Properties

Label 8036.2.a.q.1.12
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-2.47735\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.47735 q^{3} -3.49844 q^{5} +3.13725 q^{9} +O(q^{10})\) \(q+2.47735 q^{3} -3.49844 q^{5} +3.13725 q^{9} -0.886832 q^{11} -6.85228 q^{13} -8.66684 q^{15} +3.02899 q^{17} +6.07400 q^{19} -4.52270 q^{23} +7.23905 q^{25} +0.340013 q^{27} -7.22633 q^{29} +9.72069 q^{31} -2.19699 q^{33} +7.05671 q^{37} -16.9755 q^{39} -1.00000 q^{41} +4.25996 q^{43} -10.9755 q^{45} -11.7610 q^{47} +7.50385 q^{51} +6.23725 q^{53} +3.10252 q^{55} +15.0474 q^{57} +0.453451 q^{59} -1.80500 q^{61} +23.9722 q^{65} +0.386390 q^{67} -11.2043 q^{69} +0.406313 q^{71} +2.47266 q^{73} +17.9336 q^{75} +14.1588 q^{79} -8.56942 q^{81} +7.79158 q^{83} -10.5967 q^{85} -17.9021 q^{87} -5.14645 q^{89} +24.0815 q^{93} -21.2495 q^{95} -11.4082 q^{97} -2.78221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) 2.47735 1.43030 0.715149 0.698973i \(-0.246359\pi\)
0.715149 + 0.698973i \(0.246359\pi\)
\(4\) 0 0
\(5\) −3.49844 −1.56455 −0.782274 0.622935i \(-0.785940\pi\)
−0.782274 + 0.622935i \(0.785940\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.13725 1.04575
\(10\) 0 0
\(11\) −0.886832 −0.267390 −0.133695 0.991023i \(-0.542684\pi\)
−0.133695 + 0.991023i \(0.542684\pi\)
\(12\) 0 0
\(13\) −6.85228 −1.90048 −0.950240 0.311519i \(-0.899162\pi\)
−0.950240 + 0.311519i \(0.899162\pi\)
\(14\) 0 0
\(15\) −8.66684 −2.23777
\(16\) 0 0
\(17\) 3.02899 0.734637 0.367318 0.930095i \(-0.380276\pi\)
0.367318 + 0.930095i \(0.380276\pi\)
\(18\) 0 0
\(19\) 6.07400 1.39347 0.696735 0.717328i \(-0.254635\pi\)
0.696735 + 0.717328i \(0.254635\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.52270 −0.943048 −0.471524 0.881853i \(-0.656296\pi\)
−0.471524 + 0.881853i \(0.656296\pi\)
\(24\) 0 0
\(25\) 7.23905 1.44781
\(26\) 0 0
\(27\) 0.340013 0.0654355
\(28\) 0 0
\(29\) −7.22633 −1.34189 −0.670947 0.741505i \(-0.734112\pi\)
−0.670947 + 0.741505i \(0.734112\pi\)
\(30\) 0 0
\(31\) 9.72069 1.74589 0.872944 0.487821i \(-0.162208\pi\)
0.872944 + 0.487821i \(0.162208\pi\)
\(32\) 0 0
\(33\) −2.19699 −0.382447
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.05671 1.16012 0.580058 0.814575i \(-0.303030\pi\)
0.580058 + 0.814575i \(0.303030\pi\)
\(38\) 0 0
\(39\) −16.9755 −2.71825
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 4.25996 0.649638 0.324819 0.945776i \(-0.394697\pi\)
0.324819 + 0.945776i \(0.394697\pi\)
\(44\) 0 0
\(45\) −10.9755 −1.63613
\(46\) 0 0
\(47\) −11.7610 −1.71551 −0.857756 0.514056i \(-0.828142\pi\)
−0.857756 + 0.514056i \(0.828142\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 7.50385 1.05075
\(52\) 0 0
\(53\) 6.23725 0.856752 0.428376 0.903601i \(-0.359086\pi\)
0.428376 + 0.903601i \(0.359086\pi\)
\(54\) 0 0
\(55\) 3.10252 0.418344
\(56\) 0 0
\(57\) 15.0474 1.99308
\(58\) 0 0
\(59\) 0.453451 0.0590343 0.0295171 0.999564i \(-0.490603\pi\)
0.0295171 + 0.999564i \(0.490603\pi\)
\(60\) 0 0
\(61\) −1.80500 −0.231106 −0.115553 0.993301i \(-0.536864\pi\)
−0.115553 + 0.993301i \(0.536864\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 23.9722 2.97339
\(66\) 0 0
\(67\) 0.386390 0.0472050 0.0236025 0.999721i \(-0.492486\pi\)
0.0236025 + 0.999721i \(0.492486\pi\)
\(68\) 0 0
\(69\) −11.2043 −1.34884
\(70\) 0 0
\(71\) 0.406313 0.0482205 0.0241103 0.999709i \(-0.492325\pi\)
0.0241103 + 0.999709i \(0.492325\pi\)
\(72\) 0 0
\(73\) 2.47266 0.289403 0.144701 0.989475i \(-0.453778\pi\)
0.144701 + 0.989475i \(0.453778\pi\)
\(74\) 0 0
\(75\) 17.9336 2.07080
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 14.1588 1.59299 0.796497 0.604643i \(-0.206684\pi\)
0.796497 + 0.604643i \(0.206684\pi\)
\(80\) 0 0
\(81\) −8.56942 −0.952157
\(82\) 0 0
\(83\) 7.79158 0.855237 0.427618 0.903959i \(-0.359353\pi\)
0.427618 + 0.903959i \(0.359353\pi\)
\(84\) 0 0
\(85\) −10.5967 −1.14937
\(86\) 0 0
\(87\) −17.9021 −1.91931
\(88\) 0 0
