Properties

Label 8046.2.a.l.1.1
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.73396\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -3.73396 q^{5} -2.62384 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -3.73396 q^{5} -2.62384 q^{7} -1.00000 q^{8} +3.73396 q^{10} +2.14257 q^{11} -0.987139 q^{13} +2.62384 q^{14} +1.00000 q^{16} +5.24725 q^{17} -4.24478 q^{19} -3.73396 q^{20} -2.14257 q^{22} +8.14672 q^{23} +8.94247 q^{25} +0.987139 q^{26} -2.62384 q^{28} -8.43701 q^{29} -5.21821 q^{31} -1.00000 q^{32} -5.24725 q^{34} +9.79733 q^{35} +0.533584 q^{37} +4.24478 q^{38} +3.73396 q^{40} -3.88515 q^{41} +2.54110 q^{43} +2.14257 q^{44} -8.14672 q^{46} -3.35439 q^{47} -0.115449 q^{49} -8.94247 q^{50} -0.987139 q^{52} +2.52043 q^{53} -8.00028 q^{55} +2.62384 q^{56} +8.43701 q^{58} +3.22501 q^{59} -8.02184 q^{61} +5.21821 q^{62} +1.00000 q^{64} +3.68594 q^{65} +0.811742 q^{67} +5.24725 q^{68} -9.79733 q^{70} -3.95778 q^{71} -8.88304 q^{73} -0.533584 q^{74} -4.24478 q^{76} -5.62177 q^{77} -14.7166 q^{79} -3.73396 q^{80} +3.88515 q^{82} -6.87510 q^{83} -19.5930 q^{85} -2.54110 q^{86} -2.14257 q^{88} +6.07130 q^{89} +2.59010 q^{91} +8.14672 q^{92} +3.35439 q^{94} +15.8499 q^{95} -1.67775 q^{97} +0.115449 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{2} + 12q^{4} + 5q^{5} - 6q^{7} - 12q^{8} + O(q^{10}) \) \( 12q - 12q^{2} + 12q^{4} + 5q^{5} - 6q^{7} - 12q^{8} - 5q^{10} + 10q^{11} - q^{13} + 6q^{14} + 12q^{16} + 6q^{17} - 10q^{19} + 5q^{20} - 10q^{22} + 15q^{23} + 7q^{25} + q^{26} - 6q^{28} + 33q^{29} - 6q^{31} - 12q^{32} - 6q^{34} + 16q^{35} - 13q^{37} + 10q^{38} - 5q^{40} + 20q^{41} - 11q^{43} + 10q^{44} - 15q^{46} + 15q^{47} + 2q^{49} - 7q^{50} - q^{52} + 4q^{53} - 17q^{55} + 6q^{56} - 33q^{58} + 10q^{59} - 12q^{61} + 6q^{62} + 12q^{64} + 40q^{65} - 19q^{67} + 6q^{68} - 16q^{70} + 47q^{71} - 2q^{73} + 13q^{74} - 10q^{76} - 6q^{77} - 15q^{79} + 5q^{80} - 20q^{82} + 18q^{83} - 25q^{85} + 11q^{86} - 10q^{88} + 24q^{89} - 3q^{91} + 15q^{92} - 15q^{94} - 3q^{95} - 25q^{97} - 2q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −3.73396 −1.66988 −0.834939 0.550342i \(-0.814497\pi\)
−0.834939 + 0.550342i \(0.814497\pi\)
\(6\) 0 0
\(7\) −2.62384 −0.991719 −0.495860 0.868403i \(-0.665147\pi\)
−0.495860 + 0.868403i \(0.665147\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 3.73396 1.18078
\(11\) 2.14257 0.646010 0.323005 0.946397i \(-0.395307\pi\)
0.323005 + 0.946397i \(0.395307\pi\)
\(12\) 0 0
\(13\) −0.987139 −0.273783 −0.136892 0.990586i \(-0.543711\pi\)
−0.136892 + 0.990586i \(0.543711\pi\)
\(14\) 2.62384 0.701251
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.24725 1.27265 0.636323 0.771423i \(-0.280455\pi\)
0.636323 + 0.771423i \(0.280455\pi\)
\(18\) 0 0
