Properties

Label 308.2.a.b.1.2
Level 308
Weight 2
Character 308.1
Self dual Yes
Analytic conductor 2.459
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 308.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.45939238226\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.44949\)
Character \(\chi\) = 308.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.44949 q^{3} +2.00000 q^{5} -1.00000 q^{7} +3.00000 q^{9} +O(q^{10})\) \(q+2.44949 q^{3} +2.00000 q^{5} -1.00000 q^{7} +3.00000 q^{9} -1.00000 q^{11} -0.449490 q^{13} +4.89898 q^{15} -0.449490 q^{17} -4.89898 q^{19} -2.44949 q^{21} -0.898979 q^{23} -1.00000 q^{25} +2.89898 q^{29} +6.44949 q^{31} -2.44949 q^{33} -2.00000 q^{35} +4.00000 q^{37} -1.10102 q^{39} -9.34847 q^{41} +2.89898 q^{43} +6.00000 q^{45} -6.44949 q^{47} +1.00000 q^{49} -1.10102 q^{51} +9.79796 q^{53} -2.00000 q^{55} -12.0000 q^{57} +7.34847 q^{59} +5.34847 q^{61} -3.00000 q^{63} -0.898979 q^{65} -14.6969 q^{67} -2.20204 q^{69} -12.8990 q^{71} +12.4495 q^{73} -2.44949 q^{75} +1.00000 q^{77} -10.8990 q^{79} -9.00000 q^{81} -16.8990 q^{83} -0.898979 q^{85} +7.10102 q^{87} +6.00000 q^{89} +0.449490 q^{91} +15.7980 q^{93} -9.79796 q^{95} +5.10102 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{5} - 2q^{7} + 6q^{9} + O(q^{10}) \) \( 2q + 4q^{5} - 2q^{7} + 6q^{9} - 2q^{11} + 4q^{13} + 4q^{17} + 8q^{23} - 2q^{25} - 4q^{29} + 8q^{31} - 4q^{35} + 8q^{37} - 12q^{39} - 4q^{41} - 4q^{43} + 12q^{45} - 8q^{47} + 2q^{49} - 12q^{51} - 4q^{55} - 24q^{57} - 4q^{61} - 6q^{63} + 8q^{65} - 24q^{69} - 16q^{71} + 20q^{73} + 2q^{77} - 12q^{79} - 18q^{81} - 24q^{83} + 8q^{85} + 24q^{87} + 12q^{89} - 4q^{91} + 12q^{93} + 20q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 2.44949 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(4\) 0 0
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −0.449490 −0.124666 −0.0623330 0.998055i \(-0.519854\pi\)
−0.0623330 + 0.998055i \(0.519854\pi\)
\(14\) 0 0
\(15\) 4.89898 1.26491
\(16\) 0 0
\(17\) −0.449490 −0.109017 −0.0545086 0.998513i \(-0.517359\pi\)
−0.0545086 + 0.998513i \(0.517359\pi\)
\(18\) 0 0
\(19\) −4.89898 −1.12390 −0.561951 0.827170i \(-0.689949\pi\)
−0.561951 + 0.827170i \(0.689949\pi\)
\(20\) 0 0
\(21\) −2.44949 −0.534522
\(22\) 0 0
\(23\) −0.898979 −0.187450 −0.0937251 0.995598i \(-0.529877\pi\)
−0.0937251 + 0.995598i \(0.529877\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.89898 0.538327 0.269163 0.963095i \(-0.413253\pi\)
0.269163 + 0.963095i \(0.413253\pi\)
\(30\) 0 0
\(31\) 6.44949 1.15836 0.579181 0.815199i \(-0.303372\pi\)
0.579181 + 0.815199i \(0.303372\pi\)
\(32\) 0 0
\(33\) −2.44949 −0.426401
\(34\) 0 0
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) −1.10102 −0.176304
\(40\) 0 0
\(41\) −9.34847 −1.45999 −0.729993 0.683455i \(-0.760477\pi\)
−0.729993 + 0.683455i \(0.760477\pi\)
\(42\) 0 0
\(43\) 2.89898 0.442090 0.221045 0.975264i \(-0.429053\pi\)
0.221045 + 0.975264i \(0.429053\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) 0 0
\(47\) −6.44949 −0.940755 −0.470377 0.882465i \(-0.655882\pi\)
−0.470377 + 0.882465i \(0.655882\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.10102 −0.154174
\(52\) 0 0
\(53\) 9.79796 1.34585 0.672927 0.739709i \(-0.265037\pi\)
0.672927 + 0.739709i \(0.265037\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) 0 0
\(59\) 7.34847 0.956689 0.478345 0.878172i \(-0.341237\pi\)
0.478345 + 0.878172i \(0.341237\pi\)
\(60\) 0 0
\(61\) 5.34847 0.684801 0.342401 0.939554i \(-0.388760\pi\)
0.342401 + 0.939554i \(0.388760\pi\)
\(62\) 0 0
\(63\) −3.00000 −0.377964
\(64\) 0 0
\(65\) −0.898979 −0.111505
\(66\) 0 0
\(67\) −14.6969 −1.79552 −0.897758 0.440488i \(-0.854805\pi\)
−0.897758 + 0.440488i \(0.854805\pi\)
\(68\) 0 0
\(69\) −2.20204 −0.265095
\(70\) 0 0
\(71\) −12.8990 −1.53083 −0.765414 0.643539i \(-0.777466\pi\)
−0.765414 + 0.643539i \(0.777466\pi\)
\(72\) 0 0
\(73\) 12.4495 1.45710 0.728551 0.684991i \(-0.240194\pi\)
