Properties

Label 4004.2.a.j.1.2
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.78432\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78432 q^{3} +2.77311 q^{5} -1.00000 q^{7} +4.75245 q^{9} +O(q^{10})\) \(q-2.78432 q^{3} +2.77311 q^{5} -1.00000 q^{7} +4.75245 q^{9} -1.00000 q^{11} -1.00000 q^{13} -7.72124 q^{15} -2.84666 q^{17} -6.75777 q^{19} +2.78432 q^{21} +0.282040 q^{23} +2.69016 q^{25} -4.87938 q^{27} +8.65828 q^{29} -2.61339 q^{31} +2.78432 q^{33} -2.77311 q^{35} -2.19155 q^{37} +2.78432 q^{39} +9.09314 q^{41} +6.50862 q^{43} +13.1791 q^{45} +0.120836 q^{47} +1.00000 q^{49} +7.92601 q^{51} +5.22807 q^{53} -2.77311 q^{55} +18.8158 q^{57} +4.04489 q^{59} -9.87513 q^{61} -4.75245 q^{63} -2.77311 q^{65} -2.78400 q^{67} -0.785291 q^{69} -9.02475 q^{71} -9.94348 q^{73} -7.49028 q^{75} +1.00000 q^{77} +10.1171 q^{79} -0.671584 q^{81} -8.81845 q^{83} -7.89411 q^{85} -24.1074 q^{87} +17.7949 q^{89} +1.00000 q^{91} +7.27652 q^{93} -18.7401 q^{95} -8.81902 q^{97} -4.75245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.78432 −1.60753 −0.803764 0.594948i \(-0.797173\pi\)
−0.803764 + 0.594948i \(0.797173\pi\)
\(4\) 0 0
\(5\) 2.77311 1.24017 0.620087 0.784533i \(-0.287097\pi\)
0.620087 + 0.784533i \(0.287097\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 4.75245 1.58415
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −7.72124 −1.99362
\(16\) 0 0
\(17\) −2.84666 −0.690416 −0.345208 0.938526i \(-0.612192\pi\)
−0.345208 + 0.938526i \(0.612192\pi\)
\(18\) 0 0
\(19\) −6.75777 −1.55034 −0.775169 0.631754i \(-0.782335\pi\)
−0.775169 + 0.631754i \(0.782335\pi\)
\(20\) 0 0
\(21\) 2.78432 0.607589
\(22\) 0 0
\(23\) 0.282040 0.0588095 0.0294047 0.999568i \(-0.490639\pi\)
0.0294047 + 0.999568i \(0.490639\pi\)
\(24\) 0 0
\(25\) 2.69016 0.538033
\(26\) 0 0
\(27\) −4.87938 −0.939037
\(28\) 0 0
\(29\) 8.65828 1.60780 0.803901 0.594763i \(-0.202754\pi\)
0.803901 + 0.594763i \(0.202754\pi\)
\(30\) 0 0
\(31\) −2.61339 −0.469379 −0.234689 0.972070i \(-0.575407\pi\)
−0.234689 + 0.972070i \(0.575407\pi\)
\(32\) 0 0
\(33\) 2.78432 0.484688
\(34\) 0 0
\(35\) −2.77311 −0.468742
\(36\) 0 0
\(37\) −2.19155 −0.360288 −0.180144 0.983640i \(-0.557656\pi\)
−0.180144 + 0.983640i \(0.557656\pi\)
\(38\) 0 0
\(39\) 2.78432 0.445848
\(40\) 0 0
\(41\) 9.09314 1.42011 0.710055 0.704146i \(-0.248670\pi\)
0.710055 + 0.704146i \(0.248670\pi\)
\(42\) 0 0
\(43\) 6.50862 0.992556 0.496278 0.868164i \(-0.334700\pi\)
0.496278 + 0.868164i \(0.334700\pi\)
\(44\) 0 0
\(45\) 13.1791 1.96462
\(46\) 0 0
\(47\) 0.120836 0.0176257 0.00881286 0.999961i \(-0.497195\pi\)
0.00881286 + 0.999961i \(0.497195\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 7.92601 1.10986
\(52\) 0 0
\(53\) 5.22807 0.718131 0.359066 0.933312i \(-0.383095\pi\)
0.359066 + 0.933312i \(0.383095\pi\)
\(54\) 0 0
\(55\) −2.77311 −0.373927
\(56\) 0 0
\(57\) 18.8158 2.49221
\(58\) 0 0
\(59\) 4.04489 0.526600 0.263300 0.964714i \(-0.415189\pi\)
0.263300 + 0.964714i \(0.415189\pi\)
\(60\) 0 0
\(61\) −9.87513 −1.26438 −0.632190 0.774813i \(-0.717844\pi\)
−0.632190 + 0.774813i \(0.717844\pi\)
\(62\) 0 0
\(63\) −4.75245 −0.598752
\(64\) 0 0
\(65\) −2.77311 −0.343962
\(66\) 0 0
\(67\) −2.78400 −0.340119 −0.170060 0.985434i \(-0.554396\pi\)
−0.170060 + 0.985434i \(0.554396\pi\)
\(68\) 0 0
\(69\) −0.785291 −0.0945380
\(70\) 0 0
\(71\) −9.02475 −1.07104 −0.535520 0.844522i \(-0.679884\pi\)
−0.535520 + 0.844522i \(0.679884\pi\)
\(72\) 0 0
\(73\) −9.94348 −1.16380 −0.581898 0.813262i \(-0.697690\pi\)
−0.581898 + 0.813262i \(0.697690\pi\)
\(74\) 0 0
\(75\) −7.49028 −0.864903
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 10.1171 1.13827 0.569134 0.822245i \(-0.307279\pi\)
0.569134 + 0.822245i \(0.307279\pi\)
\(80\) 0 0
\(81\) −0.671584 −0.0746204
\(82\) 0 0
\(83\) −8.81845 −0.967951 −0.483975 0.875082i \(-0.660808\pi\)
−0.483975 + 0.875082i \(0.660808\pi\)
\(84\) 0 0
\(85\) −7.89411 −0.856236
\(86\) 0 0
\(87\) −24.1074 −2.58459
\(88\) 0 0
\(89\) 17.7949 1.88626 0.943128 0.332431i \(-0.107869\pi\)