\(19\) −4.24478 −0.973820 −0.486910 0.873452i \(-0.661876\pi\)
−0.486910 + 0.873452i \(0.661876\pi\)
\(20\) −3.73396 −0.834939
\(21\) 0 0
\(22\) −2.14257 −0.456798
\(23\) 8.14672 1.69871 0.849354 0.527823i \(-0.176992\pi\)
0.849354 + 0.527823i \(0.176992\pi\)
\(24\) 0 0
\(25\) 8.94247 1.78849
\(26\) 0.987139 0.193594
\(27\) 0 0
\(28\) −2.62384 −0.495860
\(29\) −8.43701 −1.56671 −0.783357 0.621573i \(-0.786494\pi\)
−0.783357 + 0.621573i \(0.786494\pi\)
\(30\) 0 0
\(31\) −5.21821 −0.937218 −0.468609 0.883406i \(-0.655245\pi\)
−0.468609 + 0.883406i \(0.655245\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −5.24725 −0.899896
\(35\) 9.79733 1.65605
\(36\) 0 0
\(37\) 0.533584 0.0877206 0.0438603 0.999038i \(-0.486034\pi\)
0.0438603 + 0.999038i \(0.486034\pi\)
\(38\) 4.24478 0.688594
\(39\) 0 0
\(40\) 3.73396 0.590391
\(41\) −3.88515 −0.606758 −0.303379 0.952870i \(-0.598115\pi\)
−0.303379 + 0.952870i \(0.598115\pi\)
\(42\) 0 0
\(43\) 2.54110 0.387514 0.193757 0.981050i \(-0.437933\pi\)
0.193757 + 0.981050i \(0.437933\pi\)
\(44\) 2.14257 0.323005
\(45\) 0 0
\(46\) −8.14672 −1.20117
\(47\) −3.35439 −0.489288 −0.244644 0.969613i \(-0.578671\pi\)
−0.244644 + 0.969613i \(0.578671\pi\)
\(48\) 0 0
\(49\) −0.115449 −0.0164927
\(50\) −8.94247 −1.26466
\(51\) 0 0
\(52\) −0.987139 −0.136892
\(53\) 2.52043 0.346208 0.173104 0.984904i \(-0.444620\pi\)
0.173104 + 0.984904i \(0.444620\pi\)
\(54\) 0 0
\(55\) −8.00028 −1.07876
\(56\) 2.62384 0.350626
\(57\) 0 0
\(58\) 8.43701 1.10783
\(59\) 3.22501 0.419860 0.209930 0.977716i \(-0.432676\pi\)
0.209930 + 0.977716i \(0.432676\pi\)
\(60\) 0 0
\(61\) −8.02184 −1.02709 −0.513545 0.858062i \(-0.671668\pi\)
−0.513545 + 0.858062i \(0.671668\pi\)
\(62\) 5.21821 0.662713
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.68594 0.457184
\(66\) 0 0
\(67\) 0.811742 0.0991700 0.0495850 0.998770i \(-0.484210\pi\)
0.0495850 + 0.998770i \(0.484210\pi\)
\(68\) 5.24725 0.636323
\(69\) 0 0
\(70\) −9.79733 −1.17100
\(71\) −3.95778 −0.469702 −0.234851 0.972031i \(-0.575460\pi\)
−0.234851 + 0.972031i \(0.575460\pi\)
\(72\) 0 0
\(73\) −8.88304 −1.03968 −0.519841 0.854263i \(-0.674009\pi\)
−0.519841 + 0.854263i \(0.674009\pi\)
\(74\) −0.533584 −0.0620279
\(75\) 0 0
\(76\) −4.24478 −0.486910
\(77\) −5.62177 −0.640660
\(78\) 0 0
\(79\) −14.7166 −1.65575 −0.827873 0.560916i \(-0.810449\pi\)
−0.827873 + 0.560916i \(0.810449\pi\)
\(80\) −3.73396 −0.417470
\(81\) 0 0
\(82\) 3.88515 0.429043
\(83\) −6.87510 −0.754641 −0.377320 0.926083i \(-0.623154\pi\)
−0.377320 + 0.926083i \(0.623154\pi\)
\(84\) 0 0
\(85\) −19.5930 −2.12516
\(86\) −2.54110 −0.274014
\(87\) 0 0
\(88\) −2.14257 −0.228399
\(89\) 6.07130 0.643556 0.321778 0.946815i \(-0.395720\pi\)
0.321778 + 0.946815i \(0.395720\pi\)
\(90\) 0 0
