Properties

Label 8036.2.a.q.1.9
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 1.9
Root \(-0.449590\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.449590 q^{3} -0.787803 q^{5} -2.79787 q^{9} +O(q^{10})\) \(q+0.449590 q^{3} -0.787803 q^{5} -2.79787 q^{9} +3.10400 q^{11} +5.59137 q^{13} -0.354188 q^{15} +5.38244 q^{17} +4.82385 q^{19} +7.02456 q^{23} -4.37937 q^{25} -2.60666 q^{27} -7.52560 q^{29} +4.90724 q^{31} +1.39553 q^{33} -9.21207 q^{37} +2.51382 q^{39} -1.00000 q^{41} +11.7730 q^{43} +2.20417 q^{45} -5.56287 q^{47} +2.41989 q^{51} +5.94752 q^{53} -2.44534 q^{55} +2.16875 q^{57} -10.2017 q^{59} +4.89403 q^{61} -4.40490 q^{65} +11.7436 q^{67} +3.15817 q^{69} -1.39569 q^{71} -4.28028 q^{73} -1.96892 q^{75} +8.10074 q^{79} +7.22168 q^{81} +2.10452 q^{83} -4.24031 q^{85} -3.38343 q^{87} -16.1614 q^{89} +2.20625 q^{93} -3.80024 q^{95} +2.23832 q^{97} -8.68459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) 0.449590 0.259571 0.129785 0.991542i \(-0.458571\pi\)
0.129785 + 0.991542i \(0.458571\pi\)
\(4\) 0 0
\(5\) −0.787803 −0.352316 −0.176158 0.984362i \(-0.556367\pi\)
−0.176158 + 0.984362i \(0.556367\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.79787 −0.932623
\(10\) 0 0
\(11\) 3.10400 0.935891 0.467946 0.883757i \(-0.344994\pi\)
0.467946 + 0.883757i \(0.344994\pi\)
\(12\) 0 0
\(13\) 5.59137 1.55077 0.775383 0.631491i \(-0.217557\pi\)
0.775383 + 0.631491i \(0.217557\pi\)
\(14\) 0 0
\(15\) −0.354188 −0.0914510
\(16\) 0 0
\(17\) 5.38244 1.30543 0.652717 0.757602i \(-0.273629\pi\)
0.652717 + 0.757602i \(0.273629\pi\)
\(18\) 0 0
\(19\) 4.82385 1.10667 0.553334 0.832960i \(-0.313355\pi\)
0.553334 + 0.832960i \(0.313355\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.02456 1.46472 0.732361 0.680917i \(-0.238419\pi\)
0.732361 + 0.680917i \(0.238419\pi\)
\(24\) 0 0
\(25\) −4.37937 −0.875873
\(26\) 0 0
\(27\) −2.60666 −0.501652
\(28\) 0 0
\(29\) −7.52560 −1.39747 −0.698734 0.715382i \(-0.746253\pi\)
−0.698734 + 0.715382i \(0.746253\pi\)
\(30\) 0 0
\(31\) 4.90724 0.881366 0.440683 0.897663i \(-0.354736\pi\)
0.440683 + 0.897663i \(0.354736\pi\)
\(32\) 0 0
\(33\) 1.39553 0.242930
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −9.21207 −1.51446 −0.757228 0.653151i \(-0.773447\pi\)
−0.757228 + 0.653151i \(0.773447\pi\)
\(38\) 0 0
\(39\) 2.51382 0.402534
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 11.7730 1.79536 0.897680 0.440648i \(-0.145251\pi\)
0.897680 + 0.440648i \(0.145251\pi\)
\(44\) 0 0
\(45\) 2.20417 0.328578
\(46\) 0 0
\(47\) −5.56287 −0.811428 −0.405714 0.914000i \(-0.632977\pi\)
−0.405714 + 0.914000i \(0.632977\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 2.41989 0.338853
\(52\) 0 0
\(53\) 5.94752 0.816955 0.408477 0.912768i \(-0.366060\pi\)
0.408477 + 0.912768i \(0.366060\pi\)
\(54\) 0 0
\(55\) −2.44534 −0.329730
\(56\) 0 0
\(57\) 2.16875 0.287259
\(58\) 0 0
\(59\) −10.2017 −1.32814 −0.664071 0.747670i \(-0.731173\pi\)
−0.664071 + 0.747670i \(0.731173\pi\)
\(60\) 0 0
\(61\) 4.89403 0.626616 0.313308 0.949652i \(-0.398563\pi\)
0.313308 + 0.949652i \(0.398563\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.40490 −0.546360
\(66\) 0 0
\(67\) 11.7436 1.43472 0.717358 0.696705i \(-0.245351\pi\)
0.717358 + 0.696705i \(0.245351\pi\)
\(68\) 0 0
\(69\) 3.15817 0.380199
\(70\) 0 0
\(71\) −1.39569 −0.165638 −0.0828188 0.996565i \(-0.526392\pi\)
−0.0828188 + 0.996565i \(0.526392\pi\)
\(72\) 0 0
\(73\) −4.28028 −0.500968 −0.250484 0.968121i \(-0.580590\pi\)
−0.250484 + 0.968121i \(0.580590\pi\)
\(74\) 0 0
\(75\) −1.96892 −0.227351
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 8.10074 0.911404 0.455702 0.890132i \(-0.349388\pi\)
0.455702 + 0.890132i \(0.349388\pi\)
\(80\) 0 0
\(81\) 7.22168 0.802409
\(82\) 0 0
\(83\) 2.10452 0.231001 0.115500 0.993307i \(-0.463153\pi\)
0.115500 + 0.993307i \(0.463153\pi\)
\(84\) 0 0
\(85\) −4.24031 −0.459926
\(86\) 0 0
\(87\) −3.38343 −0.362742
\(88\) 0 0