0.728551 + 0.684991i \(0.240194\pi\)
\(74\) 0 0
\(75\) −2.44949 −0.282843
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −10.8990 −1.22623 −0.613115 0.789993i \(-0.710084\pi\)
−0.613115 + 0.789993i \(0.710084\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) −16.8990 −1.85490 −0.927452 0.373942i \(-0.878006\pi\)
−0.927452 + 0.373942i \(0.878006\pi\)
\(84\) 0 0
\(85\) −0.898979 −0.0975080
\(86\) 0 0
\(87\) 7.10102 0.761309
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0.449490 0.0471193
\(92\) 0 0
\(93\) 15.7980 1.63817
\(94\) 0 0
\(95\) −9.79796 −1.00525
\(96\) 0 0
\(97\) 5.10102 0.517930 0.258965 0.965887i \(-0.416619\pi\)
0.258965 + 0.965887i \(0.416619\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −8.44949 −0.840756 −0.420378 0.907349i \(-0.638102\pi\)
−0.420378 + 0.907349i \(0.638102\pi\)
\(102\) 0 0
\(103\) 14.4495 1.42375 0.711875 0.702306i \(-0.247846\pi\)
0.711875 + 0.702306i \(0.247846\pi\)
\(104\) 0 0
\(105\) −4.89898 −0.478091
\(106\) 0 0
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) 14.8990 1.42706 0.713532 0.700623i \(-0.247094\pi\)
0.713532 + 0.700623i \(0.247094\pi\)
\(110\) 0 0
\(111\) 9.79796 0.929981
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.79796 −0.167661
\(116\) 0 0
\(117\) −1.34847 −0.124666
\(118\) 0 0
\(119\) 0.449490 0.0412047
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −22.8990 −2.06473
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −1.79796 −0.159543 −0.0797715 0.996813i \(-0.525419\pi\)
−0.0797715 + 0.996813i \(0.525419\pi\)
\(128\) 0 0
\(129\) 7.10102 0.625210
\(130\) 0 0
\(131\) 9.79796 0.856052 0.428026 0.903767i \(-0.359209\pi\)
0.428026 + 0.903767i \(0.359209\pi\)
\(132\) 0 0
\(133\) 4.89898 0.424795
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.79796 0.837096 0.418548 0.908195i \(-0.362539\pi\)
0.418548 + 0.908195i \(0.362539\pi\)
\(138\) 0 0
\(139\) 22.6969 1.92513 0.962565 0.271052i \(-0.0873717\pi\)
0.962565 + 0.271052i \(0.0873717\pi\)
\(140\) 0 0
\(141\) −15.7980 −1.33043
\(142\) 0 0
\(143\) 0.449490 0.0375882
\(144\) 0 0
\(145\) 5.79796 0.481494
\(146\) 0 0
\(147\) 2.44949 0.202031
\(148\) 0 0
\(149\) 11.7980 0.966526 0.483263 0.875475i \(-0.339451\pi\)
0.483263 + 0.875475i \(0.339451\pi\)
\(150\) 0 0
\(151\) 8.69694 0.707747 0.353873 0.935293i \(-0.384864\pi\)
0.353873 + 0.935293i \(0.384864\pi\)
\(152\) 0 0
\(153\) −1.34847 −0.109017
\(154\) 0 0
\(155\) 12.8990 1.03607
\(156\) 0 0
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 0 0
\(159\) 24.0000 1.90332
\(160\) 0 0
\(161\) 0.898979 0.0708495
\(162\) 0 0
\(163\) 8.89898 0.697022 0.348511 0.937305i \(-0.386687\pi\)
0.348511 + 0.937305i \(0.386687\pi\)
\(164\) 0 0
\(165\) −4.89898 −0.381385
\(166\) 0 0
\(167\) 13.7980 1.06772 0.533859 0.845573i \(-0.320741\pi\)
0.533859 + 0.845573i \(0.320741\pi\)
\(168\) 0 0
\(169\) −12.7980 −0.984458
\(170\) 0 0
\(171\) −14.6969 −1.12390
\(172\) 0 0
\(173\) 10.2474 0.779099 0.389550 0.921006i \(-0.372631\pi\)
0.389550 + 0.921006i \(0.372631\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 18.0000 1.35296
\(178\) 0 0
\(179\) −15.5959 −1.16569 −0.582847 0.812582i \(-0.698061\pi\)
−0.582847 + 0.812582i \(0.698061\pi\)
\(180\) 0 0
\(181\) 9.10102 0.676474 0.338237 0.941061i \(-0.390170\pi\)
0.338237 + 0.941061i \(0.390170\pi\)
\(182\) 0 0
\(183\) 13.1010 0.968455
\(184\) 0 0
\(185\) 8.00000 0.588172
\(186\) 0 0
\(187\) 0.449490 0.0328699
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.79796 −0.130096 −0.0650479 0.997882i \(-0.520720\pi\)
−0.0650479 + 0.997882i \(0.520720\pi\)
\(192\) 0 0
\(193\) 21.5959 1.55451 0.777254 0.629187i \(-0.216612\pi\)
0.777254 + 0.629187i \(0.216612\pi\)
\(194\) 0 0
\(195\) −2.20204 −0.157691
\(196\) 0 0
\(197\) −25.5959 −1.82363 −0.911817 0.410597i \(-0.865320\pi\)
−0.911817 + 0.410597i \(0.865320\pi\)
\(198\) 0 0
\(199\) 26.0454 1.84631 0.923155 0.384428i \(-0.125601\pi\)
0.923155 + 0.384428i \(0.125601\pi\)
\(200\) 0 0
