Properties

Label 6040.2.a.p.1.7
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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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 1.7
Root \(1.68584\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.68584 q^{3}\) \(+1.00000 q^{5}\) \(-4.78926 q^{7}\) \(-0.157936 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.68584 q^{3}\) \(+1.00000 q^{5}\) \(-4.78926 q^{7}\) \(-0.157936 q^{9}\) \(-1.17912 q^{11}\) \(+3.55016 q^{13}\) \(-1.68584 q^{15}\) \(+5.24056 q^{17}\) \(+2.24601 q^{19}\) \(+8.07394 q^{21}\) \(-8.41556 q^{23}\) \(+1.00000 q^{25}\) \(+5.32378 q^{27}\) \(-8.71732 q^{29}\) \(+3.38760 q^{31}\) \(+1.98782 q^{33}\) \(-4.78926 q^{35}\) \(+9.53075 q^{37}\) \(-5.98501 q^{39}\) \(-2.73536 q^{41}\) \(+4.70896 q^{43}\) \(-0.157936 q^{45}\) \(-11.7202 q^{47}\) \(+15.9370 q^{49}\) \(-8.83475 q^{51}\) \(-4.56229 q^{53}\) \(-1.17912 q^{55}\) \(-3.78642 q^{57}\) \(+2.95106 q^{59}\) \(+3.98085 q^{61}\) \(+0.756395 q^{63}\) \(+3.55016 q^{65}\) \(+13.8968 q^{67}\) \(+14.1873 q^{69}\) \(-3.61567 q^{71}\) \(+9.48202 q^{73}\) \(-1.68584 q^{75}\) \(+5.64713 q^{77}\) \(+1.13533 q^{79}\) \(-8.50125 q^{81}\) \(+15.4538 q^{83}\) \(+5.24056 q^{85}\) \(+14.6960 q^{87}\) \(-0.962116 q^{89}\) \(-17.0027 q^{91}\) \(-5.71097 q^{93}\) \(+2.24601 q^{95}\) \(+3.59211 q^{97}\) \(+0.186226 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.68584 −0.973322 −0.486661 0.873591i \(-0.661785\pi\)
−0.486661 + 0.873591i \(0.661785\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.78926 −1.81017 −0.905086 0.425229i \(-0.860194\pi\)
−0.905086 + 0.425229i \(0.860194\pi\)
\(8\) 0 0
\(9\) −0.157936 −0.0526452
\(10\) 0 0
\(11\) −1.17912 −0.355519 −0.177760 0.984074i \(-0.556885\pi\)
−0.177760 + 0.984074i \(0.556885\pi\)
\(12\) 0 0
\(13\) 3.55016 0.984637 0.492319 0.870415i \(-0.336149\pi\)
0.492319 + 0.870415i \(0.336149\pi\)
\(14\) 0 0
\(15\) −1.68584 −0.435283
\(16\) 0 0
\(17\) 5.24056 1.27102 0.635511 0.772092i \(-0.280790\pi\)
0.635511 + 0.772092i \(0.280790\pi\)
\(18\) 0 0
\(19\) 2.24601 0.515270 0.257635 0.966242i \(-0.417057\pi\)
0.257635 + 0.966242i \(0.417057\pi\)
\(20\) 0 0
\(21\) 8.07394 1.76188
\(22\) 0 0
\(23\) −8.41556 −1.75477 −0.877383 0.479790i \(-0.840713\pi\)
−0.877383 + 0.479790i \(0.840713\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.32378 1.02456
\(28\) 0 0
\(29\) −8.71732 −1.61877 −0.809383 0.587282i \(-0.800198\pi\)
−0.809383 + 0.587282i \(0.800198\pi\)
\(30\) 0 0
\(31\) 3.38760 0.608432 0.304216 0.952603i \(-0.401606\pi\)
0.304216 + 0.952603i \(0.401606\pi\)
\(32\) 0 0
\(33\) 1.98782 0.346034
\(34\) 0 0
\(35\) −4.78926 −0.809533
\(36\) 0 0
\(37\) 9.53075 1.56685 0.783423 0.621489i \(-0.213472\pi\)
0.783423 + 0.621489i \(0.213472\pi\)
\(38\) 0 0
\(39\) −5.98501 −0.958369
\(40\) 0 0
\(41\) −2.73536 −0.427192 −0.213596 0.976922i \(-0.568518\pi\)
−0.213596 + 0.976922i \(0.568518\pi\)
\(42\) 0 0
\(43\) 4.70896 0.718110 0.359055 0.933316i \(-0.383099\pi\)
0.359055 + 0.933316i \(0.383099\pi\)
\(44\) 0 0
\(45\) −0.157936 −0.0235436
\(46\) 0 0
\(47\) −11.7202 −1.70956 −0.854781 0.518989i \(-0.826308\pi\)
−0.854781 + 0.518989i \(0.826308\pi\)
\(48\) 0 0
\(49\) 15.9370 2.27672
\(50\) 0 0
\(51\) −8.83475 −1.23711
\(52\) 0 0
\(53\) −4.56229 −0.626679 −0.313340 0.949641i \(-0.601448\pi\)
−0.313340 + 0.949641i \(0.601448\pi\)
\(54\) 0 0
\(55\) −1.17912 −0.158993
\(56\) 0 0
\(57\) −3.78642 −0.501524
\(58\) 0 0
\(59\) 2.95106 0.384195 0.192098 0.981376i \(-0.438471\pi\)
0.192098 + 0.981376i \(0.438471\pi\)
\(60\) 0 0
\(61\) 3.98085 0.509696 0.254848 0.966981i \(-0.417975\pi\)
0.254848 + 0.966981i \(0.417975\pi\)
\(62\) 0 0
\(63\) 0.756395 0.0952968
\(64\) 0 0
\(65\) 3.55016 0.440343
\(66\) 0 0
\(67\) 13.8968 1.69776 0.848881 0.528584i \(-0.177277\pi\)
0.848881 + 0.528584i \(0.177277\pi\)
\(68\) 0 0
\(69\) 14.1873 1.70795
\(70\) 0 0
\(71\) −3.61567 −0.429101 −0.214550 0.976713i \(-0.568829\pi\)
−0.214550 + 0.976713i \(0.568829\pi\)
\(72\) 0 0
\(73\) 9.48202 1.10979 0.554893 0.831922i \(-0.312759\pi\)
0.554893 + 0.831922i \(0.312759\pi\)