\(89\) −5.14645 −0.545523 −0.272761 0.962082i \(-0.587937\pi\)
−0.272761 + 0.962082i \(0.587937\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 24.0815 2.49714
\(94\) 0 0
\(95\) −21.2495 −2.18015
\(96\) 0 0
\(97\) −11.4082 −1.15833 −0.579165 0.815211i \(-0.696621\pi\)
−0.579165 + 0.815211i \(0.696621\pi\)
\(98\) 0 0
\(99\) −2.78221 −0.279623
\(100\) 0 0
\(101\) 7.23469 0.719878 0.359939 0.932976i \(-0.382797\pi\)
0.359939 + 0.932976i \(0.382797\pi\)
\(102\) 0 0
\(103\) −9.81614 −0.967213 −0.483606 0.875286i \(-0.660673\pi\)
−0.483606 + 0.875286i \(0.660673\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.91514 0.958533 0.479266 0.877669i \(-0.340903\pi\)
0.479266 + 0.877669i \(0.340903\pi\)
\(108\) 0 0
\(109\) 4.44277 0.425540 0.212770 0.977102i \(-0.431751\pi\)
0.212770 + 0.977102i \(0.431751\pi\)
\(110\) 0 0
\(111\) 17.4819 1.65931
\(112\) 0 0
\(113\) 13.0359 1.22631 0.613157 0.789961i \(-0.289899\pi\)
0.613157 + 0.789961i \(0.289899\pi\)
\(114\) 0 0
\(115\) 15.8224 1.47544
\(116\) 0 0
\(117\) −21.4973 −1.98743
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.2135 −0.928503
\(122\) 0 0
\(123\) −2.47735 −0.223375
\(124\) 0 0
\(125\) −7.83317 −0.700620
\(126\) 0 0
\(127\) 21.6259 1.91899 0.959496 0.281722i \(-0.0909057\pi\)
0.959496 + 0.281722i \(0.0909057\pi\)
\(128\) 0 0
\(129\) 10.5534 0.929175
\(130\) 0 0
\(131\) 2.13139 0.186221 0.0931104 0.995656i \(-0.470319\pi\)
0.0931104 + 0.995656i \(0.470319\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.18951 −0.102377
\(136\) 0 0
\(137\) 2.35667 0.201344 0.100672 0.994920i \(-0.467901\pi\)
0.100672 + 0.994920i \(0.467901\pi\)
\(138\) 0 0
\(139\) 12.9520 1.09858 0.549288 0.835633i \(-0.314899\pi\)
0.549288 + 0.835633i \(0.314899\pi\)
\(140\) 0 0
\(141\) −29.1360 −2.45369
\(142\) 0 0
\(143\) 6.07682 0.508169
\(144\) 0 0
\(145\) 25.2808 2.09946
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −14.5047 −1.18827 −0.594137 0.804364i \(-0.702506\pi\)
−0.594137 + 0.804364i \(0.702506\pi\)
\(150\) 0 0
\(151\) 11.6316 0.946569 0.473285 0.880910i \(-0.343068\pi\)
0.473285 + 0.880910i \(0.343068\pi\)
\(152\) 0 0
\(153\) 9.50268 0.768246
\(154\) 0 0
\(155\) −34.0072 −2.73152
\(156\) 0 0
\(157\) 5.60289 0.447160 0.223580 0.974686i \(-0.428226\pi\)
0.223580 + 0.974686i \(0.428226\pi\)
\(158\) 0 0
\(159\) 15.4518 1.22541
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 7.42331 0.581439 0.290719 0.956808i \(-0.406105\pi\)
0.290719 + 0.956808i \(0.406105\pi\)
\(164\) 0 0
\(165\) 7.68603 0.598356
\(166\) 0 0
\(167\) 17.5163 1.35545 0.677726 0.735314i \(-0.262965\pi\)
0.677726 + 0.735314i \(0.262965\pi\)
\(168\) 0 0
\(169\) 33.9537 2.61182
\(170\) 0 0
\(171\) 19.0556 1.45722
\(172\) 0 0
\(173\) 9.59063 0.729162 0.364581 0.931172i \(-0.381212\pi\)
0.364581 + 0.931172i \(0.381212\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.12336 0.0844366
\(178\) 0 0
\(179\) 24.6408 1.84174 0.920870 0.389871i \(-0.127480\pi\)
0.920870 + 0.389871i \(0.127480\pi\)
\(180\) 0 0
\(181\) −3.27455 −0.243395 −0.121698 0.992567i \(-0.538834\pi\)
−0.121698 + 0.992567i \(0.538834\pi\)
\(182\) 0 0
\(183\) −4.47160 −0.330551
\(184\) 0 0
\(185\) −24.6874 −1.81506
\(186\) 0 0
\(187\) −2.68620 −0.196434
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.00730 0.0728855 0.0364428 0.999336i \(-0.488397\pi\)
0.0364428 + 0.999336i \(0.488397\pi\)
\(192\) 0 0
\(193\) 19.9178 1.43371 0.716857 0.697220i \(-0.245580\pi\)
0.716857 + 0.697220i \(0.245580\pi\)
\(194\) 0 0
\(195\) 59.3876 4.25283
\(196\) 0 0
\(197\) 7.96044 0.567158 0.283579 0.958949i \(-0.408478\pi\)
0.283579 + 0.958949i \(0.408478\pi\)
\(198\) 0 0
\(199\) −16.1963 −1.14813 −0.574064 0.818811i \(-0.694634\pi\)
−0.574064 + 0.818811i \(0.694634\pi\)
\(200\) 0 0
\(201\) 0.957221 0.0675172
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.49844 0.244341
\(206\) 0 0
\(207\) −14.1888 −0.986193
\(208\) 0 0
\(209\) −5.38661 −0.372600
\(210\) 0 0
\(211\) 10.1084 0.695894 0.347947 0.937514i \(-0.386879\pi\)