\(89\) −16.1614 −1.71311 −0.856553 0.516059i \(-0.827398\pi\)
−0.856553 + 0.516059i \(0.827398\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.20625 0.228777
\(94\) 0 0
\(95\) −3.80024 −0.389897
\(96\) 0 0
\(97\) 2.23832 0.227267 0.113634 0.993523i \(-0.463751\pi\)
0.113634 + 0.993523i \(0.463751\pi\)
\(98\) 0 0
\(99\) −8.68459 −0.872834
\(100\) 0 0
\(101\) −6.14466 −0.611416 −0.305708 0.952125i \(-0.598893\pi\)
−0.305708 + 0.952125i \(0.598893\pi\)
\(102\) 0 0
\(103\) 1.47349 0.145188 0.0725938 0.997362i \(-0.476872\pi\)
0.0725938 + 0.997362i \(0.476872\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.43556 0.815497 0.407748 0.913094i \(-0.366314\pi\)
0.407748 + 0.913094i \(0.366314\pi\)
\(108\) 0 0
\(109\) −10.1612 −0.973266 −0.486633 0.873607i \(-0.661775\pi\)
−0.486633 + 0.873607i \(0.661775\pi\)
\(110\) 0 0
\(111\) −4.14165 −0.393108
\(112\) 0 0
\(113\) 8.34801 0.785315 0.392657 0.919685i \(-0.371556\pi\)
0.392657 + 0.919685i \(0.371556\pi\)
\(114\) 0 0
\(115\) −5.53397 −0.516045
\(116\) 0 0
\(117\) −15.6439 −1.44628
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.36518 −0.124107
\(122\) 0 0
\(123\) −0.449590 −0.0405381
\(124\) 0 0
\(125\) 7.38909 0.660901
\(126\) 0 0
\(127\) −15.6031 −1.38455 −0.692274 0.721635i \(-0.743391\pi\)
−0.692274 + 0.721635i \(0.743391\pi\)
\(128\) 0 0
\(129\) 5.29300 0.466023
\(130\) 0 0
\(131\) −11.7626 −1.02771 −0.513853 0.857878i \(-0.671782\pi\)
−0.513853 + 0.857878i \(0.671782\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.05354 0.176740
\(136\) 0 0
\(137\) 4.49604 0.384123 0.192061 0.981383i \(-0.438483\pi\)
0.192061 + 0.981383i \(0.438483\pi\)
\(138\) 0 0
\(139\) 1.41035 0.119624 0.0598121 0.998210i \(-0.480950\pi\)
0.0598121 + 0.998210i \(0.480950\pi\)
\(140\) 0 0
\(141\) −2.50101 −0.210623
\(142\) 0 0
\(143\) 17.3556 1.45135
\(144\) 0 0
\(145\) 5.92869 0.492351
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.50284 0.696580 0.348290 0.937387i \(-0.386762\pi\)
0.348290 + 0.937387i \(0.386762\pi\)
\(150\) 0 0
\(151\) −2.68539 −0.218534 −0.109267 0.994012i \(-0.534850\pi\)
−0.109267 + 0.994012i \(0.534850\pi\)
\(152\) 0 0
\(153\) −15.0594 −1.21748
\(154\) 0 0
\(155\) −3.86594 −0.310520
\(156\) 0 0
\(157\) −4.26751 −0.340584 −0.170292 0.985394i \(-0.554471\pi\)
−0.170292 + 0.985394i \(0.554471\pi\)
\(158\) 0 0
\(159\) 2.67394 0.212058
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 18.7332 1.46730 0.733649 0.679529i \(-0.237816\pi\)
0.733649 + 0.679529i \(0.237816\pi\)
\(164\) 0 0
\(165\) −1.09940 −0.0855882
\(166\) 0 0
\(167\) 11.3399 0.877510 0.438755 0.898607i \(-0.355420\pi\)
0.438755 + 0.898607i \(0.355420\pi\)
\(168\) 0 0
\(169\) 18.2634 1.40488
\(170\) 0 0
\(171\) −13.4965 −1.03210
\(172\) 0 0
\(173\) −12.5023 −0.950531 −0.475266 0.879842i \(-0.657648\pi\)
−0.475266 + 0.879842i \(0.657648\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.58656 −0.344747
\(178\) 0 0
\(179\) −6.96188 −0.520355 −0.260178 0.965561i \(-0.583781\pi\)
−0.260178 + 0.965561i \(0.583781\pi\)
\(180\) 0 0
\(181\) 18.3297 1.36244 0.681219 0.732080i \(-0.261450\pi\)
0.681219 + 0.732080i \(0.261450\pi\)
\(182\) 0 0
\(183\) 2.20031 0.162651
\(184\) 0 0
\(185\) 7.25730 0.533567
\(186\) 0 0
\(187\) 16.7071 1.22174
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 19.2841 1.39535 0.697675 0.716414i \(-0.254218\pi\)
0.697675 + 0.716414i \(0.254218\pi\)
\(192\) 0 0
\(193\) 1.39703 0.100561 0.0502803 0.998735i \(-0.483989\pi\)
0.0502803 + 0.998735i \(0.483989\pi\)
\(194\) 0 0
\(195\) −1.98040 −0.141819
\(196\) 0 0
\(197\) 12.8161 0.913108 0.456554 0.889696i \(-0.349084\pi\)
0.456554 + 0.889696i \(0.349084\pi\)
\(198\) 0 0
\(199\) −1.67339 −0.118624 −0.0593119 0.998239i \(-0.518891\pi\)
−0.0593119 + 0.998239i \(0.518891\pi\)
\(200\) 0 0
\(201\) 5.27982 0.372410
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.787803 0.0550225
\(206\) 0 0
\(207\) −19.6538 −1.36603
\(208\) 0 0
\(209\) 14.9732 1.03572
\(210\) 0 0