\(74\) 0 0
\(75\) −1.68584 −0.194664
\(76\) 0 0
\(77\) 5.64713 0.643550
\(78\) 0 0
\(79\) 1.13533 0.127734 0.0638671 0.997958i \(-0.479657\pi\)
0.0638671 + 0.997958i \(0.479657\pi\)
\(80\) 0 0
\(81\) −8.50125 −0.944583
\(82\) 0 0
\(83\) 15.4538 1.69628 0.848138 0.529775i \(-0.177724\pi\)
0.848138 + 0.529775i \(0.177724\pi\)
\(84\) 0 0
\(85\) 5.24056 0.568418
\(86\) 0 0
\(87\) 14.6960 1.57558
\(88\) 0 0
\(89\) −0.962116 −0.101984 −0.0509920 0.998699i \(-0.516238\pi\)
−0.0509920 + 0.998699i \(0.516238\pi\)
\(90\) 0 0
\(91\) −17.0027 −1.78236
\(92\) 0 0
\(93\) −5.71097 −0.592200
\(94\) 0 0
\(95\) 2.24601 0.230436
\(96\) 0 0
\(97\) 3.59211 0.364723 0.182362 0.983232i \(-0.441626\pi\)
0.182362 + 0.983232i \(0.441626\pi\)
\(98\) 0 0
\(99\) 0.186226 0.0187164
\(100\) 0 0
\(101\) −11.2620 −1.12061 −0.560304 0.828287i \(-0.689316\pi\)
−0.560304 + 0.828287i \(0.689316\pi\)
\(102\) 0 0
\(103\) −13.2954 −1.31004 −0.655019 0.755612i \(-0.727339\pi\)
−0.655019 + 0.755612i \(0.727339\pi\)
\(104\) 0 0
\(105\) 8.07394 0.787936
\(106\) 0 0
\(107\) 0.644033 0.0622610 0.0311305 0.999515i \(-0.490089\pi\)
0.0311305 + 0.999515i \(0.490089\pi\)
\(108\) 0 0
\(109\) 14.0524 1.34598 0.672988 0.739653i \(-0.265010\pi\)
0.672988 + 0.739653i \(0.265010\pi\)
\(110\) 0 0
\(111\) −16.0673 −1.52504
\(112\) 0 0
\(113\) −6.81062 −0.640689 −0.320345 0.947301i \(-0.603799\pi\)
−0.320345 + 0.947301i \(0.603799\pi\)
\(114\) 0 0
\(115\) −8.41556 −0.784755
\(116\) 0 0
\(117\) −0.560697 −0.0518364
\(118\) 0 0
\(119\) −25.0984 −2.30077
\(120\) 0 0
\(121\) −9.60967 −0.873606
\(122\) 0 0
\(123\) 4.61139 0.415795
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 5.47889 0.486173 0.243086 0.970005i \(-0.421840\pi\)
0.243086 + 0.970005i \(0.421840\pi\)
\(128\) 0 0
\(129\) −7.93857 −0.698952
\(130\) 0 0
\(131\) −9.29141 −0.811795 −0.405897 0.913919i \(-0.633041\pi\)
−0.405897 + 0.913919i \(0.633041\pi\)
\(132\) 0 0
\(133\) −10.7567 −0.932728
\(134\) 0 0
\(135\) 5.32378 0.458198
\(136\) 0 0
\(137\) 5.97746 0.510689 0.255344 0.966850i \(-0.417811\pi\)
0.255344 + 0.966850i \(0.417811\pi\)
\(138\) 0 0
\(139\) −12.0766 −1.02433 −0.512164 0.858888i \(-0.671156\pi\)
−0.512164 + 0.858888i \(0.671156\pi\)
\(140\) 0 0
\(141\) 19.7583 1.66395
\(142\) 0 0
\(143\) −4.18608 −0.350057
\(144\) 0 0
\(145\) −8.71732 −0.723934
\(146\) 0 0
\(147\) −26.8673 −2.21598
\(148\) 0 0
\(149\) −12.0049 −0.983480 −0.491740 0.870742i \(-0.663639\pi\)
−0.491740 + 0.870742i \(0.663639\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −0.827670 −0.0669132
\(154\) 0 0
\(155\) 3.38760 0.272099
\(156\) 0 0
\(157\) −2.61722 −0.208877 −0.104438 0.994531i \(-0.533304\pi\)
−0.104438 + 0.994531i \(0.533304\pi\)
\(158\) 0 0
\(159\) 7.69131 0.609960
\(160\) 0 0
\(161\) 40.3044 3.17643
\(162\) 0 0
\(163\) 16.6073 1.30078 0.650391 0.759599i \(-0.274605\pi\)
0.650391 + 0.759599i \(0.274605\pi\)
\(164\) 0 0
\(165\) 1.98782 0.154751
\(166\) 0 0
\(167\) −20.2987 −1.57076 −0.785379 0.619015i \(-0.787532\pi\)
−0.785379 + 0.619015i \(0.787532\pi\)
\(168\) 0 0
\(169\) −0.396361 −0.0304893
\(170\) 0 0
\(171\) −0.354725 −0.0271265
\(172\) 0 0
\(173\) −19.2373 −1.46258 −0.731291 0.682066i \(-0.761082\pi\)
−0.731291 + 0.682066i \(0.761082\pi\)
\(174\) 0 0
\(175\) −4.78926 −0.362034
\(176\) 0 0
\(177\) −4.97502 −0.373945
\(178\) 0 0
\(179\) 23.5260 1.75841 0.879207 0.476439i \(-0.158073\pi\)
0.879207 + 0.476439i \(0.158073\pi\)
\(180\) 0 0
\(181\) −2.07285 −0.154074 −0.0770369 0.997028i \(-0.524546\pi\)
−0.0770369 + 0.997028i \(0.524546\pi\)
\(182\) 0 0
\(183\) −6.71109 −0.496098
\(184\) 0 0
\(185\) 9.53075 0.700715
\(186\) 0 0
\(187\) −6.17926 −0.451872
\(188\) 0 0
\(189\) −25.4970 −1.85463
\(190\) 0 0
\(191\) −16.1010 −1.16503 −0.582513 0.812821i \(-0.697931\pi\)
−0.582513 + 0.812821i \(0.697931\pi\)
\(192\) 0 0
\(193\) −20.6192 −1.48420 −0.742100 0.670290i \(-0.766170\pi\)
−0.742100 + 0.670290i \(0.766170\pi\)
\(194\) 0 0
\(195\) −5.98501 −0.428596
\(196\) 0 0
\(197\) −13.3013 −0.947677 −0.473839 0.880612i \(-0.657132\pi\)
−0.473839 + 0.880612i \(0.657132\pi\)
\(198\) 0 0
