Properties

Label 6040.2.a.p.1.16
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(-1.97307\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.97307 q^{3}\) \(+1.00000 q^{5}\) \(-0.188446 q^{7}\) \(+0.892989 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.97307 q^{3}\) \(+1.00000 q^{5}\) \(-0.188446 q^{7}\) \(+0.892989 q^{9}\) \(+1.45854 q^{11}\) \(-5.70600 q^{13}\) \(+1.97307 q^{15}\) \(-3.29442 q^{17}\) \(-2.35587 q^{19}\) \(-0.371816 q^{21}\) \(-0.811678 q^{23}\) \(+1.00000 q^{25}\) \(-4.15727 q^{27}\) \(+6.35299 q^{29}\) \(-1.00433 q^{31}\) \(+2.87780 q^{33}\) \(-0.188446 q^{35}\) \(-6.49639 q^{37}\) \(-11.2583 q^{39}\) \(-9.03633 q^{41}\) \(-10.4240 q^{43}\) \(+0.892989 q^{45}\) \(+7.03789 q^{47}\) \(-6.96449 q^{49}\) \(-6.50011 q^{51}\) \(+5.21570 q^{53}\) \(+1.45854 q^{55}\) \(-4.64828 q^{57}\) \(+7.83497 q^{59}\) \(-11.8569 q^{61}\) \(-0.168280 q^{63}\) \(-5.70600 q^{65}\) \(+0.795991 q^{67}\) \(-1.60149 q^{69}\) \(+12.6300 q^{71}\) \(+9.53942 q^{73}\) \(+1.97307 q^{75}\) \(-0.274856 q^{77}\) \(-17.1002 q^{79}\) \(-10.8815 q^{81}\) \(+6.51530 q^{83}\) \(-3.29442 q^{85}\) \(+12.5349 q^{87}\) \(-7.05591 q^{89}\) \(+1.07527 q^{91}\) \(-1.98162 q^{93}\) \(-2.35587 q^{95}\) \(+5.93164 q^{97}\) \(+1.30246 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.97307 1.13915 0.569575 0.821939i \(-0.307108\pi\)
0.569575 + 0.821939i \(0.307108\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.188446 −0.0712258 −0.0356129 0.999366i \(-0.511338\pi\)
−0.0356129 + 0.999366i \(0.511338\pi\)
\(8\) 0 0
\(9\) 0.892989 0.297663
\(10\) 0 0
\(11\) 1.45854 0.439767 0.219884 0.975526i \(-0.429432\pi\)
0.219884 + 0.975526i \(0.429432\pi\)
\(12\) 0 0
\(13\) −5.70600 −1.58256 −0.791280 0.611454i \(-0.790585\pi\)
−0.791280 + 0.611454i \(0.790585\pi\)
\(14\) 0 0
\(15\) 1.97307 0.509443
\(16\) 0 0
\(17\) −3.29442 −0.799015 −0.399507 0.916730i \(-0.630819\pi\)
−0.399507 + 0.916730i \(0.630819\pi\)
\(18\) 0 0
\(19\) −2.35587 −0.540473 −0.270237 0.962794i \(-0.587102\pi\)
−0.270237 + 0.962794i \(0.587102\pi\)
\(20\) 0 0
\(21\) −0.371816 −0.0811369
\(22\) 0 0
\(23\) −0.811678 −0.169247 −0.0846233 0.996413i \(-0.526969\pi\)
−0.0846233 + 0.996413i \(0.526969\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.15727 −0.800067
\(28\) 0 0
\(29\) 6.35299 1.17972 0.589860 0.807505i \(-0.299183\pi\)
0.589860 + 0.807505i \(0.299183\pi\)
\(30\) 0 0
\(31\) −1.00433 −0.180384 −0.0901918 0.995924i \(-0.528748\pi\)
−0.0901918 + 0.995924i \(0.528748\pi\)
\(32\) 0 0
\(33\) 2.87780 0.500961
\(34\) 0 0
\(35\) −0.188446 −0.0318531
\(36\) 0 0
\(37\) −6.49639 −1.06800 −0.534000 0.845485i \(-0.679312\pi\)
−0.534000 + 0.845485i \(0.679312\pi\)
\(38\) 0 0
\(39\) −11.2583 −1.80277
\(40\) 0 0
\(41\) −9.03633 −1.41124 −0.705619 0.708592i \(-0.749331\pi\)
−0.705619 + 0.708592i \(0.749331\pi\)
\(42\) 0 0
\(43\) −10.4240 −1.58965 −0.794825 0.606839i \(-0.792437\pi\)
−0.794825 + 0.606839i \(0.792437\pi\)
\(44\) 0 0
\(45\) 0.892989 0.133119
\(46\) 0 0
\(47\) 7.03789 1.02658 0.513291 0.858215i \(-0.328426\pi\)
0.513291 + 0.858215i \(0.328426\pi\)
\(48\) 0 0
\(49\) −6.96449 −0.994927
\(50\) 0 0
\(51\) −6.50011 −0.910198
\(52\) 0 0
\(53\) 5.21570 0.716431 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(54\) 0 0
\(55\) 1.45854 0.196670
\(56\) 0 0
\(57\) −4.64828 −0.615680
\(58\) 0 0
\(59\) 7.83497 1.02003 0.510013 0.860166i \(-0.329640\pi\)
0.510013 + 0.860166i \(0.329640\pi\)
\(60\) 0 0
\(61\) −11.8569 −1.51812 −0.759059 0.651021i \(-0.774341\pi\)
−0.759059 + 0.651021i \(0.774341\pi\)
\(62\) 0 0
\(63\) −0.168280 −0.0212013
\(64\) 0 0
\(65\) −5.70600 −0.707742
\(66\) 0 0
\(67\) 0.795991 0.0972458 0.0486229 0.998817i \(-0.484517\pi\)
0.0486229 + 0.998817i \(0.484517\pi\)
\(68\) 0 0
\(69\) −1.60149 −0.192797
\(70\) 0 0
\(71\) 12.6300 1.49891 0.749453 0.662058i \(-0.230317\pi\)
0.749453 + 0.662058i \(0.230317\pi\)
\(72\) 0 0
\(73\) 9.53942 1.11651 0.558253 0.829671i \(-0.311472\pi\)
0.558253 + 0.829671i \(0.311472\pi\)
\(74\) 0 0
\(75\) 1.97307 0.227830
\(76\) 0 0
\(77\) −0.274856 −0.0313228
\(78\) 0 0