0.943128 + 0.332431i \(0.107869\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 7.27652 0.754540
\(94\) 0 0
\(95\) −18.7401 −1.92269
\(96\) 0 0
\(97\) −8.81902 −0.895436 −0.447718 0.894175i \(-0.647763\pi\)
−0.447718 + 0.894175i \(0.647763\pi\)
\(98\) 0 0
\(99\) −4.75245 −0.477639
\(100\) 0 0
\(101\) 15.5773 1.55000 0.775000 0.631961i \(-0.217750\pi\)
0.775000 + 0.631961i \(0.217750\pi\)
\(102\) 0 0
\(103\) 7.45574 0.734636 0.367318 0.930095i \(-0.380276\pi\)
0.367318 + 0.930095i \(0.380276\pi\)
\(104\) 0 0
\(105\) 7.72124 0.753516
\(106\) 0 0
\(107\) 0.367658 0.0355428 0.0177714 0.999842i \(-0.494343\pi\)
0.0177714 + 0.999842i \(0.494343\pi\)
\(108\) 0 0
\(109\) −8.31826 −0.796745 −0.398372 0.917224i \(-0.630425\pi\)
−0.398372 + 0.917224i \(0.630425\pi\)
\(110\) 0 0
\(111\) 6.10198 0.579174
\(112\) 0 0
\(113\) 5.40717 0.508664 0.254332 0.967117i \(-0.418144\pi\)
0.254332 + 0.967117i \(0.418144\pi\)
\(114\) 0 0
\(115\) 0.782130 0.0729340
\(116\) 0 0
\(117\) −4.75245 −0.439364
\(118\) 0 0
\(119\) 2.84666 0.260953
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −25.3182 −2.28287
\(124\) 0 0
\(125\) −6.40544 −0.572920
\(126\) 0 0
\(127\) 18.7598 1.66466 0.832330 0.554280i \(-0.187006\pi\)
0.832330 + 0.554280i \(0.187006\pi\)
\(128\) 0 0
\(129\) −18.1221 −1.59556
\(130\) 0 0
\(131\) 8.13395 0.710666 0.355333 0.934740i \(-0.384367\pi\)
0.355333 + 0.934740i \(0.384367\pi\)
\(132\) 0 0
\(133\) 6.75777 0.585973
\(134\) 0 0
\(135\) −13.5311 −1.16457
\(136\) 0 0
\(137\) −12.8557 −1.09834 −0.549169 0.835711i \(-0.685056\pi\)
−0.549169 + 0.835711i \(0.685056\pi\)
\(138\) 0 0
\(139\) 22.5614 1.91364 0.956819 0.290686i \(-0.0938834\pi\)
0.956819 + 0.290686i \(0.0938834\pi\)
\(140\) 0 0
\(141\) −0.336446 −0.0283338
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 24.0104 1.99396
\(146\) 0 0
\(147\) −2.78432 −0.229647
\(148\) 0 0
\(149\) 16.9874 1.39166 0.695831 0.718205i \(-0.255036\pi\)
0.695831 + 0.718205i \(0.255036\pi\)
\(150\) 0 0
\(151\) −15.3459 −1.24883 −0.624415 0.781093i \(-0.714663\pi\)
−0.624415 + 0.781093i \(0.714663\pi\)
\(152\) 0 0
\(153\) −13.5286 −1.09372
\(154\) 0 0
\(155\) −7.24723 −0.582111
\(156\) 0 0
\(157\) 5.03408 0.401763 0.200882 0.979616i \(-0.435619\pi\)
0.200882 + 0.979616i \(0.435619\pi\)
\(158\) 0 0
\(159\) −14.5566 −1.15442
\(160\) 0 0
\(161\) −0.282040 −0.0222279
\(162\) 0 0
\(163\) −3.26771 −0.255947 −0.127973 0.991778i \(-0.540847\pi\)
−0.127973 + 0.991778i \(0.540847\pi\)
\(164\) 0 0
\(165\) 7.72124 0.601098
\(166\) 0 0
\(167\) 16.9303 1.31011 0.655054 0.755582i \(-0.272646\pi\)
0.655054 + 0.755582i \(0.272646\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −32.1159 −2.45597
\(172\) 0 0
\(173\) −17.0625 −1.29724 −0.648618 0.761114i \(-0.724653\pi\)
−0.648618 + 0.761114i \(0.724653\pi\)
\(174\) 0 0
\(175\) −2.69016 −0.203357
\(176\) 0 0
\(177\) −11.2623 −0.846524
\(178\) 0 0
\(179\) −7.73835 −0.578391 −0.289196 0.957270i \(-0.593388\pi\)
−0.289196 + 0.957270i \(0.593388\pi\)
\(180\) 0 0
\(181\) 2.18521 0.162425 0.0812125 0.996697i \(-0.474121\pi\)
0.0812125 + 0.996697i \(0.474121\pi\)
\(182\) 0 0
\(183\) 27.4955 2.03253
\(184\) 0 0
\(185\) −6.07742 −0.446820
\(186\) 0 0
\(187\) 2.84666 0.208168
\(188\) 0 0
\(189\) 4.87938 0.354923
\(190\) 0 0
\(191\) 24.1931 1.75055 0.875276 0.483623i \(-0.160680\pi\)
0.875276 + 0.483623i \(0.160680\pi\)
\(192\) 0 0
\(193\) 6.37682 0.459013 0.229507 0.973307i \(-0.426289\pi\)
0.229507 + 0.973307i \(0.426289\pi\)
\(194\) 0 0
\(195\) 7.72124 0.552930
\(196\) 0 0
\(197\) 23.1068 1.64629 0.823146 0.567830i \(-0.192217\pi\)
0.823146 + 0.567830i \(0.192217\pi\)
\(198\) 0 0
\(199\) −10.8710 −0.770626 −0.385313 0.922786i \(-0.625907\pi\)
−0.385313 + 0.922786i \(0.625907\pi\)
\(200\) 0 0
\(201\) 7.75154 0.546752
\(202\) 0 0
\(203\) −8.65828 −0.607692
\(204\) 0 0
\(205\) 25.2163 1.76118
\(206\) 0 0
\(207\) 1.34038 0.0931630
\(208\) 0 0
\(209\) 6.75777 0.467445
\(210\) 0 0
\(211\) 17.5059 1.20515 0.602577 0.798061i \(-0.294141\pi\)