\(199\) −22.8199 −1.61766 −0.808829 0.588043i \(-0.799898\pi\)
−0.808829 + 0.588043i \(0.799898\pi\)
\(200\) 0 0
\(201\) −23.4278 −1.65247
\(202\) 0 0
\(203\) 41.7495 2.93024
\(204\) 0 0
\(205\) −2.73536 −0.191046
\(206\) 0 0
\(207\) 1.32912 0.0923800
\(208\) 0 0
\(209\) −2.64832 −0.183188
\(210\) 0 0
\(211\) −9.47681 −0.652411 −0.326205 0.945299i \(-0.605770\pi\)
−0.326205 + 0.945299i \(0.605770\pi\)
\(212\) 0 0
\(213\) 6.09544 0.417653
\(214\) 0 0
\(215\) 4.70896 0.321149
\(216\) 0 0
\(217\) −16.2241 −1.10137
\(218\) 0 0
\(219\) −15.9852 −1.08018
\(220\) 0 0
\(221\) 18.6048 1.25150
\(222\) 0 0
\(223\) 19.6834 1.31810 0.659049 0.752100i \(-0.270959\pi\)
0.659049 + 0.752100i \(0.270959\pi\)
\(224\) 0 0
\(225\) −0.157936 −0.0105290
\(226\) 0 0
\(227\) −9.62635 −0.638924 −0.319462 0.947599i \(-0.603502\pi\)
−0.319462 + 0.947599i \(0.603502\pi\)
\(228\) 0 0
\(229\) 6.27899 0.414927 0.207464 0.978243i \(-0.433479\pi\)
0.207464 + 0.978243i \(0.433479\pi\)
\(230\) 0 0
\(231\) −9.52017 −0.626382
\(232\) 0 0
\(233\) 6.72540 0.440596 0.220298 0.975433i \(-0.429297\pi\)
0.220298 + 0.975433i \(0.429297\pi\)
\(234\) 0 0
\(235\) −11.7202 −0.764539
\(236\) 0 0
\(237\) −1.91398 −0.124326
\(238\) 0 0
\(239\) 23.7929 1.53903 0.769517 0.638627i \(-0.220497\pi\)
0.769517 + 0.638627i \(0.220497\pi\)
\(240\) 0 0
\(241\) −12.0919 −0.778908 −0.389454 0.921046i \(-0.627336\pi\)
−0.389454 + 0.921046i \(0.627336\pi\)
\(242\) 0 0
\(243\) −1.63958 −0.105179
\(244\) 0 0
\(245\) 15.9370 1.01818
\(246\) 0 0
\(247\) 7.97370 0.507355
\(248\) 0 0
\(249\) −26.0527 −1.65102
\(250\) 0 0
\(251\) −22.3273 −1.40929 −0.704644 0.709561i \(-0.748893\pi\)
−0.704644 + 0.709561i \(0.748893\pi\)
\(252\) 0 0
\(253\) 9.92299 0.623853
\(254\) 0 0
\(255\) −8.83475 −0.553254
\(256\) 0 0
\(257\) −8.81643 −0.549954 −0.274977 0.961451i \(-0.588670\pi\)
−0.274977 + 0.961451i \(0.588670\pi\)
\(258\) 0 0
\(259\) −45.6453 −2.83626
\(260\) 0 0
\(261\) 1.37677 0.0852202
\(262\) 0 0
\(263\) 2.64563 0.163137 0.0815683 0.996668i \(-0.474007\pi\)
0.0815683 + 0.996668i \(0.474007\pi\)
\(264\) 0 0
\(265\) −4.56229 −0.280259
\(266\) 0 0
\(267\) 1.62198 0.0992633
\(268\) 0 0
\(269\) −22.0993 −1.34742 −0.673709 0.738997i \(-0.735300\pi\)
−0.673709 + 0.738997i \(0.735300\pi\)
\(270\) 0 0
\(271\) 5.22290 0.317268 0.158634 0.987337i \(-0.449291\pi\)
0.158634 + 0.987337i \(0.449291\pi\)
\(272\) 0 0
\(273\) 28.6638 1.73481
\(274\) 0 0
\(275\) −1.17912 −0.0711038
\(276\) 0 0
\(277\) −7.22896 −0.434346 −0.217173 0.976133i \(-0.569684\pi\)
−0.217173 + 0.976133i \(0.569684\pi\)
\(278\) 0 0
\(279\) −0.535023 −0.0320310
\(280\) 0 0
\(281\) −25.5959 −1.52693 −0.763463 0.645852i \(-0.776502\pi\)
−0.763463 + 0.645852i \(0.776502\pi\)
\(282\) 0 0
\(283\) 4.62103 0.274691 0.137346 0.990523i \(-0.456143\pi\)
0.137346 + 0.990523i \(0.456143\pi\)
\(284\) 0 0
\(285\) −3.78642 −0.224288
\(286\) 0 0
\(287\) 13.1004 0.773291
\(288\) 0 0
\(289\) 10.4634 0.615496
\(290\) 0 0
\(291\) −6.05572 −0.354993
\(292\) 0 0
\(293\) 23.3315 1.36304 0.681522 0.731798i \(-0.261319\pi\)
0.681522 + 0.731798i \(0.261319\pi\)
\(294\) 0 0
\(295\) 2.95106 0.171817
\(296\) 0 0
\(297\) −6.27739 −0.364251
\(298\) 0 0
\(299\) −29.8766 −1.72781
\(300\) 0 0
\(301\) −22.5525 −1.29990
\(302\) 0 0
\(303\) 18.9859 1.09071
\(304\) 0 0
\(305\) 3.98085 0.227943
\(306\) 0 0
\(307\) 26.4097 1.50728 0.753640 0.657288i \(-0.228296\pi\)
0.753640 + 0.657288i \(0.228296\pi\)
\(308\) 0 0
\(309\) 22.4140 1.27509
\(310\) 0 0
\(311\) −14.7295 −0.835232 −0.417616 0.908624i \(-0.637134\pi\)
−0.417616 + 0.908624i \(0.637134\pi\)
\(312\) 0 0
\(313\) −17.5665 −0.992917 −0.496459 0.868060i \(-0.665367\pi\)
−0.496459 + 0.868060i \(0.665367\pi\)
\(314\) 0 0
\(315\) 0.756395 0.0426180
\(316\) 0 0
\(317\) 32.7240 1.83796 0.918981 0.394301i \(-0.129013\pi\)
0.918981 + 0.394301i \(0.129013\pi\)
\(318\) 0 0
\(319\) 10.2788 0.575502
\(320\) 0 0
\(321\) −1.08574 −0.0606000
\(322\) 0 0
\(323\) 11.7704 0.654920
\(324\) 0 0
\(325\) 3.55016 0.196927
\(326\) 0 0
\(327\) −23.6901 −1.31007
\(328\) 0 0
\(329\) 56.1309 3.09460
\(330\) 0 0