\(79\) −17.1002 −1.92392 −0.961961 0.273188i \(-0.911922\pi\)
−0.961961 + 0.273188i \(0.911922\pi\)
\(80\) 0 0
\(81\) −10.8815 −1.20906
\(82\) 0 0
\(83\) 6.51530 0.715147 0.357573 0.933885i \(-0.383604\pi\)
0.357573 + 0.933885i \(0.383604\pi\)
\(84\) 0 0
\(85\) −3.29442 −0.357330
\(86\) 0 0
\(87\) 12.5349 1.34388
\(88\) 0 0
\(89\) −7.05591 −0.747925 −0.373963 0.927444i \(-0.622001\pi\)
−0.373963 + 0.927444i \(0.622001\pi\)
\(90\) 0 0
\(91\) 1.07527 0.112719
\(92\) 0 0
\(93\) −1.98162 −0.205484
\(94\) 0 0
\(95\) −2.35587 −0.241707
\(96\) 0 0
\(97\) 5.93164 0.602266 0.301133 0.953582i \(-0.402635\pi\)
0.301133 + 0.953582i \(0.402635\pi\)
\(98\) 0 0
\(99\) 1.30246 0.130902
\(100\) 0 0
\(101\) −16.7641 −1.66809 −0.834045 0.551696i \(-0.813981\pi\)
−0.834045 + 0.551696i \(0.813981\pi\)
\(102\) 0 0
\(103\) −3.29512 −0.324678 −0.162339 0.986735i \(-0.551904\pi\)
−0.162339 + 0.986735i \(0.551904\pi\)
\(104\) 0 0
\(105\) −0.371816 −0.0362855
\(106\) 0 0
\(107\) −8.81179 −0.851868 −0.425934 0.904754i \(-0.640054\pi\)
−0.425934 + 0.904754i \(0.640054\pi\)
\(108\) 0 0
\(109\) −5.00627 −0.479514 −0.239757 0.970833i \(-0.577068\pi\)
−0.239757 + 0.970833i \(0.577068\pi\)
\(110\) 0 0
\(111\) −12.8178 −1.21661
\(112\) 0 0
\(113\) 2.81571 0.264880 0.132440 0.991191i \(-0.457719\pi\)
0.132440 + 0.991191i \(0.457719\pi\)
\(114\) 0 0
\(115\) −0.811678 −0.0756893
\(116\) 0 0
\(117\) −5.09540 −0.471070
\(118\) 0 0
\(119\) 0.620820 0.0569105
\(120\) 0 0
\(121\) −8.87265 −0.806605
\(122\) 0 0
\(123\) −17.8293 −1.60761
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −10.2700 −0.911312 −0.455656 0.890156i \(-0.650595\pi\)
−0.455656 + 0.890156i \(0.650595\pi\)
\(128\) 0 0
\(129\) −20.5673 −1.81085
\(130\) 0 0
\(131\) −7.76201 −0.678170 −0.339085 0.940756i \(-0.610117\pi\)
−0.339085 + 0.940756i \(0.610117\pi\)
\(132\) 0 0
\(133\) 0.443953 0.0384956
\(134\) 0 0
\(135\) −4.15727 −0.357801
\(136\) 0 0
\(137\) 21.0458 1.79806 0.899030 0.437887i \(-0.144273\pi\)
0.899030 + 0.437887i \(0.144273\pi\)
\(138\) 0 0
\(139\) 10.4634 0.887498 0.443749 0.896151i \(-0.353648\pi\)
0.443749 + 0.896151i \(0.353648\pi\)
\(140\) 0 0
\(141\) 13.8862 1.16943
\(142\) 0 0
\(143\) −8.32245 −0.695958
\(144\) 0 0
\(145\) 6.35299 0.527587
\(146\) 0 0
\(147\) −13.7414 −1.13337
\(148\) 0 0
\(149\) −6.55983 −0.537402 −0.268701 0.963224i \(-0.586594\pi\)
−0.268701 + 0.963224i \(0.586594\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −2.94188 −0.237837
\(154\) 0 0
\(155\) −1.00433 −0.0806700
\(156\) 0 0
\(157\) −7.86962 −0.628064 −0.314032 0.949412i \(-0.601680\pi\)
−0.314032 + 0.949412i \(0.601680\pi\)
\(158\) 0 0
\(159\) 10.2909 0.816123
\(160\) 0 0
\(161\) 0.152957 0.0120547
\(162\) 0 0
\(163\) 5.89611 0.461819 0.230909 0.972975i \(-0.425830\pi\)
0.230909 + 0.972975i \(0.425830\pi\)
\(164\) 0 0
\(165\) 2.87780 0.224036
\(166\) 0 0
\(167\) −3.46843 −0.268395 −0.134197 0.990955i \(-0.542846\pi\)
−0.134197 + 0.990955i \(0.542846\pi\)
\(168\) 0 0
\(169\) 19.5585 1.50450
\(170\) 0 0
\(171\) −2.10376 −0.160879
\(172\) 0 0
\(173\) 1.82521 0.138768 0.0693841 0.997590i \(-0.477897\pi\)
0.0693841 + 0.997590i \(0.477897\pi\)
\(174\) 0 0
\(175\) −0.188446 −0.0142452
\(176\) 0 0
\(177\) 15.4589 1.16196
\(178\) 0 0
\(179\) 14.2727 1.06679 0.533396 0.845866i \(-0.320916\pi\)
0.533396 + 0.845866i \(0.320916\pi\)
\(180\) 0 0
\(181\) 2.07528 0.154254 0.0771270 0.997021i \(-0.475425\pi\)
0.0771270 + 0.997021i \(0.475425\pi\)
\(182\) 0 0
\(183\) −23.3944 −1.72937
\(184\) 0 0
\(185\) −6.49639 −0.477624
\(186\) 0 0
\(187\) −4.80505 −0.351380
\(188\) 0 0
\(189\) 0.783420 0.0569854
\(190\) 0 0
\(191\) −15.3436 −1.11023 −0.555113 0.831775i \(-0.687325\pi\)
−0.555113 + 0.831775i \(0.687325\pi\)
\(192\) 0 0
\(193\) 8.13361 0.585470 0.292735 0.956194i \(-0.405435\pi\)
0.292735 + 0.956194i \(0.405435\pi\)
\(194\) 0 0
\(195\) −11.2583 −0.806225
\(196\) 0 0
\(197\) 7.89099 0.562209 0.281105 0.959677i \(-0.409299\pi\)
0.281105 + 0.959677i \(0.409299\pi\)
\(198\) 0 0
\(199\) −9.71038 −0.688351 −0.344175 0.938905i \(-0.611841\pi\)
−0.344175 + 0.938905i \(0.611841\pi\)
\(200\) 0 0