0.602577 + 0.798061i \(0.294141\pi\)
\(212\) 0 0
\(213\) 25.1278 1.72173
\(214\) 0 0
\(215\) 18.0492 1.23094
\(216\) 0 0
\(217\) 2.61339 0.177408
\(218\) 0 0
\(219\) 27.6858 1.87084
\(220\) 0 0
\(221\) 2.84666 0.191487
\(222\) 0 0
\(223\) −21.8649 −1.46418 −0.732092 0.681206i \(-0.761456\pi\)
−0.732092 + 0.681206i \(0.761456\pi\)
\(224\) 0 0
\(225\) 12.7849 0.852324
\(226\) 0 0
\(227\) 4.85493 0.322233 0.161117 0.986935i \(-0.448490\pi\)
0.161117 + 0.986935i \(0.448490\pi\)
\(228\) 0 0
\(229\) 2.87378 0.189905 0.0949525 0.995482i \(-0.469730\pi\)
0.0949525 + 0.995482i \(0.469730\pi\)
\(230\) 0 0
\(231\) −2.78432 −0.183195
\(232\) 0 0
\(233\) 0.953404 0.0624596 0.0312298 0.999512i \(-0.490058\pi\)
0.0312298 + 0.999512i \(0.490058\pi\)
\(234\) 0 0
\(235\) 0.335091 0.0218590
\(236\) 0 0
\(237\) −28.1694 −1.82980
\(238\) 0 0
\(239\) 2.47685 0.160214 0.0801071 0.996786i \(-0.474474\pi\)
0.0801071 + 0.996786i \(0.474474\pi\)
\(240\) 0 0
\(241\) −16.2269 −1.04527 −0.522634 0.852557i \(-0.675050\pi\)
−0.522634 + 0.852557i \(0.675050\pi\)
\(242\) 0 0
\(243\) 16.5080 1.05899
\(244\) 0 0
\(245\) 2.77311 0.177168
\(246\) 0 0
\(247\) 6.75777 0.429986
\(248\) 0 0
\(249\) 24.5534 1.55601
\(250\) 0 0
\(251\) −3.84609 −0.242763 −0.121381 0.992606i \(-0.538732\pi\)
−0.121381 + 0.992606i \(0.538732\pi\)
\(252\) 0 0
\(253\) −0.282040 −0.0177317
\(254\) 0 0
\(255\) 21.9797 1.37642
\(256\) 0 0
\(257\) 27.2096 1.69729 0.848645 0.528963i \(-0.177419\pi\)
0.848645 + 0.528963i \(0.177419\pi\)
\(258\) 0 0
\(259\) 2.19155 0.136176
\(260\) 0 0
\(261\) 41.1480 2.54700
\(262\) 0 0
\(263\) 16.2641 1.00289 0.501445 0.865190i \(-0.332802\pi\)
0.501445 + 0.865190i \(0.332802\pi\)
\(264\) 0 0
\(265\) 14.4980 0.890608
\(266\) 0 0
\(267\) −49.5467 −3.03221
\(268\) 0 0
\(269\) 21.0343 1.28249 0.641243 0.767338i \(-0.278419\pi\)
0.641243 + 0.767338i \(0.278419\pi\)
\(270\) 0 0
\(271\) −14.6237 −0.888325 −0.444163 0.895946i \(-0.646499\pi\)
−0.444163 + 0.895946i \(0.646499\pi\)
\(272\) 0 0
\(273\) −2.78432 −0.168515
\(274\) 0 0
\(275\) −2.69016 −0.162223
\(276\) 0 0
\(277\) 26.4258 1.58777 0.793885 0.608067i \(-0.208055\pi\)
0.793885 + 0.608067i \(0.208055\pi\)
\(278\) 0 0
\(279\) −12.4200 −0.743566
\(280\) 0 0
\(281\) 5.10347 0.304448 0.152224 0.988346i \(-0.451357\pi\)
0.152224 + 0.988346i \(0.451357\pi\)
\(282\) 0 0
\(283\) 12.2991 0.731104 0.365552 0.930791i \(-0.380880\pi\)
0.365552 + 0.930791i \(0.380880\pi\)
\(284\) 0 0
\(285\) 52.1784 3.09078
\(286\) 0 0
\(287\) −9.09314 −0.536751
\(288\) 0 0
\(289\) −8.89653 −0.523326
\(290\) 0 0
\(291\) 24.5550 1.43944
\(292\) 0 0
\(293\) 11.6569 0.681001 0.340500 0.940244i \(-0.389404\pi\)
0.340500 + 0.940244i \(0.389404\pi\)
\(294\) 0 0
\(295\) 11.2169 0.653076
\(296\) 0 0
\(297\) 4.87938 0.283130
\(298\) 0 0
\(299\) −0.282040 −0.0163108
\(300\) 0 0
\(301\) −6.50862 −0.375151
\(302\) 0 0
\(303\) −43.3722 −2.49167
\(304\) 0 0
\(305\) −27.3849 −1.56805
\(306\) 0 0
\(307\) 7.07652 0.403878 0.201939 0.979398i \(-0.435276\pi\)
0.201939 + 0.979398i \(0.435276\pi\)
\(308\) 0 0
\(309\) −20.7592 −1.18095
\(310\) 0 0
\(311\) −3.96382 −0.224768 −0.112384 0.993665i \(-0.535849\pi\)
−0.112384 + 0.993665i \(0.535849\pi\)
\(312\) 0 0
\(313\) 13.3806 0.756316 0.378158 0.925741i \(-0.376558\pi\)
0.378158 + 0.925741i \(0.376558\pi\)
\(314\) 0 0
\(315\) −13.1791 −0.742557
\(316\) 0 0
\(317\) −31.2650 −1.75602 −0.878008 0.478646i \(-0.841128\pi\)
−0.878008 + 0.478646i \(0.841128\pi\)
\(318\) 0 0
\(319\) −8.65828 −0.484771
\(320\) 0 0
\(321\) −1.02368 −0.0571361
\(322\) 0 0
\(323\) 19.2371 1.07038
\(324\) 0 0
\(325\) −2.69016 −0.149223
\(326\) 0 0
\(327\) 23.1607 1.28079
\(328\) 0 0
\(329\) −0.120836 −0.00666189
\(330\) 0 0
\(331\) 8.97026 0.493050 0.246525 0.969136i \(-0.420711\pi\)
0.246525 + 0.969136i \(0.420711\pi\)
\(332\) 0 0
\(333\) −10.4152 −0.570751
\(334\) 0 0
\(335\) −7.72034 −0.421807
\(336\) 0 0
\(337\) 21.0738 1.14796 0.573981 0.818869i \(-0.305398\pi\)
0.573981 + 0.818869i \(0.305398\pi\)
\(338\) 0 0
\(339\) −15.0553 −0.817692
\(340\) 0 0