\(331\) −3.28802 −0.180726 −0.0903628 0.995909i \(-0.528803\pi\)
−0.0903628 + 0.995909i \(0.528803\pi\)
\(332\) 0 0
\(333\) −1.50524 −0.0824869
\(334\) 0 0
\(335\) 13.8968 0.759262
\(336\) 0 0
\(337\) 0.972333 0.0529663 0.0264832 0.999649i \(-0.491569\pi\)
0.0264832 + 0.999649i \(0.491569\pi\)
\(338\) 0 0
\(339\) 11.4816 0.623597
\(340\) 0 0
\(341\) −3.99440 −0.216309
\(342\) 0 0
\(343\) −42.8019 −2.31108
\(344\) 0 0
\(345\) 14.1873 0.763819
\(346\) 0 0
\(347\) −10.3706 −0.556722 −0.278361 0.960477i \(-0.589791\pi\)
−0.278361 + 0.960477i \(0.589791\pi\)
\(348\) 0 0
\(349\) −11.6433 −0.623252 −0.311626 0.950205i \(-0.600874\pi\)
−0.311626 + 0.950205i \(0.600874\pi\)
\(350\) 0 0
\(351\) 18.9003 1.00882
\(352\) 0 0
\(353\) 15.5832 0.829412 0.414706 0.909955i \(-0.363884\pi\)
0.414706 + 0.909955i \(0.363884\pi\)
\(354\) 0 0
\(355\) −3.61567 −0.191900
\(356\) 0 0
\(357\) 42.3120 2.23939
\(358\) 0 0
\(359\) −2.08463 −0.110023 −0.0550113 0.998486i \(-0.517519\pi\)
−0.0550113 + 0.998486i \(0.517519\pi\)
\(360\) 0 0
\(361\) −13.9554 −0.734496
\(362\) 0 0
\(363\) 16.2004 0.850300
\(364\) 0 0
\(365\) 9.48202 0.496311
\(366\) 0 0
\(367\) −27.8275 −1.45258 −0.726291 0.687387i \(-0.758758\pi\)
−0.726291 + 0.687387i \(0.758758\pi\)
\(368\) 0 0
\(369\) 0.432011 0.0224896
\(370\) 0 0
\(371\) 21.8500 1.13440
\(372\) 0 0
\(373\) −23.5229 −1.21797 −0.608984 0.793182i \(-0.708423\pi\)
−0.608984 + 0.793182i \(0.708423\pi\)
\(374\) 0 0
\(375\) −1.68584 −0.0870565
\(376\) 0 0
\(377\) −30.9479 −1.59390
\(378\) 0 0
\(379\) −22.7298 −1.16755 −0.583777 0.811914i \(-0.698426\pi\)
−0.583777 + 0.811914i \(0.698426\pi\)
\(380\) 0 0
\(381\) −9.23654 −0.473202
\(382\) 0 0
\(383\) −24.4353 −1.24858 −0.624291 0.781191i \(-0.714612\pi\)
−0.624291 + 0.781191i \(0.714612\pi\)
\(384\) 0 0
\(385\) 5.64713 0.287805
\(386\) 0 0
\(387\) −0.743713 −0.0378050
\(388\) 0 0
\(389\) −6.54041 −0.331612 −0.165806 0.986158i \(-0.553023\pi\)
−0.165806 + 0.986158i \(0.553023\pi\)
\(390\) 0 0
\(391\) −44.1022 −2.23035
\(392\) 0 0
\(393\) 15.6639 0.790137
\(394\) 0 0
\(395\) 1.13533 0.0571244
\(396\) 0 0
\(397\) 24.1816 1.21364 0.606820 0.794839i \(-0.292445\pi\)
0.606820 + 0.794839i \(0.292445\pi\)
\(398\) 0 0
\(399\) 18.1342 0.907844
\(400\) 0 0
\(401\) 18.4253 0.920115 0.460057 0.887889i \(-0.347829\pi\)
0.460057 + 0.887889i \(0.347829\pi\)
\(402\) 0 0
\(403\) 12.0265 0.599084
\(404\) 0 0
\(405\) −8.50125 −0.422430
\(406\) 0 0
\(407\) −11.2379 −0.557043
\(408\) 0 0
\(409\) 6.95826 0.344064 0.172032 0.985091i \(-0.444967\pi\)
0.172032 + 0.985091i \(0.444967\pi\)
\(410\) 0 0
\(411\) −10.0771 −0.497065
\(412\) 0 0
\(413\) −14.1334 −0.695459
\(414\) 0 0
\(415\) 15.4538 0.758598
\(416\) 0 0
\(417\) 20.3593 0.997000
\(418\) 0 0
\(419\) −25.2342 −1.23277 −0.616387 0.787444i \(-0.711404\pi\)
−0.616387 + 0.787444i \(0.711404\pi\)
\(420\) 0 0
\(421\) −7.85171 −0.382669 −0.191335 0.981525i \(-0.561282\pi\)
−0.191335 + 0.981525i \(0.561282\pi\)
\(422\) 0 0
\(423\) 1.85103 0.0900002
\(424\) 0 0
\(425\) 5.24056 0.254204
\(426\) 0 0
\(427\) −19.0653 −0.922637
\(428\) 0 0
\(429\) 7.05707 0.340718
\(430\) 0 0
\(431\) 28.4386 1.36984 0.684920 0.728619i \(-0.259837\pi\)
0.684920 + 0.728619i \(0.259837\pi\)
\(432\) 0 0
\(433\) 2.45235 0.117853 0.0589263 0.998262i \(-0.481232\pi\)
0.0589263 + 0.998262i \(0.481232\pi\)
\(434\) 0 0
\(435\) 14.6960 0.704620
\(436\) 0 0
\(437\) −18.9015 −0.904179
\(438\) 0 0
\(439\) −12.6622 −0.604333 −0.302167 0.953255i \(-0.597710\pi\)
−0.302167 + 0.953255i \(0.597710\pi\)
\(440\) 0 0
\(441\) −2.51703 −0.119858
\(442\) 0 0
\(443\) 3.19950 0.152013 0.0760064 0.997107i \(-0.475783\pi\)
0.0760064 + 0.997107i \(0.475783\pi\)
\(444\) 0 0
\(445\) −0.962116 −0.0456087
\(446\) 0 0
\(447\) 20.2384 0.957243
\(448\) 0 0
\(449\) −15.5437 −0.733550 −0.366775 0.930310i \(-0.619538\pi\)
−0.366775 + 0.930310i \(0.619538\pi\)
\(450\) 0 0
\(451\) 3.22533 0.151875
\(452\) 0 0
\(453\) −1.68584 −0.0792078
\(454\) 0 0
\(455\) −17.0027 −0.797097
\(456\) 0 0
\(457\) −2.88086 −0.134761 −0.0673806 0.997727i \(-0.521464\pi\)
−0.0673806 + 0.997727i \(0.521464\pi\)
\(458\) 0 0
\(459\) 27.8996 1.30224
