Properties

Label 6036.2.a.g.1.4
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.04745\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.04745 q^{5} +3.89716 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.04745 q^{5} +3.89716 q^{7} +1.00000 q^{9} -4.70738 q^{11} -0.326886 q^{13} -2.04745 q^{15} -5.01396 q^{17} +1.82435 q^{19} +3.89716 q^{21} -1.20909 q^{23} -0.807938 q^{25} +1.00000 q^{27} +2.55087 q^{29} +7.52387 q^{31} -4.70738 q^{33} -7.97926 q^{35} +9.54315 q^{37} -0.326886 q^{39} -8.47431 q^{41} -4.76687 q^{43} -2.04745 q^{45} -4.57901 q^{47} +8.18789 q^{49} -5.01396 q^{51} -1.27828 q^{53} +9.63813 q^{55} +1.82435 q^{57} -7.43663 q^{59} -0.825352 q^{61} +3.89716 q^{63} +0.669283 q^{65} -4.57998 q^{67} -1.20909 q^{69} +5.48910 q^{71} -13.0048 q^{73} -0.807938 q^{75} -18.3454 q^{77} -13.2651 q^{79} +1.00000 q^{81} +3.86744 q^{83} +10.2659 q^{85} +2.55087 q^{87} -4.91231 q^{89} -1.27393 q^{91} +7.52387 q^{93} -3.73527 q^{95} -9.32029 q^{97} -4.70738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 15q^{3} - 11q^{5} - 4q^{7} + 15q^{9} + O(q^{10}) \) \( 15q + 15q^{3} - 11q^{5} - 4q^{7} + 15q^{9} - 5q^{11} - 14q^{13} - 11q^{15} - 5q^{17} + 3q^{19} - 4q^{21} - 32q^{23} + 2q^{25} + 15q^{27} - 23q^{29} - 13q^{31} - 5q^{33} - 16q^{35} - 10q^{37} - 14q^{39} - 14q^{41} + 4q^{43} - 11q^{45} - 20q^{47} - 9q^{49} - 5q^{51} - 30q^{53} - 10q^{55} + 3q^{57} - 14q^{59} - 38q^{61} - 4q^{63} - 24q^{65} - 8q^{67} - 32q^{69} - 41q^{71} - 19q^{73} + 2q^{75} - 39q^{77} - 27q^{79} + 15q^{81} - 17q^{83} - 6q^{85} - 23q^{87} - 23q^{89} + 4q^{91} - 13q^{93} - 30q^{95} - 18q^{97} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −2.04745 −0.915649 −0.457824 0.889043i \(-0.651371\pi\)
−0.457824 + 0.889043i \(0.651371\pi\)
\(6\) 0 0
\(7\) 3.89716 1.47299 0.736495 0.676443i \(-0.236480\pi\)
0.736495 + 0.676443i \(0.236480\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.70738 −1.41933 −0.709664 0.704541i \(-0.751153\pi\)
−0.709664 + 0.704541i \(0.751153\pi\)
\(12\) 0 0
\(13\) −0.326886 −0.0906618 −0.0453309 0.998972i \(-0.514434\pi\)
−0.0453309 + 0.998972i \(0.514434\pi\)
\(14\) 0 0
\(15\) −2.04745 −0.528650
\(16\) 0 0
\(17\) −5.01396 −1.21606 −0.608032 0.793912i \(-0.708041\pi\)
−0.608032 + 0.793912i \(0.708041\pi\)
\(18\) 0 0
\(19\) 1.82435 0.418535 0.209267 0.977858i \(-0.432892\pi\)
0.209267 + 0.977858i \(0.432892\pi\)
\(20\) 0 0
\(21\) 3.89716 0.850431
\(22\) 0 0
\(23\) −1.20909 −0.252112 −0.126056 0.992023i \(-0.540232\pi\)
−0.126056 + 0.992023i \(0.540232\pi\)
\(24\) 0 0
\(25\) −0.807938 −0.161588
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.55087 0.473685 0.236843 0.971548i \(-0.423887\pi\)
0.236843 + 0.971548i \(0.423887\pi\)
\(30\) 0 0
\(31\) 7.52387 1.35133 0.675663 0.737210i \(-0.263857\pi\)
0.675663 + 0.737210i \(0.263857\pi\)
\(32\) 0 0
\(33\) −4.70738 −0.819449
\(34\) 0 0
\(35\) −7.97926 −1.34874
\(36\) 0 0
\(37\) 9.54315 1.56888 0.784442 0.620202i \(-0.212949\pi\)
0.784442 + 0.620202i \(0.212949\pi\)
\(38\) 0 0
\(39\) −0.326886 −0.0523436
\(40\) 0 0
\(41\) −8.47431 −1.32346 −0.661732 0.749740i \(-0.730178\pi\)
−0.661732 + 0.749740i \(0.730178\pi\)
\(42\) 0 0
\(43\) −4.76687 −0.726941 −0.363470 0.931606i \(-0.618408\pi\)
−0.363470 + 0.931606i \(0.618408\pi\)
\(44\) 0 0
\(45\) −2.04745 −0.305216
\(46\) 0 0
\(47\) −4.57901 −0.667917 −0.333959 0.942588i \(-0.608385\pi\)
−0.333959 + 0.942588i \(0.608385\pi\)
\(48\) 0 0
\(49\) 8.18789 1.16970
\(50\) 0 0
\(51\) −5.01396 −0.702095
\(52\) 0 0
\(53\) −1.27828 −0.175586 −0.0877928 0.996139i \(-0.527981\pi\)
−0.0877928 + 0.996139i \(0.527981\pi\)
\(54\) 0 0
\(55\) 9.63813 1.29960
\(56\) 0 0
\(57\) 1.82435 0.241641
\(58\) 0 0
\(59\) −7.43663 −0.968167 −0.484083 0.875022i \(-0.660847\pi\)
−0.484083 + 0.875022i \(0.660847\pi\)
\(60\) 0 0
\(61\) −0.825352 −0.105675 −0.0528377 0.998603i \(-0.516827\pi\)
−0.0528377 + 0.998603i \(0.516827\pi\)
\(62\) 0 0
\(63\) 3.89716 0.490997
\(64\) 0 0
\(65\) 0.669283 0.0830144
\(66\) 0 0
\(67\) −4.57998 −0.559533 −0.279767 0.960068i \(-0.590257\pi\)
−0.279767 + 0.960068i \(0.590257\pi\)
\(68\) 0 0
\(69\) −1.20909 −0.145557