\(201\) −36.0000 −2.53924
\(202\) 0 0
\(203\) −2.89898 −0.203468
\(204\) 0 0
\(205\) −18.6969 −1.30585
\(206\) 0 0
\(207\) −2.69694 −0.187450
\(208\) 0 0
\(209\) 4.89898 0.338869
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) −31.5959 −2.16492
\(214\) 0 0
\(215\) 5.79796 0.395418
\(216\) 0 0
\(217\) −6.44949 −0.437820
\(218\) 0 0
\(219\) 30.4949 2.06065
\(220\) 0 0
\(221\) 0.202041 0.0135908
\(222\) 0 0
\(223\) −13.1464 −0.880350 −0.440175 0.897912i \(-0.645084\pi\)
−0.440175 + 0.897912i \(0.645084\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) 1.79796 0.119335 0.0596674 0.998218i \(-0.480996\pi\)
0.0596674 + 0.998218i \(0.480996\pi\)
\(228\) 0 0
\(229\) −5.10102 −0.337085 −0.168542 0.985694i \(-0.553906\pi\)
−0.168542 + 0.985694i \(0.553906\pi\)
\(230\) 0 0
\(231\) 2.44949 0.161165
\(232\) 0 0
\(233\) −1.10102 −0.0721303 −0.0360651 0.999349i \(-0.511482\pi\)
−0.0360651 + 0.999349i \(0.511482\pi\)
\(234\) 0 0
\(235\) −12.8990 −0.841437
\(236\) 0 0
\(237\) −26.6969 −1.73415
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −1.34847 −0.0868625 −0.0434313 0.999056i \(-0.513829\pi\)
−0.0434313 + 0.999056i \(0.513829\pi\)
\(242\) 0 0
\(243\) −22.0454 −1.41421
\(244\) 0 0
\(245\) 2.00000 0.127775
\(246\) 0 0
\(247\) 2.20204 0.140113
\(248\) 0 0
\(249\) −41.3939 −2.62323
\(250\) 0 0
\(251\) 2.44949 0.154610 0.0773052 0.997007i \(-0.475368\pi\)
0.0773052 + 0.997007i \(0.475368\pi\)
\(252\) 0 0
\(253\) 0.898979 0.0565184
\(254\) 0 0
\(255\) −2.20204 −0.137897
\(256\) 0 0
\(257\) −3.79796 −0.236910 −0.118455 0.992959i \(-0.537794\pi\)
−0.118455 + 0.992959i \(0.537794\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) 8.69694 0.538327
\(262\) 0 0
\(263\) 19.5959 1.20834 0.604168 0.796857i \(-0.293506\pi\)
0.604168 + 0.796857i \(0.293506\pi\)
\(264\) 0 0
\(265\) 19.5959 1.20377
\(266\) 0 0
\(267\) 14.6969 0.899438
\(268\) 0 0
\(269\) −13.1010 −0.798783 −0.399392 0.916780i \(-0.630779\pi\)
−0.399392 + 0.916780i \(0.630779\pi\)
\(270\) 0 0
\(271\) 1.30306 0.0791554 0.0395777 0.999216i \(-0.487399\pi\)
0.0395777 + 0.999216i \(0.487399\pi\)
\(272\) 0 0
\(273\) 1.10102 0.0666368
\(274\) 0 0
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 15.7980 0.949207 0.474604 0.880200i \(-0.342591\pi\)
0.474604 + 0.880200i \(0.342591\pi\)
\(278\) 0 0
\(279\) 19.3485 1.15836
\(280\) 0 0
\(281\) −5.10102 −0.304301 −0.152151 0.988357i \(-0.548620\pi\)
−0.152151 + 0.988357i \(0.548620\pi\)
\(282\) 0 0
\(283\) −24.0000 −1.42665 −0.713326 0.700832i \(-0.752812\pi\)
−0.713326 + 0.700832i \(0.752812\pi\)
\(284\) 0 0
\(285\) −24.0000 −1.42164
\(286\) 0 0
\(287\) 9.34847 0.551823
\(288\) 0 0
\(289\) −16.7980 −0.988115
\(290\) 0 0
\(291\) 12.4949 0.732464
\(292\) 0 0
\(293\) −10.6515 −0.622269 −0.311135 0.950366i \(-0.600709\pi\)
−0.311135 + 0.950366i \(0.600709\pi\)
\(294\) 0 0
\(295\) 14.6969 0.855689
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.404082 0.0233687
\(300\) 0 0
\(301\) −2.89898 −0.167094
\(302\) 0 0
\(303\) −20.6969 −1.18901
\(304\) 0 0
\(305\) 10.6969 0.612505
\(306\) 0 0
\(307\) −1.79796 −0.102615 −0.0513075 0.998683i \(-0.516339\pi\)
−0.0513075 + 0.998683i \(0.516339\pi\)
\(308\) 0 0
\(309\) 35.3939 2.01349
\(310\) 0 0
\(311\) −1.55051 −0.0879214 −0.0439607 0.999033i \(-0.513998\pi\)
−0.0439607 + 0.999033i \(0.513998\pi\)
\(312\) 0 0
\(313\) 5.59592 0.316300 0.158150 0.987415i \(-0.449447\pi\)
0.158150 + 0.987415i \(0.449447\pi\)
\(314\) 0 0
\(315\) −6.00000 −0.338062
\(316\) 0 0
\(317\) −13.5959 −0.763623 −0.381811 0.924240i \(-0.624700\pi\)
−0.381811 + 0.924240i \(0.624700\pi\)
\(318\) 0 0
\(319\) −2.89898 −0.162312
\(320\) 0 0
\(321\) −9.79796 −0.546869
\(322\) 0 0
\(323\) 2.20204 0.122525
\(324\) 0 0
\(325\) 0.449490 0.0249332
\(326\) 0 0
\(327\) 36.4949 2.01817
\(328\) 0 0
\(329\) 6.44949 0.355572
\(330\) 0 0
\(331\) −32.0000 −1.75888 −0.879440 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 0 0
\(333\) 12.0000 0.657596
\(334\) 0 0