\(460\) 0 0
\(461\) −13.2623 −0.617686 −0.308843 0.951113i \(-0.599942\pi\)
−0.308843 + 0.951113i \(0.599942\pi\)
\(462\) 0 0
\(463\) −37.1104 −1.72467 −0.862333 0.506342i \(-0.830998\pi\)
−0.862333 + 0.506342i \(0.830998\pi\)
\(464\) 0 0
\(465\) −5.71097 −0.264840
\(466\) 0 0
\(467\) 29.3945 1.36021 0.680107 0.733112i \(-0.261933\pi\)
0.680107 + 0.733112i \(0.261933\pi\)
\(468\) 0 0
\(469\) −66.5553 −3.07324
\(470\) 0 0
\(471\) 4.41222 0.203304
\(472\) 0 0
\(473\) −5.55245 −0.255302
\(474\) 0 0
\(475\) 2.24601 0.103054
\(476\) 0 0
\(477\) 0.720548 0.0329916
\(478\) 0 0
\(479\) 29.2253 1.33534 0.667670 0.744457i \(-0.267292\pi\)
0.667670 + 0.744457i \(0.267292\pi\)
\(480\) 0 0
\(481\) 33.8357 1.54277
\(482\) 0 0
\(483\) −67.9468 −3.09169
\(484\) 0 0
\(485\) 3.59211 0.163109
\(486\) 0 0
\(487\) 33.6969 1.52695 0.763476 0.645836i \(-0.223491\pi\)
0.763476 + 0.645836i \(0.223491\pi\)
\(488\) 0 0
\(489\) −27.9973 −1.26608
\(490\) 0 0
\(491\) −34.9759 −1.57844 −0.789220 0.614111i \(-0.789515\pi\)
−0.789220 + 0.614111i \(0.789515\pi\)
\(492\) 0 0
\(493\) −45.6836 −2.05749
\(494\) 0 0
\(495\) 0.186226 0.00837021
\(496\) 0 0
\(497\) 17.3164 0.776746
\(498\) 0 0
\(499\) −19.9030 −0.890981 −0.445491 0.895287i \(-0.646971\pi\)
−0.445491 + 0.895287i \(0.646971\pi\)
\(500\) 0 0
\(501\) 34.2204 1.52885
\(502\) 0 0
\(503\) −21.4091 −0.954585 −0.477293 0.878744i \(-0.658382\pi\)
−0.477293 + 0.878744i \(0.658382\pi\)
\(504\) 0 0
\(505\) −11.2620 −0.501151
\(506\) 0 0
\(507\) 0.668202 0.0296759
\(508\) 0 0
\(509\) 20.1679 0.893928 0.446964 0.894552i \(-0.352505\pi\)
0.446964 + 0.894552i \(0.352505\pi\)
\(510\) 0 0
\(511\) −45.4119 −2.00890
\(512\) 0 0
\(513\) 11.9573 0.527927
\(514\) 0 0
\(515\) −13.2954 −0.585867
\(516\) 0 0
\(517\) 13.8195 0.607782
\(518\) 0 0
\(519\) 32.4310 1.42356
\(520\) 0 0
\(521\) −27.0068 −1.18319 −0.591596 0.806235i \(-0.701502\pi\)
−0.591596 + 0.806235i \(0.701502\pi\)
\(522\) 0 0
\(523\) 37.5250 1.64085 0.820427 0.571751i \(-0.193736\pi\)
0.820427 + 0.571751i \(0.193736\pi\)
\(524\) 0 0
\(525\) 8.07394 0.352376
\(526\) 0 0
\(527\) 17.7529 0.773330
\(528\) 0 0
\(529\) 47.8217 2.07921
\(530\) 0 0
\(531\) −0.466077 −0.0202260
\(532\) 0 0
\(533\) −9.71098 −0.420629
\(534\) 0 0
\(535\) 0.644033 0.0278440
\(536\) 0 0
\(537\) −39.6611 −1.71150
\(538\) 0 0
\(539\) −18.7917 −0.809418
\(540\) 0 0
\(541\) 9.04100 0.388703 0.194352 0.980932i \(-0.437740\pi\)
0.194352 + 0.980932i \(0.437740\pi\)
\(542\) 0 0
\(543\) 3.49450 0.149963
\(544\) 0 0
\(545\) 14.0524 0.601939
\(546\) 0 0
\(547\) −1.72613 −0.0738039 −0.0369020 0.999319i \(-0.511749\pi\)
−0.0369020 + 0.999319i \(0.511749\pi\)
\(548\) 0 0
\(549\) −0.628718 −0.0268330
\(550\) 0 0
\(551\) −19.5792 −0.834102
\(552\) 0 0
\(553\) −5.43738 −0.231221
\(554\) 0 0
\(555\) −16.0673 −0.682021
\(556\) 0 0
\(557\) −10.8157 −0.458276 −0.229138 0.973394i \(-0.573591\pi\)
−0.229138 + 0.973394i \(0.573591\pi\)
\(558\) 0 0
\(559\) 16.7176 0.707078
\(560\) 0 0
\(561\) 10.4173 0.439817
\(562\) 0 0
\(563\) −28.3778 −1.19598 −0.597991 0.801503i \(-0.704034\pi\)
−0.597991 + 0.801503i \(0.704034\pi\)
\(564\) 0 0
\(565\) −6.81062 −0.286525
\(566\) 0 0
\(567\) 40.7147 1.70986
\(568\) 0 0
\(569\) −9.33414 −0.391307 −0.195654 0.980673i \(-0.562683\pi\)
−0.195654 + 0.980673i \(0.562683\pi\)
\(570\) 0 0
\(571\) 19.2264 0.804599 0.402300 0.915508i \(-0.368211\pi\)
0.402300 + 0.915508i \(0.368211\pi\)
\(572\) 0 0
\(573\) 27.1437 1.13395
\(574\) 0 0
\(575\) −8.41556 −0.350953
\(576\) 0 0
\(577\) 30.6039 1.27406 0.637028 0.770841i \(-0.280164\pi\)
0.637028 + 0.770841i \(0.280164\pi\)
\(578\) 0 0
\(579\) 34.7606 1.44460
\(580\) 0 0
\(581\) −74.0124 −3.07055
\(582\) 0 0
\(583\) 5.37951 0.222796
\(584\) 0 0
\(585\) −0.560697 −0.0231820
\(586\) 0 0
\(587\) −14.9701 −0.617884 −0.308942 0.951081i \(-0.599975\pi\)
−0.308942 + 0.951081i \(0.599975\pi\)
\(588\) 0 0
\(589\) 7.60860 0.313507
\(590\) 0 0
\(591\) 22.4239 0.922395
\(592\) 0 0
\(593\) −20.1585 −0.827810 −0.413905 0.910320i \(-0.635835\pi\)
−0.413905 + 0.910320i \(0.635835\pi\)
\(594\) 0 0
\(595\) −25.0984 −1.02893