\(201\) 1.57054 0.110778
\(202\) 0 0
\(203\) −1.19719 −0.0840266
\(204\) 0 0
\(205\) −9.03633 −0.631124
\(206\) 0 0
\(207\) −0.724820 −0.0503784
\(208\) 0 0
\(209\) −3.43613 −0.237682
\(210\) 0 0
\(211\) −3.00745 −0.207041 −0.103521 0.994627i \(-0.533011\pi\)
−0.103521 + 0.994627i \(0.533011\pi\)
\(212\) 0 0
\(213\) 24.9198 1.70748
\(214\) 0 0
\(215\) −10.4240 −0.710913
\(216\) 0 0
\(217\) 0.189262 0.0128480
\(218\) 0 0
\(219\) 18.8219 1.27187
\(220\) 0 0
\(221\) 18.7980 1.26449
\(222\) 0 0
\(223\) 24.7060 1.65443 0.827217 0.561882i \(-0.189922\pi\)
0.827217 + 0.561882i \(0.189922\pi\)
\(224\) 0 0
\(225\) 0.892989 0.0595326
\(226\) 0 0
\(227\) 3.61489 0.239928 0.119964 0.992778i \(-0.461722\pi\)
0.119964 + 0.992778i \(0.461722\pi\)
\(228\) 0 0
\(229\) 2.41310 0.159462 0.0797309 0.996816i \(-0.474594\pi\)
0.0797309 + 0.996816i \(0.474594\pi\)
\(230\) 0 0
\(231\) −0.542309 −0.0356813
\(232\) 0 0
\(233\) −2.73549 −0.179208 −0.0896038 0.995977i \(-0.528560\pi\)
−0.0896038 + 0.995977i \(0.528560\pi\)
\(234\) 0 0
\(235\) 7.03789 0.459101
\(236\) 0 0
\(237\) −33.7398 −2.19164
\(238\) 0 0
\(239\) 20.1982 1.30651 0.653257 0.757136i \(-0.273402\pi\)
0.653257 + 0.757136i \(0.273402\pi\)
\(240\) 0 0
\(241\) 19.1210 1.23169 0.615847 0.787865i \(-0.288814\pi\)
0.615847 + 0.787865i \(0.288814\pi\)
\(242\) 0 0
\(243\) −8.99818 −0.577233
\(244\) 0 0
\(245\) −6.96449 −0.444945
\(246\) 0 0
\(247\) 13.4426 0.855331
\(248\) 0 0
\(249\) 12.8551 0.814660
\(250\) 0 0
\(251\) −12.2432 −0.772784 −0.386392 0.922335i \(-0.626279\pi\)
−0.386392 + 0.922335i \(0.626279\pi\)
\(252\) 0 0
\(253\) −1.18387 −0.0744291
\(254\) 0 0
\(255\) −6.50011 −0.407053
\(256\) 0 0
\(257\) 17.4727 1.08992 0.544958 0.838463i \(-0.316546\pi\)
0.544958 + 0.838463i \(0.316546\pi\)
\(258\) 0 0
\(259\) 1.22422 0.0760692
\(260\) 0 0
\(261\) 5.67315 0.351159
\(262\) 0 0
\(263\) −27.0884 −1.67034 −0.835171 0.549990i \(-0.814631\pi\)
−0.835171 + 0.549990i \(0.814631\pi\)
\(264\) 0 0
\(265\) 5.21570 0.320398
\(266\) 0 0
\(267\) −13.9218 −0.851999
\(268\) 0 0
\(269\) −21.8420 −1.33173 −0.665865 0.746072i \(-0.731938\pi\)
−0.665865 + 0.746072i \(0.731938\pi\)
\(270\) 0 0
\(271\) −25.2195 −1.53198 −0.765989 0.642854i \(-0.777750\pi\)
−0.765989 + 0.642854i \(0.777750\pi\)
\(272\) 0 0
\(273\) 2.12158 0.128404
\(274\) 0 0
\(275\) 1.45854 0.0879534
\(276\) 0 0
\(277\) −22.0957 −1.32760 −0.663802 0.747908i \(-0.731058\pi\)
−0.663802 + 0.747908i \(0.731058\pi\)
\(278\) 0 0
\(279\) −0.896859 −0.0536936
\(280\) 0 0
\(281\) 12.9881 0.774808 0.387404 0.921910i \(-0.373372\pi\)
0.387404 + 0.921910i \(0.373372\pi\)
\(282\) 0 0
\(283\) 19.0522 1.13254 0.566268 0.824221i \(-0.308387\pi\)
0.566268 + 0.824221i \(0.308387\pi\)
\(284\) 0 0
\(285\) −4.64828 −0.275340
\(286\) 0 0
\(287\) 1.70286 0.100516
\(288\) 0 0
\(289\) −6.14678 −0.361576
\(290\) 0 0
\(291\) 11.7035 0.686072
\(292\) 0 0
\(293\) −6.24228 −0.364678 −0.182339 0.983236i \(-0.558367\pi\)
−0.182339 + 0.983236i \(0.558367\pi\)
\(294\) 0 0
\(295\) 7.83497 0.456170
\(296\) 0 0
\(297\) −6.06356 −0.351843
\(298\) 0 0
\(299\) 4.63143 0.267843
\(300\) 0 0
\(301\) 1.96436 0.113224
\(302\) 0 0
\(303\) −33.0767 −1.90021
\(304\) 0 0
\(305\) −11.8569 −0.678923
\(306\) 0 0
\(307\) −2.96401 −0.169165 −0.0845825 0.996416i \(-0.526956\pi\)
−0.0845825 + 0.996416i \(0.526956\pi\)
\(308\) 0 0
\(309\) −6.50149 −0.369857
\(310\) 0 0
\(311\) −21.7783 −1.23493 −0.617467 0.786597i \(-0.711841\pi\)
−0.617467 + 0.786597i \(0.711841\pi\)
\(312\) 0 0
\(313\) −8.27014 −0.467456 −0.233728 0.972302i \(-0.575093\pi\)
−0.233728 + 0.972302i \(0.575093\pi\)
\(314\) 0 0
\(315\) −0.168280 −0.00948151
\(316\) 0 0
\(317\) 25.2152 1.41623 0.708114 0.706098i \(-0.249546\pi\)
0.708114 + 0.706098i \(0.249546\pi\)
\(318\) 0 0
\(319\) 9.26611 0.518802
\(320\) 0 0
\(321\) −17.3862 −0.970406
\(322\) 0 0
\(323\) 7.76122 0.431846
\(324\) 0 0
\(325\) −5.70600 −0.316512
\(326\) 0 0
\(327\) −9.87771 −0.546238
\(328\) 0 0
\(329\) −1.32626 −0.0731191
\(330\) 0 0
\(331\) −13.3441 −0.733456 −0.366728 0.930328i \(-0.619522\pi\)
−0.366728 + 0.930328i \(0.619522\pi\)