0.347947 + 0.937514i \(0.386879\pi\)
\(212\) 0 0
\(213\) 1.00658 0.0689696
\(214\) 0 0
\(215\) −14.9032 −1.01639
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.12564 0.413932
\(220\) 0 0
\(221\) −20.7554 −1.39616
\(222\) 0 0
\(223\) 5.60799 0.375539 0.187770 0.982213i \(-0.439874\pi\)
0.187770 + 0.982213i \(0.439874\pi\)
\(224\) 0 0
\(225\) 22.7107 1.51405
\(226\) 0 0
\(227\) −5.16589 −0.342872 −0.171436 0.985195i \(-0.554841\pi\)
−0.171436 + 0.985195i \(0.554841\pi\)
\(228\) 0 0
\(229\) 6.39496 0.422591 0.211296 0.977422i \(-0.432232\pi\)
0.211296 + 0.977422i \(0.432232\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.1923 0.929771 0.464885 0.885371i \(-0.346096\pi\)
0.464885 + 0.885371i \(0.346096\pi\)
\(234\) 0 0
\(235\) 41.1450 2.68400
\(236\) 0 0
\(237\) 35.0763 2.27845
\(238\) 0 0
\(239\) −15.2318 −0.985266 −0.492633 0.870237i \(-0.663966\pi\)
−0.492633 + 0.870237i \(0.663966\pi\)
\(240\) 0 0
\(241\) −6.90521 −0.444804 −0.222402 0.974955i \(-0.571390\pi\)
−0.222402 + 0.974955i \(0.571390\pi\)
\(242\) 0 0
\(243\) −22.2495 −1.42730
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −41.6207 −2.64826
\(248\) 0 0
\(249\) 19.3024 1.22324
\(250\) 0 0
\(251\) −21.2459 −1.34103 −0.670515 0.741896i \(-0.733927\pi\)
−0.670515 + 0.741896i \(0.733927\pi\)
\(252\) 0 0
\(253\) 4.01088 0.252162
\(254\) 0 0
\(255\) −26.2517 −1.64395
\(256\) 0 0
\(257\) −6.06200 −0.378137 −0.189068 0.981964i \(-0.560547\pi\)
−0.189068 + 0.981964i \(0.560547\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −22.6708 −1.40329
\(262\) 0 0
\(263\) −15.1984 −0.937171 −0.468586 0.883418i \(-0.655236\pi\)
−0.468586 + 0.883418i \(0.655236\pi\)
\(264\) 0 0
\(265\) −21.8206 −1.34043
\(266\) 0 0
\(267\) −12.7495 −0.780260
\(268\) 0 0
\(269\) 18.8933 1.15195 0.575973 0.817469i \(-0.304623\pi\)
0.575973 + 0.817469i \(0.304623\pi\)
\(270\) 0 0
\(271\) 14.9578 0.908621 0.454310 0.890843i \(-0.349886\pi\)
0.454310 + 0.890843i \(0.349886\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.41982 −0.387130
\(276\) 0 0
\(277\) −13.0971 −0.786931 −0.393465 0.919339i \(-0.628724\pi\)
−0.393465 + 0.919339i \(0.628724\pi\)
\(278\) 0 0
\(279\) 30.4962 1.82576
\(280\) 0 0
\(281\) −21.2844 −1.26972 −0.634860 0.772627i \(-0.718942\pi\)
−0.634860 + 0.772627i \(0.718942\pi\)
\(282\) 0 0
\(283\) 22.7683 1.35343 0.676717 0.736243i \(-0.263402\pi\)
0.676717 + 0.736243i \(0.263402\pi\)
\(284\) 0 0
\(285\) −52.6424 −3.11826
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −7.82525 −0.460309
\(290\) 0 0
\(291\) −28.2621 −1.65675
\(292\) 0 0
\(293\) 4.51752 0.263916 0.131958 0.991255i \(-0.457874\pi\)
0.131958 + 0.991255i \(0.457874\pi\)
\(294\) 0 0
\(295\) −1.58637 −0.0923620
\(296\) 0 0
\(297\) −0.301534 −0.0174968
\(298\) 0 0
\(299\) 30.9908 1.79224
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 17.9228 1.02964
\(304\) 0 0
\(305\) 6.31467 0.361577
\(306\) 0 0
\(307\) 4.60882 0.263039 0.131520 0.991314i \(-0.458014\pi\)
0.131520 + 0.991314i \(0.458014\pi\)
\(308\) 0 0
\(309\) −24.3180 −1.38340
\(310\) 0 0
\(311\) −15.9788 −0.906077 −0.453039 0.891491i \(-0.649660\pi\)
−0.453039 + 0.891491i \(0.649660\pi\)
\(312\) 0 0
\(313\) −32.4129 −1.83208 −0.916042 0.401082i \(-0.868634\pi\)
−0.916042 + 0.401082i \(0.868634\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.1162 −0.736679 −0.368340 0.929691i \(-0.620074\pi\)
−0.368340 + 0.929691i \(0.620074\pi\)
\(318\) 0 0
\(319\) 6.40854 0.358809
\(320\) 0 0
\(321\) 24.5632 1.37099
\(322\) 0 0
\(323\) 18.3981 1.02370
\(324\) 0 0
\(325\) −49.6040 −2.75153
\(326\) 0 0
\(327\) 11.0063 0.608649
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 26.6358 1.46403 0.732017 0.681286i \(-0.238579\pi\)
0.732017 + 0.681286i \(0.238579\pi\)
\(332\) 0 0
\(333\) 22.1387 1.21319
\(334\) 0 0
\(335\) −1.35176 −0.0738545
\(336\) 0 0
\(337\) −22.0648 −1.20194 −0.600972 0.799270i \(-0.705220\pi\)
−0.600972 + 0.799270i \(0.705220\pi\)
\(338\) 0 0