\(211\) −13.1602 −0.905984 −0.452992 0.891515i \(-0.649643\pi\)
−0.452992 + 0.891515i \(0.649643\pi\)
\(212\) 0 0
\(213\) −0.627487 −0.0429947
\(214\) 0 0
\(215\) −9.27478 −0.632535
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.92437 −0.130037
\(220\) 0 0
\(221\) 30.0952 2.02442
\(222\) 0 0
\(223\) 11.1114 0.744072 0.372036 0.928218i \(-0.378660\pi\)
0.372036 + 0.928218i \(0.378660\pi\)
\(224\) 0 0
\(225\) 12.2529 0.816860
\(226\) 0 0
\(227\) −16.0652 −1.06628 −0.533142 0.846026i \(-0.678989\pi\)
−0.533142 + 0.846026i \(0.678989\pi\)
\(228\) 0 0
\(229\) −25.4126 −1.67931 −0.839655 0.543120i \(-0.817243\pi\)
−0.839655 + 0.543120i \(0.817243\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.0557 1.31390 0.656948 0.753936i \(-0.271847\pi\)
0.656948 + 0.753936i \(0.271847\pi\)
\(234\) 0 0
\(235\) 4.38245 0.285879
\(236\) 0 0
\(237\) 3.64201 0.236574
\(238\) 0 0
\(239\) 6.32352 0.409034 0.204517 0.978863i \(-0.434438\pi\)
0.204517 + 0.978863i \(0.434438\pi\)
\(240\) 0 0
\(241\) 25.2122 1.62406 0.812030 0.583616i \(-0.198363\pi\)
0.812030 + 0.583616i \(0.198363\pi\)
\(242\) 0 0
\(243\) 11.0668 0.709934
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 26.9719 1.71618
\(248\) 0 0
\(249\) 0.946169 0.0599610
\(250\) 0 0
\(251\) 15.3360 0.967998 0.483999 0.875069i \(-0.339184\pi\)
0.483999 + 0.875069i \(0.339184\pi\)
\(252\) 0 0
\(253\) 21.8042 1.37082
\(254\) 0 0
\(255\) −1.90640 −0.119383
\(256\) 0 0
\(257\) 15.2711 0.952587 0.476293 0.879286i \(-0.341980\pi\)
0.476293 + 0.879286i \(0.341980\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 21.0556 1.30331
\(262\) 0 0
\(263\) 25.2720 1.55834 0.779169 0.626814i \(-0.215642\pi\)
0.779169 + 0.626814i \(0.215642\pi\)
\(264\) 0 0
\(265\) −4.68547 −0.287826
\(266\) 0 0
\(267\) −7.26600 −0.444672
\(268\) 0 0
\(269\) −7.10754 −0.433355 −0.216677 0.976243i \(-0.569522\pi\)
−0.216677 + 0.976243i \(0.569522\pi\)
\(270\) 0 0
\(271\) 1.01526 0.0616727 0.0308363 0.999524i \(-0.490183\pi\)
0.0308363 + 0.999524i \(0.490183\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13.5936 −0.819722
\(276\) 0 0
\(277\) −23.0775 −1.38659 −0.693296 0.720653i \(-0.743842\pi\)
−0.693296 + 0.720653i \(0.743842\pi\)
\(278\) 0 0
\(279\) −13.7298 −0.821983
\(280\) 0 0
\(281\) −19.3572 −1.15475 −0.577377 0.816478i \(-0.695924\pi\)
−0.577377 + 0.816478i \(0.695924\pi\)
\(282\) 0 0
\(283\) 0.177467 0.0105493 0.00527466 0.999986i \(-0.498321\pi\)
0.00527466 + 0.999986i \(0.498321\pi\)
\(284\) 0 0
\(285\) −1.70855 −0.101206
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 11.9707 0.704159
\(290\) 0 0
\(291\) 1.00633 0.0589919
\(292\) 0 0
\(293\) 27.8143 1.62493 0.812465 0.583010i \(-0.198125\pi\)
0.812465 + 0.583010i \(0.198125\pi\)
\(294\) 0 0
\(295\) 8.03689 0.467926
\(296\) 0 0
\(297\) −8.09108 −0.469492
\(298\) 0 0
\(299\) 39.2769 2.27144
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.76257 −0.158706
\(304\) 0 0
\(305\) −3.85553 −0.220767
\(306\) 0 0
\(307\) 25.7021 1.46690 0.733448 0.679745i \(-0.237910\pi\)
0.733448 + 0.679745i \(0.237910\pi\)
\(308\) 0 0
\(309\) 0.662468 0.0376865
\(310\) 0 0
\(311\) −15.5756 −0.883213 −0.441606 0.897209i \(-0.645591\pi\)
−0.441606 + 0.897209i \(0.645591\pi\)
\(312\) 0 0
\(313\) 21.6373 1.22301 0.611505 0.791241i \(-0.290564\pi\)
0.611505 + 0.791241i \(0.290564\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 23.9737 1.34650 0.673248 0.739417i \(-0.264899\pi\)
0.673248 + 0.739417i \(0.264899\pi\)
\(318\) 0 0
\(319\) −23.3595 −1.30788
\(320\) 0 0
\(321\) 3.79254 0.211679
\(322\) 0 0
\(323\) 25.9641 1.44468
\(324\) 0 0
\(325\) −24.4867 −1.35828
\(326\) 0 0
\(327\) −4.56837 −0.252631
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −9.64917 −0.530366 −0.265183 0.964198i \(-0.585432\pi\)
−0.265183 + 0.964198i \(0.585432\pi\)
\(332\) 0 0
\(333\) 25.7742 1.41242
\(334\) 0 0
\(335\) −9.25168 −0.505473
\(336\) 0 0
\(337\) −0.606481 −0.0330371 −0.0165186 0.999864i \(-0.505258\pi\)
−0.0165186 + 0.999864i \(0.505258\pi\)