\(335\) −29.3939 −1.60596
\(336\) 0 0
\(337\) 20.6969 1.12743 0.563717 0.825968i \(-0.309371\pi\)
0.563717 + 0.825968i \(0.309371\pi\)
\(338\) 0 0
\(339\) −24.4949 −1.33038
\(340\) 0 0
\(341\) −6.44949 −0.349259
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −4.40408 −0.237108
\(346\) 0 0
\(347\) 26.4949 1.42232 0.711160 0.703030i \(-0.248170\pi\)
0.711160 + 0.703030i \(0.248170\pi\)
\(348\) 0 0
\(349\) 1.75255 0.0938119 0.0469060 0.998899i \(-0.485064\pi\)
0.0469060 + 0.998899i \(0.485064\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 25.5959 1.36233 0.681167 0.732128i \(-0.261473\pi\)
0.681167 + 0.732128i \(0.261473\pi\)
\(354\) 0 0
\(355\) −25.7980 −1.36921
\(356\) 0 0
\(357\) 1.10102 0.0582722
\(358\) 0 0
\(359\) −24.6969 −1.30345 −0.651727 0.758453i \(-0.725955\pi\)
−0.651727 + 0.758453i \(0.725955\pi\)
\(360\) 0 0
\(361\) 5.00000 0.263158
\(362\) 0 0
\(363\) 2.44949 0.128565
\(364\) 0 0
\(365\) 24.8990 1.30327
\(366\) 0 0
\(367\) 21.1464 1.10383 0.551917 0.833899i \(-0.313896\pi\)
0.551917 + 0.833899i \(0.313896\pi\)
\(368\) 0 0
\(369\) −28.0454 −1.45999
\(370\) 0 0
\(371\) −9.79796 −0.508685
\(372\) 0 0
\(373\) 4.20204 0.217573 0.108787 0.994065i \(-0.465303\pi\)
0.108787 + 0.994065i \(0.465303\pi\)
\(374\) 0 0
\(375\) −29.3939 −1.51789
\(376\) 0 0
\(377\) −1.30306 −0.0671111
\(378\) 0 0
\(379\) −3.10102 −0.159289 −0.0796444 0.996823i \(-0.525378\pi\)
−0.0796444 + 0.996823i \(0.525378\pi\)
\(380\) 0 0
\(381\) −4.40408 −0.225628
\(382\) 0 0
\(383\) 27.3485 1.39744 0.698721 0.715395i \(-0.253753\pi\)
0.698721 + 0.715395i \(0.253753\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) 0 0
\(387\) 8.69694 0.442090
\(388\) 0 0
\(389\) −13.5959 −0.689340 −0.344670 0.938724i \(-0.612009\pi\)
−0.344670 + 0.938724i \(0.612009\pi\)
\(390\) 0 0
\(391\) 0.404082 0.0204353
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 0 0
\(395\) −21.7980 −1.09677
\(396\) 0 0
\(397\) −25.5959 −1.28462 −0.642311 0.766444i \(-0.722024\pi\)
−0.642311 + 0.766444i \(0.722024\pi\)
\(398\) 0 0
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) −27.7980 −1.38816 −0.694082 0.719896i \(-0.744189\pi\)
−0.694082 + 0.719896i \(0.744189\pi\)
\(402\) 0 0
\(403\) −2.89898 −0.144408
\(404\) 0 0
\(405\) −18.0000 −0.894427
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −11.5505 −0.571136 −0.285568 0.958358i \(-0.592182\pi\)
−0.285568 + 0.958358i \(0.592182\pi\)
\(410\) 0 0
\(411\) 24.0000 1.18383
\(412\) 0 0
\(413\) −7.34847 −0.361595
\(414\) 0 0
\(415\) −33.7980 −1.65908
\(416\) 0 0
\(417\) 55.5959 2.72254
\(418\) 0 0
\(419\) 18.4495 0.901317 0.450658 0.892697i \(-0.351189\pi\)
0.450658 + 0.892697i \(0.351189\pi\)
\(420\) 0 0
\(421\) −5.79796 −0.282575 −0.141288 0.989969i \(-0.545124\pi\)
−0.141288 + 0.989969i \(0.545124\pi\)
\(422\) 0 0
\(423\) −19.3485 −0.940755
\(424\) 0 0
\(425\) 0.449490 0.0218035
\(426\) 0 0
\(427\) −5.34847 −0.258831
\(428\) 0 0
\(429\) 1.10102 0.0531578
\(430\) 0 0
\(431\) −9.10102 −0.438381 −0.219190 0.975682i \(-0.570342\pi\)
−0.219190 + 0.975682i \(0.570342\pi\)
\(432\) 0 0
\(433\) 21.1010 1.01405 0.507025 0.861931i \(-0.330745\pi\)
0.507025 + 0.861931i \(0.330745\pi\)
\(434\) 0 0
\(435\) 14.2020 0.680936
\(436\) 0 0
\(437\) 4.40408 0.210676
\(438\) 0 0
\(439\) −24.8990 −1.18836 −0.594182 0.804331i \(-0.702524\pi\)
−0.594182 + 0.804331i \(0.702524\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 0 0
\(445\) 12.0000 0.568855
\(446\) 0 0
\(447\) 28.8990 1.36687
\(448\) 0 0
\(449\) 19.5959 0.924789 0.462394 0.886674i \(-0.346990\pi\)
0.462394 + 0.886674i \(0.346990\pi\)
\(450\) 0 0
\(451\) 9.34847 0.440202
\(452\) 0 0
\(453\) 21.3031 1.00091
\(454\) 0 0
\(455\) 0.898979 0.0421448
\(456\) 0 0
\(457\) 19.3939 0.907207 0.453604 0.891204i \(-0.350138\pi\)
0.453604 + 0.891204i \(0.350138\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −37.3485 −1.73949 −0.869746 0.493500i \(-0.835717\pi\)
−0.869746 + 0.493500i \(0.835717\pi\)
\(462\) 0 0