\(70\) 0 0
\(71\) 5.48910 0.651437 0.325718 0.945467i \(-0.394394\pi\)
0.325718 + 0.945467i \(0.394394\pi\)
\(72\) 0 0
\(73\) −13.0048 −1.52209 −0.761046 0.648698i \(-0.775314\pi\)
−0.761046 + 0.648698i \(0.775314\pi\)
\(74\) 0 0
\(75\) −0.807938 −0.0932927
\(76\) 0 0
\(77\) −18.3454 −2.09065
\(78\) 0 0
\(79\) −13.2651 −1.49244 −0.746222 0.665697i \(-0.768134\pi\)
−0.746222 + 0.665697i \(0.768134\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.86744 0.424507 0.212254 0.977215i \(-0.431920\pi\)
0.212254 + 0.977215i \(0.431920\pi\)
\(84\) 0 0
\(85\) 10.2659 1.11349
\(86\) 0 0
\(87\) 2.55087 0.273482
\(88\) 0 0
\(89\) −4.91231 −0.520704 −0.260352 0.965514i \(-0.583839\pi\)
−0.260352 + 0.965514i \(0.583839\pi\)
\(90\) 0 0
\(91\) −1.27393 −0.133544
\(92\) 0 0
\(93\) 7.52387 0.780189
\(94\) 0 0
\(95\) −3.73527 −0.383231
\(96\) 0 0
\(97\) −9.32029 −0.946332 −0.473166 0.880973i \(-0.656889\pi\)
−0.473166 + 0.880973i \(0.656889\pi\)
\(98\) 0 0
\(99\) −4.70738 −0.473109
\(100\) 0 0
\(101\) 2.59179 0.257893 0.128946 0.991652i \(-0.458841\pi\)
0.128946 + 0.991652i \(0.458841\pi\)
\(102\) 0 0
\(103\) −10.1898 −1.00403 −0.502015 0.864859i \(-0.667408\pi\)
−0.502015 + 0.864859i \(0.667408\pi\)
\(104\) 0 0
\(105\) −7.97926 −0.778696
\(106\) 0 0
\(107\) 2.11685 0.204644 0.102322 0.994751i \(-0.467373\pi\)
0.102322 + 0.994751i \(0.467373\pi\)
\(108\) 0 0
\(109\) −6.58991 −0.631198 −0.315599 0.948893i \(-0.602206\pi\)
−0.315599 + 0.948893i \(0.602206\pi\)
\(110\) 0 0
\(111\) 9.54315 0.905796
\(112\) 0 0
\(113\) 0.987955 0.0929390 0.0464695 0.998920i \(-0.485203\pi\)
0.0464695 + 0.998920i \(0.485203\pi\)
\(114\) 0 0
\(115\) 2.47554 0.230846
\(116\) 0 0
\(117\) −0.326886 −0.0302206
\(118\) 0 0
\(119\) −19.5402 −1.79125
\(120\) 0 0
\(121\) 11.1594 1.01449
\(122\) 0 0
\(123\) −8.47431 −0.764102
\(124\) 0 0
\(125\) 11.8915 1.06361
\(126\) 0 0
\(127\) −0.523002 −0.0464089 −0.0232045 0.999731i \(-0.507387\pi\)
−0.0232045 + 0.999731i \(0.507387\pi\)
\(128\) 0 0
\(129\) −4.76687 −0.419699
\(130\) 0 0
\(131\) −11.8830 −1.03823 −0.519113 0.854706i \(-0.673737\pi\)
−0.519113 + 0.854706i \(0.673737\pi\)
\(132\) 0 0
\(133\) 7.10980 0.616498
\(134\) 0 0
\(135\) −2.04745 −0.176217
\(136\) 0 0
\(137\) −6.31909 −0.539876 −0.269938 0.962878i \(-0.587003\pi\)
−0.269938 + 0.962878i \(0.587003\pi\)
\(138\) 0 0
\(139\) 0.794226 0.0673654 0.0336827 0.999433i \(-0.489276\pi\)
0.0336827 + 0.999433i \(0.489276\pi\)
\(140\) 0 0
\(141\) −4.57901 −0.385622
\(142\) 0 0
\(143\) 1.53877 0.128679
\(144\) 0 0
\(145\) −5.22279 −0.433729
\(146\) 0 0
\(147\) 8.18789 0.675326
\(148\) 0 0
\(149\) −8.51557 −0.697623 −0.348811 0.937193i \(-0.613415\pi\)
−0.348811 + 0.937193i \(0.613415\pi\)
\(150\) 0 0
\(151\) −5.19256 −0.422565 −0.211282 0.977425i \(-0.567764\pi\)
−0.211282 + 0.977425i \(0.567764\pi\)
\(152\) 0 0
\(153\) −5.01396 −0.405355
\(154\) 0 0
\(155\) −15.4048 −1.23734
\(156\) 0 0
\(157\) 22.7694 1.81720 0.908598 0.417672i \(-0.137154\pi\)
0.908598 + 0.417672i \(0.137154\pi\)
\(158\) 0 0
\(159\) −1.27828 −0.101374
\(160\) 0 0
\(161\) −4.71200 −0.371358
\(162\) 0 0
\(163\) −19.9768 −1.56471 −0.782353 0.622835i \(-0.785981\pi\)
−0.782353 + 0.622835i \(0.785981\pi\)
\(164\) 0 0
\(165\) 9.63813 0.750327
\(166\) 0 0
\(167\) −4.06406 −0.314486 −0.157243 0.987560i \(-0.550261\pi\)
−0.157243 + 0.987560i \(0.550261\pi\)
\(168\) 0 0
\(169\) −12.8931 −0.991780
\(170\) 0 0
\(171\) 1.82435 0.139512
\(172\) 0 0
\(173\) 14.4948 1.10202 0.551009 0.834499i \(-0.314243\pi\)
0.551009 + 0.834499i \(0.314243\pi\)
\(174\) 0 0
\(175\) −3.14867 −0.238017
\(176\) 0 0
\(177\) −7.43663 −0.558971
\(178\) 0 0
\(179\) 14.8963 1.11340 0.556700 0.830714i \(-0.312067\pi\)
0.556700 + 0.830714i \(0.312067\pi\)
\(180\) 0 0
\(181\) 0.0958839 0.00712699 0.00356350 0.999994i \(-0.498866\pi\)
0.00356350 + 0.999994i \(0.498866\pi\)
\(182\) 0 0
\(183\) −0.825352 −0.0610118
\(184\) 0 0
\(185\) −19.5391 −1.43655
\(186\) 0 0
\(187\) 23.6026 1.72599
\(188\) 0 0
\(189\) 3.89716 0.283477
\(190\) 0 0
\(191\) −12.2133 −0.883721 −0.441860 0.897084i \(-0.645681\pi\)
−0.441860 + 0.897084i \(0.645681\pi\)