\(596\) 0 0
\(597\) 38.4707 1.57450
\(598\) 0 0
\(599\) 44.0047 1.79798 0.898992 0.437964i \(-0.144300\pi\)
0.898992 + 0.437964i \(0.144300\pi\)
\(600\) 0 0
\(601\) −1.87877 −0.0766366 −0.0383183 0.999266i \(-0.512200\pi\)
−0.0383183 + 0.999266i \(0.512200\pi\)
\(602\) 0 0
\(603\) −2.19480 −0.0893790
\(604\) 0 0
\(605\) −9.60967 −0.390689
\(606\) 0 0
\(607\) 31.4087 1.27484 0.637420 0.770517i \(-0.280002\pi\)
0.637420 + 0.770517i \(0.280002\pi\)
\(608\) 0 0
\(609\) −70.3831 −2.85207
\(610\) 0 0
\(611\) −41.6085 −1.68330
\(612\) 0 0
\(613\) −38.5568 −1.55729 −0.778647 0.627462i \(-0.784094\pi\)
−0.778647 + 0.627462i \(0.784094\pi\)
\(614\) 0 0
\(615\) 4.61139 0.185949
\(616\) 0 0
\(617\) 10.6786 0.429903 0.214951 0.976625i \(-0.431041\pi\)
0.214951 + 0.976625i \(0.431041\pi\)
\(618\) 0 0
\(619\) −15.0106 −0.603328 −0.301664 0.953414i \(-0.597542\pi\)
−0.301664 + 0.953414i \(0.597542\pi\)
\(620\) 0 0
\(621\) −44.8026 −1.79787
\(622\) 0 0
\(623\) 4.60783 0.184609
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 4.46466 0.178301
\(628\) 0 0
\(629\) 49.9464 1.99149
\(630\) 0 0
\(631\) −12.9588 −0.515882 −0.257941 0.966161i \(-0.583044\pi\)
−0.257941 + 0.966161i \(0.583044\pi\)
\(632\) 0 0
\(633\) 15.9764 0.635005
\(634\) 0 0
\(635\) 5.47889 0.217423
\(636\) 0 0
\(637\) 56.5791 2.24174
\(638\) 0 0
\(639\) 0.571042 0.0225901
\(640\) 0 0
\(641\) −29.9531 −1.18308 −0.591539 0.806277i \(-0.701479\pi\)
−0.591539 + 0.806277i \(0.701479\pi\)
\(642\) 0 0
\(643\) −40.4514 −1.59525 −0.797624 0.603155i \(-0.793910\pi\)
−0.797624 + 0.603155i \(0.793910\pi\)
\(644\) 0 0
\(645\) −7.93857 −0.312581
\(646\) 0 0
\(647\) 16.0943 0.632732 0.316366 0.948637i \(-0.397537\pi\)
0.316366 + 0.948637i \(0.397537\pi\)
\(648\) 0 0
\(649\) −3.47966 −0.136589
\(650\) 0 0
\(651\) 27.3513 1.07198
\(652\) 0 0
\(653\) −33.9810 −1.32978 −0.664889 0.746942i \(-0.731521\pi\)
−0.664889 + 0.746942i \(0.731521\pi\)
\(654\) 0 0
\(655\) −9.29141 −0.363046
\(656\) 0 0
\(657\) −1.49755 −0.0584249
\(658\) 0 0
\(659\) 5.84598 0.227727 0.113863 0.993496i \(-0.463677\pi\)
0.113863 + 0.993496i \(0.463677\pi\)
\(660\) 0 0
\(661\) 10.5250 0.409375 0.204688 0.978827i \(-0.434382\pi\)
0.204688 + 0.978827i \(0.434382\pi\)
\(662\) 0 0
\(663\) −31.3648 −1.21811
\(664\) 0 0
\(665\) −10.7567 −0.417129
\(666\) 0 0
\(667\) 73.3612 2.84056
\(668\) 0 0
\(669\) −33.1831 −1.28293
\(670\) 0 0
\(671\) −4.69391 −0.181207
\(672\) 0 0
\(673\) −3.99228 −0.153891 −0.0769454 0.997035i \(-0.524517\pi\)
−0.0769454 + 0.997035i \(0.524517\pi\)
\(674\) 0 0
\(675\) 5.32378 0.204912
\(676\) 0 0
\(677\) −1.59882 −0.0614478 −0.0307239 0.999528i \(-0.509781\pi\)
−0.0307239 + 0.999528i \(0.509781\pi\)
\(678\) 0 0
\(679\) −17.2035 −0.660211
\(680\) 0 0
\(681\) 16.2285 0.621878
\(682\) 0 0
\(683\) 1.23339 0.0471944 0.0235972 0.999722i \(-0.492488\pi\)
0.0235972 + 0.999722i \(0.492488\pi\)
\(684\) 0 0
\(685\) 5.97746 0.228387
\(686\) 0 0
\(687\) −10.5854 −0.403858
\(688\) 0 0
\(689\) −16.1969 −0.617052
\(690\) 0 0
\(691\) −1.55289 −0.0590746 −0.0295373 0.999564i \(-0.509403\pi\)
−0.0295373 + 0.999564i \(0.509403\pi\)
\(692\) 0 0
\(693\) −0.891883 −0.0338798
\(694\) 0 0
\(695\) −12.0766 −0.458093
\(696\) 0 0
\(697\) −14.3348 −0.542970
\(698\) 0 0
\(699\) −11.3380 −0.428841
\(700\) 0 0
\(701\) −13.4906 −0.509532 −0.254766 0.967003i \(-0.581998\pi\)
−0.254766 + 0.967003i \(0.581998\pi\)
\(702\) 0 0
\(703\) 21.4062 0.807349
\(704\) 0 0
\(705\) 19.7583 0.744142
\(706\) 0 0
\(707\) 53.9365 2.02849
\(708\) 0 0
\(709\) 15.1429 0.568703 0.284351 0.958720i \(-0.408222\pi\)
0.284351 + 0.958720i \(0.408222\pi\)
\(710\) 0 0
\(711\) −0.179308 −0.00672459
\(712\) 0 0
\(713\) −28.5086 −1.06766
\(714\) 0 0
\(715\) −4.18608 −0.156550
\(716\) 0 0
\(717\) −40.1110 −1.49797
\(718\) 0 0
\(719\) −27.5067 −1.02583 −0.512913 0.858441i \(-0.671434\pi\)
−0.512913 + 0.858441i \(0.671434\pi\)
\(720\) 0 0
\(721\) 63.6753 2.37139
\(722\) 0 0
\(723\) 20.3851 0.758128
\(724\) 0 0
\(725\) −8.71732 −0.323753
\(726\) 0 0
\(727\) −7.40922 −0.274793 −0.137396 0.990516i \(-0.543873\pi\)
−0.137396 + 0.990516i \(0.543873\pi\)