\(339\) 32.2945 1.75399
\(340\) 0 0
\(341\) −8.62062 −0.466833
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 39.1975 2.11032
\(346\) 0 0
\(347\) 29.4858 1.58288 0.791440 0.611246i \(-0.209332\pi\)
0.791440 + 0.611246i \(0.209332\pi\)
\(348\) 0 0
\(349\) −14.9842 −0.802084 −0.401042 0.916060i \(-0.631352\pi\)
−0.401042 + 0.916060i \(0.631352\pi\)
\(350\) 0 0
\(351\) −2.32986 −0.124359
\(352\) 0 0
\(353\) 18.2650 0.972149 0.486075 0.873917i \(-0.338428\pi\)
0.486075 + 0.873917i \(0.338428\pi\)
\(354\) 0 0
\(355\) −1.42146 −0.0754433
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.1774 1.06492 0.532462 0.846454i \(-0.321267\pi\)
0.532462 + 0.846454i \(0.321267\pi\)
\(360\) 0 0
\(361\) 17.8935 0.941761
\(362\) 0 0
\(363\) −25.3025 −1.32803
\(364\) 0 0
\(365\) −8.65044 −0.452785
\(366\) 0 0
\(367\) 17.2336 0.899585 0.449792 0.893133i \(-0.351498\pi\)
0.449792 + 0.893133i \(0.351498\pi\)
\(368\) 0 0
\(369\) −3.13725 −0.163319
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.7019 −0.554125 −0.277062 0.960852i \(-0.589361\pi\)
−0.277062 + 0.960852i \(0.589361\pi\)
\(374\) 0 0
\(375\) −19.4055 −1.00209
\(376\) 0 0
\(377\) 49.5168 2.55024
\(378\) 0 0
\(379\) 24.9770 1.28298 0.641492 0.767130i \(-0.278316\pi\)
0.641492 + 0.767130i \(0.278316\pi\)
\(380\) 0 0
\(381\) 53.5750 2.74473
\(382\) 0 0
\(383\) −4.22751 −0.216016 −0.108008 0.994150i \(-0.534447\pi\)
−0.108008 + 0.994150i \(0.534447\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 13.3646 0.679359
\(388\) 0 0
\(389\) 25.5041 1.29311 0.646555 0.762867i \(-0.276209\pi\)
0.646555 + 0.762867i \(0.276209\pi\)
\(390\) 0 0
\(391\) −13.6992 −0.692798
\(392\) 0 0
\(393\) 5.28020 0.266351
\(394\) 0 0
\(395\) −49.5338 −2.49231
\(396\) 0 0
\(397\) −30.2426 −1.51783 −0.758917 0.651187i \(-0.774271\pi\)
−0.758917 + 0.651187i \(0.774271\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.81709 0.290491 0.145246 0.989396i \(-0.453603\pi\)
0.145246 + 0.989396i \(0.453603\pi\)
\(402\) 0 0
\(403\) −66.6089 −3.31802
\(404\) 0 0
\(405\) 29.9796 1.48970
\(406\) 0 0
\(407\) −6.25812 −0.310203
\(408\) 0 0
\(409\) −0.436763 −0.0215965 −0.0107983 0.999942i \(-0.503437\pi\)
−0.0107983 + 0.999942i \(0.503437\pi\)
\(410\) 0 0
\(411\) 5.83829 0.287982
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −27.2583 −1.33806
\(416\) 0 0
\(417\) 32.0867 1.57129
\(418\) 0 0
\(419\) −7.44035 −0.363485 −0.181743 0.983346i \(-0.558174\pi\)
−0.181743 + 0.983346i \(0.558174\pi\)
\(420\) 0 0
\(421\) 22.7010 1.10638 0.553189 0.833056i \(-0.313411\pi\)
0.553189 + 0.833056i \(0.313411\pi\)
\(422\) 0 0
\(423\) −36.8971 −1.79400
\(424\) 0 0
\(425\) 21.9270 1.06361
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 15.0544 0.726833
\(430\) 0 0
\(431\) 33.3117 1.60457 0.802285 0.596942i \(-0.203618\pi\)
0.802285 + 0.596942i \(0.203618\pi\)
\(432\) 0 0
\(433\) −13.8756 −0.666816 −0.333408 0.942783i \(-0.608199\pi\)
−0.333408 + 0.942783i \(0.608199\pi\)
\(434\) 0 0
\(435\) 62.6294 3.00285
\(436\) 0 0
\(437\) −27.4709 −1.31411
\(438\) 0 0
\(439\) 25.0594 1.19602 0.598010 0.801488i \(-0.295958\pi\)
0.598010 + 0.801488i \(0.295958\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.6739 0.602154 0.301077 0.953600i \(-0.402654\pi\)
0.301077 + 0.953600i \(0.402654\pi\)
\(444\) 0 0
\(445\) 18.0045 0.853497
\(446\) 0 0
\(447\) −35.9333 −1.69959
\(448\) 0 0
\(449\) −35.8184 −1.69037 −0.845187 0.534470i \(-0.820511\pi\)
−0.845187 + 0.534470i \(0.820511\pi\)
\(450\) 0 0
\(451\) 0.886832 0.0417593
\(452\) 0 0
\(453\) 28.8156 1.35388
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −21.1037 −0.987190 −0.493595 0.869692i \(-0.664318\pi\)
−0.493595 + 0.869692i \(0.664318\pi\)
\(458\) 0 0
\(459\) 1.02989 0.0480713
\(460\) 0 0
\(461\) −33.8364 −1.57592 −0.787958 0.615729i \(-0.788862\pi\)
−0.787958 + 0.615729i \(0.788862\pi\)
\(462\) 0 0
\(463\) 31.5226 1.46498 0.732490 0.680778i \(-0.238358\pi\)
0.732490 + 0.680778i \(0.238358\pi\)
\(464\) 0 0