\(338\) 0 0
\(339\) 3.75318 0.203845
\(340\) 0 0
\(341\) 15.2321 0.824863
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.48801 −0.133950
\(346\) 0 0
\(347\) 18.7135 1.00459 0.502296 0.864696i \(-0.332489\pi\)
0.502296 + 0.864696i \(0.332489\pi\)
\(348\) 0 0
\(349\) 20.5477 1.09989 0.549945 0.835201i \(-0.314649\pi\)
0.549945 + 0.835201i \(0.314649\pi\)
\(350\) 0 0
\(351\) −14.5748 −0.777946
\(352\) 0 0
\(353\) −3.94997 −0.210235 −0.105118 0.994460i \(-0.533522\pi\)
−0.105118 + 0.994460i \(0.533522\pi\)
\(354\) 0 0
\(355\) 1.09953 0.0583568
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.04134 0.107738 0.0538690 0.998548i \(-0.482845\pi\)
0.0538690 + 0.998548i \(0.482845\pi\)
\(360\) 0 0
\(361\) 4.26954 0.224713
\(362\) 0 0
\(363\) −0.613771 −0.0322146
\(364\) 0 0
\(365\) 3.37201 0.176499
\(366\) 0 0
\(367\) −16.6087 −0.866969 −0.433485 0.901161i \(-0.642716\pi\)
−0.433485 + 0.901161i \(0.642716\pi\)
\(368\) 0 0
\(369\) 2.79787 0.145651
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −13.8375 −0.716479 −0.358239 0.933630i \(-0.616623\pi\)
−0.358239 + 0.933630i \(0.616623\pi\)
\(374\) 0 0
\(375\) 3.32206 0.171550
\(376\) 0 0
\(377\) −42.0784 −2.16715
\(378\) 0 0
\(379\) −5.23579 −0.268944 −0.134472 0.990917i \(-0.542934\pi\)
−0.134472 + 0.990917i \(0.542934\pi\)
\(380\) 0 0
\(381\) −7.01498 −0.359388
\(382\) 0 0
\(383\) 8.45623 0.432093 0.216047 0.976383i \(-0.430684\pi\)
0.216047 + 0.976383i \(0.430684\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −32.9392 −1.67439
\(388\) 0 0
\(389\) −26.0414 −1.32035 −0.660175 0.751112i \(-0.729518\pi\)
−0.660175 + 0.751112i \(0.729518\pi\)
\(390\) 0 0
\(391\) 37.8093 1.91210
\(392\) 0 0
\(393\) −5.28836 −0.266762
\(394\) 0 0
\(395\) −6.38179 −0.321103
\(396\) 0 0
\(397\) −3.42795 −0.172044 −0.0860220 0.996293i \(-0.527416\pi\)
−0.0860220 + 0.996293i \(0.527416\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.26799 0.113258 0.0566289 0.998395i \(-0.481965\pi\)
0.0566289 + 0.998395i \(0.481965\pi\)
\(402\) 0 0
\(403\) 27.4382 1.36679
\(404\) 0 0
\(405\) −5.68926 −0.282702
\(406\) 0 0
\(407\) −28.5943 −1.41737
\(408\) 0 0
\(409\) −11.0462 −0.546198 −0.273099 0.961986i \(-0.588049\pi\)
−0.273099 + 0.961986i \(0.588049\pi\)
\(410\) 0 0
\(411\) 2.02138 0.0997071
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.65794 −0.0813853
\(416\) 0 0
\(417\) 0.634078 0.0310509
\(418\) 0 0
\(419\) −29.0178 −1.41761 −0.708805 0.705404i \(-0.750765\pi\)
−0.708805 + 0.705404i \(0.750765\pi\)
\(420\) 0 0
\(421\) 11.2610 0.548827 0.274414 0.961612i \(-0.411516\pi\)
0.274414 + 0.961612i \(0.411516\pi\)
\(422\) 0 0
\(423\) 15.5642 0.756756
\(424\) 0 0
\(425\) −23.5717 −1.14340
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 7.80291 0.376728
\(430\) 0 0
\(431\) 16.5476 0.797071 0.398535 0.917153i \(-0.369519\pi\)
0.398535 + 0.917153i \(0.369519\pi\)
\(432\) 0 0
\(433\) −4.65533 −0.223721 −0.111860 0.993724i \(-0.535681\pi\)
−0.111860 + 0.993724i \(0.535681\pi\)
\(434\) 0 0
\(435\) 2.66548 0.127800
\(436\) 0 0
\(437\) 33.8854 1.62096
\(438\) 0 0
\(439\) −22.7846 −1.08745 −0.543725 0.839263i \(-0.682987\pi\)
−0.543725 + 0.839263i \(0.682987\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −29.6057 −1.40661 −0.703305 0.710888i \(-0.748293\pi\)
−0.703305 + 0.710888i \(0.748293\pi\)
\(444\) 0 0
\(445\) 12.7320 0.603555
\(446\) 0 0
\(447\) 3.82279 0.180812
\(448\) 0 0
\(449\) −2.83513 −0.133798 −0.0668990 0.997760i \(-0.521311\pi\)
−0.0668990 + 0.997760i \(0.521311\pi\)
\(450\) 0 0
\(451\) −3.10400 −0.146162
\(452\) 0 0
\(453\) −1.20732 −0.0567250
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 27.6601 1.29389 0.646943 0.762538i \(-0.276047\pi\)
0.646943 + 0.762538i \(0.276047\pi\)
\(458\) 0 0
\(459\) −14.0302 −0.654874
\(460\) 0 0
\(461\) 4.80680 0.223875 0.111937 0.993715i \(-0.464294\pi\)
0.111937 + 0.993715i \(0.464294\pi\)
\(462\) 0 0
\(463\) 31.2899 1.45416 0.727082 0.686551i \(-0.240876\pi\)