\(341\) 2.61339 0.141523
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −2.17770 −0.117244
\(346\) 0 0
\(347\) 6.15858 0.330610 0.165305 0.986243i \(-0.447139\pi\)
0.165305 + 0.986243i \(0.447139\pi\)
\(348\) 0 0
\(349\) −10.1993 −0.545956 −0.272978 0.962020i \(-0.588009\pi\)
−0.272978 + 0.962020i \(0.588009\pi\)
\(350\) 0 0
\(351\) 4.87938 0.260442
\(352\) 0 0
\(353\) −15.5664 −0.828518 −0.414259 0.910159i \(-0.635959\pi\)
−0.414259 + 0.910159i \(0.635959\pi\)
\(354\) 0 0
\(355\) −25.0267 −1.32828
\(356\) 0 0
\(357\) −7.92601 −0.419489
\(358\) 0 0
\(359\) 17.2948 0.912784 0.456392 0.889779i \(-0.349142\pi\)
0.456392 + 0.889779i \(0.349142\pi\)
\(360\) 0 0
\(361\) 26.6674 1.40355
\(362\) 0 0
\(363\) −2.78432 −0.146139
\(364\) 0 0
\(365\) −27.5744 −1.44331
\(366\) 0 0
\(367\) −27.7144 −1.44668 −0.723339 0.690493i \(-0.757394\pi\)
−0.723339 + 0.690493i \(0.757394\pi\)
\(368\) 0 0
\(369\) 43.2147 2.24967
\(370\) 0 0
\(371\) −5.22807 −0.271428
\(372\) 0 0
\(373\) 1.19168 0.0617030 0.0308515 0.999524i \(-0.490178\pi\)
0.0308515 + 0.999524i \(0.490178\pi\)
\(374\) 0 0
\(375\) 17.8348 0.920986
\(376\) 0 0
\(377\) −8.65828 −0.445924
\(378\) 0 0
\(379\) 13.2714 0.681706 0.340853 0.940117i \(-0.389284\pi\)
0.340853 + 0.940117i \(0.389284\pi\)
\(380\) 0 0
\(381\) −52.2333 −2.67599
\(382\) 0 0
\(383\) −3.88242 −0.198383 −0.0991913 0.995068i \(-0.531626\pi\)
−0.0991913 + 0.995068i \(0.531626\pi\)
\(384\) 0 0
\(385\) 2.77311 0.141331
\(386\) 0 0
\(387\) 30.9319 1.57236
\(388\) 0 0
\(389\) 18.0201 0.913657 0.456829 0.889555i \(-0.348985\pi\)
0.456829 + 0.889555i \(0.348985\pi\)
\(390\) 0 0
\(391\) −0.802873 −0.0406030
\(392\) 0 0
\(393\) −22.6475 −1.14242
\(394\) 0 0
\(395\) 28.0560 1.41165
\(396\) 0 0
\(397\) 36.6325 1.83853 0.919266 0.393637i \(-0.128783\pi\)
0.919266 + 0.393637i \(0.128783\pi\)
\(398\) 0 0
\(399\) −18.8158 −0.941968
\(400\) 0 0
\(401\) 24.6288 1.22990 0.614952 0.788564i \(-0.289175\pi\)
0.614952 + 0.788564i \(0.289175\pi\)
\(402\) 0 0
\(403\) 2.61339 0.130182
\(404\) 0 0
\(405\) −1.86238 −0.0925423
\(406\) 0 0
\(407\) 2.19155 0.108631
\(408\) 0 0
\(409\) −15.2688 −0.754992 −0.377496 0.926011i \(-0.623215\pi\)
−0.377496 + 0.926011i \(0.623215\pi\)
\(410\) 0 0
\(411\) 35.7945 1.76561
\(412\) 0 0
\(413\) −4.04489 −0.199036
\(414\) 0 0
\(415\) −24.4546 −1.20043
\(416\) 0 0
\(417\) −62.8183 −3.07623
\(418\) 0 0
\(419\) −21.5160 −1.05113 −0.525564 0.850754i \(-0.676146\pi\)
−0.525564 + 0.850754i \(0.676146\pi\)
\(420\) 0 0
\(421\) 26.8404 1.30812 0.654059 0.756443i \(-0.273065\pi\)
0.654059 + 0.756443i \(0.273065\pi\)
\(422\) 0 0
\(423\) 0.574266 0.0279218
\(424\) 0 0
\(425\) −7.65798 −0.371466
\(426\) 0 0
\(427\) 9.87513 0.477891
\(428\) 0 0
\(429\) −2.78432 −0.134428
\(430\) 0 0
\(431\) 37.9193 1.82651 0.913254 0.407390i \(-0.133561\pi\)
0.913254 + 0.407390i \(0.133561\pi\)
\(432\) 0 0
\(433\) −30.1766 −1.45020 −0.725098 0.688646i \(-0.758206\pi\)
−0.725098 + 0.688646i \(0.758206\pi\)
\(434\) 0 0
\(435\) −66.8527 −3.20534
\(436\) 0 0
\(437\) −1.90596 −0.0911746
\(438\) 0 0
\(439\) 13.0983 0.625149 0.312575 0.949893i \(-0.398809\pi\)
0.312575 + 0.949893i \(0.398809\pi\)
\(440\) 0 0
\(441\) 4.75245 0.226307
\(442\) 0 0
\(443\) −14.1509 −0.672329 −0.336164 0.941803i \(-0.609130\pi\)
−0.336164 + 0.941803i \(0.609130\pi\)
\(444\) 0 0
\(445\) 49.3473 2.33929
\(446\) 0 0
\(447\) −47.2984 −2.23714
\(448\) 0 0
\(449\) 1.37721 0.0649946 0.0324973 0.999472i \(-0.489654\pi\)
0.0324973 + 0.999472i \(0.489654\pi\)
\(450\) 0 0
\(451\) −9.09314 −0.428179
\(452\) 0 0
\(453\) 42.7279 2.00753
\(454\) 0 0
\(455\) 2.77311 0.130006
\(456\) 0 0
\(457\) −3.44269 −0.161042 −0.0805212 0.996753i \(-0.525658\pi\)
−0.0805212 + 0.996753i \(0.525658\pi\)
\(458\) 0 0
\(459\) 13.8899 0.648326
\(460\) 0 0
\(461\) −10.5969 −0.493547 −0.246774 0.969073i \(-0.579370\pi\)
−0.246774 + 0.969073i \(0.579370\pi\)
\(462\) 0 0
\(463\) 17.4442 0.810699 0.405349 0.914162i \(-0.367150\pi\)
0.405349 + 0.914162i \(0.367150\pi\)
\(464\) 0 0
\(465\) 20.1786 0.935761