\(463\) −24.8990 −1.15715 −0.578577 0.815628i \(-0.696392\pi\)
−0.578577 + 0.815628i \(0.696392\pi\)
\(464\) 0 0
\(465\) 31.5959 1.46523
\(466\) 0 0
\(467\) 7.34847 0.340047 0.170023 0.985440i \(-0.445616\pi\)
0.170023 + 0.985440i \(0.445616\pi\)
\(468\) 0 0
\(469\) 14.6969 0.678642
\(470\) 0 0
\(471\) 24.4949 1.12867
\(472\) 0 0
\(473\) −2.89898 −0.133295
\(474\) 0 0
\(475\) 4.89898 0.224781
\(476\) 0 0
\(477\) 29.3939 1.34585
\(478\) 0 0
\(479\) 0.898979 0.0410754 0.0205377 0.999789i \(-0.493462\pi\)
0.0205377 + 0.999789i \(0.493462\pi\)
\(480\) 0 0
\(481\) −1.79796 −0.0819799
\(482\) 0 0
\(483\) 2.20204 0.100196
\(484\) 0 0
\(485\) 10.2020 0.463251
\(486\) 0 0
\(487\) 36.8990 1.67205 0.836026 0.548690i \(-0.184873\pi\)
0.836026 + 0.548690i \(0.184873\pi\)
\(488\) 0 0
\(489\) 21.7980 0.985738
\(490\) 0 0
\(491\) 32.6969 1.47559 0.737796 0.675024i \(-0.235867\pi\)
0.737796 + 0.675024i \(0.235867\pi\)
\(492\) 0 0
\(493\) −1.30306 −0.0586869
\(494\) 0 0
\(495\) −6.00000 −0.269680
\(496\) 0 0
\(497\) 12.8990 0.578598
\(498\) 0 0
\(499\) −42.6969 −1.91138 −0.955689 0.294379i \(-0.904887\pi\)
−0.955689 + 0.294379i \(0.904887\pi\)
\(500\) 0 0
\(501\) 33.7980 1.50998
\(502\) 0 0
\(503\) −24.4949 −1.09217 −0.546087 0.837729i \(-0.683883\pi\)
−0.546087 + 0.837729i \(0.683883\pi\)
\(504\) 0 0
\(505\) −16.8990 −0.751995
\(506\) 0 0
\(507\) −31.3485 −1.39223
\(508\) 0 0
\(509\) −24.6969 −1.09467 −0.547336 0.836913i \(-0.684358\pi\)
−0.547336 + 0.836913i \(0.684358\pi\)
\(510\) 0 0
\(511\) −12.4495 −0.550733
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 28.8990 1.27344
\(516\) 0 0
\(517\) 6.44949 0.283648
\(518\) 0 0
\(519\) 25.1010 1.10181
\(520\) 0 0
\(521\) −9.10102 −0.398723 −0.199361 0.979926i \(-0.563887\pi\)
−0.199361 + 0.979926i \(0.563887\pi\)
\(522\) 0 0
\(523\) 25.3939 1.11040 0.555198 0.831718i \(-0.312642\pi\)
0.555198 + 0.831718i \(0.312642\pi\)
\(524\) 0 0
\(525\) 2.44949 0.106904
\(526\) 0 0
\(527\) −2.89898 −0.126282
\(528\) 0 0
\(529\) −22.1918 −0.964862
\(530\) 0 0
\(531\) 22.0454 0.956689
\(532\) 0 0
\(533\) 4.20204 0.182011
\(534\) 0 0
\(535\) −8.00000 −0.345870
\(536\) 0 0
\(537\) −38.2020 −1.64854
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −17.5959 −0.756508 −0.378254 0.925702i \(-0.623475\pi\)
−0.378254 + 0.925702i \(0.623475\pi\)
\(542\) 0 0
\(543\) 22.2929 0.956678
\(544\) 0 0
\(545\) 29.7980 1.27640
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) 16.0454 0.684801
\(550\) 0 0
\(551\) −14.2020 −0.605027
\(552\) 0 0
\(553\) 10.8990 0.463472
\(554\) 0 0
\(555\) 19.5959 0.831800
\(556\) 0 0
\(557\) −43.7980 −1.85578 −0.927890 0.372855i \(-0.878379\pi\)
−0.927890 + 0.372855i \(0.878379\pi\)
\(558\) 0 0
\(559\) −1.30306 −0.0551136
\(560\) 0 0
\(561\) 1.10102 0.0464851
\(562\) 0 0
\(563\) −26.2929 −1.10811 −0.554056 0.832479i \(-0.686921\pi\)
−0.554056 + 0.832479i \(0.686921\pi\)
\(564\) 0 0
\(565\) −20.0000 −0.841406
\(566\) 0 0
\(567\) 9.00000 0.377964
\(568\) 0 0
\(569\) −8.69694 −0.364595 −0.182297 0.983243i \(-0.558353\pi\)
−0.182297 + 0.983243i \(0.558353\pi\)
\(570\) 0 0
\(571\) −10.2020 −0.426942 −0.213471 0.976949i \(-0.568477\pi\)
−0.213471 + 0.976949i \(0.568477\pi\)
\(572\) 0 0
\(573\) −4.40408 −0.183983
\(574\) 0 0
\(575\) 0.898979 0.0374900
\(576\) 0 0
\(577\) −22.4949 −0.936475 −0.468237 0.883603i \(-0.655111\pi\)
−0.468237 + 0.883603i \(0.655111\pi\)
\(578\) 0 0
\(579\) 52.8990 2.19841
\(580\) 0 0
\(581\) 16.8990 0.701088
\(582\) 0 0
\(583\) −9.79796 −0.405790
\(584\) 0 0
\(585\) −2.69694 −0.111505
\(586\) 0 0
\(587\) 21.5505 0.889485 0.444742 0.895659i \(-0.353295\pi\)
0.444742 + 0.895659i \(0.353295\pi\)
\(588\) 0 0
\(589\) −31.5959 −1.30189
\(590\) 0 0
\(591\) −62.6969 −2.57901
\(592\) 0 0
\(593\) −0.853572 −0.0350520 −0.0175260 0.999846i \(-0.505579\pi\)
−0.0175260 + 0.999846i \(0.505579\pi\)
\(594\) 0 0
\(595\) 0.898979 0.0368546
\(596\) 0 0
\(597\) 63.7980 2.61108
\(598\) 0 0
\(599\) −7.10102 −0.290140 −0.145070 0.989421i \(-0.546341\pi\)
