\)
\(678\) 0 0
\(679\) −11.0495 −0.424041
\(680\) 0 0
\(681\) 5.37540 0.205986
\(682\) 0 0
\(683\) 8.58263 0.328405 0.164203 0.986427i \(-0.447495\pi\)
0.164203 + 0.986427i \(0.447495\pi\)
\(684\) 0 0
\(685\) −25.5982 −0.978055
\(686\) 0 0
\(687\) 7.85562 0.299711
\(688\) 0 0
\(689\) −7.60230 −0.289625
\(690\) 0 0
\(691\) 6.22154 0.236679 0.118339 0.992973i \(-0.462243\pi\)
0.118339 + 0.992973i \(0.462243\pi\)
\(692\) 0 0
\(693\) 3.55542 0.135059
\(694\) 0 0
\(695\) 15.9925 0.606630
\(696\) 0 0
\(697\) 24.2061 0.916873
\(698\) 0 0
\(699\) −5.08638 −0.192385
\(700\) 0 0
\(701\) −17.5201 −0.661724 −0.330862 0.943679i \(-0.607339\pi\)
−0.330862 + 0.943679i \(0.607339\pi\)
\(702\) 0 0
\(703\) 26.2803 0.991181
\(704\) 0 0
\(705\) −6.32930 −0.238375
\(706\) 0 0
\(707\) 2.15957 0.0812190
\(708\) 0 0
\(709\) 38.8631 1.45953 0.729766 0.683697i \(-0.239629\pi\)
0.729766 + 0.683697i \(0.239629\pi\)
\(710\) 0 0
\(711\) 12.4674 0.467563
\(712\) 0 0
\(713\) −19.4692 −0.729129
\(714\) 0 0
\(715\) 42.8635 1.60300
\(716\) 0 0
\(717\) −12.8450 −0.479707
\(718\) 0 0
\(719\) 10.3606 0.386383 0.193192 0.981161i \(-0.438116\pi\)
0.193192 + 0.981161i \(0.438116\pi\)
\(720\) 0 0
\(721\) 4.39901 0.163828
\(722\) 0 0
\(723\) −5.56580 −0.206994
\(724\) 0 0
\(725\) −3.40137 −0.126324
\(726\) 0 0
\(727\) 51.7807 1.92044 0.960220 0.279244i \(-0.0900840\pi\)
0.960220 + 0.279244i \(0.0900840\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 21.3684 0.790340
\(732\) 0 0
\(733\) 10.7091 0.395550 0.197775 0.980247i \(-0.436628\pi\)
0.197775 + 0.980247i \(0.436628\pi\)
\(734\) 0 0
\(735\) 10.9383 0.403465
\(736\) 0 0
\(737\) 57.3647 2.11306
\(738\) 0 0
\(739\) 40.3746 1.48520 0.742602 0.669734i \(-0.233592\pi\)
0.742602 + 0.669734i \(0.233592\pi\)
\(740\) 0 0
\(741\) −16.6553 −0.611849
\(742\) 0 0
\(743\) 16.6651 0.611383 0.305692 0.952131i \(-0.401112\pi\)
0.305692 + 0.952131i \(0.401112\pi\)
\(744\) 0 0
\(745\) 25.9321 0.950080
\(746\) 0 0
\(747\) 2.96218 0.108380
\(748\) 0 0
\(749\) 8.84169 0.323068
\(750\) 0 0
\(751\) −25.7654 −0.940191 −0.470096 0.882615i \(-0.655781\pi\)
−0.470096 + 0.882615i \(0.655781\pi\)
\(752\) 0 0
\(753\) −13.4878 −0.491523
\(754\) 0 0
\(755\) 21.7085 0.790054
\(756\) 0 0
\(757\) −3.58635 −0.130348 −0.0651740 0.997874i \(-0.520760\pi\)
−0.0651740 + 0.997874i \(0.520760\pi\)
\(758\) 0 0
\(759\) −44.8979 −1.62969
\(760\) 0 0