\(466\) 0 0
\(467\) −3.55369 −0.164445 −0.0822226 0.996614i \(-0.526202\pi\)
−0.0822226 + 0.996614i \(0.526202\pi\)
\(468\) 0 0
\(469\) 2.78400 0.128553
\(470\) 0 0
\(471\) −14.0165 −0.645846
\(472\) 0 0
\(473\) −6.50862 −0.299267
\(474\) 0 0
\(475\) −18.1795 −0.834133
\(476\) 0 0
\(477\) 24.8462 1.13763
\(478\) 0 0
\(479\) 12.3749 0.565422 0.282711 0.959205i \(-0.408766\pi\)
0.282711 + 0.959205i \(0.408766\pi\)
\(480\) 0 0
\(481\) 2.19155 0.0999260
\(482\) 0 0
\(483\) 0.785291 0.0357320
\(484\) 0 0
\(485\) −24.4562 −1.11050
\(486\) 0 0
\(487\) −33.8091 −1.53204 −0.766018 0.642819i \(-0.777765\pi\)
−0.766018 + 0.642819i \(0.777765\pi\)
\(488\) 0 0
\(489\) 9.09836 0.411442
\(490\) 0 0
\(491\) 39.7317 1.79307 0.896533 0.442977i \(-0.146078\pi\)
0.896533 + 0.442977i \(0.146078\pi\)
\(492\) 0 0
\(493\) −24.6472 −1.11005
\(494\) 0 0
\(495\) −13.1791 −0.592356
\(496\) 0 0
\(497\) 9.02475 0.404815
\(498\) 0 0
\(499\) −13.2331 −0.592393 −0.296196 0.955127i \(-0.595718\pi\)
−0.296196 + 0.955127i \(0.595718\pi\)
\(500\) 0 0
\(501\) −47.1395 −2.10604
\(502\) 0 0
\(503\) −9.47397 −0.422423 −0.211212 0.977440i \(-0.567741\pi\)
−0.211212 + 0.977440i \(0.567741\pi\)
\(504\) 0 0
\(505\) 43.1977 1.92227
\(506\) 0 0
\(507\) −2.78432 −0.123656
\(508\) 0 0
\(509\) 5.62864 0.249485 0.124743 0.992189i \(-0.460190\pi\)
0.124743 + 0.992189i \(0.460190\pi\)
\(510\) 0 0
\(511\) 9.94348 0.439874
\(512\) 0 0
\(513\) 32.9737 1.45582
\(514\) 0 0
\(515\) 20.6756 0.911076
\(516\) 0 0
\(517\) −0.120836 −0.00531435
\(518\) 0 0
\(519\) 47.5075 2.08535
\(520\) 0 0
\(521\) 34.8219 1.52557 0.762786 0.646650i \(-0.223831\pi\)
0.762786 + 0.646650i \(0.223831\pi\)
\(522\) 0 0
\(523\) −9.12215 −0.398884 −0.199442 0.979910i \(-0.563913\pi\)
−0.199442 + 0.979910i \(0.563913\pi\)
\(524\) 0 0
\(525\) 7.49028 0.326903
\(526\) 0 0
\(527\) 7.43943 0.324067
\(528\) 0 0
\(529\) −22.9205 −0.996541
\(530\) 0 0
\(531\) 19.2231 0.834213
\(532\) 0 0
\(533\) −9.09314 −0.393868
\(534\) 0 0
\(535\) 1.01956 0.0440793
\(536\) 0 0
\(537\) 21.5460 0.929781
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 23.7767 1.02224 0.511119 0.859510i \(-0.329231\pi\)
0.511119 + 0.859510i \(0.329231\pi\)
\(542\) 0 0
\(543\) −6.08432 −0.261103
\(544\) 0 0
\(545\) −23.0675 −0.988102
\(546\) 0 0
\(547\) −38.6086 −1.65079 −0.825393 0.564558i \(-0.809046\pi\)
−0.825393 + 0.564558i \(0.809046\pi\)
\(548\) 0 0
\(549\) −46.9310 −2.00297
\(550\) 0 0
\(551\) −58.5106 −2.49264
\(552\) 0 0
\(553\) −10.1171 −0.430225
\(554\) 0 0
\(555\) 16.9215 0.718277
\(556\) 0 0
\(557\) 0.470484 0.0199351 0.00996753 0.999950i \(-0.496827\pi\)
0.00996753 + 0.999950i \(0.496827\pi\)
\(558\) 0 0
\(559\) −6.50862 −0.275285
\(560\) 0 0
\(561\) −7.92601 −0.334637
\(562\) 0 0
\(563\) 30.9553 1.30461 0.652305 0.757957i \(-0.273802\pi\)
0.652305 + 0.757957i \(0.273802\pi\)
\(564\) 0 0
\(565\) 14.9947 0.630832
\(566\) 0 0
\(567\) 0.671584 0.0282039
\(568\) 0 0
\(569\) −4.38784 −0.183948 −0.0919740 0.995761i \(-0.529318\pi\)
−0.0919740 + 0.995761i \(0.529318\pi\)
\(570\) 0 0
\(571\) 27.5135 1.15140 0.575702 0.817659i \(-0.304729\pi\)
0.575702 + 0.817659i \(0.304729\pi\)
\(572\) 0 0
\(573\) −67.3614 −2.81406
\(574\) 0 0
\(575\) 0.758735 0.0316414
\(576\) 0 0
\(577\) −21.5703 −0.897985 −0.448992 0.893536i \(-0.648217\pi\)
−0.448992 + 0.893536i \(0.648217\pi\)
\(578\) 0 0
\(579\) −17.7551 −0.737877
\(580\) 0 0
\(581\) 8.81845 0.365851
\(582\) 0 0
\(583\) −5.22807 −0.216525
\(584\) 0 0
\(585\) −13.1791 −0.544888
\(586\) 0 0
\(587\) −35.9394 −1.48338 −0.741689 0.670744i \(-0.765975\pi\)
−0.741689 + 0.670744i \(0.765975\pi\)
\(588\) 0 0
\(589\) 17.6607 0.727696
\(590\) 0 0
\(591\) −64.3368 −2.64646
\(592\) 0 0
\(593\) 6.58399 0.270372 0.135186 0.990820i \(-0.456837\pi\)
0.135186 + 0.990820i \(0.456837\pi\)
\(594\) 0 0
\(595\) 7.89411 0.323627
\(596\) 0 0
\(597\) 30.2684 1.23880
\(598\) 0 0
\(599\) 29.8135 1.21814 0.609072 0.793115i \(-0.291542\pi\)
0.609072 + 0.793115i \(0.291542\pi\)
\(600\) 0 0
\(601\) −8.33001 −0.339788 −0.169894 0.985462i \(-0.554343\pi\)