\(332\) 0 0
\(333\) −5.80121 −0.317904
\(334\) 0 0
\(335\) 0.795991 0.0434896
\(336\) 0 0
\(337\) 16.7055 0.910007 0.455004 0.890490i \(-0.349638\pi\)
0.455004 + 0.890490i \(0.349638\pi\)
\(338\) 0 0
\(339\) 5.55558 0.301738
\(340\) 0 0
\(341\) −1.46486 −0.0793268
\(342\) 0 0
\(343\) 2.63155 0.142090
\(344\) 0 0
\(345\) −1.60149 −0.0862215
\(346\) 0 0
\(347\) −1.16196 −0.0623774 −0.0311887 0.999514i \(-0.509929\pi\)
−0.0311887 + 0.999514i \(0.509929\pi\)
\(348\) 0 0
\(349\) −36.9214 −1.97636 −0.988180 0.153301i \(-0.951010\pi\)
−0.988180 + 0.153301i \(0.951010\pi\)
\(350\) 0 0
\(351\) 23.7214 1.26615
\(352\) 0 0
\(353\) 13.2601 0.705761 0.352881 0.935668i \(-0.385202\pi\)
0.352881 + 0.935668i \(0.385202\pi\)
\(354\) 0 0
\(355\) 12.6300 0.670331
\(356\) 0 0
\(357\) 1.22492 0.0648296
\(358\) 0 0
\(359\) −7.26636 −0.383504 −0.191752 0.981443i \(-0.561417\pi\)
−0.191752 + 0.981443i \(0.561417\pi\)
\(360\) 0 0
\(361\) −13.4499 −0.707889
\(362\) 0 0
\(363\) −17.5063 −0.918844
\(364\) 0 0
\(365\) 9.53942 0.499316
\(366\) 0 0
\(367\) −18.3390 −0.957286 −0.478643 0.878010i \(-0.658871\pi\)
−0.478643 + 0.878010i \(0.658871\pi\)
\(368\) 0 0
\(369\) −8.06934 −0.420073
\(370\) 0 0
\(371\) −0.982876 −0.0510284
\(372\) 0 0
\(373\) 22.5544 1.16782 0.583911 0.811817i \(-0.301522\pi\)
0.583911 + 0.811817i \(0.301522\pi\)
\(374\) 0 0
\(375\) 1.97307 0.101889
\(376\) 0 0
\(377\) −36.2502 −1.86698
\(378\) 0 0
\(379\) 21.9228 1.12610 0.563049 0.826423i \(-0.309628\pi\)
0.563049 + 0.826423i \(0.309628\pi\)
\(380\) 0 0
\(381\) −20.2633 −1.03812
\(382\) 0 0
\(383\) 31.6390 1.61668 0.808340 0.588716i \(-0.200366\pi\)
0.808340 + 0.588716i \(0.200366\pi\)
\(384\) 0 0
\(385\) −0.274856 −0.0140080
\(386\) 0 0
\(387\) −9.30855 −0.473180
\(388\) 0 0
\(389\) 28.4167 1.44079 0.720393 0.693567i \(-0.243962\pi\)
0.720393 + 0.693567i \(0.243962\pi\)
\(390\) 0 0
\(391\) 2.67401 0.135230
\(392\) 0 0
\(393\) −15.3150 −0.772538
\(394\) 0 0
\(395\) −17.1002 −0.860404
\(396\) 0 0
\(397\) −17.4172 −0.874146 −0.437073 0.899426i \(-0.643985\pi\)
−0.437073 + 0.899426i \(0.643985\pi\)
\(398\) 0 0
\(399\) 0.875949 0.0438523
\(400\) 0 0
\(401\) −18.6095 −0.929314 −0.464657 0.885491i \(-0.653822\pi\)
−0.464657 + 0.885491i \(0.653822\pi\)
\(402\) 0 0
\(403\) 5.73073 0.285468
\(404\) 0 0
\(405\) −10.8815 −0.540708
\(406\) 0 0
\(407\) −9.47526 −0.469671
\(408\) 0 0
\(409\) 27.2564 1.34774 0.673871 0.738849i \(-0.264631\pi\)
0.673871 + 0.738849i \(0.264631\pi\)
\(410\) 0 0
\(411\) 41.5247 2.04826
\(412\) 0 0
\(413\) −1.47647 −0.0726522
\(414\) 0 0
\(415\) 6.51530 0.319823
\(416\) 0 0
\(417\) 20.6451 1.01099
\(418\) 0 0
\(419\) 24.3451 1.18934 0.594669 0.803971i \(-0.297283\pi\)
0.594669 + 0.803971i \(0.297283\pi\)
\(420\) 0 0
\(421\) 25.6110 1.24820 0.624102 0.781343i \(-0.285465\pi\)
0.624102 + 0.781343i \(0.285465\pi\)
\(422\) 0 0
\(423\) 6.28476 0.305575
\(424\) 0 0
\(425\) −3.29442 −0.159803
\(426\) 0 0
\(427\) 2.23438 0.108129
\(428\) 0 0
\(429\) −16.4207 −0.792800
\(430\) 0 0
\(431\) 9.10491 0.438568 0.219284 0.975661i \(-0.429628\pi\)
0.219284 + 0.975661i \(0.429628\pi\)
\(432\) 0 0
\(433\) 32.1652 1.54576 0.772880 0.634552i \(-0.218815\pi\)
0.772880 + 0.634552i \(0.218815\pi\)
\(434\) 0 0
\(435\) 12.5349 0.601001
\(436\) 0 0
\(437\) 1.91221 0.0914732
\(438\) 0 0
\(439\) 13.6927 0.653515 0.326757 0.945108i \(-0.394044\pi\)
0.326757 + 0.945108i \(0.394044\pi\)
\(440\) 0 0
\(441\) −6.21921 −0.296153
\(442\) 0 0
\(443\) −34.4325 −1.63594 −0.817969 0.575263i \(-0.804900\pi\)
−0.817969 + 0.575263i \(0.804900\pi\)
\(444\) 0 0
\(445\) −7.05591 −0.334482
\(446\) 0 0
\(447\) −12.9430 −0.612182
\(448\) 0 0
\(449\) 25.2783 1.19296 0.596479 0.802628i \(-0.296566\pi\)
0.596479 + 0.802628i \(0.296566\pi\)
\(450\) 0 0
\(451\) −13.1799 −0.620616
\(452\) 0 0
\(453\) 1.97307 0.0927027
\(454\) 0 0
\(455\) 1.07527 0.0504095
\(456\) 0 0
\(457\) −30.9143 −1.44611 −0.723056 0.690790i \(-0.757263\pi\)
−0.723056 + 0.690790i \(0.757263\pi\)
\(458\) 0 0
\(459\) 13.6958 0.639265
\(460\) 0 0
\(461\) 35.7687 1.66592 0.832958 0.553336i \(-0.186645\pi\)