\(465\) −84.2477 −3.90689
\(466\) 0 0
\(467\) 33.1549 1.53422 0.767112 0.641513i \(-0.221693\pi\)
0.767112 + 0.641513i \(0.221693\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 13.8803 0.639571
\(472\) 0 0
\(473\) −3.77787 −0.173707
\(474\) 0 0
\(475\) 43.9700 2.01748
\(476\) 0 0
\(477\) 19.5678 0.895948
\(478\) 0 0
\(479\) −7.80316 −0.356536 −0.178268 0.983982i \(-0.557049\pi\)
−0.178268 + 0.983982i \(0.557049\pi\)
\(480\) 0 0
\(481\) −48.3545 −2.20478
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 39.9109 1.81226
\(486\) 0 0
\(487\) 11.9654 0.542202 0.271101 0.962551i \(-0.412612\pi\)
0.271101 + 0.962551i \(0.412612\pi\)
\(488\) 0 0
\(489\) 18.3901 0.831630
\(490\) 0 0
\(491\) 4.00762 0.180861 0.0904307 0.995903i \(-0.471176\pi\)
0.0904307 + 0.995903i \(0.471176\pi\)
\(492\) 0 0
\(493\) −21.8884 −0.985806
\(494\) 0 0
\(495\) 9.73339 0.437483
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −11.7405 −0.525578 −0.262789 0.964853i \(-0.584642\pi\)
−0.262789 + 0.964853i \(0.584642\pi\)
\(500\) 0 0
\(501\) 43.3940 1.93870
\(502\) 0 0
\(503\) −5.10200 −0.227487 −0.113743 0.993510i \(-0.536284\pi\)
−0.113743 + 0.993510i \(0.536284\pi\)
\(504\) 0 0
\(505\) −25.3101 −1.12628
\(506\) 0 0
\(507\) 84.1151 3.73568
\(508\) 0 0
\(509\) −22.1952 −0.983784 −0.491892 0.870656i \(-0.663695\pi\)
−0.491892 + 0.870656i \(0.663695\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 2.06524 0.0911824
\(514\) 0 0
\(515\) 34.3411 1.51325
\(516\) 0 0
\(517\) 10.4300 0.458711
\(518\) 0 0
\(519\) 23.7593 1.04292
\(520\) 0 0
\(521\) −26.9053 −1.17874 −0.589370 0.807863i \(-0.700624\pi\)
−0.589370 + 0.807863i \(0.700624\pi\)
\(522\) 0 0
\(523\) 28.5119 1.24674 0.623369 0.781928i \(-0.285764\pi\)
0.623369 + 0.781928i \(0.285764\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.4438 1.28259
\(528\) 0 0
\(529\) −2.54517 −0.110660
\(530\) 0 0
\(531\) 1.42259 0.0617351
\(532\) 0 0
\(533\) 6.85228 0.296805
\(534\) 0 0
\(535\) −34.6875 −1.49967
\(536\) 0 0
\(537\) 61.0438 2.63423
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −13.1630 −0.565920 −0.282960 0.959132i \(-0.591316\pi\)
−0.282960 + 0.959132i \(0.591316\pi\)
\(542\) 0 0
\(543\) −8.11220 −0.348128
\(544\) 0 0
\(545\) −15.5427 −0.665778
\(546\) 0 0
\(547\) −13.8254 −0.591133 −0.295567 0.955322i \(-0.595508\pi\)
−0.295567 + 0.955322i \(0.595508\pi\)
\(548\) 0 0
\(549\) −5.66273 −0.241679
\(550\) 0 0
\(551\) −43.8927 −1.86989
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −61.1594 −2.59607
\(556\) 0 0
\(557\) −34.3090 −1.45372 −0.726861 0.686785i \(-0.759021\pi\)
−0.726861 + 0.686785i \(0.759021\pi\)
\(558\) 0 0
\(559\) −29.1904 −1.23462
\(560\) 0 0
\(561\) −6.65465 −0.280960
\(562\) 0 0
\(563\) −13.4964 −0.568806 −0.284403 0.958705i \(-0.591795\pi\)
−0.284403 + 0.958705i \(0.591795\pi\)
\(564\) 0 0
\(565\) −45.6053 −1.91863
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.21418 −0.302434 −0.151217 0.988501i \(-0.548319\pi\)
−0.151217 + 0.988501i \(0.548319\pi\)
\(570\) 0 0
\(571\) −9.09658 −0.380680 −0.190340 0.981718i \(-0.560959\pi\)
−0.190340 + 0.981718i \(0.560959\pi\)
\(572\) 0 0
\(573\) 2.49543 0.104248
\(574\) 0 0
\(575\) −32.7401 −1.36536
\(576\) 0 0
\(577\) −25.5931 −1.06545 −0.532727 0.846287i \(-0.678833\pi\)
−0.532727 + 0.846287i \(0.678833\pi\)
\(578\) 0 0
\(579\) 49.3433 2.05064
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5.53139 −0.229087
\(584\) 0 0
\(585\) 75.2069 3.10942
\(586\) 0 0
\(587\) 14.8861 0.614416 0.307208 0.951642i \(-0.400605\pi\)
0.307208 + 0.951642i \(0.400605\pi\)
\(588\) 0 0
\(589\) 59.0435 2.43284
\(590\) 0 0
\(591\) 19.7208 0.811204
\(592\) 0 0
\(593\) 9.85853 0.404841 0.202421 0.979299i \(-0.435119\pi\)
0.202421 + 0.979299i \(0.435119\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −40.1239 −1.64216
\(598\) 0 0
\(599\) 11.2816 0.460953 0.230476 0.973078i \(-0.425972\pi\)
0.230476 + 0.973078i \(0.425972\pi\)
\(600\) 0 0