0.727082 + 0.686551i \(0.240876\pi\)
\(464\) 0 0
\(465\) −1.73809 −0.0806018
\(466\) 0 0
\(467\) 10.8937 0.504100 0.252050 0.967714i \(-0.418895\pi\)
0.252050 + 0.967714i \(0.418895\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.91863 −0.0884057
\(472\) 0 0
\(473\) 36.5433 1.68026
\(474\) 0 0
\(475\) −21.1254 −0.969300
\(476\) 0 0
\(477\) −16.6404 −0.761911
\(478\) 0 0
\(479\) 14.1384 0.646000 0.323000 0.946399i \(-0.395309\pi\)
0.323000 + 0.946399i \(0.395309\pi\)
\(480\) 0 0
\(481\) −51.5081 −2.34857
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.76336 −0.0800699
\(486\) 0 0
\(487\) −34.7768 −1.57589 −0.787945 0.615746i \(-0.788855\pi\)
−0.787945 + 0.615746i \(0.788855\pi\)
\(488\) 0 0
\(489\) 8.42226 0.380868
\(490\) 0 0
\(491\) 31.6187 1.42693 0.713466 0.700690i \(-0.247124\pi\)
0.713466 + 0.700690i \(0.247124\pi\)
\(492\) 0 0
\(493\) −40.5061 −1.82430
\(494\) 0 0
\(495\) 6.84174 0.307514
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 30.8653 1.38172 0.690860 0.722989i \(-0.257232\pi\)
0.690860 + 0.722989i \(0.257232\pi\)
\(500\) 0 0
\(501\) 5.09832 0.227776
\(502\) 0 0
\(503\) −18.3660 −0.818900 −0.409450 0.912333i \(-0.634279\pi\)
−0.409450 + 0.912333i \(0.634279\pi\)
\(504\) 0 0
\(505\) 4.84078 0.215412
\(506\) 0 0
\(507\) 8.21104 0.364665
\(508\) 0 0
\(509\) −37.0290 −1.64128 −0.820641 0.571444i \(-0.806384\pi\)
−0.820641 + 0.571444i \(0.806384\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −12.5742 −0.555162
\(514\) 0 0
\(515\) −1.16082 −0.0511520
\(516\) 0 0
\(517\) −17.2672 −0.759408
\(518\) 0 0
\(519\) −5.62090 −0.246730
\(520\) 0 0
\(521\) −26.2351 −1.14938 −0.574690 0.818371i \(-0.694878\pi\)
−0.574690 + 0.818371i \(0.694878\pi\)
\(522\) 0 0
\(523\) 1.74603 0.0763485 0.0381742 0.999271i \(-0.487846\pi\)
0.0381742 + 0.999271i \(0.487846\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 26.4129 1.15057
\(528\) 0 0
\(529\) 26.3444 1.14541
\(530\) 0 0
\(531\) 28.5429 1.23866
\(532\) 0 0
\(533\) −5.59137 −0.242189
\(534\) 0 0
\(535\) −6.64556 −0.287313
\(536\) 0 0
\(537\) −3.12999 −0.135069
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 14.3096 0.615219 0.307609 0.951513i \(-0.400471\pi\)
0.307609 + 0.951513i \(0.400471\pi\)
\(542\) 0 0
\(543\) 8.24086 0.353649
\(544\) 0 0
\(545\) 8.00502 0.342897
\(546\) 0 0
\(547\) 1.40140 0.0599194 0.0299597 0.999551i \(-0.490462\pi\)
0.0299597 + 0.999551i \(0.490462\pi\)
\(548\) 0 0
\(549\) −13.6929 −0.584397
\(550\) 0 0
\(551\) −36.3024 −1.54653
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 3.26281 0.138498
\(556\) 0 0
\(557\) −13.4128 −0.568318 −0.284159 0.958777i \(-0.591714\pi\)
−0.284159 + 0.958777i \(0.591714\pi\)
\(558\) 0 0
\(559\) 65.8270 2.78419
\(560\) 0 0
\(561\) 7.51135 0.317129
\(562\) 0 0
\(563\) −20.3679 −0.858404 −0.429202 0.903208i \(-0.641205\pi\)
−0.429202 + 0.903208i \(0.641205\pi\)
\(564\) 0 0
\(565\) −6.57659 −0.276679
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.9245 −0.583746 −0.291873 0.956457i \(-0.594278\pi\)
−0.291873 + 0.956457i \(0.594278\pi\)
\(570\) 0 0
\(571\) 40.0547 1.67624 0.838118 0.545489i \(-0.183656\pi\)
0.838118 + 0.545489i \(0.183656\pi\)
\(572\) 0 0
\(573\) 8.66995 0.362192
\(574\) 0 0
\(575\) −30.7631 −1.28291
\(576\) 0 0
\(577\) 41.8713 1.74312 0.871562 0.490285i \(-0.163107\pi\)
0.871562 + 0.490285i \(0.163107\pi\)
\(578\) 0 0
\(579\) 0.628092 0.0261026
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 18.4611 0.764581
\(584\) 0 0
\(585\) 12.3243 0.509548
\(586\) 0 0
\(587\) 12.4478 0.513775 0.256888 0.966441i \(-0.417303\pi\)
0.256888 + 0.966441i \(0.417303\pi\)
\(588\) 0 0
\(589\) 23.6718 0.975379
\(590\) 0 0
\(591\) 5.76198 0.237016
\(592\) 0 0
\(593\) −12.6955 −0.521342 −0.260671 0.965428i \(-0.583944\pi\)
−0.260671 + 0.965428i \(0.583944\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.752341 −0.0307913
\(598\) 0 0
\(599\) 37.9084 1.54890 0.774448 0.632637i \(-0.218028\pi\)
0.774448 + 0.632637i \(0.218028\pi\)
\(600\) 0 0