\(192\) 0 0
\(193\) 26.3900 1.89960 0.949798 0.312863i \(-0.101288\pi\)
0.949798 + 0.312863i \(0.101288\pi\)
\(194\) 0 0
\(195\) 0.669283 0.0479284
\(196\) 0 0
\(197\) 0.655343 0.0466913 0.0233456 0.999727i \(-0.492568\pi\)
0.0233456 + 0.999727i \(0.492568\pi\)
\(198\) 0 0
\(199\) −7.47514 −0.529899 −0.264949 0.964262i \(-0.585355\pi\)
−0.264949 + 0.964262i \(0.585355\pi\)
\(200\) 0 0
\(201\) −4.57998 −0.323047
\(202\) 0 0
\(203\) 9.94118 0.697734
\(204\) 0 0
\(205\) 17.3507 1.21183
\(206\) 0 0
\(207\) −1.20909 −0.0840372
\(208\) 0 0
\(209\) −8.58791 −0.594038
\(210\) 0 0
\(211\) −5.77812 −0.397782 −0.198891 0.980022i \(-0.563734\pi\)
−0.198891 + 0.980022i \(0.563734\pi\)
\(212\) 0 0
\(213\) 5.48910 0.376107
\(214\) 0 0
\(215\) 9.75994 0.665622
\(216\) 0 0
\(217\) 29.3218 1.99049
\(218\) 0 0
\(219\) −13.0048 −0.878780
\(220\) 0 0
\(221\) 1.63899 0.110251
\(222\) 0 0
\(223\) 23.7158 1.58813 0.794064 0.607835i \(-0.207962\pi\)
0.794064 + 0.607835i \(0.207962\pi\)
\(224\) 0 0
\(225\) −0.807938 −0.0538626
\(226\) 0 0
\(227\) −19.1401 −1.27038 −0.635188 0.772358i \(-0.719077\pi\)
−0.635188 + 0.772358i \(0.719077\pi\)
\(228\) 0 0
\(229\) −17.0306 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(230\) 0 0
\(231\) −18.3454 −1.20704
\(232\) 0 0
\(233\) 0.00287566 0.000188391 0 9.41955e−5 1.00000i \(-0.499970\pi\)
9.41955e−5 1.00000i \(0.499970\pi\)
\(234\) 0 0
\(235\) 9.37530 0.611577
\(236\) 0 0
\(237\) −13.2651 −0.861663
\(238\) 0 0
\(239\) 16.7797 1.08539 0.542693 0.839931i \(-0.317405\pi\)
0.542693 + 0.839931i \(0.317405\pi\)
\(240\) 0 0
\(241\) 2.01472 0.129780 0.0648898 0.997892i \(-0.479330\pi\)
0.0648898 + 0.997892i \(0.479330\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −16.7643 −1.07103
\(246\) 0 0
\(247\) −0.596355 −0.0379451
\(248\) 0 0
\(249\) 3.86744 0.245089
\(250\) 0 0
\(251\) −3.46557 −0.218745 −0.109372 0.994001i \(-0.534884\pi\)
−0.109372 + 0.994001i \(0.534884\pi\)
\(252\) 0 0
\(253\) 5.69162 0.357829
\(254\) 0 0
\(255\) 10.2659 0.642873
\(256\) 0 0
\(257\) −1.64966 −0.102903 −0.0514514 0.998676i \(-0.516385\pi\)
−0.0514514 + 0.998676i \(0.516385\pi\)
\(258\) 0 0
\(259\) 37.1912 2.31095
\(260\) 0 0
\(261\) 2.55087 0.157895
\(262\) 0 0
\(263\) 11.1195 0.685660 0.342830 0.939397i \(-0.388614\pi\)
0.342830 + 0.939397i \(0.388614\pi\)
\(264\) 0 0
\(265\) 2.61722 0.160775
\(266\) 0 0
\(267\) −4.91231 −0.300629
\(268\) 0 0
\(269\) −0.751890 −0.0458435 −0.0229218 0.999737i \(-0.507297\pi\)
−0.0229218 + 0.999737i \(0.507297\pi\)
\(270\) 0 0
\(271\) −18.2087 −1.10610 −0.553051 0.833148i \(-0.686536\pi\)
−0.553051 + 0.833148i \(0.686536\pi\)
\(272\) 0 0
\(273\) −1.27393 −0.0771016
\(274\) 0 0
\(275\) 3.80327 0.229346
\(276\) 0 0
\(277\) −25.2198 −1.51531 −0.757654 0.652656i \(-0.773655\pi\)
−0.757654 + 0.652656i \(0.773655\pi\)
\(278\) 0 0
\(279\) 7.52387 0.450442
\(280\) 0 0
\(281\) 2.79663 0.166833 0.0834166 0.996515i \(-0.473417\pi\)
0.0834166 + 0.996515i \(0.473417\pi\)
\(282\) 0 0
\(283\) −13.4378 −0.798792 −0.399396 0.916779i \(-0.630780\pi\)
−0.399396 + 0.916779i \(0.630780\pi\)
\(284\) 0 0
\(285\) −3.73527 −0.221258
\(286\) 0 0
\(287\) −33.0258 −1.94945
\(288\) 0 0
\(289\) 8.13983 0.478814
\(290\) 0 0
\(291\) −9.32029 −0.546365
\(292\) 0 0
\(293\) 23.3446 1.36381 0.681903 0.731443i \(-0.261153\pi\)
0.681903 + 0.731443i \(0.261153\pi\)
\(294\) 0 0
\(295\) 15.2261 0.886501
\(296\) 0 0
\(297\) −4.70738 −0.273150
\(298\) 0 0
\(299\) 0.395233 0.0228569
\(300\) 0 0
\(301\) −18.5773 −1.07078
\(302\) 0 0
\(303\) 2.59179 0.148894
\(304\) 0 0
\(305\) 1.68987 0.0967616
\(306\) 0 0
\(307\) −33.2791 −1.89934 −0.949670 0.313253i \(-0.898581\pi\)
−0.949670 + 0.313253i \(0.898581\pi\)
\(308\) 0 0
\(309\) −10.1898 −0.579677
\(310\) 0 0
\(311\) 14.4700 0.820519 0.410260 0.911969i \(-0.365438\pi\)
0.410260 + 0.911969i \(0.365438\pi\)
\(312\) 0 0
\(313\) −22.2012 −1.25488 −0.627442 0.778663i \(-0.715898\pi\)
−0.627442 + 0.778663i \(0.715898\pi\)
\(314\) 0 0
\(315\) −7.97926 −0.449580
\(316\) 0 0
\(317\) −6.95963 −0.390892 −0.195446 0.980714i \(-0.562615\pi\)
−0.195446 + 0.980714i \(0.562615\pi\)
\(318\) 0 0