\(601\) 4.84169 0.197497 0.0987483 0.995112i \(-0.468516\pi\)
0.0987483 + 0.995112i \(0.468516\pi\)
\(602\) 0 0
\(603\) 1.21220 0.0493646
\(604\) 0 0
\(605\) 35.7314 1.45269
\(606\) 0 0
\(607\) −28.9727 −1.17596 −0.587982 0.808874i \(-0.700077\pi\)
−0.587982 + 0.808874i \(0.700077\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 80.5894 3.26030
\(612\) 0 0
\(613\) 4.05986 0.163976 0.0819881 0.996633i \(-0.473873\pi\)
0.0819881 + 0.996633i \(0.473873\pi\)
\(614\) 0 0
\(615\) 8.66684 0.349481
\(616\) 0 0
\(617\) 31.0323 1.24931 0.624657 0.780900i \(-0.285239\pi\)
0.624657 + 0.780900i \(0.285239\pi\)
\(618\) 0 0
\(619\) −12.8594 −0.516862 −0.258431 0.966030i \(-0.583206\pi\)
−0.258431 + 0.966030i \(0.583206\pi\)
\(620\) 0 0
\(621\) −1.53778 −0.0617088
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −8.79140 −0.351656
\(626\) 0 0
\(627\) −13.3445 −0.532929
\(628\) 0 0
\(629\) 21.3747 0.852264
\(630\) 0 0
\(631\) −28.0819 −1.11792 −0.558961 0.829194i \(-0.688800\pi\)
−0.558961 + 0.829194i \(0.688800\pi\)
\(632\) 0 0
\(633\) 25.0421 0.995335
\(634\) 0 0
\(635\) −75.6570 −3.00235
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.27471 0.0504266
\(640\) 0 0
\(641\) −29.1285 −1.15051 −0.575253 0.817976i \(-0.695096\pi\)
−0.575253 + 0.817976i \(0.695096\pi\)
\(642\) 0 0
\(643\) −34.0791 −1.34395 −0.671974 0.740575i \(-0.734553\pi\)
−0.671974 + 0.740575i \(0.734553\pi\)
\(644\) 0 0
\(645\) −36.9204 −1.45374
\(646\) 0 0
\(647\) 7.04612 0.277012 0.138506 0.990362i \(-0.455770\pi\)
0.138506 + 0.990362i \(0.455770\pi\)
\(648\) 0 0
\(649\) −0.402135 −0.0157852
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.5790 0.531388 0.265694 0.964057i \(-0.414399\pi\)
0.265694 + 0.964057i \(0.414399\pi\)
\(654\) 0 0
\(655\) −7.45654 −0.291351
\(656\) 0 0
\(657\) 7.75735 0.302643
\(658\) 0 0
\(659\) 38.7358 1.50893 0.754466 0.656339i \(-0.227896\pi\)
0.754466 + 0.656339i \(0.227896\pi\)
\(660\) 0 0
\(661\) 26.6698 1.03734 0.518668 0.854976i \(-0.326428\pi\)
0.518668 + 0.854976i \(0.326428\pi\)
\(662\) 0 0
\(663\) −51.4184 −1.99693
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 32.6825 1.26547
\(668\) 0 0
\(669\) 13.8929 0.537132
\(670\) 0 0
\(671\) 1.60073 0.0617955
\(672\) 0 0
\(673\) −43.4682 −1.67558 −0.837789 0.545995i \(-0.816152\pi\)
−0.837789 + 0.545995i \(0.816152\pi\)
\(674\) 0 0
\(675\) 2.46137 0.0947381
\(676\) 0 0
\(677\) −37.2749 −1.43259 −0.716296 0.697797i \(-0.754164\pi\)
−0.716296 + 0.697797i \(0.754164\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −12.7977 −0.490409
\(682\) 0 0
\(683\) −27.7986 −1.06368 −0.531842 0.846844i \(-0.678500\pi\)
−0.531842 + 0.846844i \(0.678500\pi\)
\(684\) 0 0
\(685\) −8.24466 −0.315012
\(686\) 0 0
\(687\) 15.8425 0.604431
\(688\) 0 0
\(689\) −42.7394 −1.62824
\(690\) 0 0
\(691\) 31.1281 1.18417 0.592084 0.805876i \(-0.298305\pi\)
0.592084 + 0.805876i \(0.298305\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −45.3118 −1.71877
\(696\) 0 0
\(697\) −3.02899 −0.114731
\(698\) 0 0
\(699\) 35.1593 1.32985
\(700\) 0 0
\(701\) −12.0547 −0.455301 −0.227651 0.973743i \(-0.573104\pi\)
−0.227651 + 0.973743i \(0.573104\pi\)
\(702\) 0 0
\(703\) 42.8625 1.61659
\(704\) 0 0
\(705\) 101.930 3.83892
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 46.4903 1.74598 0.872989 0.487739i \(-0.162178\pi\)
0.872989 + 0.487739i \(0.162178\pi\)
\(710\) 0 0
\(711\) 44.4198 1.66587
\(712\) 0 0
\(713\) −43.9638 −1.64646
\(714\) 0 0
\(715\) −21.2594 −0.795055
\(716\) 0 0
\(717\) −37.7346 −1.40922
\(718\) 0 0
\(719\) 12.5884 0.469467 0.234734 0.972060i \(-0.424578\pi\)
0.234734 + 0.972060i \(0.424578\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −17.1066 −0.636201
\(724\) 0 0
\(725\) −52.3117 −1.94281
\(726\) 0 0
\(727\) −6.55299 −0.243037 −0.121519 0.992589i \(-0.538776\pi\)
−0.121519 + 0.992589i \(0.538776\pi\)
\(728\) 0 0
\(729\) −29.4114 −1.08931
\(730\) 0 0
\(731\) 12.9034 0.477248
\(732\) 0 0
\(733\) 6.10776 0.225595 0.112798 0.993618i \(-0.464019\pi\)