\(601\) 22.3859 0.913139 0.456569 0.889688i \(-0.349078\pi\)
0.456569 + 0.889688i \(0.349078\pi\)
\(602\) 0 0
\(603\) −32.8572 −1.33805
\(604\) 0 0
\(605\) 1.07549 0.0437250
\(606\) 0 0
\(607\) 46.7440 1.89728 0.948640 0.316357i \(-0.102460\pi\)
0.948640 + 0.316357i \(0.102460\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −31.1041 −1.25834
\(612\) 0 0
\(613\) −0.295420 −0.0119319 −0.00596596 0.999982i \(-0.501899\pi\)
−0.00596596 + 0.999982i \(0.501899\pi\)
\(614\) 0 0
\(615\) 0.354188 0.0142822
\(616\) 0 0
\(617\) −42.2704 −1.70174 −0.850871 0.525375i \(-0.823925\pi\)
−0.850871 + 0.525375i \(0.823925\pi\)
\(618\) 0 0
\(619\) 31.9134 1.28271 0.641354 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(620\) 0 0
\(621\) −18.3106 −0.734781
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 16.0757 0.643027
\(626\) 0 0
\(627\) 6.73181 0.268843
\(628\) 0 0
\(629\) −49.5835 −1.97702
\(630\) 0 0
\(631\) −5.19942 −0.206986 −0.103493 0.994630i \(-0.533002\pi\)
−0.103493 + 0.994630i \(0.533002\pi\)
\(632\) 0 0
\(633\) −5.91668 −0.235167
\(634\) 0 0
\(635\) 12.2921 0.487799
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3.90495 0.154478
\(640\) 0 0
\(641\) −8.90534 −0.351740 −0.175870 0.984413i \(-0.556274\pi\)
−0.175870 + 0.984413i \(0.556274\pi\)
\(642\) 0 0
\(643\) −24.4281 −0.963350 −0.481675 0.876350i \(-0.659971\pi\)
−0.481675 + 0.876350i \(0.659971\pi\)
\(644\) 0 0
\(645\) −4.16984 −0.164187
\(646\) 0 0
\(647\) −24.8284 −0.976104 −0.488052 0.872814i \(-0.662292\pi\)
−0.488052 + 0.872814i \(0.662292\pi\)
\(648\) 0 0
\(649\) −31.6659 −1.24300
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.0715 −0.941990 −0.470995 0.882136i \(-0.656105\pi\)
−0.470995 + 0.882136i \(0.656105\pi\)
\(654\) 0 0
\(655\) 9.26663 0.362077
\(656\) 0 0
\(657\) 11.9756 0.467215
\(658\) 0 0
\(659\) −3.61093 −0.140662 −0.0703310 0.997524i \(-0.522406\pi\)
−0.0703310 + 0.997524i \(0.522406\pi\)
\(660\) 0 0
\(661\) −28.0885 −1.09252 −0.546258 0.837617i \(-0.683948\pi\)
−0.546258 + 0.837617i \(0.683948\pi\)
\(662\) 0 0
\(663\) 13.5305 0.525481
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −52.8640 −2.04690
\(668\) 0 0
\(669\) 4.99556 0.193139
\(670\) 0 0
\(671\) 15.1911 0.586445
\(672\) 0 0
\(673\) 34.0798 1.31368 0.656840 0.754030i \(-0.271893\pi\)
0.656840 + 0.754030i \(0.271893\pi\)
\(674\) 0 0
\(675\) 11.4155 0.439384
\(676\) 0 0
\(677\) 9.32910 0.358546 0.179273 0.983799i \(-0.442625\pi\)
0.179273 + 0.983799i \(0.442625\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −7.22274 −0.276776
\(682\) 0 0
\(683\) −14.7903 −0.565933 −0.282967 0.959130i \(-0.591319\pi\)
−0.282967 + 0.959130i \(0.591319\pi\)
\(684\) 0 0
\(685\) −3.54200 −0.135333
\(686\) 0 0
\(687\) −11.4252 −0.435900
\(688\) 0 0
\(689\) 33.2548 1.26691
\(690\) 0 0
\(691\) −27.7101 −1.05414 −0.527072 0.849821i \(-0.676710\pi\)
−0.527072 + 0.849821i \(0.676710\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.11108 −0.0421455
\(696\) 0 0
\(697\) −5.38244 −0.203875
\(698\) 0 0
\(699\) 9.01686 0.341049
\(700\) 0 0
\(701\) −3.12039 −0.117856 −0.0589278 0.998262i \(-0.518768\pi\)
−0.0589278 + 0.998262i \(0.518768\pi\)
\(702\) 0 0
\(703\) −44.4377 −1.67600
\(704\) 0 0
\(705\) 1.97030 0.0742059
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 34.9063 1.31093 0.655467 0.755224i \(-0.272472\pi\)
0.655467 + 0.755224i \(0.272472\pi\)
\(710\) 0 0
\(711\) −22.6648 −0.849997
\(712\) 0 0
\(713\) 34.4712 1.29096
\(714\) 0 0
\(715\) −13.6728 −0.511334
\(716\) 0 0
\(717\) 2.84299 0.106173
\(718\) 0 0
\(719\) −35.8654 −1.33755 −0.668777 0.743463i \(-0.733182\pi\)
−0.668777 + 0.743463i \(0.733182\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 11.3351 0.421558
\(724\) 0 0
\(725\) 32.9573 1.22400
\(726\) 0 0
\(727\) −8.15799 −0.302563 −0.151282 0.988491i \(-0.548340\pi\)
−0.151282 + 0.988491i \(0.548340\pi\)
\(728\) 0 0
\(729\) −16.6895 −0.618131
\(730\) 0 0
\(731\) 63.3673 2.34373
\(732\) 0 0