−0.169894 + 0.985462i \(0.554343\pi\)
\(602\) 0 0
\(603\) −13.2308 −0.538800
\(604\) 0 0
\(605\) 2.77311 0.112743
\(606\) 0 0
\(607\) 12.4632 0.505864 0.252932 0.967484i \(-0.418605\pi\)
0.252932 + 0.967484i \(0.418605\pi\)
\(608\) 0 0
\(609\) 24.1074 0.976883
\(610\) 0 0
\(611\) −0.120836 −0.00488849
\(612\) 0 0
\(613\) 35.4426 1.43151 0.715757 0.698350i \(-0.246082\pi\)
0.715757 + 0.698350i \(0.246082\pi\)
\(614\) 0 0
\(615\) −70.2103 −2.83115
\(616\) 0 0
\(617\) −22.5862 −0.909288 −0.454644 0.890673i \(-0.650233\pi\)
−0.454644 + 0.890673i \(0.650233\pi\)
\(618\) 0 0
\(619\) 25.4026 1.02101 0.510507 0.859873i \(-0.329458\pi\)
0.510507 + 0.859873i \(0.329458\pi\)
\(620\) 0 0
\(621\) −1.37618 −0.0552243
\(622\) 0 0
\(623\) −17.7949 −0.712937
\(624\) 0 0
\(625\) −31.2138 −1.24855
\(626\) 0 0
\(627\) −18.8158 −0.751431
\(628\) 0 0
\(629\) 6.23859 0.248749
\(630\) 0 0
\(631\) 27.1228 1.07974 0.539871 0.841748i \(-0.318473\pi\)
0.539871 + 0.841748i \(0.318473\pi\)
\(632\) 0 0
\(633\) −48.7420 −1.93732
\(634\) 0 0
\(635\) 52.0230 2.06447
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −42.8896 −1.69669
\(640\) 0 0
\(641\) 21.1087 0.833742 0.416871 0.908966i \(-0.363127\pi\)
0.416871 + 0.908966i \(0.363127\pi\)
\(642\) 0 0
\(643\) 44.7611 1.76520 0.882602 0.470120i \(-0.155789\pi\)
0.882602 + 0.470120i \(0.155789\pi\)
\(644\) 0 0
\(645\) −50.2547 −1.97878
\(646\) 0 0
\(647\) 11.8839 0.467202 0.233601 0.972332i \(-0.424949\pi\)
0.233601 + 0.972332i \(0.424949\pi\)
\(648\) 0 0
\(649\) −4.04489 −0.158776
\(650\) 0 0
\(651\) −7.27652 −0.285189
\(652\) 0 0
\(653\) −41.5792 −1.62712 −0.813559 0.581482i \(-0.802473\pi\)
−0.813559 + 0.581482i \(0.802473\pi\)
\(654\) 0 0
\(655\) 22.5564 0.881350
\(656\) 0 0
\(657\) −47.2559 −1.84363
\(658\) 0 0
\(659\) −13.5696 −0.528598 −0.264299 0.964441i \(-0.585141\pi\)
−0.264299 + 0.964441i \(0.585141\pi\)
\(660\) 0 0
\(661\) 4.59269 0.178635 0.0893175 0.996003i \(-0.471531\pi\)
0.0893175 + 0.996003i \(0.471531\pi\)
\(662\) 0 0
\(663\) −7.92601 −0.307821
\(664\) 0 0
\(665\) 18.7401 0.726708
\(666\) 0 0
\(667\) 2.44198 0.0945540
\(668\) 0 0
\(669\) 60.8790 2.35372
\(670\) 0 0
\(671\) 9.87513 0.381225
\(672\) 0 0
\(673\) −40.5588 −1.56343 −0.781714 0.623637i \(-0.785654\pi\)
−0.781714 + 0.623637i \(0.785654\pi\)
\(674\) 0 0
\(675\) −13.1263 −0.505232
\(676\) 0 0
\(677\) −39.9393 −1.53499 −0.767496 0.641053i \(-0.778498\pi\)
−0.767496 + 0.641053i \(0.778498\pi\)
\(678\) 0 0
\(679\) 8.81902 0.338443
\(680\) 0 0
\(681\) −13.5177 −0.517999
\(682\) 0 0
\(683\) −16.6904 −0.638639 −0.319319 0.947647i \(-0.603454\pi\)
−0.319319 + 0.947647i \(0.603454\pi\)
\(684\) 0 0
\(685\) −35.6504 −1.36213
\(686\) 0 0
\(687\) −8.00154 −0.305278
\(688\) 0 0
\(689\) −5.22807 −0.199174
\(690\) 0 0
\(691\) −18.0484 −0.686593 −0.343297 0.939227i \(-0.611544\pi\)
−0.343297 + 0.939227i \(0.611544\pi\)
\(692\) 0 0
\(693\) 4.75245 0.180531
\(694\) 0 0
\(695\) 62.5655 2.37324
\(696\) 0 0
\(697\) −25.8851 −0.980467
\(698\) 0 0
\(699\) −2.65458 −0.100406
\(700\) 0 0
\(701\) 13.1741 0.497578 0.248789 0.968558i \(-0.419967\pi\)
0.248789 + 0.968558i \(0.419967\pi\)
\(702\) 0 0
\(703\) 14.8100 0.558569
\(704\) 0 0
\(705\) −0.933002 −0.0351389
\(706\) 0 0
\(707\) −15.5773 −0.585845
\(708\) 0 0
\(709\) −8.31848 −0.312407 −0.156204 0.987725i \(-0.549926\pi\)
−0.156204 + 0.987725i \(0.549926\pi\)
\(710\) 0 0
\(711\) 48.0812 1.80318
\(712\) 0 0
\(713\) −0.737081 −0.0276039
\(714\) 0 0
\(715\) 2.77311 0.103709
\(716\) 0 0
\(717\) −6.89635 −0.257549
\(718\) 0 0
\(719\) −11.6582 −0.434778 −0.217389 0.976085i \(-0.569754\pi\)
−0.217389 + 0.976085i \(0.569754\pi\)
\(720\) 0 0
\(721\) −7.45574 −0.277666
\(722\) 0 0
\(723\) 45.1809 1.68030
\(724\) 0 0
\(725\) 23.2922 0.865050
\(726\) 0 0
\(727\) −5.08052 −0.188426 −0.0942131 0.995552i \(-0.530034\pi\)
−0.0942131 + 0.995552i \(0.530034\pi\)
\(728\) 0 0
\(729\) −43.9489 −1.62774
\(730\) 0 0
\(731\) −18.5278 −0.685277
\(732\) 0 0
\(733\) 9.48835 0.350460 0.175230 0.984528i \(-0.443933\pi\)