0.112798 + 0.993618i \(0.464019\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.342663 −0.0126221
\(738\) 0 0
\(739\) 22.0038 0.809421 0.404711 0.914445i \(-0.367372\pi\)
0.404711 + 0.914445i \(0.367372\pi\)
\(740\) 0 0
\(741\) −103.109 −3.78780
\(742\) 0 0
\(743\) 34.6353 1.27065 0.635323 0.772247i \(-0.280867\pi\)
0.635323 + 0.772247i \(0.280867\pi\)
\(744\) 0 0
\(745\) 50.7439 1.85911
\(746\) 0 0
\(747\) 24.4441 0.894363
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −20.3539 −0.742725 −0.371363 0.928488i \(-0.621109\pi\)
−0.371363 + 0.928488i \(0.621109\pi\)
\(752\) 0 0
\(753\) −52.6335 −1.91807
\(754\) 0 0
\(755\) −40.6925 −1.48095
\(756\) 0 0
\(757\) 29.9426 1.08828 0.544141 0.838994i \(-0.316856\pi\)
0.544141 + 0.838994i \(0.316856\pi\)
\(758\) 0 0
\(759\) 9.93633 0.360666
\(760\) 0 0
\(761\) 53.3438 1.93371 0.966855 0.255326i \(-0.0821830\pi\)
0.966855 + 0.255326i \(0.0821830\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −33.2445 −1.20196
\(766\) 0 0
\(767\) −3.10717 −0.112193
\(768\) 0 0
\(769\) 0.577705 0.0208326 0.0104163 0.999946i \(-0.496684\pi\)
0.0104163 + 0.999946i \(0.496684\pi\)
\(770\) 0 0
\(771\) −15.0177 −0.540848
\(772\) 0 0
\(773\) −7.91026 −0.284512 −0.142256 0.989830i \(-0.545436\pi\)
−0.142256 + 0.989830i \(0.545436\pi\)
\(774\) 0 0
\(775\) 70.3686 2.52771
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.07400 −0.217624
\(780\) 0 0
\(781\) −0.360331 −0.0128937
\(782\) 0 0
\(783\) −2.45704 −0.0878075
\(784\) 0 0
\(785\) −19.6014 −0.699603
\(786\) 0 0
\(787\) −24.6891 −0.880072 −0.440036 0.897980i \(-0.645034\pi\)
−0.440036 + 0.897980i \(0.645034\pi\)
\(788\) 0 0
\(789\) −37.6516 −1.34043
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 12.3683 0.439213
\(794\) 0 0
\(795\) −54.0572 −1.91721
\(796\) 0 0
\(797\) −11.1868 −0.396258 −0.198129 0.980176i \(-0.563486\pi\)
−0.198129 + 0.980176i \(0.563486\pi\)
\(798\) 0 0
\(799\) −35.6238 −1.26028
\(800\) 0 0
\(801\) −16.1457 −0.570480
\(802\) 0 0
\(803\) −2.19283 −0.0773834
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 46.8053 1.64763
\(808\) 0 0
\(809\) 4.29964 0.151167 0.0755836 0.997139i \(-0.475918\pi\)
0.0755836 + 0.997139i \(0.475918\pi\)
\(810\) 0 0
\(811\) 19.4277 0.682199 0.341100 0.940027i \(-0.389201\pi\)
0.341100 + 0.940027i \(0.389201\pi\)
\(812\) 0 0
\(813\) 37.0556 1.29960
\(814\) 0 0
\(815\) −25.9700 −0.909689
\(816\) 0 0
\(817\) 25.8750 0.905252
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 47.1341 1.64499 0.822495 0.568772i \(-0.192581\pi\)
0.822495 + 0.568772i \(0.192581\pi\)
\(822\) 0 0
\(823\) 5.94967 0.207392 0.103696 0.994609i \(-0.466933\pi\)
0.103696 + 0.994609i \(0.466933\pi\)
\(824\) 0 0
\(825\) −15.9041 −0.553710
\(826\) 0 0
\(827\) 4.01224 0.139519 0.0697596 0.997564i \(-0.477777\pi\)
0.0697596 + 0.997564i \(0.477777\pi\)
\(828\) 0 0
\(829\) 3.09097 0.107354 0.0536769 0.998558i \(-0.482906\pi\)
0.0536769 + 0.998558i \(0.482906\pi\)
\(830\) 0 0
\(831\) −32.4462 −1.12555
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −61.2797 −2.12067
\(836\) 0 0
\(837\) 3.30516 0.114243
\(838\) 0 0
\(839\) 35.1218 1.21254 0.606270 0.795259i \(-0.292665\pi\)
0.606270 + 0.795259i \(0.292665\pi\)
\(840\) 0 0
\(841\) 23.2198 0.800682
\(842\) 0 0
\(843\) −52.7288 −1.81608
\(844\) 0 0
\(845\) −118.785 −4.08632
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 56.4050 1.93581
\(850\) 0 0
\(851\) −31.9154 −1.09405
\(852\) 0 0
\(853\) −21.6536 −0.741405 −0.370702 0.928752i \(-0.620883\pi\)
−0.370702 + 0.928752i \(0.620883\pi\)
\(854\) 0 0
\(855\) −66.6649 −2.27989
\(856\) 0 0
\(857\) −54.7616 −1.87062 −0.935310 0.353828i \(-0.884880\pi\)
−0.935310 + 0.353828i \(0.884880\pi\)
\(858\) 0 0
\(859\) 0.263155 0.00897874 0.00448937 0.999990i \(-0.498571\pi\)
0.00448937 + 0.999990i \(0.498571\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −54.0124 −1.83860 −0.919302 0.393552i \(-0.871246\pi\)
−0.919302 + 0.393552i \(0.871246\pi\)