\(319\) −12.0079 −0.672315
\(320\) 0 0
\(321\) 2.11685 0.118151
\(322\) 0 0
\(323\) −9.14723 −0.508966
\(324\) 0 0
\(325\) 0.264104 0.0146498
\(326\) 0 0
\(327\) −6.58991 −0.364423
\(328\) 0 0
\(329\) −17.8452 −0.983835
\(330\) 0 0
\(331\) −13.9114 −0.764640 −0.382320 0.924030i \(-0.624875\pi\)
−0.382320 + 0.924030i \(0.624875\pi\)
\(332\) 0 0
\(333\) 9.54315 0.522961
\(334\) 0 0
\(335\) 9.37729 0.512336
\(336\) 0 0
\(337\) 1.97814 0.107756 0.0538782 0.998548i \(-0.482842\pi\)
0.0538782 + 0.998548i \(0.482842\pi\)
\(338\) 0 0
\(339\) 0.987955 0.0536584
\(340\) 0 0
\(341\) −35.4177 −1.91797
\(342\) 0 0
\(343\) 4.62940 0.249964
\(344\) 0 0
\(345\) 2.47554 0.133279
\(346\) 0 0
\(347\) −9.00457 −0.483391 −0.241695 0.970352i \(-0.577703\pi\)
−0.241695 + 0.970352i \(0.577703\pi\)
\(348\) 0 0
\(349\) 0.401688 0.0215019 0.0107509 0.999942i \(-0.496578\pi\)
0.0107509 + 0.999942i \(0.496578\pi\)
\(350\) 0 0
\(351\) −0.326886 −0.0174479
\(352\) 0 0
\(353\) −9.46991 −0.504032 −0.252016 0.967723i \(-0.581094\pi\)
−0.252016 + 0.967723i \(0.581094\pi\)
\(354\) 0 0
\(355\) −11.2387 −0.596487
\(356\) 0 0
\(357\) −19.5402 −1.03418
\(358\) 0 0
\(359\) 23.7941 1.25581 0.627903 0.778292i \(-0.283914\pi\)
0.627903 + 0.778292i \(0.283914\pi\)
\(360\) 0 0
\(361\) −15.6717 −0.824828
\(362\) 0 0
\(363\) 11.1594 0.585716
\(364\) 0 0
\(365\) 26.6266 1.39370
\(366\) 0 0
\(367\) −13.3921 −0.699061 −0.349531 0.936925i \(-0.613659\pi\)
−0.349531 + 0.936925i \(0.613659\pi\)
\(368\) 0 0
\(369\) −8.47431 −0.441155
\(370\) 0 0
\(371\) −4.98167 −0.258636
\(372\) 0 0
\(373\) −1.99893 −0.103501 −0.0517503 0.998660i \(-0.516480\pi\)
−0.0517503 + 0.998660i \(0.516480\pi\)
\(374\) 0 0
\(375\) 11.8915 0.614073
\(376\) 0 0
\(377\) −0.833845 −0.0429452
\(378\) 0 0
\(379\) −13.9518 −0.716654 −0.358327 0.933596i \(-0.616653\pi\)
−0.358327 + 0.933596i \(0.616653\pi\)
\(380\) 0 0
\(381\) −0.523002 −0.0267942
\(382\) 0 0
\(383\) −27.3853 −1.39932 −0.699661 0.714475i \(-0.746666\pi\)
−0.699661 + 0.714475i \(0.746666\pi\)
\(384\) 0 0
\(385\) 37.5614 1.91430
\(386\) 0 0
\(387\) −4.76687 −0.242314
\(388\) 0 0
\(389\) 4.95165 0.251059 0.125529 0.992090i \(-0.459937\pi\)
0.125529 + 0.992090i \(0.459937\pi\)
\(390\) 0 0
\(391\) 6.06231 0.306584
\(392\) 0 0
\(393\) −11.8830 −0.599420
\(394\) 0 0
\(395\) 27.1597 1.36656
\(396\) 0 0
\(397\) 5.20465 0.261214 0.130607 0.991434i \(-0.458307\pi\)
0.130607 + 0.991434i \(0.458307\pi\)
\(398\) 0 0
\(399\) 7.10980 0.355935
\(400\) 0 0
\(401\) 25.0630 1.25158 0.625792 0.779990i \(-0.284776\pi\)
0.625792 + 0.779990i \(0.284776\pi\)
\(402\) 0 0
\(403\) −2.45945 −0.122514
\(404\) 0 0
\(405\) −2.04745 −0.101739
\(406\) 0 0
\(407\) −44.9232 −2.22676
\(408\) 0 0
\(409\) −21.9726 −1.08648 −0.543239 0.839578i \(-0.682802\pi\)
−0.543239 + 0.839578i \(0.682802\pi\)
\(410\) 0 0
\(411\) −6.31909 −0.311698
\(412\) 0 0
\(413\) −28.9818 −1.42610
\(414\) 0 0
\(415\) −7.91841 −0.388699
\(416\) 0 0
\(417\) 0.794226 0.0388934
\(418\) 0 0
\(419\) 27.1619 1.32694 0.663472 0.748201i \(-0.269082\pi\)
0.663472 + 0.748201i \(0.269082\pi\)
\(420\) 0 0
\(421\) 23.0600 1.12388 0.561938 0.827179i \(-0.310056\pi\)
0.561938 + 0.827179i \(0.310056\pi\)
\(422\) 0 0
\(423\) −4.57901 −0.222639
\(424\) 0 0
\(425\) 4.05097 0.196501
\(426\) 0 0
\(427\) −3.21653 −0.155659
\(428\) 0 0
\(429\) 1.53877 0.0742927
\(430\) 0 0
\(431\) 16.0875 0.774906 0.387453 0.921890i \(-0.373355\pi\)
0.387453 + 0.921890i \(0.373355\pi\)
\(432\) 0 0
\(433\) −0.424933 −0.0204210 −0.0102105 0.999948i \(-0.503250\pi\)
−0.0102105 + 0.999948i \(0.503250\pi\)
\(434\) 0 0
\(435\) −5.22279 −0.250414
\(436\) 0 0
\(437\) −2.20580 −0.105518
\(438\) 0 0
\(439\) −18.7546 −0.895110 −0.447555 0.894257i \(-0.647705\pi\)
−0.447555 + 0.894257i \(0.647705\pi\)
\(440\) 0 0
\(441\) 8.18789 0.389900
\(442\) 0 0
\(443\) −2.60334 −0.123689 −0.0618443 0.998086i \(-0.519698\pi\)
−0.0618443 + 0.998086i \(0.519698\pi\)
\(444\) 0 0
\(445\) 10.0577 0.476782
\(446\) 0 0
\(447\) −8.51557 −0.402773
\(448\) 0 0
\(449\) −2.69027 −0.126962 −0.0634808 0.997983i \(-0.520220\pi\)
−0.0634808 + 0.997983i \(0.520220\pi\)
\(450\) 0 0