\(728\) 0 0
\(729\) 28.2678 1.04696
\(730\) 0 0
\(731\) 24.6776 0.912734
\(732\) 0 0
\(733\) 15.9022 0.587361 0.293680 0.955904i \(-0.405120\pi\)
0.293680 + 0.955904i \(0.405120\pi\)
\(734\) 0 0
\(735\) −26.8673 −0.991017
\(736\) 0 0
\(737\) −16.3860 −0.603587
\(738\) 0 0
\(739\) 33.4462 1.23034 0.615169 0.788395i \(-0.289088\pi\)
0.615169 + 0.788395i \(0.289088\pi\)
\(740\) 0 0
\(741\) −13.4424 −0.493819
\(742\) 0 0
\(743\) 46.9482 1.72236 0.861182 0.508297i \(-0.169725\pi\)
0.861182 + 0.508297i \(0.169725\pi\)
\(744\) 0 0
\(745\) −12.0049 −0.439826
\(746\) 0 0
\(747\) −2.44071 −0.0893008
\(748\) 0 0
\(749\) −3.08444 −0.112703
\(750\) 0 0
\(751\) −39.3367 −1.43542 −0.717708 0.696345i \(-0.754809\pi\)
−0.717708 + 0.696345i \(0.754809\pi\)
\(752\) 0 0
\(753\) 37.6404 1.37169
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 38.7559 1.40861 0.704304 0.709899i \(-0.251259\pi\)
0.704304 + 0.709899i \(0.251259\pi\)
\(758\) 0 0
\(759\) −16.7286 −0.607209
\(760\) 0 0
\(761\) −19.3171 −0.700245 −0.350123 0.936704i \(-0.613860\pi\)
−0.350123 + 0.936704i \(0.613860\pi\)
\(762\) 0 0
\(763\) −67.3007 −2.43645
\(764\) 0 0
\(765\) −0.827670 −0.0299245
\(766\) 0 0
\(767\) 10.4767 0.378293
\(768\) 0 0
\(769\) −11.2909 −0.407161 −0.203581 0.979058i \(-0.565258\pi\)
−0.203581 + 0.979058i \(0.565258\pi\)
\(770\) 0 0
\(771\) 14.8631 0.535282
\(772\) 0 0
\(773\) 7.11477 0.255900 0.127950 0.991781i \(-0.459160\pi\)
0.127950 + 0.991781i \(0.459160\pi\)
\(774\) 0 0
\(775\) 3.38760 0.121686
\(776\) 0 0
\(777\) 76.9507 2.76059
\(778\) 0 0
\(779\) −6.14366 −0.220119
\(780\) 0 0
\(781\) 4.26332 0.152553
\(782\) 0 0
\(783\) −46.4091 −1.65853
\(784\) 0 0
\(785\) −2.61722 −0.0934125
\(786\) 0 0
\(787\) −17.0445 −0.607572 −0.303786 0.952740i \(-0.598251\pi\)
−0.303786 + 0.952740i \(0.598251\pi\)
\(788\) 0 0
\(789\) −4.46012 −0.158784
\(790\) 0 0
\(791\) 32.6179 1.15976
\(792\) 0 0
\(793\) 14.1327 0.501865
\(794\) 0 0
\(795\) 7.69131 0.272783
\(796\) 0 0
\(797\) −44.7936 −1.58667 −0.793335 0.608785i \(-0.791657\pi\)
−0.793335 + 0.608785i \(0.791657\pi\)
\(798\) 0 0
\(799\) −61.4202 −2.17289
\(800\) 0 0
\(801\) 0.151952 0.00536897
\(802\) 0 0
\(803\) −11.1805 −0.394550
\(804\) 0 0
\(805\) 40.3044 1.42054
\(806\) 0 0
\(807\) 37.2559 1.31147
\(808\) 0 0
\(809\) 8.60627 0.302580 0.151290 0.988489i \(-0.451657\pi\)
0.151290 + 0.988489i \(0.451657\pi\)
\(810\) 0 0
\(811\) −53.1530 −1.86646 −0.933228 0.359286i \(-0.883020\pi\)
−0.933228 + 0.359286i \(0.883020\pi\)
\(812\) 0 0
\(813\) −8.80498 −0.308804
\(814\) 0 0
\(815\) 16.6073 0.581728
\(816\) 0 0
\(817\) 10.5764 0.370021
\(818\) 0 0
\(819\) 2.68532 0.0938328
\(820\) 0 0
\(821\) 14.5588 0.508104 0.254052 0.967191i \(-0.418236\pi\)
0.254052 + 0.967191i \(0.418236\pi\)
\(822\) 0 0
\(823\) −45.4404 −1.58395 −0.791977 0.610551i \(-0.790948\pi\)
−0.791977 + 0.610551i \(0.790948\pi\)
\(824\) 0 0
\(825\) 1.98782 0.0692069
\(826\) 0 0
\(827\) −36.4041 −1.26589 −0.632947 0.774195i \(-0.718155\pi\)
−0.632947 + 0.774195i \(0.718155\pi\)
\(828\) 0 0
\(829\) −25.3060 −0.878913 −0.439457 0.898264i \(-0.644829\pi\)
−0.439457 + 0.898264i \(0.644829\pi\)
\(830\) 0 0
\(831\) 12.1869 0.422758
\(832\) 0 0
\(833\) 83.5190 2.89376
\(834\) 0 0
\(835\) −20.2987 −0.702465
\(836\) 0 0
\(837\) 18.0349 0.623376
\(838\) 0 0
\(839\) 29.8613 1.03093 0.515463 0.856912i \(-0.327620\pi\)
0.515463 + 0.856912i \(0.327620\pi\)
\(840\) 0 0
\(841\) 46.9916 1.62040
\(842\) 0 0
\(843\) 43.1507 1.48619
\(844\) 0 0
\(845\) −0.396361 −0.0136352
\(846\) 0 0
\(847\) 46.0232 1.58138
\(848\) 0 0
\(849\) −7.79032 −0.267363
\(850\) 0 0
\(851\) −80.2066 −2.74945
\(852\) 0 0
\(853\) −0.462410 −0.0158326 −0.00791631 0.999969i \(-0.502520\pi\)
−0.00791631 + 0.999969i \(0.502520\pi\)
\(854\) 0 0
\(855\) −0.354725 −0.0121313
\(856\) 0 0
\(857\) 10.9521 0.374118 0.187059 0.982349i \(-0.440105\pi\)
0.187059 + 0.982349i \(0.440105\pi\)
\(858\) 0 0
\(859\) −30.6640 −1.04624 −0.523121 0.852259i \(-0.675232\pi\)
−0.523121 + 0.852259i \(0.675232\pi\)
\(860\) 0 0
\(861\) −22.0852 −0.752660
\(862\) 0 0