\(91\) 2.59010 0.271516
\(92\) 8.14672 0.849354
\(93\) 0 0
\(94\) 3.35439 0.345979
\(95\) 15.8499 1.62616
\(96\) 0 0
\(97\) −1.67775 −0.170350 −0.0851750 0.996366i \(-0.527145\pi\)
−0.0851750 + 0.996366i \(0.527145\pi\)
\(98\) 0.115449 0.0116621
\(99\) 0 0
\(100\) 8.94247 0.894247
\(101\) 17.2529 1.71673 0.858364 0.513042i \(-0.171481\pi\)
0.858364 + 0.513042i \(0.171481\pi\)
\(102\) 0 0
\(103\) −0.973885 −0.0959597 −0.0479799 0.998848i \(-0.515278\pi\)
−0.0479799 + 0.998848i \(0.515278\pi\)
\(104\) 0.987139 0.0967969
\(105\) 0 0
\(106\) −2.52043 −0.244806
\(107\) 13.1499 1.27125 0.635626 0.771998i \(-0.280742\pi\)
0.635626 + 0.771998i \(0.280742\pi\)
\(108\) 0 0
\(109\) 6.48190 0.620853 0.310427 0.950597i \(-0.399528\pi\)
0.310427 + 0.950597i \(0.399528\pi\)
\(110\) 8.00028 0.762797
\(111\) 0 0
\(112\) −2.62384 −0.247930
\(113\) −9.79815 −0.921733 −0.460866 0.887470i \(-0.652461\pi\)
−0.460866 + 0.887470i \(0.652461\pi\)
\(114\) 0 0
\(115\) −30.4195 −2.83664
\(116\) −8.43701 −0.783357
\(117\) 0 0
\(118\) −3.22501 −0.296886
\(119\) −13.7680 −1.26211
\(120\) 0 0
\(121\) −6.40939 −0.582672
\(122\) 8.02184 0.726263
\(123\) 0 0
\(124\) −5.21821 −0.468609
\(125\) −14.7210 −1.31669
\(126\) 0 0
\(127\) −4.34198 −0.385289 −0.192644 0.981269i \(-0.561706\pi\)
−0.192644 + 0.981269i \(0.561706\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −3.68594 −0.323278
\(131\) 3.82187 0.333919 0.166959 0.985964i \(-0.446605\pi\)
0.166959 + 0.985964i \(0.446605\pi\)
\(132\) 0 0
\(133\) 11.1376 0.965756
\(134\) −0.811742 −0.0701238
\(135\) 0 0
\(136\) −5.24725 −0.449948
\(137\) −11.0978 −0.948148 −0.474074 0.880485i \(-0.657217\pi\)
−0.474074 + 0.880485i \(0.657217\pi\)
\(138\) 0 0
\(139\) 2.47689 0.210087 0.105043 0.994468i \(-0.466502\pi\)
0.105043 + 0.994468i \(0.466502\pi\)
\(140\) 9.79733 0.828025
\(141\) 0 0
\(142\) 3.95778 0.332130
\(143\) −2.11502 −0.176867
\(144\) 0 0
\(145\) 31.5035 2.61622
\(146\) 8.88304 0.735166
\(147\) 0 0
\(148\) 0.533584 0.0438603
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −15.4626 −1.25833 −0.629165 0.777272i \(-0.716603\pi\)
−0.629165 + 0.777272i \(0.716603\pi\)
\(152\) 4.24478 0.344297
\(153\) 0 0
\(154\) 5.62177 0.453015
\(155\) 19.4846 1.56504
\(156\) 0 0
\(157\) −20.0843 −1.60290 −0.801452 0.598060i \(-0.795939\pi\)
−0.801452 + 0.598060i \(0.795939\pi\)
\(158\) 14.7166 1.17079
\(159\) 0 0
\(160\) 3.73396 0.295196
\(161\) −21.3757 −1.68464
\(162\) 0 0
\(163\) −6.48075 −0.507612 −0.253806 0.967255i \(-0.581682\pi\)
−0.253806 + 0.967255i \(0.581682\pi\)
\(164\) −3.88515 −0.303379
\(165\) 0 0
\(166\) 6.87510 0.533612
\(167\) 2.40489 0.186096 0.0930479 0.995662i \(-0.470339\pi\)
0.0930479 + 0.995662i \(0.470339\pi\)
\(168\) 0 0
\(169\) −12.0256 −0.925043