\(451\) 39.8917 1.87843
\(452\) 0 0
\(453\) −5.19256 −0.243968
\(454\) 0 0
\(455\) 2.60831 0.122279
\(456\) 0 0
\(457\) 3.37173 0.157723 0.0788613 0.996886i \(-0.474872\pi\)
0.0788613 + 0.996886i \(0.474872\pi\)
\(458\) 0 0
\(459\) −5.01396 −0.234032
\(460\) 0 0
\(461\) 17.8684 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(462\) 0 0
\(463\) −29.6764 −1.37918 −0.689589 0.724201i \(-0.742209\pi\)
−0.689589 + 0.724201i \(0.742209\pi\)
\(464\) 0 0
\(465\) −15.4048 −0.714379
\(466\) 0 0
\(467\) −24.8093 −1.14804 −0.574018 0.818843i \(-0.694616\pi\)
−0.574018 + 0.818843i \(0.694616\pi\)
\(468\) 0 0
\(469\) −17.8489 −0.824187
\(470\) 0 0
\(471\) 22.7694 1.04916
\(472\) 0 0
\(473\) 22.4394 1.03177
\(474\) 0 0
\(475\) −1.47396 −0.0676301
\(476\) 0 0
\(477\) −1.27828 −0.0585285
\(478\) 0 0
\(479\) −20.2970 −0.927394 −0.463697 0.885994i \(-0.653477\pi\)
−0.463697 + 0.885994i \(0.653477\pi\)
\(480\) 0 0
\(481\) −3.11952 −0.142238
\(482\) 0 0
\(483\) −4.71200 −0.214404
\(484\) 0 0
\(485\) 19.0828 0.866507
\(486\) 0 0
\(487\) −1.05720 −0.0479061 −0.0239530 0.999713i \(-0.507625\pi\)
−0.0239530 + 0.999713i \(0.507625\pi\)
\(488\) 0 0
\(489\) −19.9768 −0.903383
\(490\) 0 0
\(491\) −11.2245 −0.506556 −0.253278 0.967393i \(-0.581509\pi\)
−0.253278 + 0.967393i \(0.581509\pi\)
\(492\) 0 0
\(493\) −12.7900 −0.576032
\(494\) 0 0
\(495\) 9.63813 0.433202
\(496\) 0 0
\(497\) 21.3919 0.959559
\(498\) 0 0
\(499\) 6.38326 0.285754 0.142877 0.989740i \(-0.454365\pi\)
0.142877 + 0.989740i \(0.454365\pi\)
\(500\) 0 0
\(501\) −4.06406 −0.181569
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −5.30656 −0.236139
\(506\) 0 0
\(507\) −12.8931 −0.572605
\(508\) 0 0
\(509\) −20.9545 −0.928794 −0.464397 0.885627i \(-0.653729\pi\)
−0.464397 + 0.885627i \(0.653729\pi\)
\(510\) 0 0
\(511\) −50.6817 −2.24202
\(512\) 0 0
\(513\) 1.82435 0.0805471
\(514\) 0 0
\(515\) 20.8631 0.919338
\(516\) 0 0
\(517\) 21.5551 0.947993
\(518\) 0 0
\(519\) 14.4948 0.636250
\(520\) 0 0
\(521\) −14.5474 −0.637331 −0.318666 0.947867i \(-0.603235\pi\)
−0.318666 + 0.947867i \(0.603235\pi\)
\(522\) 0 0
\(523\) 37.6429 1.64601 0.823004 0.568036i \(-0.192297\pi\)
0.823004 + 0.568036i \(0.192297\pi\)
\(524\) 0 0
\(525\) −3.14867 −0.137419
\(526\) 0 0
\(527\) −37.7244 −1.64330
\(528\) 0 0
\(529\) −21.5381 −0.936440
\(530\) 0 0
\(531\) −7.43663 −0.322722
\(532\) 0 0
\(533\) 2.77013 0.119988
\(534\) 0 0
\(535\) −4.33415 −0.187382
\(536\) 0 0
\(537\) 14.8963 0.642822
\(538\) 0 0
\(539\) −38.5435 −1.66018
\(540\) 0 0
\(541\) 0.131363 0.00564775 0.00282387 0.999996i \(-0.499101\pi\)
0.00282387 + 0.999996i \(0.499101\pi\)
\(542\) 0 0
\(543\) 0.0958839 0.00411477
\(544\) 0 0
\(545\) 13.4925 0.577956
\(546\) 0 0
\(547\) 14.9179 0.637843 0.318922 0.947781i \(-0.396679\pi\)
0.318922 + 0.947781i \(0.396679\pi\)
\(548\) 0 0
\(549\) −0.825352 −0.0352252
\(550\) 0 0
\(551\) 4.65369 0.198254
\(552\) 0 0
\(553\) −51.6964 −2.19836
\(554\) 0 0
\(555\) −19.5391 −0.829390
\(556\) 0 0
\(557\) −5.52271 −0.234005 −0.117002 0.993132i \(-0.537329\pi\)
−0.117002 + 0.993132i \(0.537329\pi\)
\(558\) 0 0
\(559\) 1.55822 0.0659057
\(560\) 0 0
\(561\) 23.6026 0.996503
\(562\) 0 0
\(563\) 18.3716 0.774271 0.387135 0.922023i \(-0.373465\pi\)
0.387135 + 0.922023i \(0.373465\pi\)
\(564\) 0 0
\(565\) −2.02279 −0.0850995
\(566\) 0 0
\(567\) 3.89716 0.163666
\(568\) 0 0
\(569\) 21.1494 0.886627 0.443313 0.896367i \(-0.353803\pi\)
0.443313 + 0.896367i \(0.353803\pi\)
\(570\) 0 0
\(571\) 44.9516 1.88117 0.940583 0.339564i \(-0.110279\pi\)
0.940583 + 0.339564i \(0.110279\pi\)
\(572\) 0 0
\(573\) −12.2133 −0.510216
\(574\) 0 0
\(575\) 0.976866 0.0407381
\(576\) 0 0
\(577\) 8.14898 0.339247 0.169623 0.985509i \(-0.445745\pi\)
0.169623 + 0.985509i \(0.445745\pi\)
\(578\) 0 0
\(579\) 26.3900 1.09673
\(580\) 0 0
\(581\) 15.0721 0.625295
\(582\) 0 0
\(583\) 6.01735 0.249213
\(584\) 0 0
\(585\) 0.669283 0.0276715
\(586\) 0 0
\(587\) 34.6714 1.43104 0.715521 0.698592i \(-0.246190\pi\)
0.715521 + 0.698592i \(0.246190\pi\)
\(588\) 0 0
\(589\) 13.7262 0.565578
\(590\) 0 0
\(591\) 0.655343 0.0269572
\(592\) 0 0