0.832958 + 0.553336i \(0.186645\pi\)
\(462\) 0 0
\(463\) −32.8482 −1.52659 −0.763293 0.646053i \(-0.776419\pi\)
−0.763293 + 0.646053i \(0.776419\pi\)
\(464\) 0 0
\(465\) −1.98162 −0.0918953
\(466\) 0 0
\(467\) 25.0429 1.15885 0.579423 0.815027i \(-0.303278\pi\)
0.579423 + 0.815027i \(0.303278\pi\)
\(468\) 0 0
\(469\) −0.150001 −0.00692641
\(470\) 0 0
\(471\) −15.5273 −0.715459
\(472\) 0 0
\(473\) −15.2039 −0.699076
\(474\) 0 0
\(475\) −2.35587 −0.108095
\(476\) 0 0
\(477\) 4.65756 0.213255
\(478\) 0 0
\(479\) −22.9908 −1.05048 −0.525238 0.850955i \(-0.676024\pi\)
−0.525238 + 0.850955i \(0.676024\pi\)
\(480\) 0 0
\(481\) 37.0684 1.69017
\(482\) 0 0
\(483\) 0.301795 0.0137321
\(484\) 0 0
\(485\) 5.93164 0.269342
\(486\) 0 0
\(487\) −26.1531 −1.18511 −0.592555 0.805530i \(-0.701881\pi\)
−0.592555 + 0.805530i \(0.701881\pi\)
\(488\) 0 0
\(489\) 11.6334 0.526081
\(490\) 0 0
\(491\) −15.1841 −0.685247 −0.342623 0.939473i \(-0.611316\pi\)
−0.342623 + 0.939473i \(0.611316\pi\)
\(492\) 0 0
\(493\) −20.9294 −0.942614
\(494\) 0 0
\(495\) 1.30246 0.0585413
\(496\) 0 0
\(497\) −2.38007 −0.106761
\(498\) 0 0
\(499\) −1.95963 −0.0877250 −0.0438625 0.999038i \(-0.513966\pi\)
−0.0438625 + 0.999038i \(0.513966\pi\)
\(500\) 0 0
\(501\) −6.84343 −0.305742
\(502\) 0 0
\(503\) 37.7556 1.68344 0.841718 0.539917i \(-0.181544\pi\)
0.841718 + 0.539917i \(0.181544\pi\)
\(504\) 0 0
\(505\) −16.7641 −0.745993
\(506\) 0 0
\(507\) 38.5901 1.71385
\(508\) 0 0
\(509\) 34.1891 1.51541 0.757703 0.652600i \(-0.226322\pi\)
0.757703 + 0.652600i \(0.226322\pi\)
\(510\) 0 0
\(511\) −1.79766 −0.0795240
\(512\) 0 0
\(513\) 9.79398 0.432415
\(514\) 0 0
\(515\) −3.29512 −0.145200
\(516\) 0 0
\(517\) 10.2651 0.451457
\(518\) 0 0
\(519\) 3.60126 0.158078
\(520\) 0 0
\(521\) −17.2394 −0.755272 −0.377636 0.925954i \(-0.623263\pi\)
−0.377636 + 0.925954i \(0.623263\pi\)
\(522\) 0 0
\(523\) 28.7547 1.25735 0.628677 0.777666i \(-0.283597\pi\)
0.628677 + 0.777666i \(0.283597\pi\)
\(524\) 0 0
\(525\) −0.371816 −0.0162274
\(526\) 0 0
\(527\) 3.30870 0.144129
\(528\) 0 0
\(529\) −22.3412 −0.971356
\(530\) 0 0
\(531\) 6.99655 0.303624
\(532\) 0 0
\(533\) 51.5613 2.23337
\(534\) 0 0
\(535\) −8.81179 −0.380967
\(536\) 0 0
\(537\) 28.1610 1.21524
\(538\) 0 0
\(539\) −10.1580 −0.437536
\(540\) 0 0
\(541\) −32.4085 −1.39335 −0.696676 0.717386i \(-0.745338\pi\)
−0.696676 + 0.717386i \(0.745338\pi\)
\(542\) 0 0
\(543\) 4.09466 0.175718
\(544\) 0 0
\(545\) −5.00627 −0.214445
\(546\) 0 0
\(547\) −35.8456 −1.53265 −0.766323 0.642456i \(-0.777916\pi\)
−0.766323 + 0.642456i \(0.777916\pi\)
\(548\) 0 0
\(549\) −10.5881 −0.451888
\(550\) 0 0
\(551\) −14.9668 −0.637607
\(552\) 0 0
\(553\) 3.22246 0.137033
\(554\) 0 0
\(555\) −12.8178 −0.544086
\(556\) 0 0
\(557\) −33.2005 −1.40675 −0.703375 0.710819i \(-0.748325\pi\)
−0.703375 + 0.710819i \(0.748325\pi\)
\(558\) 0 0
\(559\) 59.4795 2.51572
\(560\) 0 0
\(561\) −9.48069 −0.400275
\(562\) 0 0
\(563\) 5.48206 0.231041 0.115521 0.993305i \(-0.463146\pi\)
0.115521 + 0.993305i \(0.463146\pi\)
\(564\) 0 0
\(565\) 2.81571 0.118458
\(566\) 0 0
\(567\) 2.05058 0.0861163
\(568\) 0 0
\(569\) 3.11243 0.130480 0.0652399 0.997870i \(-0.479219\pi\)
0.0652399 + 0.997870i \(0.479219\pi\)
\(570\) 0 0
\(571\) −34.7084 −1.45250 −0.726252 0.687429i \(-0.758739\pi\)
−0.726252 + 0.687429i \(0.758739\pi\)
\(572\) 0 0
\(573\) −30.2740 −1.26471
\(574\) 0 0
\(575\) −0.811678 −0.0338493
\(576\) 0 0
\(577\) 21.4814 0.894284 0.447142 0.894463i \(-0.352442\pi\)
0.447142 + 0.894463i \(0.352442\pi\)
\(578\) 0 0
\(579\) 16.0482 0.666938
\(580\) 0 0
\(581\) −1.22778 −0.0509369
\(582\) 0 0
\(583\) 7.60732 0.315063
\(584\) 0 0
\(585\) −5.09540 −0.210669
\(586\) 0 0
\(587\) 7.03865 0.290516 0.145258 0.989394i \(-0.453599\pi\)
0.145258 + 0.989394i \(0.453599\pi\)
\(588\) 0 0
\(589\) 2.36608 0.0974925
\(590\) 0 0
\(591\) 15.5694 0.640441
\(592\) 0 0
\(593\) −4.63627 −0.190389 −0.0951943 0.995459i \(-0.530347\pi\)
−0.0951943 + 0.995459i \(0.530347\pi\)
\(594\) 0 0
\(595\) 0.620820 0.0254511
\(596\) 0 0
\(597\) −19.1592 −0.784135