−0.145070 + 0.989421i \(0.546341\pi\)
\(600\) 0 0
\(601\) 6.65153 0.271322 0.135661 0.990755i \(-0.456684\pi\)
0.135661 + 0.990755i \(0.456684\pi\)
\(602\) 0 0
\(603\) −44.0908 −1.79552
\(604\) 0 0
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) 15.5959 0.633019 0.316509 0.948589i \(-0.397489\pi\)
0.316509 + 0.948589i \(0.397489\pi\)
\(608\) 0 0
\(609\) −7.10102 −0.287748
\(610\) 0 0
\(611\) 2.89898 0.117280
\(612\) 0 0
\(613\) −16.6969 −0.674383 −0.337191 0.941436i \(-0.609477\pi\)
−0.337191 + 0.941436i \(0.609477\pi\)
\(614\) 0 0
\(615\) −45.7980 −1.84675
\(616\) 0 0
\(617\) −29.3939 −1.18335 −0.591676 0.806176i \(-0.701534\pi\)
−0.591676 + 0.806176i \(0.701534\pi\)
\(618\) 0 0
\(619\) 5.55051 0.223094 0.111547 0.993759i \(-0.464419\pi\)
0.111547 + 0.993759i \(0.464419\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 12.0000 0.479234
\(628\) 0 0
\(629\) −1.79796 −0.0716893
\(630\) 0 0
\(631\) −2.20204 −0.0876619 −0.0438309 0.999039i \(-0.513956\pi\)
−0.0438309 + 0.999039i \(0.513956\pi\)
\(632\) 0 0
\(633\) −48.9898 −1.94717
\(634\) 0 0
\(635\) −3.59592 −0.142700
\(636\) 0 0
\(637\) −0.449490 −0.0178094
\(638\) 0 0
\(639\) −38.6969 −1.53083
\(640\) 0 0
\(641\) −7.59592 −0.300021 −0.150010 0.988684i \(-0.547931\pi\)
−0.150010 + 0.988684i \(0.547931\pi\)
\(642\) 0 0
\(643\) 4.24745 0.167503 0.0837515 0.996487i \(-0.473310\pi\)
0.0837515 + 0.996487i \(0.473310\pi\)
\(644\) 0 0
\(645\) 14.2020 0.559205
\(646\) 0 0
\(647\) 0.247449 0.00972821 0.00486411 0.999988i \(-0.498452\pi\)
0.00486411 + 0.999988i \(0.498452\pi\)
\(648\) 0 0
\(649\) −7.34847 −0.288453
\(650\) 0 0
\(651\) −15.7980 −0.619171
\(652\) 0 0
\(653\) 15.3939 0.602409 0.301204 0.953560i \(-0.402611\pi\)
0.301204 + 0.953560i \(0.402611\pi\)
\(654\) 0 0
\(655\) 19.5959 0.765676
\(656\) 0 0
\(657\) 37.3485 1.45710
\(658\) 0 0
\(659\) 5.10102 0.198708 0.0993538 0.995052i \(-0.468322\pi\)
0.0993538 + 0.995052i \(0.468322\pi\)
\(660\) 0 0
\(661\) −29.5959 −1.15115 −0.575574 0.817750i \(-0.695221\pi\)
−0.575574 + 0.817750i \(0.695221\pi\)
\(662\) 0 0
\(663\) 0.494897 0.0192202
\(664\) 0 0
\(665\) 9.79796 0.379949
\(666\) 0 0
\(667\) −2.60612 −0.100909
\(668\) 0 0
\(669\) −32.2020 −1.24500
\(670\) 0 0
\(671\) −5.34847 −0.206475
\(672\) 0 0
\(673\) 7.30306 0.281512 0.140756 0.990044i \(-0.455047\pi\)
0.140756 + 0.990044i \(0.455047\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 28.9444 1.11242 0.556212 0.831041i \(-0.312254\pi\)
0.556212 + 0.831041i \(0.312254\pi\)
\(678\) 0 0
\(679\) −5.10102 −0.195759
\(680\) 0 0
\(681\) 4.40408 0.168765
\(682\) 0 0
\(683\) −26.2020 −1.00259 −0.501297 0.865276i \(-0.667143\pi\)
−0.501297 + 0.865276i \(0.667143\pi\)
\(684\) 0 0
\(685\) 19.5959 0.748722
\(686\) 0 0
\(687\) −12.4949 −0.476710
\(688\) 0 0
\(689\) −4.40408 −0.167782
\(690\) 0 0
\(691\) −41.1464 −1.56528 −0.782642 0.622472i \(-0.786128\pi\)
−0.782642 + 0.622472i \(0.786128\pi\)
\(692\) 0 0
\(693\) 3.00000 0.113961
\(694\) 0 0
\(695\) 45.3939 1.72189
\(696\) 0 0
\(697\) 4.20204 0.159164
\(698\) 0 0
\(699\) −2.69694 −0.102008
\(700\) 0 0
\(701\) −20.6969 −0.781713 −0.390856 0.920452i \(-0.627821\pi\)
−0.390856 + 0.920452i \(0.627821\pi\)
\(702\) 0 0
\(703\) −19.5959 −0.739074
\(704\) 0 0
\(705\) −31.5959 −1.18997
\(706\) 0 0
\(707\) 8.44949 0.317776
\(708\) 0 0
\(709\) 3.79796 0.142635 0.0713177 0.997454i \(-0.477280\pi\)
0.0713177 + 0.997454i \(0.477280\pi\)
\(710\) 0 0
\(711\) −32.6969 −1.22623
\(712\) 0 0
\(713\) −5.79796 −0.217135
\(714\) 0 0
\(715\) 0.898979 0.0336199
\(716\) 0 0
\(717\) 39.1918 1.46365
\(718\) 0 0
\(719\) 45.1464 1.68368 0.841839 0.539729i \(-0.181473\pi\)
0.841839 + 0.539729i \(0.181473\pi\)
\(720\) 0 0
\(721\) −14.4495 −0.538127
\(722\) 0 0
\(723\) −3.30306 −0.122842
\(724\) 0 0
\(725\) −2.89898 −0.107665
\(726\) 0 0
\(727\) −1.55051 −0.0575052 −0.0287526 0.999587i \(-0.509154\pi\)
−0.0287526 + 0.999587i \(0.509154\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −1.30306 −0.0481955