\(593\) 17.4584 0.716930 0.358465 0.933543i \(-0.383300\pi\)
0.358465 + 0.933543i \(0.383300\pi\)
\(594\) 0 0
\(595\) 40.0077 1.64016
\(596\) 0 0
\(597\) −7.47514 −0.305937
\(598\) 0 0
\(599\) −33.2755 −1.35960 −0.679801 0.733397i \(-0.737934\pi\)
−0.679801 + 0.733397i \(0.737934\pi\)
\(600\) 0 0
\(601\) −21.3864 −0.872368 −0.436184 0.899857i \(-0.643670\pi\)
−0.436184 + 0.899857i \(0.643670\pi\)
\(602\) 0 0
\(603\) −4.57998 −0.186511
\(604\) 0 0
\(605\) −22.8483 −0.928916
\(606\) 0 0
\(607\) 4.03385 0.163729 0.0818645 0.996643i \(-0.473913\pi\)
0.0818645 + 0.996643i \(0.473913\pi\)
\(608\) 0 0
\(609\) 9.94118 0.402837
\(610\) 0 0
\(611\) 1.49681 0.0605546
\(612\) 0 0
\(613\) 18.8434 0.761079 0.380539 0.924765i \(-0.375738\pi\)
0.380539 + 0.924765i \(0.375738\pi\)
\(614\) 0 0
\(615\) 17.3507 0.699649
\(616\) 0 0
\(617\) 21.9673 0.884372 0.442186 0.896923i \(-0.354203\pi\)
0.442186 + 0.896923i \(0.354203\pi\)
\(618\) 0 0
\(619\) 44.2152 1.77716 0.888579 0.458723i \(-0.151693\pi\)
0.888579 + 0.458723i \(0.151693\pi\)
\(620\) 0 0
\(621\) −1.20909 −0.0485189
\(622\) 0 0
\(623\) −19.1441 −0.766992
\(624\) 0 0
\(625\) −20.3075 −0.812302
\(626\) 0 0
\(627\) −8.58791 −0.342968
\(628\) 0 0
\(629\) −47.8490 −1.90786
\(630\) 0 0
\(631\) −10.3264 −0.411087 −0.205543 0.978648i \(-0.565896\pi\)
−0.205543 + 0.978648i \(0.565896\pi\)
\(632\) 0 0
\(633\) −5.77812 −0.229660
\(634\) 0 0
\(635\) 1.07082 0.0424942
\(636\) 0 0
\(637\) −2.67651 −0.106047
\(638\) 0 0
\(639\) 5.48910 0.217146
\(640\) 0 0
\(641\) −17.9443 −0.708759 −0.354379 0.935102i \(-0.615308\pi\)
−0.354379 + 0.935102i \(0.615308\pi\)
\(642\) 0 0
\(643\) −8.52846 −0.336330 −0.168165 0.985759i \(-0.553784\pi\)
−0.168165 + 0.985759i \(0.553784\pi\)
\(644\) 0 0
\(645\) 9.75994 0.384297
\(646\) 0 0
\(647\) 13.9515 0.548490 0.274245 0.961660i \(-0.411572\pi\)
0.274245 + 0.961660i \(0.411572\pi\)
\(648\) 0 0
\(649\) 35.0070 1.37415
\(650\) 0 0
\(651\) 29.3218 1.14921
\(652\) 0 0
\(653\) 36.8740 1.44299 0.721496 0.692418i \(-0.243455\pi\)
0.721496 + 0.692418i \(0.243455\pi\)
\(654\) 0 0
\(655\) 24.3299 0.950650
\(656\) 0 0
\(657\) −13.0048 −0.507364
\(658\) 0 0
\(659\) 47.4745 1.84935 0.924673 0.380763i \(-0.124339\pi\)
0.924673 + 0.380763i \(0.124339\pi\)
\(660\) 0 0
\(661\) 22.2703 0.866213 0.433107 0.901343i \(-0.357417\pi\)
0.433107 + 0.901343i \(0.357417\pi\)
\(662\) 0 0
\(663\) 1.63899 0.0636532
\(664\) 0 0
\(665\) −14.5570 −0.564495
\(666\) 0 0
\(667\) −3.08422 −0.119422
\(668\) 0 0
\(669\) 23.7158 0.916906
\(670\) 0 0
\(671\) 3.88524 0.149988
\(672\) 0 0
\(673\) −3.63814 −0.140240 −0.0701201 0.997539i \(-0.522338\pi\)
−0.0701201 + 0.997539i \(0.522338\pi\)
\(674\) 0 0
\(675\) −0.807938 −0.0310976
\(676\) 0 0
\(677\) −11.8147 −0.454075 −0.227037 0.973886i \(-0.572904\pi\)
−0.227037 + 0.973886i \(0.572904\pi\)
\(678\) 0 0
\(679\) −36.3227 −1.39394
\(680\) 0 0
\(681\) −19.1401 −0.733451
\(682\) 0 0
\(683\) 8.99351 0.344127 0.172064 0.985086i \(-0.444957\pi\)
0.172064 + 0.985086i \(0.444957\pi\)
\(684\) 0 0
\(685\) 12.9380 0.494337
\(686\) 0 0
\(687\) −17.0306 −0.649759
\(688\) 0 0
\(689\) 0.417852 0.0159189
\(690\) 0 0
\(691\) 33.2929 1.26652 0.633260 0.773939i \(-0.281716\pi\)
0.633260 + 0.773939i \(0.281716\pi\)
\(692\) 0 0
\(693\) −18.3454 −0.696885
\(694\) 0 0
\(695\) −1.62614 −0.0616830
\(696\) 0 0
\(697\) 42.4899 1.60942
\(698\) 0 0
\(699\) 0.00287566 0.000108768 0
\(700\) 0 0
\(701\) −18.6421 −0.704103 −0.352051 0.935981i \(-0.614516\pi\)
−0.352051 + 0.935981i \(0.614516\pi\)
\(702\) 0 0
\(703\) 17.4101 0.656633
\(704\) 0 0
\(705\) 9.37530 0.353094
\(706\) 0 0
\(707\) 10.1006 0.379873
\(708\) 0 0
\(709\) −14.0309 −0.526943 −0.263471 0.964667i \(-0.584867\pi\)
−0.263471 + 0.964667i \(0.584867\pi\)
\(710\) 0 0
\(711\) −13.2651 −0.497482
\(712\) 0 0
\(713\) −9.09700 −0.340685
\(714\) 0 0
\(715\) −3.15057 −0.117825
\(716\) 0 0
\(717\) 16.7797 0.626648
\(718\) 0 0
\(719\) −41.6576 −1.55357 −0.776784 0.629767i \(-0.783150\pi\)
−0.776784 + 0.629767i \(0.783150\pi\)
\(720\) 0 0
\(721\) −39.7113 −1.47892
\(722\) 0 0
\(723\) 2.01472 0.0749283
\(724\) 0 0
\(725\) −2.06095 −0.0765417
\(726\) 0 0