\(598\) 0 0
\(599\) −19.8199 −0.809820 −0.404910 0.914357i \(-0.632697\pi\)
−0.404910 + 0.914357i \(0.632697\pi\)
\(600\) 0 0
\(601\) 20.5664 0.838923 0.419461 0.907773i \(-0.362219\pi\)
0.419461 + 0.907773i \(0.362219\pi\)
\(602\) 0 0
\(603\) 0.710811 0.0289465
\(604\) 0 0
\(605\) −8.87265 −0.360725
\(606\) 0 0
\(607\) −45.1910 −1.83424 −0.917122 0.398606i \(-0.869494\pi\)
−0.917122 + 0.398606i \(0.869494\pi\)
\(608\) 0 0
\(609\) −2.36214 −0.0957189
\(610\) 0 0
\(611\) −40.1582 −1.62463
\(612\) 0 0
\(613\) 1.56705 0.0632927 0.0316463 0.999499i \(-0.489925\pi\)
0.0316463 + 0.999499i \(0.489925\pi\)
\(614\) 0 0
\(615\) −17.8293 −0.718945
\(616\) 0 0
\(617\) −13.9257 −0.560630 −0.280315 0.959908i \(-0.590439\pi\)
−0.280315 + 0.959908i \(0.590439\pi\)
\(618\) 0 0
\(619\) −15.2910 −0.614596 −0.307298 0.951613i \(-0.599425\pi\)
−0.307298 + 0.951613i \(0.599425\pi\)
\(620\) 0 0
\(621\) 3.37436 0.135409
\(622\) 0 0
\(623\) 1.32966 0.0532716
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −6.77972 −0.270756
\(628\) 0 0
\(629\) 21.4018 0.853348
\(630\) 0 0
\(631\) −33.6021 −1.33768 −0.668840 0.743406i \(-0.733209\pi\)
−0.668840 + 0.743406i \(0.733209\pi\)
\(632\) 0 0
\(633\) −5.93389 −0.235851
\(634\) 0 0
\(635\) −10.2700 −0.407551
\(636\) 0 0
\(637\) 39.7394 1.57453
\(638\) 0 0
\(639\) 11.2785 0.446169
\(640\) 0 0
\(641\) −5.98940 −0.236567 −0.118283 0.992980i \(-0.537739\pi\)
−0.118283 + 0.992980i \(0.537739\pi\)
\(642\) 0 0
\(643\) 17.3369 0.683699 0.341850 0.939755i \(-0.388947\pi\)
0.341850 + 0.939755i \(0.388947\pi\)
\(644\) 0 0
\(645\) −20.5673 −0.809837
\(646\) 0 0
\(647\) −39.0043 −1.53342 −0.766708 0.641996i \(-0.778106\pi\)
−0.766708 + 0.641996i \(0.778106\pi\)
\(648\) 0 0
\(649\) 11.4276 0.448574
\(650\) 0 0
\(651\) 0.373427 0.0146358
\(652\) 0 0
\(653\) 21.5523 0.843407 0.421704 0.906734i \(-0.361432\pi\)
0.421704 + 0.906734i \(0.361432\pi\)
\(654\) 0 0
\(655\) −7.76201 −0.303287
\(656\) 0 0
\(657\) 8.51860 0.332342
\(658\) 0 0
\(659\) 18.2891 0.712441 0.356221 0.934402i \(-0.384065\pi\)
0.356221 + 0.934402i \(0.384065\pi\)
\(660\) 0 0
\(661\) −16.2982 −0.633926 −0.316963 0.948438i \(-0.602663\pi\)
−0.316963 + 0.948438i \(0.602663\pi\)
\(662\) 0 0
\(663\) 37.0896 1.44044
\(664\) 0 0
\(665\) 0.443953 0.0172158
\(666\) 0 0
\(667\) −5.15658 −0.199664
\(668\) 0 0
\(669\) 48.7465 1.88465
\(670\) 0 0
\(671\) −17.2938 −0.667619
\(672\) 0 0
\(673\) 7.35910 0.283672 0.141836 0.989890i \(-0.454699\pi\)
0.141836 + 0.989890i \(0.454699\pi\)
\(674\) 0 0
\(675\) −4.15727 −0.160013
\(676\) 0 0
\(677\) 20.9604 0.805574 0.402787 0.915294i \(-0.368042\pi\)
0.402787 + 0.915294i \(0.368042\pi\)
\(678\) 0 0
\(679\) −1.11779 −0.0428969
\(680\) 0 0
\(681\) 7.13241 0.273315
\(682\) 0 0
\(683\) −28.9997 −1.10964 −0.554822 0.831969i \(-0.687214\pi\)
−0.554822 + 0.831969i \(0.687214\pi\)
\(684\) 0 0
\(685\) 21.0458 0.804117
\(686\) 0 0
\(687\) 4.76120 0.181651
\(688\) 0 0
\(689\) −29.7608 −1.13380
\(690\) 0 0
\(691\) −2.84746 −0.108323 −0.0541613 0.998532i \(-0.517249\pi\)
−0.0541613 + 0.998532i \(0.517249\pi\)
\(692\) 0 0
\(693\) −0.245444 −0.00932363
\(694\) 0 0
\(695\) 10.4634 0.396901
\(696\) 0 0
\(697\) 29.7695 1.12760
\(698\) 0 0
\(699\) −5.39729 −0.204144
\(700\) 0 0
\(701\) −14.7745 −0.558024 −0.279012 0.960288i \(-0.590007\pi\)
−0.279012 + 0.960288i \(0.590007\pi\)
\(702\) 0 0
\(703\) 15.3046 0.577225
\(704\) 0 0
\(705\) 13.8862 0.522985
\(706\) 0 0
\(707\) 3.15913 0.118811
\(708\) 0 0
\(709\) 0.381680 0.0143343 0.00716714 0.999974i \(-0.497719\pi\)
0.00716714 + 0.999974i \(0.497719\pi\)
\(710\) 0 0
\(711\) −15.2703 −0.572680
\(712\) 0 0
\(713\) 0.815195 0.0305293
\(714\) 0 0
\(715\) −8.32245 −0.311242
\(716\) 0 0
\(717\) 39.8524 1.48832
\(718\) 0 0
\(719\) 28.8978 1.07771 0.538853 0.842400i \(-0.318858\pi\)
0.538853 + 0.842400i \(0.318858\pi\)
\(720\) 0 0
\(721\) 0.620952 0.0231255
\(722\) 0 0
\(723\) 37.7271 1.40309
\(724\) 0 0
\(725\) 6.35299 0.235944
\(726\) 0 0
\(727\) −3.75757 −0.139361 −0.0696803 0.997569i \(-0.522198\pi\)
−0.0696803 + 0.997569i \(0.522198\pi\)
\(728\) 0 0