\(732\) 0 0
\(733\) 45.3485 1.67498 0.837492 0.546450i \(-0.184021\pi\)
0.837492 + 0.546450i \(0.184021\pi\)
\(734\) 0 0
\(735\) 4.89898 0.180702
\(736\) 0 0
\(737\) 14.6969 0.541369
\(738\) 0 0
\(739\) −41.3939 −1.52270 −0.761349 0.648342i \(-0.775463\pi\)
−0.761349 + 0.648342i \(0.775463\pi\)
\(740\) 0 0
\(741\) 5.39388 0.198149
\(742\) 0 0
\(743\) −19.5959 −0.718905 −0.359452 0.933163i \(-0.617036\pi\)
−0.359452 + 0.933163i \(0.617036\pi\)
\(744\) 0 0
\(745\) 23.5959 0.864488
\(746\) 0 0
\(747\) −50.6969 −1.85490
\(748\) 0 0
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) −12.8990 −0.470690 −0.235345 0.971912i \(-0.575622\pi\)
−0.235345 + 0.971912i \(0.575622\pi\)
\(752\) 0 0
\(753\) 6.00000 0.218652
\(754\) 0 0
\(755\) 17.3939 0.633028
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 2.20204 0.0799290
\(760\) 0 0
\(761\) 49.8434 1.80682 0.903410 0.428777i \(-0.141055\pi\)
0.903410 + 0.428777i \(0.141055\pi\)
\(762\) 0 0
\(763\) −14.8990 −0.539379
\(764\) 0 0
\(765\) −2.69694 −0.0975080
\(766\) 0 0
\(767\) −3.30306 −0.119267
\(768\) 0 0
\(769\) 39.1464 1.41166 0.705828 0.708383i \(-0.250575\pi\)
0.705828 + 0.708383i \(0.250575\pi\)
\(770\) 0 0
\(771\) −9.30306 −0.335042
\(772\) 0 0
\(773\) 3.30306 0.118803 0.0594014 0.998234i \(-0.481081\pi\)
0.0594014 + 0.998234i \(0.481081\pi\)
\(774\) 0 0
\(775\) −6.44949 −0.231673
\(776\) 0 0
\(777\) −9.79796 −0.351500
\(778\) 0 0
\(779\) 45.7980 1.64088
\(780\) 0 0
\(781\) 12.8990 0.461562
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 20.0000 0.713831
\(786\) 0 0
\(787\) 10.6969 0.381305 0.190652 0.981658i \(-0.438940\pi\)
0.190652 + 0.981658i \(0.438940\pi\)
\(788\) 0 0
\(789\) 48.0000 1.70885
\(790\) 0 0
\(791\) 10.0000 0.355559
\(792\) 0 0
\(793\) −2.40408 −0.0853715
\(794\) 0 0
\(795\) 48.0000 1.70238
\(796\) 0 0
\(797\) −31.7980 −1.12634 −0.563171 0.826341i \(-0.690419\pi\)
−0.563171 + 0.826341i \(0.690419\pi\)
\(798\) 0 0
\(799\) 2.89898 0.102559
\(800\) 0 0
\(801\) 18.0000 0.635999
\(802\) 0 0
\(803\) −12.4495 −0.439333
\(804\) 0 0
\(805\) 1.79796 0.0633697
\(806\) 0 0
\(807\) −32.0908 −1.12965
\(808\) 0 0
\(809\) −25.5959 −0.899905 −0.449952 0.893053i \(-0.648559\pi\)
−0.449952 + 0.893053i \(0.648559\pi\)
\(810\) 0 0
\(811\) −23.5959 −0.828565 −0.414282 0.910148i \(-0.635967\pi\)
−0.414282 + 0.910148i \(0.635967\pi\)
\(812\) 0 0
\(813\) 3.19184 0.111943
\(814\) 0 0
\(815\) 17.7980 0.623435
\(816\) 0 0
\(817\) −14.2020 −0.496867
\(818\) 0 0
\(819\) 1.34847 0.0471193
\(820\) 0 0
\(821\) −15.7980 −0.551353 −0.275676 0.961251i \(-0.588902\pi\)
−0.275676 + 0.961251i \(0.588902\pi\)
\(822\) 0 0
\(823\) 35.1918 1.22671 0.613355 0.789807i \(-0.289819\pi\)
0.613355 + 0.789807i \(0.289819\pi\)
\(824\) 0 0
\(825\) 2.44949 0.0852803
\(826\) 0 0
\(827\) 52.6969 1.83245 0.916226 0.400662i \(-0.131220\pi\)
0.916226 + 0.400662i \(0.131220\pi\)
\(828\) 0 0
\(829\) −14.0000 −0.486240 −0.243120 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 0 0
\(831\) 38.6969 1.34238
\(832\) 0 0
\(833\) −0.449490 −0.0155739
\(834\) 0 0
\(835\) 27.5959 0.954996
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9.55051 0.329720 0.164860 0.986317i \(-0.447283\pi\)
0.164860 + 0.986317i \(0.447283\pi\)
\(840\) 0 0
\(841\) −20.5959 −0.710204
\(842\) 0 0
\(843\) −12.4949 −0.430347
\(844\) 0 0
\(845\) −25.5959 −0.880526
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −58.7878 −2.01759
\(850\) 0 0
\(851\) −3.59592 −0.123266
\(852\) 0 0
\(853\) 43.1464 1.47731 0.738653 0.674086i \(-0.235462\pi\)
0.738653 + 0.674086i \(0.235462\pi\)
\(854\) 0 0
\(855\) −29.3939 −1.00525
\(856\) 0 0
\(857\) 8.85357 0.302432 0.151216 0.988501i \(-0.451681\pi\)
0.151216 + 0.988501i \(0.451681\pi\)
\(858\) 0 0
\(859\) 23.8434 0.813525 0.406763 0.913534i \(-0.366658\pi\)
0.406763 + 0.913534i \(0.366658\pi\)
\(860\) 0 0
\(861\) 22.8990 0.780395
\(862\) 0 0
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 0 0