0.175230 + 0.984528i \(0.443933\pi\)
\(734\) 0 0
\(735\) −7.72124 −0.284802
\(736\) 0 0
\(737\) 2.78400 0.102550
\(738\) 0 0
\(739\) −33.5555 −1.23436 −0.617179 0.786823i \(-0.711724\pi\)
−0.617179 + 0.786823i \(0.711724\pi\)
\(740\) 0 0
\(741\) −18.8158 −0.691216
\(742\) 0 0
\(743\) −10.5003 −0.385218 −0.192609 0.981276i \(-0.561695\pi\)
−0.192609 + 0.981276i \(0.561695\pi\)
\(744\) 0 0
\(745\) 47.1080 1.72590
\(746\) 0 0
\(747\) −41.9092 −1.53338
\(748\) 0 0
\(749\) −0.367658 −0.0134339
\(750\) 0 0
\(751\) 23.5350 0.858803 0.429401 0.903114i \(-0.358725\pi\)
0.429401 + 0.903114i \(0.358725\pi\)
\(752\) 0 0
\(753\) 10.7087 0.390248
\(754\) 0 0
\(755\) −42.5559 −1.54877
\(756\) 0 0
\(757\) −20.6595 −0.750884 −0.375442 0.926846i \(-0.622509\pi\)
−0.375442 + 0.926846i \(0.622509\pi\)
\(758\) 0 0
\(759\) 0.785291 0.0285043
\(760\) 0 0
\(761\) −12.1303 −0.439723 −0.219862 0.975531i \(-0.570561\pi\)
−0.219862 + 0.975531i \(0.570561\pi\)
\(762\) 0 0
\(763\) 8.31826 0.301141
\(764\) 0 0
\(765\) −37.5163 −1.35641
\(766\) 0 0
\(767\) −4.04489 −0.146052
\(768\) 0 0
\(769\) −11.8917 −0.428827 −0.214414 0.976743i \(-0.568784\pi\)
−0.214414 + 0.976743i \(0.568784\pi\)
\(770\) 0 0
\(771\) −75.7604 −2.72844
\(772\) 0 0
\(773\) −28.0728 −1.00971 −0.504854 0.863205i \(-0.668454\pi\)
−0.504854 + 0.863205i \(0.668454\pi\)
\(774\) 0 0
\(775\) −7.03044 −0.252541
\(776\) 0 0
\(777\) −6.10198 −0.218907
\(778\) 0 0
\(779\) −61.4493 −2.20165
\(780\) 0 0
\(781\) 9.02475 0.322931
\(782\) 0 0
\(783\) −42.2470 −1.50979
\(784\) 0 0
\(785\) 13.9601 0.498256
\(786\) 0 0
\(787\) −2.73641 −0.0975426 −0.0487713 0.998810i \(-0.515531\pi\)
−0.0487713 + 0.998810i \(0.515531\pi\)
\(788\) 0 0
\(789\) −45.2846 −1.61217
\(790\) 0 0
\(791\) −5.40717 −0.192257
\(792\) 0 0
\(793\) 9.87513 0.350676
\(794\) 0 0
\(795\) −40.3672 −1.43168
\(796\) 0 0
\(797\) 26.7258 0.946676 0.473338 0.880881i \(-0.343049\pi\)
0.473338 + 0.880881i \(0.343049\pi\)
\(798\) 0 0
\(799\) −0.343978 −0.0121691
\(800\) 0 0
\(801\) 84.5693 2.98811
\(802\) 0 0
\(803\) 9.94348 0.350898
\(804\) 0 0
\(805\) −0.782130 −0.0275665
\(806\) 0 0
\(807\) −58.5663 −2.06163
\(808\) 0 0
\(809\) 15.7871 0.555045 0.277523 0.960719i \(-0.410487\pi\)
0.277523 + 0.960719i \(0.410487\pi\)
\(810\) 0 0
\(811\) 13.0434 0.458014 0.229007 0.973425i \(-0.426452\pi\)
0.229007 + 0.973425i \(0.426452\pi\)
\(812\) 0 0
\(813\) 40.7170 1.42801
\(814\) 0 0
\(815\) −9.06173 −0.317419
\(816\) 0 0
\(817\) −43.9838 −1.53880
\(818\) 0 0
\(819\) 4.75245 0.166064
\(820\) 0 0
\(821\) 18.8379 0.657448 0.328724 0.944426i \(-0.393381\pi\)
0.328724 + 0.944426i \(0.393381\pi\)
\(822\) 0 0
\(823\) 25.7084 0.896139 0.448069 0.893999i \(-0.352112\pi\)
0.448069 + 0.893999i \(0.352112\pi\)
\(824\) 0 0
\(825\) 7.49028 0.260778
\(826\) 0 0
\(827\) −13.5146 −0.469949 −0.234975 0.972002i \(-0.575501\pi\)
−0.234975 + 0.972002i \(0.575501\pi\)
\(828\) 0 0
\(829\) −28.1334 −0.977114 −0.488557 0.872532i \(-0.662477\pi\)
−0.488557 + 0.872532i \(0.662477\pi\)
\(830\) 0 0
\(831\) −73.5779 −2.55239
\(832\) 0 0
\(833\) −2.84666 −0.0986309
\(834\) 0 0
\(835\) 46.9497 1.62476
\(836\) 0 0
\(837\) 12.7517 0.440764
\(838\) 0 0
\(839\) −43.7578 −1.51069 −0.755343 0.655329i \(-0.772530\pi\)
−0.755343 + 0.655329i \(0.772530\pi\)
\(840\) 0 0
\(841\) 45.9658 1.58503
\(842\) 0 0
\(843\) −14.2097 −0.489408
\(844\) 0 0
\(845\) 2.77311 0.0953980
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −34.2446 −1.17527
\(850\) 0 0
\(851\) −0.618105 −0.0211884
\(852\) 0 0
\(853\) 20.8971 0.715502 0.357751 0.933817i \(-0.383544\pi\)
0.357751 + 0.933817i \(0.383544\pi\)
\(854\) 0 0
\(855\) −89.0612 −3.04583
\(856\) 0 0
\(857\) −57.0628 −1.94923 −0.974614 0.223894i \(-0.928123\pi\)
−0.974614 + 0.223894i \(0.928123\pi\)
\(858\) 0 0
\(859\) 27.1516 0.926399 0.463200 0.886254i \(-0.346701\pi\)
0.463200 + 0.886254i \(0.346701\pi\)
\(860\) 0 0
\(861\) 25.3182 0.862843
\(862\) 0 0
\(863\) 1.68942 0.0575084 0.0287542 0.999587i \(-0.490846\pi\)