\(727\) 34.2156 1.26898 0.634492 0.772929i \(-0.281209\pi\)
0.634492 + 0.772929i \(0.281209\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 23.9009 0.884007
\(732\) 0 0
\(733\) 16.0439 0.592595 0.296297 0.955096i \(-0.404248\pi\)
0.296297 + 0.955096i \(0.404248\pi\)
\(734\) 0 0
\(735\) −16.7643 −0.618361
\(736\) 0 0
\(737\) 21.5597 0.794161
\(738\) 0 0
\(739\) 30.2862 1.11410 0.557048 0.830480i \(-0.311934\pi\)
0.557048 + 0.830480i \(0.311934\pi\)
\(740\) 0 0
\(741\) −0.596355 −0.0219076
\(742\) 0 0
\(743\) 23.4411 0.859971 0.429985 0.902836i \(-0.358519\pi\)
0.429985 + 0.902836i \(0.358519\pi\)
\(744\) 0 0
\(745\) 17.4352 0.638777
\(746\) 0 0
\(747\) 3.86744 0.141502
\(748\) 0 0
\(749\) 8.24971 0.301438
\(750\) 0 0
\(751\) 24.5229 0.894854 0.447427 0.894321i \(-0.352340\pi\)
0.447427 + 0.894321i \(0.352340\pi\)
\(752\) 0 0
\(753\) −3.46557 −0.126292
\(754\) 0 0
\(755\) 10.6315 0.386921
\(756\) 0 0
\(757\) −18.1214 −0.658634 −0.329317 0.944219i \(-0.606819\pi\)
−0.329317 + 0.944219i \(0.606819\pi\)
\(758\) 0 0
\(759\) 5.69162 0.206593
\(760\) 0 0
\(761\) 13.7164 0.497217 0.248609 0.968604i \(-0.420027\pi\)
0.248609 + 0.968604i \(0.420027\pi\)
\(762\) 0 0
\(763\) −25.6819 −0.929749
\(764\) 0 0
\(765\) 10.2659 0.371163
\(766\) 0 0
\(767\) 2.43093 0.0877758
\(768\) 0 0
\(769\) −8.23898 −0.297105 −0.148553 0.988905i \(-0.547461\pi\)
−0.148553 + 0.988905i \(0.547461\pi\)
\(770\) 0 0
\(771\) −1.64966 −0.0594109
\(772\) 0 0
\(773\) −47.1354 −1.69534 −0.847671 0.530523i \(-0.821996\pi\)
−0.847671 + 0.530523i \(0.821996\pi\)
\(774\) 0 0
\(775\) −6.07882 −0.218358
\(776\) 0 0
\(777\) 37.1912 1.33423
\(778\) 0 0
\(779\) −15.4601 −0.553916
\(780\) 0 0
\(781\) −25.8393 −0.924602
\(782\) 0 0
\(783\) 2.55087 0.0911608
\(784\) 0 0
\(785\) −46.6193 −1.66391
\(786\) 0 0
\(787\) −26.4429 −0.942589 −0.471295 0.881976i \(-0.656213\pi\)
−0.471295 + 0.881976i \(0.656213\pi\)
\(788\) 0 0
\(789\) 11.1195 0.395866
\(790\) 0 0
\(791\) 3.85022 0.136898
\(792\) 0 0
\(793\) 0.269796 0.00958073
\(794\) 0 0
\(795\) 2.61722 0.0928233
\(796\) 0 0
\(797\) −15.0538 −0.533231 −0.266616 0.963803i \(-0.585905\pi\)
−0.266616 + 0.963803i \(0.585905\pi\)
\(798\) 0 0
\(799\) 22.9590 0.812231
\(800\) 0 0
\(801\) −4.91231 −0.173568
\(802\) 0 0
\(803\) 61.2183 2.16035
\(804\) 0 0
\(805\) 9.64760 0.340033
\(806\) 0 0
\(807\) −0.751890 −0.0264678
\(808\) 0 0
\(809\) 43.4681 1.52826 0.764129 0.645064i \(-0.223169\pi\)
0.764129 + 0.645064i \(0.223169\pi\)
\(810\) 0 0
\(811\) 23.5643 0.827453 0.413727 0.910401i \(-0.364227\pi\)
0.413727 + 0.910401i \(0.364227\pi\)
\(812\) 0 0
\(813\) −18.2087 −0.638608
\(814\) 0 0
\(815\) 40.9016 1.43272
\(816\) 0 0
\(817\) −8.69644 −0.304250
\(818\) 0 0
\(819\) −1.27393 −0.0445146
\(820\) 0 0
\(821\) 32.1403 1.12170 0.560852 0.827916i \(-0.310474\pi\)
0.560852 + 0.827916i \(0.310474\pi\)
\(822\) 0 0
\(823\) 26.4882 0.923320 0.461660 0.887057i \(-0.347254\pi\)
0.461660 + 0.887057i \(0.347254\pi\)
\(824\) 0 0
\(825\) 3.80327 0.132413
\(826\) 0 0
\(827\) 47.0849 1.63730 0.818651 0.574292i \(-0.194722\pi\)
0.818651 + 0.574292i \(0.194722\pi\)
\(828\) 0 0
\(829\) 16.1417 0.560626 0.280313 0.959909i \(-0.409562\pi\)
0.280313 + 0.959909i \(0.409562\pi\)
\(830\) 0 0
\(831\) −25.2198 −0.874863
\(832\) 0 0
\(833\) −41.0538 −1.42243
\(834\) 0 0
\(835\) 8.32096 0.287959
\(836\) 0 0
\(837\) 7.52387 0.260063
\(838\) 0 0
\(839\) 8.36319 0.288729 0.144365 0.989525i \(-0.453886\pi\)
0.144365 + 0.989525i \(0.453886\pi\)
\(840\) 0 0
\(841\) −22.4930 −0.775622
\(842\) 0 0
\(843\) 2.79663 0.0963211
\(844\) 0 0
\(845\) 26.3981 0.908122
\(846\) 0 0
\(847\) 43.4899 1.49433
\(848\) 0 0
\(849\) −13.4378 −0.461183
\(850\) 0 0
\(851\) −11.5385 −0.395534
\(852\) 0 0
\(853\) 8.87310 0.303809 0.151905 0.988395i \(-0.451459\pi\)
0.151905 + 0.988395i \(0.451459\pi\)
\(854\) 0 0
\(855\) −3.73527 −0.127744
\(856\) 0 0
\(857\) −53.7147 −1.83486 −0.917429 0.397899i \(-0.869739\pi\)
−0.917429 + 0.397899i \(0.869739\pi\)
\(858\) 0 0
\(859\) 48.4400 1.65275 0.826376 0.563119i \(-0.190399\pi\)
0.826376 + 0.563119i \(0.190399\pi\)
\(860\) 0 0
\(861\) −33.0258 −1.12551