\(864\) 0 0
\(865\) −33.5522 −1.14081
\(866\) 0 0
\(867\) −19.3859 −0.658378
\(868\) 0 0
\(869\) −12.5565 −0.425950
\(870\) 0 0
\(871\) −2.64765 −0.0897122
\(872\) 0 0
\(873\) −35.7904 −1.21132
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.54025 0.0520105 0.0260053 0.999662i \(-0.491721\pi\)
0.0260053 + 0.999662i \(0.491721\pi\)
\(878\) 0 0
\(879\) 11.1915 0.377478
\(880\) 0 0
\(881\) 6.28992 0.211913 0.105956 0.994371i \(-0.466210\pi\)
0.105956 + 0.994371i \(0.466210\pi\)
\(882\) 0 0
\(883\) −6.57266 −0.221188 −0.110594 0.993866i \(-0.535275\pi\)
−0.110594 + 0.993866i \(0.535275\pi\)
\(884\) 0 0
\(885\) −3.92999 −0.132105
\(886\) 0 0
\(887\) −24.6143 −0.826468 −0.413234 0.910625i \(-0.635601\pi\)
−0.413234 + 0.910625i \(0.635601\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 7.59963 0.254597
\(892\) 0 0
\(893\) −71.4361 −2.39052
\(894\) 0 0
\(895\) −86.2042 −2.88149
\(896\) 0 0
\(897\) 76.7750 2.56344
\(898\) 0 0
\(899\) −70.2449 −2.34280
\(900\) 0 0
\(901\) 18.8925 0.629402
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 11.4558 0.380804
\(906\) 0 0
\(907\) −21.4285 −0.711522 −0.355761 0.934577i \(-0.615778\pi\)
−0.355761 + 0.934577i \(0.615778\pi\)
\(908\) 0 0
\(909\) 22.6970 0.752812
\(910\) 0 0
\(911\) 20.6989 0.685786 0.342893 0.939374i \(-0.388593\pi\)
0.342893 + 0.939374i \(0.388593\pi\)
\(912\) 0 0
\(913\) −6.90982 −0.228682
\(914\) 0 0
\(915\) 15.6436 0.517162
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −13.5900 −0.448292 −0.224146 0.974556i \(-0.571959\pi\)
−0.224146 + 0.974556i \(0.571959\pi\)
\(920\) 0 0
\(921\) 11.4176 0.376224
\(922\) 0 0
\(923\) −2.78417 −0.0916421
\(924\) 0 0
\(925\) 51.0839 1.67963
\(926\) 0 0
\(927\) −30.7957 −1.01146
\(928\) 0 0
\(929\) −42.8414 −1.40558 −0.702790 0.711398i \(-0.748063\pi\)
−0.702790 + 0.711398i \(0.748063\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −39.5852 −1.29596
\(934\) 0 0
\(935\) 9.39750 0.307331
\(936\) 0 0
\(937\) −17.0062 −0.555568 −0.277784 0.960644i \(-0.589600\pi\)
−0.277784 + 0.960644i \(0.589600\pi\)
\(938\) 0 0
\(939\) −80.2979 −2.62042
\(940\) 0 0
\(941\) 43.8180 1.42843 0.714213 0.699928i \(-0.246785\pi\)
0.714213 + 0.699928i \(0.246785\pi\)
\(942\) 0 0
\(943\) 4.52270 0.147279
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.2023 −0.494008 −0.247004 0.969014i \(-0.579446\pi\)
−0.247004 + 0.969014i \(0.579446\pi\)
\(948\) 0 0
\(949\) −16.9434 −0.550004
\(950\) 0 0
\(951\) −32.4934 −1.05367
\(952\) 0 0
\(953\) 19.0486 0.617044 0.308522 0.951217i \(-0.400166\pi\)
0.308522 + 0.951217i \(0.400166\pi\)
\(954\) 0 0
\(955\) −3.52397 −0.114033
\(956\) 0 0
\(957\) 15.8762 0.513204
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 63.4918 2.04812
\(962\) 0 0
\(963\) 31.1063 1.00239
\(964\) 0 0
\(965\) −69.6812 −2.24312
\(966\) 0 0
\(967\) −12.3278 −0.396435 −0.198218 0.980158i \(-0.563515\pi\)
−0.198218 + 0.980158i \(0.563515\pi\)
\(968\) 0 0
\(969\) 45.5784 1.46419
\(970\) 0 0
\(971\) −0.959044 −0.0307772 −0.0153886 0.999882i \(-0.504899\pi\)
−0.0153886 + 0.999882i \(0.504899\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −122.886 −3.93551
\(976\) 0 0
\(977\) −37.7183 −1.20672 −0.603358 0.797471i \(-0.706171\pi\)
−0.603358 + 0.797471i \(0.706171\pi\)
\(978\) 0 0
\(979\) 4.56404 0.145867
\(980\) 0 0
\(981\) 13.9381 0.445008
\(982\) 0 0
\(983\) −32.2162 −1.02754 −0.513768 0.857929i \(-0.671751\pi\)
−0.513768 + 0.857929i \(0.671751\pi\)
\(984\) 0 0
\(985\) −27.8491 −0.887345
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −19.2665 −0.612640
\(990\) 0 0
\(991\) 11.3658 0.361048 0.180524 0.983571i \(-0.442221\pi\)
0.180524 + 0.983571i \(0.442221\pi\)
\(992\) 0 0
\(993\) 65.9861 2.09400
\(994\) 0 0
\(995\) 56.6618 1.79630
\(996\) 0 0
\(997\) −10.3504 −0.327799 −0.163900 0.986477i \(-0.552407\pi\)
−0.163900 + 0.986477i \(0.552407\pi\)
\(998\) 0 0
\(999\) 2.39937 0.0759127
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 \(a_p\))