\(729\) 14.8906 0.551504
\(730\) 0 0
\(731\) 34.3411 1.27015
\(732\) 0 0
\(733\) 18.1481 0.670317 0.335158 0.942162i \(-0.391210\pi\)
0.335158 + 0.942162i \(0.391210\pi\)
\(734\) 0 0
\(735\) −13.7414 −0.506859
\(736\) 0 0
\(737\) 1.16099 0.0427655
\(738\) 0 0
\(739\) −26.9893 −0.992817 −0.496409 0.868089i \(-0.665348\pi\)
−0.496409 + 0.868089i \(0.665348\pi\)
\(740\) 0 0
\(741\) 26.5231 0.974351
\(742\) 0 0
\(743\) −19.4932 −0.715136 −0.357568 0.933887i \(-0.616394\pi\)
−0.357568 + 0.933887i \(0.616394\pi\)
\(744\) 0 0
\(745\) −6.55983 −0.240334
\(746\) 0 0
\(747\) 5.81809 0.212873
\(748\) 0 0
\(749\) 1.66054 0.0606750
\(750\) 0 0
\(751\) 0.248167 0.00905574 0.00452787 0.999990i \(-0.498559\pi\)
0.00452787 + 0.999990i \(0.498559\pi\)
\(752\) 0 0
\(753\) −24.1567 −0.880317
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 27.1317 0.986120 0.493060 0.869995i \(-0.335878\pi\)
0.493060 + 0.869995i \(0.335878\pi\)
\(758\) 0 0
\(759\) −2.33585 −0.0847859
\(760\) 0 0
\(761\) −13.3758 −0.484873 −0.242436 0.970167i \(-0.577947\pi\)
−0.242436 + 0.970167i \(0.577947\pi\)
\(762\) 0 0
\(763\) 0.943411 0.0341538
\(764\) 0 0
\(765\) −2.94188 −0.106364
\(766\) 0 0
\(767\) −44.7064 −1.61425
\(768\) 0 0
\(769\) 27.6141 0.995791 0.497896 0.867237i \(-0.334106\pi\)
0.497896 + 0.867237i \(0.334106\pi\)
\(770\) 0 0
\(771\) 34.4748 1.24158
\(772\) 0 0
\(773\) 10.5348 0.378912 0.189456 0.981889i \(-0.439328\pi\)
0.189456 + 0.981889i \(0.439328\pi\)
\(774\) 0 0
\(775\) −1.00433 −0.0360767
\(776\) 0 0
\(777\) 2.41546 0.0866542
\(778\) 0 0
\(779\) 21.2884 0.762736
\(780\) 0 0
\(781\) 18.4214 0.659169
\(782\) 0 0
\(783\) −26.4111 −0.943856
\(784\) 0 0
\(785\) −7.86962 −0.280879
\(786\) 0 0
\(787\) −21.4949 −0.766209 −0.383105 0.923705i \(-0.625145\pi\)
−0.383105 + 0.923705i \(0.625145\pi\)
\(788\) 0 0
\(789\) −53.4472 −1.90277
\(790\) 0 0
\(791\) −0.530608 −0.0188663
\(792\) 0 0
\(793\) 67.6554 2.40251
\(794\) 0 0
\(795\) 10.2909 0.364981
\(796\) 0 0
\(797\) −39.6938 −1.40603 −0.703013 0.711177i \(-0.748163\pi\)
−0.703013 + 0.711177i \(0.748163\pi\)
\(798\) 0 0
\(799\) −23.1858 −0.820254
\(800\) 0 0
\(801\) −6.30085 −0.222630
\(802\) 0 0
\(803\) 13.9137 0.491002
\(804\) 0 0
\(805\) 0.152957 0.00539103
\(806\) 0 0
\(807\) −43.0957 −1.51704
\(808\) 0 0
\(809\) 32.9520 1.15853 0.579265 0.815140i \(-0.303340\pi\)
0.579265 + 0.815140i \(0.303340\pi\)
\(810\) 0 0
\(811\) −32.7754 −1.15090 −0.575450 0.817837i \(-0.695173\pi\)
−0.575450 + 0.817837i \(0.695173\pi\)
\(812\) 0 0
\(813\) −49.7598 −1.74515
\(814\) 0 0
\(815\) 5.89611 0.206532
\(816\) 0 0
\(817\) 24.5576 0.859163
\(818\) 0 0
\(819\) 0.960206 0.0335523
\(820\) 0 0
\(821\) 50.6760 1.76861 0.884303 0.466914i \(-0.154634\pi\)
0.884303 + 0.466914i \(0.154634\pi\)
\(822\) 0 0
\(823\) 5.91318 0.206121 0.103060 0.994675i \(-0.467137\pi\)
0.103060 + 0.994675i \(0.467137\pi\)
\(824\) 0 0
\(825\) 2.87780 0.100192
\(826\) 0 0
\(827\) 51.9688 1.80713 0.903566 0.428448i \(-0.140940\pi\)
0.903566 + 0.428448i \(0.140940\pi\)
\(828\) 0 0
\(829\) 6.38328 0.221700 0.110850 0.993837i \(-0.464643\pi\)
0.110850 + 0.993837i \(0.464643\pi\)
\(830\) 0 0
\(831\) −43.5964 −1.51234
\(832\) 0 0
\(833\) 22.9440 0.794961
\(834\) 0 0
\(835\) −3.46843 −0.120030
\(836\) 0 0
\(837\) 4.17529 0.144319
\(838\) 0 0
\(839\) −54.0976 −1.86766 −0.933829 0.357720i \(-0.883554\pi\)
−0.933829 + 0.357720i \(0.883554\pi\)
\(840\) 0 0
\(841\) 11.3605 0.391741
\(842\) 0 0
\(843\) 25.6265 0.882622
\(844\) 0 0
\(845\) 19.5585 0.672831
\(846\) 0 0
\(847\) 1.67201 0.0574511
\(848\) 0 0
\(849\) 37.5912 1.29013
\(850\) 0 0
\(851\) 5.27298 0.180755
\(852\) 0 0
\(853\) 17.6041 0.602753 0.301377 0.953505i \(-0.402554\pi\)
0.301377 + 0.953505i \(0.402554\pi\)
\(854\) 0 0
\(855\) −2.10376 −0.0719472
\(856\) 0 0
\(857\) 11.4769 0.392042 0.196021 0.980600i \(-0.437198\pi\)
0.196021 + 0.980600i \(0.437198\pi\)
\(858\) 0 0
\(859\) −18.3629 −0.626533 −0.313266 0.949665i \(-0.601423\pi\)
−0.313266 + 0.949665i \(0.601423\pi\)
\(860\) 0 0
\(861\) 3.35985 0.114503
\(862\) 0 0
\(863\) −56.7078 −1.93035 −0.965177 0.261597i \(-0.915751\pi\)