\(862\) 0 0
\(863\) −23.7291 −0.807747 −0.403874 0.914815i \(-0.632336\pi\)
−0.403874 + 0.914815i \(0.632336\pi\)
\(864\) 0 0
\(865\) −29.6774 −1.00906
\(866\) 0 0
\(867\) 8.13983 0.276443
\(868\) 0 0
\(869\) 62.4440 2.11827
\(870\) 0 0
\(871\) 1.49713 0.0507283
\(872\) 0 0
\(873\) −9.32029 −0.315444
\(874\) 0 0
\(875\) 46.3430 1.56668
\(876\) 0 0
\(877\) −10.5283 −0.355514 −0.177757 0.984074i \(-0.556884\pi\)
−0.177757 + 0.984074i \(0.556884\pi\)
\(878\) 0 0
\(879\) 23.3446 0.787394
\(880\) 0 0
\(881\) −31.9326 −1.07584 −0.537918 0.842997i \(-0.680789\pi\)
−0.537918 + 0.842997i \(0.680789\pi\)
\(882\) 0 0
\(883\) −38.5893 −1.29863 −0.649316 0.760519i \(-0.724945\pi\)
−0.649316 + 0.760519i \(0.724945\pi\)
\(884\) 0 0
\(885\) 15.2261 0.511821
\(886\) 0 0
\(887\) 47.1741 1.58395 0.791976 0.610552i \(-0.209053\pi\)
0.791976 + 0.610552i \(0.209053\pi\)
\(888\) 0 0
\(889\) −2.03822 −0.0683598
\(890\) 0 0
\(891\) −4.70738 −0.157703
\(892\) 0 0
\(893\) −8.35372 −0.279547
\(894\) 0 0
\(895\) −30.4994 −1.01948
\(896\) 0 0
\(897\) 0.395233 0.0131964
\(898\) 0 0
\(899\) 19.1924 0.640104
\(900\) 0 0
\(901\) 6.40926 0.213523
\(902\) 0 0
\(903\) −18.5773 −0.618213
\(904\) 0 0
\(905\) −0.196318 −0.00652582
\(906\) 0 0
\(907\) 2.31330 0.0768120 0.0384060 0.999262i \(-0.487772\pi\)
0.0384060 + 0.999262i \(0.487772\pi\)
\(908\) 0 0
\(909\) 2.59179 0.0859642
\(910\) 0 0
\(911\) −42.4575 −1.40668 −0.703340 0.710854i \(-0.748309\pi\)
−0.703340 + 0.710854i \(0.748309\pi\)
\(912\) 0 0
\(913\) −18.2055 −0.602514
\(914\) 0 0
\(915\) 1.68987 0.0558653
\(916\) 0 0
\(917\) −46.3101 −1.52930
\(918\) 0 0
\(919\) −6.19226 −0.204264 −0.102132 0.994771i \(-0.532566\pi\)
−0.102132 + 0.994771i \(0.532566\pi\)
\(920\) 0 0
\(921\) −33.2791 −1.09658
\(922\) 0 0
\(923\) −1.79431 −0.0590604
\(924\) 0 0
\(925\) −7.71028 −0.253512
\(926\) 0 0
\(927\) −10.1898 −0.334676
\(928\) 0 0
\(929\) −36.0820 −1.18381 −0.591906 0.806007i \(-0.701624\pi\)
−0.591906 + 0.806007i \(0.701624\pi\)
\(930\) 0 0
\(931\) 14.9376 0.489560
\(932\) 0 0
\(933\) 14.4700 0.473727
\(934\) 0 0
\(935\) −48.3252 −1.58040
\(936\) 0 0
\(937\) 26.8658 0.877668 0.438834 0.898568i \(-0.355392\pi\)
0.438834 + 0.898568i \(0.355392\pi\)
\(938\) 0 0
\(939\) −22.2012 −0.724508
\(940\) 0 0
\(941\) 26.4271 0.861500 0.430750 0.902471i \(-0.358249\pi\)
0.430750 + 0.902471i \(0.358249\pi\)
\(942\) 0 0
\(943\) 10.2462 0.333661
\(944\) 0 0
\(945\) −7.97926 −0.259565
\(946\) 0 0
\(947\) −35.4368 −1.15154 −0.575770 0.817612i \(-0.695298\pi\)
−0.575770 + 0.817612i \(0.695298\pi\)
\(948\) 0 0
\(949\) 4.25107 0.137996
\(950\) 0 0
\(951\) −6.95963 −0.225682
\(952\) 0 0
\(953\) 13.3955 0.433922 0.216961 0.976180i \(-0.430386\pi\)
0.216961 + 0.976180i \(0.430386\pi\)
\(954\) 0 0
\(955\) 25.0061 0.809177
\(956\) 0 0
\(957\) −12.0079 −0.388161
\(958\) 0 0
\(959\) −24.6265 −0.795232
\(960\) 0 0
\(961\) 25.6086 0.826084
\(962\) 0 0
\(963\) 2.11685 0.0682145
\(964\) 0 0
\(965\) −54.0323 −1.73936
\(966\) 0 0
\(967\) 13.6998 0.440557 0.220278 0.975437i \(-0.429303\pi\)
0.220278 + 0.975437i \(0.429303\pi\)
\(968\) 0 0
\(969\) −9.14723 −0.293851
\(970\) 0 0
\(971\) 20.8360 0.668658 0.334329 0.942457i \(-0.391490\pi\)
0.334329 + 0.942457i \(0.391490\pi\)
\(972\) 0 0
\(973\) 3.09523 0.0992285
\(974\) 0 0
\(975\) 0.264104 0.00845809
\(976\) 0 0
\(977\) 21.2444 0.679668 0.339834 0.940485i \(-0.389629\pi\)
0.339834 + 0.940485i \(0.389629\pi\)
\(978\) 0 0
\(979\) 23.1241 0.739049
\(980\) 0 0
\(981\) −6.58991 −0.210399
\(982\) 0 0
\(983\) 22.2204 0.708720 0.354360 0.935109i \(-0.384699\pi\)
0.354360 + 0.935109i \(0.384699\pi\)
\(984\) 0 0
\(985\) −1.34178 −0.0427528
\(986\) 0 0
\(987\) −17.8452 −0.568017
\(988\) 0 0
\(989\) 5.76355 0.183270
\(990\) 0 0
\(991\) 12.9681 0.411944 0.205972 0.978558i \(-0.433964\pi\)
0.205972 + 0.978558i \(0.433964\pi\)
\(992\) 0 0
\(993\) −13.9114 −0.441465
\(994\) 0 0
\(995\) 15.3050 0.485201
\(996\) 0 0
\(997\) 38.7803 1.22818 0.614092 0.789235i \(-0.289522\pi\)
0.614092 + 0.789235i \(0.289522\pi\)
\(998\) 0 0
\(999\) 9.54315 0.301932
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 \(a_p\))