0.0287542 + 0.999587i \(0.490846\pi\)
\(864\) 0 0
\(865\) −47.3162 −1.60880
\(866\) 0 0
\(867\) 24.7708 0.841261
\(868\) 0 0
\(869\) −10.1171 −0.343200
\(870\) 0 0
\(871\) 2.78400 0.0943321
\(872\) 0 0
\(873\) −41.9120 −1.41850
\(874\) 0 0
\(875\) 6.40544 0.216543
\(876\) 0 0
\(877\) −31.6006 −1.06708 −0.533539 0.845776i \(-0.679138\pi\)
−0.533539 + 0.845776i \(0.679138\pi\)
\(878\) 0 0
\(879\) −32.4564 −1.09473
\(880\) 0 0
\(881\) −42.6087 −1.43552 −0.717762 0.696289i \(-0.754833\pi\)
−0.717762 + 0.696289i \(0.754833\pi\)
\(882\) 0 0
\(883\) 47.7599 1.60725 0.803624 0.595137i \(-0.202902\pi\)
0.803624 + 0.595137i \(0.202902\pi\)
\(884\) 0 0
\(885\) −31.2316 −1.04984
\(886\) 0 0
\(887\) −35.8277 −1.20298 −0.601488 0.798882i \(-0.705425\pi\)
−0.601488 + 0.798882i \(0.705425\pi\)
\(888\) 0 0
\(889\) −18.7598 −0.629183
\(890\) 0 0
\(891\) 0.671584 0.0224989
\(892\) 0 0
\(893\) −0.816580 −0.0273258
\(894\) 0 0
\(895\) −21.4593 −0.717306
\(896\) 0 0
\(897\) 0.785291 0.0262201
\(898\) 0 0
\(899\) −22.6275 −0.754668
\(900\) 0 0
\(901\) −14.8825 −0.495809
\(902\) 0 0
\(903\) 18.1221 0.603066
\(904\) 0 0
\(905\) 6.05982 0.201435
\(906\) 0 0
\(907\) −10.7825 −0.358027 −0.179013 0.983847i \(-0.557291\pi\)
−0.179013 + 0.983847i \(0.557291\pi\)
\(908\) 0 0
\(909\) 74.0303 2.45543
\(910\) 0 0
\(911\) 18.7105 0.619905 0.309953 0.950752i \(-0.399687\pi\)
0.309953 + 0.950752i \(0.399687\pi\)
\(912\) 0 0
\(913\) 8.81845 0.291848
\(914\) 0 0
\(915\) 76.2483 2.52069
\(916\) 0 0
\(917\) −8.13395 −0.268607
\(918\) 0 0
\(919\) −38.8166 −1.28044 −0.640221 0.768191i \(-0.721157\pi\)
−0.640221 + 0.768191i \(0.721157\pi\)
\(920\) 0 0
\(921\) −19.7033 −0.649246
\(922\) 0 0
\(923\) 9.02475 0.297053
\(924\) 0 0
\(925\) −5.89562 −0.193847
\(926\) 0 0
\(927\) 35.4330 1.16377
\(928\) 0 0
\(929\) −7.44831 −0.244371 −0.122186 0.992507i \(-0.538990\pi\)
−0.122186 + 0.992507i \(0.538990\pi\)
\(930\) 0 0
\(931\) −6.75777 −0.221477
\(932\) 0 0
\(933\) 11.0365 0.361320
\(934\) 0 0
\(935\) 7.89411 0.258165
\(936\) 0 0
\(937\) −5.01746 −0.163913 −0.0819567 0.996636i \(-0.526117\pi\)
−0.0819567 + 0.996636i \(0.526117\pi\)
\(938\) 0 0
\(939\) −37.2559 −1.21580
\(940\) 0 0
\(941\) 39.4944 1.28748 0.643740 0.765244i \(-0.277382\pi\)
0.643740 + 0.765244i \(0.277382\pi\)
\(942\) 0 0
\(943\) 2.56463 0.0835159
\(944\) 0 0
\(945\) 13.5311 0.440166
\(946\) 0 0
\(947\) 39.0353 1.26848 0.634239 0.773137i \(-0.281314\pi\)
0.634239 + 0.773137i \(0.281314\pi\)
\(948\) 0 0
\(949\) 9.94348 0.322779
\(950\) 0 0
\(951\) 87.0518 2.82285
\(952\) 0 0
\(953\) −20.2554 −0.656136 −0.328068 0.944654i \(-0.606398\pi\)
−0.328068 + 0.944654i \(0.606398\pi\)
\(954\) 0 0
\(955\) 67.0903 2.17099
\(956\) 0 0
\(957\) 24.1074 0.779283
\(958\) 0 0
\(959\) 12.8557 0.415133
\(960\) 0 0
\(961\) −24.1702 −0.779684
\(962\) 0 0
\(963\) 1.74728 0.0563052
\(964\) 0 0
\(965\) 17.6836 0.569256
\(966\) 0 0
\(967\) 8.74658 0.281271 0.140635 0.990061i \(-0.455085\pi\)
0.140635 + 0.990061i \(0.455085\pi\)
\(968\) 0 0
\(969\) −53.5622 −1.72066
\(970\) 0 0
\(971\) −12.3035 −0.394839 −0.197420 0.980319i \(-0.563256\pi\)
−0.197420 + 0.980319i \(0.563256\pi\)
\(972\) 0 0
\(973\) −22.5614 −0.723287
\(974\) 0 0
\(975\) 7.49028 0.239881
\(976\) 0 0
\(977\) −10.6015 −0.339172 −0.169586 0.985515i \(-0.554243\pi\)
−0.169586 + 0.985515i \(0.554243\pi\)
\(978\) 0 0
\(979\) −17.7949 −0.568727
\(980\) 0 0
\(981\) −39.5321 −1.26216
\(982\) 0 0
\(983\) 57.3622 1.82957 0.914785 0.403940i \(-0.132360\pi\)
0.914785 + 0.403940i \(0.132360\pi\)
\(984\) 0 0
\(985\) 64.0778 2.04169
\(986\) 0 0
\(987\) 0.336446 0.0107092
\(988\) 0 0
\(989\) 1.83570 0.0583717
\(990\) 0 0
\(991\) −33.1355 −1.05258 −0.526291 0.850304i \(-0.676418\pi\)
−0.526291 + 0.850304i \(0.676418\pi\)
\(992\) 0 0
\(993\) −24.9761 −0.792592
\(994\) 0 0
\(995\) −30.1466 −0.955711
\(996\) 0 0
\(997\) 4.24210 0.134349 0.0671743 0.997741i \(-0.478602\pi\)
0.0671743 + 0.997741i \(0.478602\pi\)
\(998\) 0 0
\(999\) 10.6934 0.338324
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 \(a_p\))