−0.965177 + 0.261597i \(0.915751\pi\)
\(864\) 0 0
\(865\) 1.82521 0.0620590
\(866\) 0 0
\(867\) −12.1280 −0.411889
\(868\) 0 0
\(869\) −24.9414 −0.846077
\(870\) 0 0
\(871\) −4.54193 −0.153897
\(872\) 0 0
\(873\) 5.29689 0.179272
\(874\) 0 0
\(875\) −0.188446 −0.00637063
\(876\) 0 0
\(877\) −14.0790 −0.475413 −0.237706 0.971337i \(-0.576396\pi\)
−0.237706 + 0.971337i \(0.576396\pi\)
\(878\) 0 0
\(879\) −12.3164 −0.415423
\(880\) 0 0
\(881\) −28.2110 −0.950454 −0.475227 0.879863i \(-0.657634\pi\)
−0.475227 + 0.879863i \(0.657634\pi\)
\(882\) 0 0
\(883\) −30.9124 −1.04028 −0.520142 0.854080i \(-0.674121\pi\)
−0.520142 + 0.854080i \(0.674121\pi\)
\(884\) 0 0
\(885\) 15.4589 0.519646
\(886\) 0 0
\(887\) 23.2352 0.780163 0.390082 0.920780i \(-0.372447\pi\)
0.390082 + 0.920780i \(0.372447\pi\)
\(888\) 0 0
\(889\) 1.93533 0.0649090
\(890\) 0 0
\(891\) −15.8712 −0.531705
\(892\) 0 0
\(893\) −16.5803 −0.554840
\(894\) 0 0
\(895\) 14.2727 0.477084
\(896\) 0 0
\(897\) 9.13813 0.305113
\(898\) 0 0
\(899\) −6.38052 −0.212802
\(900\) 0 0
\(901\) −17.1827 −0.572439
\(902\) 0 0
\(903\) 3.87582 0.128979
\(904\) 0 0
\(905\) 2.07528 0.0689845
\(906\) 0 0
\(907\) 23.7548 0.788765 0.394382 0.918946i \(-0.370959\pi\)
0.394382 + 0.918946i \(0.370959\pi\)
\(908\) 0 0
\(909\) −14.9702 −0.496529
\(910\) 0 0
\(911\) −16.0249 −0.530930 −0.265465 0.964121i \(-0.585525\pi\)
−0.265465 + 0.964121i \(0.585525\pi\)
\(912\) 0 0
\(913\) 9.50284 0.314498
\(914\) 0 0
\(915\) −23.3944 −0.773396
\(916\) 0 0
\(917\) 1.46272 0.0483032
\(918\) 0 0
\(919\) 49.0903 1.61934 0.809670 0.586885i \(-0.199646\pi\)
0.809670 + 0.586885i \(0.199646\pi\)
\(920\) 0 0
\(921\) −5.84819 −0.192704
\(922\) 0 0
\(923\) −72.0668 −2.37211
\(924\) 0 0
\(925\) −6.49639 −0.213600
\(926\) 0 0
\(927\) −2.94251 −0.0966447
\(928\) 0 0
\(929\) −54.0620 −1.77372 −0.886858 0.462042i \(-0.847117\pi\)
−0.886858 + 0.462042i \(0.847117\pi\)
\(930\) 0 0
\(931\) 16.4074 0.537731
\(932\) 0 0
\(933\) −42.9700 −1.40678
\(934\) 0 0
\(935\) −4.80505 −0.157142
\(936\) 0 0
\(937\) 25.2934 0.826301 0.413150 0.910663i \(-0.364428\pi\)
0.413150 + 0.910663i \(0.364428\pi\)
\(938\) 0 0
\(939\) −16.3175 −0.532502
\(940\) 0 0
\(941\) −44.1481 −1.43919 −0.719593 0.694396i \(-0.755671\pi\)
−0.719593 + 0.694396i \(0.755671\pi\)
\(942\) 0 0
\(943\) 7.33459 0.238847
\(944\) 0 0
\(945\) 0.783420 0.0254847
\(946\) 0 0
\(947\) −20.5571 −0.668017 −0.334008 0.942570i \(-0.608401\pi\)
−0.334008 + 0.942570i \(0.608401\pi\)
\(948\) 0 0
\(949\) −54.4320 −1.76694
\(950\) 0 0
\(951\) 49.7513 1.61330
\(952\) 0 0
\(953\) −3.33150 −0.107918 −0.0539590 0.998543i \(-0.517184\pi\)
−0.0539590 + 0.998543i \(0.517184\pi\)
\(954\) 0 0
\(955\) −15.3436 −0.496508
\(956\) 0 0
\(957\) 18.2826 0.590994
\(958\) 0 0
\(959\) −3.96598 −0.128068
\(960\) 0 0
\(961\) −29.9913 −0.967462
\(962\) 0 0
\(963\) −7.86884 −0.253570
\(964\) 0 0
\(965\) 8.13361 0.261830
\(966\) 0 0
\(967\) 17.3673 0.558496 0.279248 0.960219i \(-0.409915\pi\)
0.279248 + 0.960219i \(0.409915\pi\)
\(968\) 0 0
\(969\) 15.3134 0.491937
\(970\) 0 0
\(971\) −28.6022 −0.917890 −0.458945 0.888465i \(-0.651772\pi\)
−0.458945 + 0.888465i \(0.651772\pi\)
\(972\) 0 0
\(973\) −1.97179 −0.0632127
\(974\) 0 0
\(975\) −11.2583 −0.360555
\(976\) 0 0
\(977\) −29.1725 −0.933310 −0.466655 0.884440i \(-0.654541\pi\)
−0.466655 + 0.884440i \(0.654541\pi\)
\(978\) 0 0
\(979\) −10.2913 −0.328913
\(980\) 0 0
\(981\) −4.47055 −0.142734
\(982\) 0 0
\(983\) 6.10404 0.194689 0.0973443 0.995251i \(-0.468965\pi\)
0.0973443 + 0.995251i \(0.468965\pi\)
\(984\) 0 0
\(985\) 7.89099 0.251428
\(986\) 0 0
\(987\) −2.61680 −0.0832936
\(988\) 0 0
\(989\) 8.46095 0.269043
\(990\) 0 0
\(991\) −25.6212 −0.813883 −0.406942 0.913454i \(-0.633405\pi\)
−0.406942 + 0.913454i \(0.633405\pi\)
\(992\) 0 0
\(993\) −26.3287 −0.835517
\(994\) 0 0
\(995\) −9.71038 −0.307840
\(996\) 0 0
\(997\) 20.2770 0.642181 0.321090 0.947049i \(-0.395951\pi\)
0.321090 + 0.947049i \(0.395951\pi\)
\(998\) 0 0
\(999\) 27.0073 0.854472
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 \(a_p\))