\(733\) 37.3000 1.37771 0.688854 0.724900i \(-0.258114\pi\)
0.688854 + 0.724900i \(0.258114\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36.4523 1.34274
\(738\) 0 0
\(739\) 0.801245 0.0294743 0.0147371 0.999891i \(-0.495309\pi\)
0.0147371 + 0.999891i \(0.495309\pi\)
\(740\) 0 0
\(741\) 12.1263 0.445471
\(742\) 0 0
\(743\) 16.3460 0.599678 0.299839 0.953990i \(-0.403067\pi\)
0.299839 + 0.953990i \(0.403067\pi\)
\(744\) 0 0
\(745\) −6.69856 −0.245416
\(746\) 0 0
\(747\) −5.88816 −0.215437
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −39.8775 −1.45515 −0.727575 0.686028i \(-0.759353\pi\)
−0.727575 + 0.686028i \(0.759353\pi\)
\(752\) 0 0
\(753\) 6.89489 0.251264
\(754\) 0 0
\(755\) 2.11556 0.0769930
\(756\) 0 0
\(757\) 24.7946 0.901177 0.450588 0.892732i \(-0.351214\pi\)
0.450588 + 0.892732i \(0.351214\pi\)
\(758\) 0 0
\(759\) 9.80296 0.355825
\(760\) 0 0
\(761\) 12.8427 0.465549 0.232774 0.972531i \(-0.425220\pi\)
0.232774 + 0.972531i \(0.425220\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 11.8638 0.428937
\(766\) 0 0
\(767\) −57.0412 −2.05964
\(768\) 0 0
\(769\) −43.3315 −1.56258 −0.781288 0.624171i \(-0.785437\pi\)
−0.781288 + 0.624171i \(0.785437\pi\)
\(770\) 0 0
\(771\) 6.86574 0.247264
\(772\) 0 0
\(773\) 44.3550 1.59534 0.797669 0.603096i \(-0.206066\pi\)
0.797669 + 0.603096i \(0.206066\pi\)
\(774\) 0 0
\(775\) −21.4906 −0.771965
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.82385 −0.172832
\(780\) 0 0
\(781\) −4.33222 −0.155019
\(782\) 0 0
\(783\) 19.6167 0.701043
\(784\) 0 0
\(785\) 3.36195 0.119993
\(786\) 0 0
\(787\) −38.8939 −1.38642 −0.693208 0.720737i \(-0.743803\pi\)
−0.693208 + 0.720737i \(0.743803\pi\)
\(788\) 0 0
\(789\) 11.3620 0.404499
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 27.3643 0.971736
\(794\) 0 0
\(795\) −2.10654 −0.0747113
\(796\) 0 0
\(797\) −18.0342 −0.638803 −0.319401 0.947619i \(-0.603482\pi\)
−0.319401 + 0.947619i \(0.603482\pi\)
\(798\) 0 0
\(799\) −29.9418 −1.05927
\(800\) 0 0
\(801\) 45.2175 1.59768
\(802\) 0 0
\(803\) −13.2860 −0.468852
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −3.19548 −0.112486
\(808\) 0 0
\(809\) −49.9425 −1.75589 −0.877943 0.478765i \(-0.841085\pi\)
−0.877943 + 0.478765i \(0.841085\pi\)
\(810\) 0 0
\(811\) 2.43604 0.0855409 0.0427705 0.999085i \(-0.486382\pi\)
0.0427705 + 0.999085i \(0.486382\pi\)
\(812\) 0 0
\(813\) 0.456451 0.0160084
\(814\) 0 0
\(815\) −14.7581 −0.516953
\(816\) 0 0
\(817\) 56.7910 1.98687
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10.6180 −0.370572 −0.185286 0.982685i \(-0.559321\pi\)
−0.185286 + 0.982685i \(0.559321\pi\)
\(822\) 0 0
\(823\) 50.4401 1.75823 0.879116 0.476608i \(-0.158134\pi\)
0.879116 + 0.476608i \(0.158134\pi\)
\(824\) 0 0
\(825\) −6.11152 −0.212776
\(826\) 0 0
\(827\) 16.6086 0.577538 0.288769 0.957399i \(-0.406754\pi\)
0.288769 + 0.957399i \(0.406754\pi\)
\(828\) 0 0
\(829\) −15.8505 −0.550512 −0.275256 0.961371i \(-0.588763\pi\)
−0.275256 + 0.961371i \(0.588763\pi\)
\(830\) 0 0
\(831\) −10.3754 −0.359919
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −8.93363 −0.309161
\(836\) 0 0
\(837\) −12.7915 −0.442140
\(838\) 0 0
\(839\) −20.4364 −0.705544 −0.352772 0.935709i \(-0.614761\pi\)
−0.352772 + 0.935709i \(0.614761\pi\)
\(840\) 0 0
\(841\) 27.6346 0.952917
\(842\) 0 0
\(843\) −8.70280 −0.299740
\(844\) 0 0
\(845\) −14.3880 −0.494961
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0.0797873 0.00273829
\(850\) 0 0
\(851\) −64.7107 −2.21825
\(852\) 0 0
\(853\) −38.5432 −1.31969 −0.659847 0.751400i \(-0.729379\pi\)
−0.659847 + 0.751400i \(0.729379\pi\)
\(854\) 0 0
\(855\) 10.6326 0.363627
\(856\) 0 0
\(857\) 42.1391 1.43945 0.719723 0.694261i \(-0.244269\pi\)
0.719723 + 0.694261i \(0.244269\pi\)
\(858\) 0 0
\(859\) −14.2451 −0.486037 −0.243018 0.970022i \(-0.578138\pi\)
−0.243018 + 0.970022i \(0.578138\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10.4037 0.354146 0.177073 0.984198i \(-0.443337\pi\)
0.177073 + 0.984198i \(0.443337\pi\)