\(863\) −18.5123 −0.630166 −0.315083 0.949064i \(-0.602032\pi\)
−0.315083 + 0.949064i \(0.602032\pi\)
\(864\) 0 0
\(865\) −19.2373 −0.654086
\(866\) 0 0
\(867\) −17.6397 −0.599076
\(868\) 0 0
\(869\) −1.33869 −0.0454119
\(870\) 0 0
\(871\) 49.3358 1.67168
\(872\) 0 0
\(873\) −0.567321 −0.0192009
\(874\) 0 0
\(875\) −4.78926 −0.161907
\(876\) 0 0
\(877\) 21.7724 0.735202 0.367601 0.929984i \(-0.380179\pi\)
0.367601 + 0.929984i \(0.380179\pi\)
\(878\) 0 0
\(879\) −39.3333 −1.32668
\(880\) 0 0
\(881\) 39.6883 1.33713 0.668566 0.743653i \(-0.266908\pi\)
0.668566 + 0.743653i \(0.266908\pi\)
\(882\) 0 0
\(883\) 3.71364 0.124974 0.0624869 0.998046i \(-0.480097\pi\)
0.0624869 + 0.998046i \(0.480097\pi\)
\(884\) 0 0
\(885\) −4.97502 −0.167233
\(886\) 0 0
\(887\) −1.81200 −0.0608410 −0.0304205 0.999537i \(-0.509685\pi\)
−0.0304205 + 0.999537i \(0.509685\pi\)
\(888\) 0 0
\(889\) −26.2398 −0.880056
\(890\) 0 0
\(891\) 10.0240 0.335817
\(892\) 0 0
\(893\) −26.3236 −0.880886
\(894\) 0 0
\(895\) 23.5260 0.786387
\(896\) 0 0
\(897\) 50.3672 1.68171
\(898\) 0 0
\(899\) −29.5308 −0.984908
\(900\) 0 0
\(901\) −23.9090 −0.796523
\(902\) 0 0
\(903\) 38.0199 1.26522
\(904\) 0 0
\(905\) −2.07285 −0.0689039
\(906\) 0 0
\(907\) 47.9592 1.59246 0.796230 0.604994i \(-0.206824\pi\)
0.796230 + 0.604994i \(0.206824\pi\)
\(908\) 0 0
\(909\) 1.77867 0.0589946
\(910\) 0 0
\(911\) −3.77083 −0.124933 −0.0624666 0.998047i \(-0.519897\pi\)
−0.0624666 + 0.998047i \(0.519897\pi\)
\(912\) 0 0
\(913\) −18.2219 −0.603058
\(914\) 0 0
\(915\) −6.71109 −0.221862
\(916\) 0 0
\(917\) 44.4990 1.46949
\(918\) 0 0
\(919\) −15.1021 −0.498174 −0.249087 0.968481i \(-0.580130\pi\)
−0.249087 + 0.968481i \(0.580130\pi\)
\(920\) 0 0
\(921\) −44.5225 −1.46707
\(922\) 0 0
\(923\) −12.8362 −0.422508
\(924\) 0 0
\(925\) 9.53075 0.313369
\(926\) 0 0
\(927\) 2.09982 0.0689672
\(928\) 0 0
\(929\) 25.5880 0.839517 0.419758 0.907636i \(-0.362115\pi\)
0.419758 + 0.907636i \(0.362115\pi\)
\(930\) 0 0
\(931\) 35.7948 1.17313
\(932\) 0 0
\(933\) 24.8316 0.812950
\(934\) 0 0
\(935\) −6.17926 −0.202084
\(936\) 0 0
\(937\) 44.0737 1.43983 0.719913 0.694064i \(-0.244182\pi\)
0.719913 + 0.694064i \(0.244182\pi\)
\(938\) 0 0
\(939\) 29.6143 0.966428
\(940\) 0 0
\(941\) 2.47251 0.0806016 0.0403008 0.999188i \(-0.487168\pi\)
0.0403008 + 0.999188i \(0.487168\pi\)
\(942\) 0 0
\(943\) 23.0196 0.749622
\(944\) 0 0
\(945\) −25.4970 −0.829417
\(946\) 0 0
\(947\) 11.1441 0.362135 0.181067 0.983471i \(-0.442045\pi\)
0.181067 + 0.983471i \(0.442045\pi\)
\(948\) 0 0
\(949\) 33.6627 1.09274
\(950\) 0 0
\(951\) −55.1675 −1.78893
\(952\) 0 0
\(953\) 34.8520 1.12897 0.564483 0.825444i \(-0.309075\pi\)
0.564483 + 0.825444i \(0.309075\pi\)
\(954\) 0 0
\(955\) −16.1010 −0.521016
\(956\) 0 0
\(957\) −17.3284 −0.560148
\(958\) 0 0
\(959\) −28.6276 −0.924435
\(960\) 0 0
\(961\) −19.5241 −0.629811
\(962\) 0 0
\(963\) −0.101716 −0.00327774
\(964\) 0 0
\(965\) −20.6192 −0.663754
\(966\) 0 0
\(967\) −8.05008 −0.258873 −0.129437 0.991588i \(-0.541317\pi\)
−0.129437 + 0.991588i \(0.541317\pi\)
\(968\) 0 0
\(969\) −19.8430 −0.637448
\(970\) 0 0
\(971\) 15.0168 0.481911 0.240956 0.970536i \(-0.422539\pi\)
0.240956 + 0.970536i \(0.422539\pi\)
\(972\) 0 0
\(973\) 57.8382 1.85421
\(974\) 0 0
\(975\) −5.98501 −0.191674
\(976\) 0 0
\(977\) −56.4400 −1.80567 −0.902837 0.429983i \(-0.858520\pi\)
−0.902837 + 0.429983i \(0.858520\pi\)
\(978\) 0 0
\(979\) 1.13445 0.0362573
\(980\) 0 0
\(981\) −2.21938 −0.0708592
\(982\) 0 0
\(983\) 46.5036 1.48324 0.741618 0.670823i \(-0.234059\pi\)
0.741618 + 0.670823i \(0.234059\pi\)
\(984\) 0 0
\(985\) −13.3013 −0.423814
\(986\) 0 0
\(987\) −94.6279 −3.01204
\(988\) 0 0
\(989\) −39.6286 −1.26012
\(990\) 0 0
\(991\) −12.6757 −0.402656 −0.201328 0.979524i \(-0.564526\pi\)
−0.201328 + 0.979524i \(0.564526\pi\)
\(992\) 0 0
\(993\) 5.54308 0.175904
\(994\) 0 0
\(995\) −22.8199 −0.723439
\(996\) 0 0
\(997\) −45.8365 −1.45166 −0.725829 0.687876i \(-0.758543\pi\)
−0.725829 + 0.687876i \(0.758543\pi\)
\(998\) 0 0
\(999\) 50.7396 1.60533
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 \(a_p\))