\(761\) 2.56070 0.0928255 0.0464127 0.998922i \(-0.485221\pi\)
0.0464127 + 0.998922i \(0.485221\pi\)
\(762\) 0 0
\(763\) −12.8388 −0.464797
\(764\) 0 0
\(765\) 7.60056 0.274799
\(766\) 0 0
\(767\) 16.1084 0.581641
\(768\) 0 0
\(769\) −14.5797 −0.525756 −0.262878 0.964829i \(-0.584672\pi\)
−0.262878 + 0.964829i \(0.584672\pi\)
\(770\) 0 0
\(771\) −15.0902 −0.543459
\(772\) 0 0
\(773\) −21.4680 −0.772151 −0.386076 0.922467i \(-0.626170\pi\)
−0.386076 + 0.922467i \(0.626170\pi\)
\(774\) 0 0
\(775\) −4.58923 −0.164850
\(776\) 0 0
\(777\) −5.87470 −0.210754
\(778\) 0 0
\(779\) −17.3694 −0.622323
\(780\) 0 0
\(781\) −67.4435 −2.41332
\(782\) 0 0
\(783\) −1.58248 −0.0565533
\(784\) 0 0
\(785\) −7.44938 −0.265880
\(786\) 0 0
\(787\) 2.87234 0.102388 0.0511939 0.998689i \(-0.483697\pi\)
0.0511939 + 0.998689i \(0.483697\pi\)
\(788\) 0 0
\(789\) 11.8686 0.422532
\(790\) 0 0
\(791\) −10.4213 −0.370538
\(792\) 0 0
\(793\) −47.0263 −1.66995
\(794\) 0 0
\(795\) −2.48941 −0.0882902
\(796\) 0 0
\(797\) 39.8716 1.41232 0.706162 0.708050i \(-0.250425\pi\)
0.706162 + 0.708050i \(0.250425\pi\)
\(798\) 0 0
\(799\) 16.8758 0.597022
\(800\) 0 0
\(801\) 7.54127 0.266458
\(802\) 0 0
\(803\) 12.3600 0.436176
\(804\) 0 0
\(805\) 11.1169 0.391820
\(806\) 0 0
\(807\) −0.857197 −0.0301748
\(808\) 0 0
\(809\) −41.6315 −1.46369 −0.731843 0.681473i \(-0.761339\pi\)
−0.731843 + 0.681473i \(0.761339\pi\)
\(810\) 0 0
\(811\) −42.3043 −1.48551 −0.742753 0.669565i \(-0.766480\pi\)
−0.742753 + 0.669565i \(0.766480\pi\)
\(812\) 0 0
\(813\) 16.9528 0.594561
\(814\) 0 0
\(815\) 14.2796 0.500192
\(816\) 0 0
\(817\) −15.3332 −0.536439
\(818\) 0 0
\(819\) 3.72313 0.130097
\(820\) 0 0
\(821\) −44.9001 −1.56702 −0.783512 0.621377i \(-0.786574\pi\)
−0.783512 + 0.621377i \(0.786574\pi\)
\(822\) 0 0
\(823\) 21.8823 0.762769 0.381385 0.924416i \(-0.375447\pi\)
0.381385 + 0.924416i \(0.375447\pi\)
\(824\) 0 0
\(825\) −10.5832 −0.368459
\(826\) 0 0
\(827\) 17.5690 0.610934 0.305467 0.952203i \(-0.401187\pi\)
0.305467 + 0.952203i \(0.401187\pi\)
\(828\) 0 0
\(829\) 10.8075 0.375361 0.187680 0.982230i \(-0.439903\pi\)
0.187680 + 0.982230i \(0.439903\pi\)
\(830\) 0 0
\(831\) −31.3840 −1.08870
\(832\) 0 0
\(833\) −29.1647 −1.01050
\(834\) 0 0
\(835\) 1.68837 0.0584286
\(836\) 0 0
\(837\) −2.13513 −0.0738008
\(838\) 0 0
\(839\) 29.0750 1.00378 0.501891 0.864931i \(-0.332638\pi\)