\(864\) 0 0
\(865\) 9.84934 0.334888
\(866\) 0 0
\(867\) 5.38191 0.182779
\(868\) 0 0
\(869\) 25.1447 0.852975
\(870\) 0 0
\(871\) 65.6631 2.22491
\(872\) 0 0
\(873\) −6.26253 −0.211955
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.38200 −0.0804344 −0.0402172 0.999191i \(-0.512805\pi\)
−0.0402172 + 0.999191i \(0.512805\pi\)
\(878\) 0 0
\(879\) 12.5050 0.421784
\(880\) 0 0
\(881\) −38.7986 −1.30716 −0.653579 0.756858i \(-0.726733\pi\)
−0.653579 + 0.756858i \(0.726733\pi\)
\(882\) 0 0
\(883\) −35.8165 −1.20532 −0.602660 0.797998i \(-0.705892\pi\)
−0.602660 + 0.797998i \(0.705892\pi\)
\(884\) 0 0
\(885\) 3.61330 0.121460
\(886\) 0 0
\(887\) 34.4998 1.15839 0.579196 0.815189i \(-0.303367\pi\)
0.579196 + 0.815189i \(0.303367\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 22.4161 0.750967
\(892\) 0 0
\(893\) −26.8345 −0.897981
\(894\) 0 0
\(895\) 5.48459 0.183330
\(896\) 0 0
\(897\) 17.6585 0.589600
\(898\) 0 0
\(899\) −36.9299 −1.23168
\(900\) 0 0
\(901\) 32.0122 1.06648
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14.4402 −0.480009
\(906\) 0 0
\(907\) 2.75723 0.0915523 0.0457761 0.998952i \(-0.485424\pi\)
0.0457761 + 0.998952i \(0.485424\pi\)
\(908\) 0 0
\(909\) 17.1919 0.570221
\(910\) 0 0
\(911\) 4.19693 0.139051 0.0695253 0.997580i \(-0.477852\pi\)
0.0695253 + 0.997580i \(0.477852\pi\)
\(912\) 0 0
\(913\) 6.53242 0.216192
\(914\) 0 0
\(915\) −1.73341 −0.0573047
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 10.8130 0.356689 0.178344 0.983968i \(-0.442926\pi\)
0.178344 + 0.983968i \(0.442926\pi\)
\(920\) 0 0
\(921\) 11.5554 0.380763
\(922\) 0 0
\(923\) −7.80381 −0.256865
\(924\) 0 0
\(925\) 40.3430 1.32647
\(926\) 0 0
\(927\) −4.12264 −0.135405
\(928\) 0 0
\(929\) −28.3572 −0.930370 −0.465185 0.885214i \(-0.654012\pi\)
−0.465185 + 0.885214i \(0.654012\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −7.00264 −0.229256
\(934\) 0 0
\(935\) −13.1619 −0.430441
\(936\) 0 0
\(937\) −11.1289 −0.363565 −0.181783 0.983339i \(-0.558187\pi\)
−0.181783 + 0.983339i \(0.558187\pi\)
\(938\) 0 0
\(939\) 9.72789 0.317458
\(940\) 0 0
\(941\) −43.0876 −1.40462 −0.702308 0.711873i \(-0.747847\pi\)
−0.702308 + 0.711873i \(0.747847\pi\)
\(942\) 0 0
\(943\) −7.02456 −0.228751
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18.7408 0.608996 0.304498 0.952513i \(-0.401511\pi\)
0.304498 + 0.952513i \(0.401511\pi\)
\(948\) 0 0
\(949\) −23.9326 −0.776885
\(950\) 0 0
\(951\) 10.7783 0.349511
\(952\) 0 0
\(953\) −13.7933 −0.446807 −0.223404 0.974726i \(-0.571717\pi\)
−0.223404 + 0.974726i \(0.571717\pi\)
\(954\) 0 0
\(955\) −15.1921 −0.491605
\(956\) 0 0
\(957\) −10.5022 −0.339487
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −6.91899 −0.223193
\(962\) 0 0
\(963\) −23.6016 −0.760551
\(964\) 0 0
\(965\) −1.10059 −0.0354291
\(966\) 0 0
\(967\) −9.71189 −0.312313 −0.156157 0.987732i \(-0.549910\pi\)
−0.156157 + 0.987732i \(0.549910\pi\)
\(968\) 0 0
\(969\) 11.6732 0.374997
\(970\) 0 0
\(971\) −58.4091 −1.87444 −0.937218 0.348743i \(-0.886609\pi\)
−0.937218 + 0.348743i \(0.886609\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −11.0089 −0.352569
\(976\) 0 0
\(977\) 51.0637 1.63367 0.816837 0.576869i \(-0.195726\pi\)
0.816837 + 0.576869i \(0.195726\pi\)
\(978\) 0 0
\(979\) −50.1650 −1.60328
\(980\) 0 0
\(981\) 28.4297 0.907690
\(982\) 0 0
\(983\) −61.7375 −1.96912 −0.984560 0.175046i \(-0.943993\pi\)
−0.984560 + 0.175046i \(0.943993\pi\)
\(984\) 0 0
\(985\) −10.0965 −0.321703
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 82.6998 2.62970
\(990\) 0 0
\(991\) −36.0099 −1.14389 −0.571946 0.820292i \(-0.693811\pi\)
−0.571946 + 0.820292i \(0.693811\pi\)
\(992\) 0 0
\(993\) −4.33817 −0.137668
\(994\) 0 0
\(995\) 1.31831 0.0417931
\(996\) 0 0
\(997\) −15.7614 −0.499169 −0.249585 0.968353i \(-0.580294\pi\)
−0.249585 + 0.968353i \(0.580294\pi\)
\(998\) 0 0
\(999\) 24.0128 0.759730
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 \(a_p\))