\(865\) 20.4949 0.696847
\(866\) 0 0
\(867\) −41.1464 −1.39741
\(868\) 0 0
\(869\) 10.8990 0.369723
\(870\) 0 0
\(871\) 6.60612 0.223840
\(872\) 0 0
\(873\) 15.3031 0.517930
\(874\) 0 0
\(875\) 12.0000 0.405674
\(876\) 0 0
\(877\) 36.6969 1.23917 0.619584 0.784931i \(-0.287301\pi\)
0.619584 + 0.784931i \(0.287301\pi\)
\(878\) 0 0
\(879\) −26.0908 −0.880021
\(880\) 0 0
\(881\) −20.6969 −0.697298 −0.348649 0.937253i \(-0.613359\pi\)
−0.348649 + 0.937253i \(0.613359\pi\)
\(882\) 0 0
\(883\) −29.7980 −1.00278 −0.501391 0.865221i \(-0.667178\pi\)
−0.501391 + 0.865221i \(0.667178\pi\)
\(884\) 0 0
\(885\) 36.0000 1.21013
\(886\) 0 0
\(887\) −30.2929 −1.01713 −0.508567 0.861022i \(-0.669825\pi\)
−0.508567 + 0.861022i \(0.669825\pi\)
\(888\) 0 0
\(889\) 1.79796 0.0603016
\(890\) 0 0
\(891\) 9.00000 0.301511
\(892\) 0 0
\(893\) 31.5959 1.05732
\(894\) 0 0
\(895\) −31.1918 −1.04263
\(896\) 0 0
\(897\) 0.989795 0.0330483
\(898\) 0 0
\(899\) 18.6969 0.623578
\(900\) 0 0
\(901\) −4.40408 −0.146721
\(902\) 0 0
\(903\) −7.10102 −0.236307
\(904\) 0 0
\(905\) 18.2020 0.605056
\(906\) 0 0
\(907\) 3.10102 0.102968 0.0514838 0.998674i \(-0.483605\pi\)
0.0514838 + 0.998674i \(0.483605\pi\)
\(908\) 0 0
\(909\) −25.3485 −0.840756
\(910\) 0 0
\(911\) 36.4949 1.20913 0.604565 0.796556i \(-0.293347\pi\)
0.604565 + 0.796556i \(0.293347\pi\)
\(912\) 0 0
\(913\) 16.8990 0.559275
\(914\) 0 0
\(915\) 26.2020 0.866213
\(916\) 0 0
\(917\) −9.79796 −0.323557
\(918\) 0 0
\(919\) 4.40408 0.145277 0.0726386 0.997358i \(-0.476858\pi\)
0.0726386 + 0.997358i \(0.476858\pi\)
\(920\) 0 0
\(921\) −4.40408 −0.145119
\(922\) 0 0
\(923\) 5.79796 0.190842
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 0 0
\(927\) 43.3485 1.42375
\(928\) 0 0
\(929\) −52.2929 −1.71567 −0.857836 0.513923i \(-0.828192\pi\)
−0.857836 + 0.513923i \(0.828192\pi\)
\(930\) 0 0
\(931\) −4.89898 −0.160558
\(932\) 0 0
\(933\) −3.79796 −0.124340
\(934\) 0 0
\(935\) 0.898979 0.0293998
\(936\) 0 0
\(937\) 32.9444 1.07625 0.538123 0.842866i \(-0.319134\pi\)
0.538123 + 0.842866i \(0.319134\pi\)
\(938\) 0 0
\(939\) 13.7071 0.447316
\(940\) 0 0
\(941\) 43.5505 1.41971 0.709853 0.704350i \(-0.248761\pi\)
0.709853 + 0.704350i \(0.248761\pi\)
\(942\) 0 0
\(943\) 8.40408 0.273675
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.404082 0.0131309 0.00656545 0.999978i \(-0.497910\pi\)
0.00656545 + 0.999978i \(0.497910\pi\)
\(948\) 0 0
\(949\) −5.59592 −0.181651
\(950\) 0 0
\(951\) −33.3031 −1.07993
\(952\) 0 0
\(953\) −43.7980 −1.41876 −0.709378 0.704829i \(-0.751024\pi\)
−0.709378 + 0.704829i \(0.751024\pi\)
\(954\) 0 0
\(955\) −3.59592 −0.116361
\(956\) 0 0
\(957\) −7.10102 −0.229543
\(958\) 0 0
\(959\) −9.79796 −0.316393
\(960\) 0 0
\(961\) 10.5959 0.341804
\(962\) 0 0
\(963\) −12.0000 −0.386695
\(964\) 0 0
\(965\) 43.1918 1.39039
\(966\) 0 0
\(967\) −38.8990 −1.25091 −0.625453 0.780262i \(-0.715086\pi\)
−0.625453 + 0.780262i \(0.715086\pi\)
\(968\) 0 0
\(969\) 5.39388 0.173276
\(970\) 0 0
\(971\) −38.0454 −1.22094 −0.610468 0.792041i \(-0.709018\pi\)
−0.610468 + 0.792041i \(0.709018\pi\)
\(972\) 0 0
\(973\) −22.6969 −0.727630
\(974\) 0 0
\(975\) 1.10102 0.0352609
\(976\) 0 0
\(977\) 4.20204 0.134435 0.0672176 0.997738i \(-0.478588\pi\)
0.0672176 + 0.997738i \(0.478588\pi\)
\(978\) 0 0
\(979\) −6.00000 −0.191761
\(980\) 0 0
\(981\) 44.6969 1.42706
\(982\) 0 0
\(983\) 19.3485 0.617120 0.308560 0.951205i \(-0.400153\pi\)
0.308560 + 0.951205i \(0.400153\pi\)
\(984\) 0 0
\(985\) −51.1918 −1.63111
\(986\) 0 0
\(987\) 15.7980 0.502855
\(988\) 0 0
\(989\) −2.60612 −0.0828699
\(990\) 0 0
\(991\) 60.0908 1.90885 0.954424 0.298455i \(-0.0964711\pi\)
0.954424 + 0.298455i \(0.0964711\pi\)
\(992\) 0 0
\(993\) −78.3837 −2.48743
\(994\) 0 0
\(995\) 52.0908 1.65139
\(996\) 0 0
\(997\) −20.9444 −0.663315 −0.331658 0.943400i \(-0.607608\pi\)
−0.331658 + 0.943400i \(0.607608\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))