0.501891 + 0.864931i \(0.332638\pi\)
\(840\) 0 0
\(841\) −26.4958 −0.913647
\(842\) 0 0
\(843\) 8.26822 0.284773
\(844\) 0 0
\(845\) 22.9364 0.789038
\(846\) 0 0
\(847\) −9.56324 −0.328597
\(848\) 0 0
\(849\) −6.24839 −0.214444
\(850\) 0 0
\(851\) 74.1858 2.54305
\(852\) 0 0
\(853\) 48.6140 1.66451 0.832256 0.554392i \(-0.187049\pi\)
0.832256 + 0.554392i \(0.187049\pi\)
\(854\) 0 0
\(855\) −5.45386 −0.186518
\(856\) 0 0
\(857\) 36.4623 1.24553 0.622763 0.782410i \(-0.286010\pi\)
0.622763 + 0.782410i \(0.286010\pi\)
\(858\) 0 0
\(859\) 8.60352 0.293548 0.146774 0.989170i \(-0.453111\pi\)
0.146774 + 0.989170i \(0.453111\pi\)
\(860\) 0 0
\(861\) 3.88275 0.132324
\(862\) 0 0
\(863\) 26.4936 0.901852 0.450926 0.892561i \(-0.351094\pi\)
0.450926 + 0.892561i \(0.351094\pi\)
\(864\) 0 0
\(865\) −7.17024 −0.243795
\(866\) 0 0
\(867\) −3.26531 −0.110896
\(868\) 0 0
\(869\) −61.3869 −2.08241
\(870\) 0 0
\(871\) 60.0706 2.03541
\(872\) 0 0
\(873\) 15.3021 0.517898
\(874\) 0 0
\(875\) 8.71623 0.294662
\(876\) 0 0
\(877\) 17.8702 0.603432 0.301716 0.953398i \(-0.402441\pi\)
0.301716 + 0.953398i \(0.402441\pi\)
\(878\) 0 0
\(879\) 22.7074 0.765900
\(880\) 0 0
\(881\) 23.2404 0.782990 0.391495 0.920180i \(-0.371958\pi\)
0.391495 + 0.920180i \(0.371958\pi\)
\(882\) 0 0
\(883\) −33.2781 −1.11990 −0.559948 0.828528i \(-0.689179\pi\)
−0.559948 + 0.828528i \(0.689179\pi\)
\(884\) 0 0
\(885\) 5.27478 0.177310
\(886\) 0 0
\(887\) −15.3015 −0.513775 −0.256887 0.966441i \(-0.582697\pi\)
−0.256887 + 0.966441i \(0.582697\pi\)
\(888\) 0 0
\(889\) −9.16212 −0.307288
\(890\) 0 0
\(891\) −4.92380 −0.164954
\(892\) 0 0
\(893\) −12.1094 −0.405226
\(894\) 0 0
\(895\) −1.01187 −0.0338229
\(896\) 0 0
\(897\) −47.0157 −1.56981
\(898\) 0 0
\(899\) 3.37880 0.112689
\(900\) 0 0
\(901\) 6.63749 0.221127
\(902\) 0 0
\(903\) 3.42757 0.114063
\(904\) 0 0
\(905\) −41.0864 −1.36576
\(906\) 0 0
\(907\) −26.7007 −0.886583 −0.443292 0.896377i \(-0.646189\pi\)
−0.443292 + 0.896377i \(0.646189\pi\)
\(908\) 0 0
\(909\) −2.99072 −0.0991961
\(910\) 0 0
\(911\) 15.6323 0.517920 0.258960 0.965888i \(-0.416620\pi\)
0.258960 + 0.965888i \(0.416620\pi\)
\(912\) 0 0
\(913\) −14.5852 −0.482699
\(914\) 0 0
\(915\) −15.3990 −0.509074
\(916\) 0 0
\(917\) −9.91409 −0.327392
\(918\) 0 0
\(919\) 18.3950 0.606795 0.303398 0.952864i \(-0.401879\pi\)
0.303398 + 0.952864i \(0.401879\pi\)
\(920\) 0 0
\(921\) −9.71355 −0.320072
\(922\) 0 0
\(923\) −70.6248 −2.32464
\(924\) 0 0
\(925\) 17.4868 0.574963
\(926\) 0 0
\(927\) −6.09205 −0.200089
\(928\) 0 0
\(929\) 18.2625 0.599174 0.299587 0.954069i \(-0.403151\pi\)
0.299587 + 0.954069i \(0.403151\pi\)
\(930\) 0 0
\(931\) 20.9274 0.685869
\(932\) 0 0
\(933\) −30.6568 −1.00366
\(934\) 0 0
\(935\) −37.4236 −1.22388
\(936\) 0 0
\(937\) 3.89282 0.127173 0.0635864 0.997976i \(-0.479746\pi\)
0.0635864 + 0.997976i \(0.479746\pi\)
\(938\) 0 0
\(939\) −3.88725 −0.126856
\(940\) 0 0
\(941\) −46.3525 −1.51105 −0.755524 0.655121i \(-0.772618\pi\)
−0.755524 + 0.655121i \(0.772618\pi\)
\(942\) 0 0
\(943\) −49.0314 −1.59668
\(944\) 0 0
\(945\) 1.21916 0.0396592
\(946\) 0 0
\(947\) 10.6858 0.347243 0.173622 0.984812i \(-0.444453\pi\)
0.173622 + 0.984812i \(0.444453\pi\)
\(948\) 0 0
\(949\) 12.9431 0.420149
\(950\) 0 0
\(951\) 18.2051 0.590340
\(952\) 0 0
\(953\) −9.70387 −0.314339 −0.157170 0.987572i \(-0.550237\pi\)
−0.157170 + 0.987572i \(0.550237\pi\)
\(954\) 0 0
\(955\) −22.5940 −0.731124
\(956\) 0 0
\(957\) 7.79183 0.251874
\(958\) 0 0
\(959\) 10.9479 0.353526
\(960\) 0 0
\(961\) −26.4412 −0.852943
\(962\) 0 0
\(963\) −12.2446 −0.394577
\(964\) 0 0
\(965\) −20.0744 −0.646219
\(966\) 0 0
\(967\) −2.89854 −0.0932107 −0.0466054 0.998913i \(-0.514840\pi\)
−0.0466054 + 0.998913i \(0.514840\pi\)
\(968\) 0 0
\(969\) 14.5416 0.467143
\(970\) 0 0
\(971\) 26.8901 0.862944 0.431472 0.902126i \(-0.357994\pi\)
0.431472 + 0.902126i \(0.357994\pi\)
\(972\) 0 0
\(973\) −6.83972 −0.219271
\(974\) 0 0
\(975\) −11.0824 −0.354921
\(976\) 0 0
\(977\) −27.0951 −0.866849 −0.433425 0.901190i \(-0.642695\pi\)
−0.433425 + 0.901190i \(0.642695\pi\)
\(978\) 0 0
\(979\) −37.1317 −1.18674
\(980\) 0 0
\(981\) 17.7801 0.567676
\(982\) 0 0
\(983\) 37.8416 1.20696 0.603481 0.797378i \(-0.293780\pi\)
0.603481 + 0.797378i \(0.293780\pi\)
\(984\) 0 0
\(985\) 32.0306 1.02058
\(986\) 0 0
\(987\) 2.70694 0.0861627
\(988\) 0 0
\(989\) −43.2834 −1.37633
\(990\) 0 0
\(991\) 36.3760 1.15552 0.577761 0.816206i \(-0.303927\pi\)
0.577761 + 0.816206i \(0.303927\pi\)
\(992\) 0 0
\(993\) 24.8334 0.788063
\(994\) 0 0
\(995\) −34.4323 −1.09158
\(996\) 0 0
\(997\) −59.9879 −1.89984 −0.949918 0.312501i \(-0.898833\pi\)
−0.949918 + 0.312501i \(0.898833\pi\)
\(998\) 0 0
\(999\) 8.13571 0.257402
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 \(a_p\))