\(170\) 19.5930 1.50272
\(171\) 0 0
\(172\) 2.54110 0.193757
\(173\) −15.9773 −1.21473 −0.607365 0.794423i \(-0.707773\pi\)
−0.607365 + 0.794423i \(0.707773\pi\)
\(174\) 0 0
\(175\) −23.4636 −1.77368
\(176\) 2.14257 0.161502
\(177\) 0 0
\(178\) −6.07130 −0.455063
\(179\) −3.98077 −0.297537 −0.148768 0.988872i \(-0.547531\pi\)
−0.148768 + 0.988872i \(0.547531\pi\)
\(180\) 0 0
\(181\) 19.7064 1.46476 0.732381 0.680895i \(-0.238409\pi\)
0.732381 + 0.680895i \(0.238409\pi\)
\(182\) −2.59010 −0.191991
\(183\) 0 0
\(184\) −8.14672 −0.600584
\(185\) −1.99238 −0.146483
\(186\) 0 0
\(187\) 11.2426 0.822141
\(188\) −3.35439 −0.244644
\(189\) 0 0
\(190\) −15.8499 −1.14987
\(191\) 19.7320 1.42775 0.713877 0.700271i \(-0.246938\pi\)
0.713877 + 0.700271i \(0.246938\pi\)
\(192\) 0 0
\(193\) 8.55331 0.615680 0.307840 0.951438i \(-0.400394\pi\)
0.307840 + 0.951438i \(0.400394\pi\)
\(194\) 1.67775 0.120456
\(195\) 0 0
\(196\) −0.115449 −0.00824636
\(197\) 2.35388 0.167707 0.0838533 0.996478i \(-0.473277\pi\)
0.0838533 + 0.996478i \(0.473277\pi\)
\(198\) 0 0
\(199\) 13.9149 0.986399 0.493200 0.869916i \(-0.335827\pi\)
0.493200 + 0.869916i \(0.335827\pi\)
\(200\) −8.94247 −0.632328
\(201\) 0 0
\(202\) −17.2529 −1.21391
\(203\) 22.1374 1.55374
\(204\) 0 0
\(205\) 14.5070 1.01321
\(206\) 0.973885 0.0678538
\(207\) 0 0
\(208\) −0.987139 −0.0684458
\(209\) −9.09475 −0.629097
\(210\) 0 0
\(211\) 1.13848 0.0783765 0.0391883 0.999232i \(-0.487523\pi\)
0.0391883 + 0.999232i \(0.487523\pi\)
\(212\) 2.52043 0.173104
\(213\) 0 0
\(214\) −13.1499 −0.898910
\(215\) −9.48837 −0.647102
\(216\) 0 0
\(217\) 13.6918 0.929457
\(218\) −6.48190 −0.439009
\(219\) 0 0
\(220\) −8.00028 −0.539379
\(221\) −5.17977 −0.348429
\(222\) 0 0
\(223\) −6.72193 −0.450134 −0.225067 0.974343i \(-0.572260\pi\)
−0.225067 + 0.974343i \(0.572260\pi\)
\(224\) 2.62384 0.175313
\(225\) 0 0
\(226\) 9.79815 0.651763
\(227\) −8.37087 −0.555594 −0.277797 0.960640i \(-0.589604\pi\)
−0.277797 + 0.960640i \(0.589604\pi\)
\(228\) 0 0
\(229\) 9.32680 0.616332 0.308166 0.951333i \(-0.400285\pi\)
0.308166 + 0.951333i \(0.400285\pi\)
\(230\) 30.4195 2.00581
\(231\) 0 0
\(232\) 8.43701 0.553917
\(233\) 10.2941 0.674391 0.337196 0.941435i \(-0.390522\pi\)
0.337196 + 0.941435i \(0.390522\pi\)
\(234\) 0 0
\(235\) 12.5252 0.817051
\(236\) 3.22501 0.209930
\(237\) 0 0
\(238\) 13.7680 0.892445
\(239\) 12.0117 0.776972 0.388486 0.921455i \(-0.372998\pi\)
0.388486 + 0.921455i \(0.372998\pi\)
\(240\) 0 0
\(241\) 24.9677 1.60831 0.804155 0.594420i \(-0.202618\pi\)
0.804155 + 0.594420i \(0.202618\pi\)
\(242\) 6.40939 0.412011
\(243\) 0 0
\(244\) −8.02184 −0.513545
\(245\) 0.431082 0.0275408
\(246\) 0 0
\(247\) 4.19019 0.266615
\(248\) 5.21821 0.331357
\(249\) 0 0
\(250\) 14.7210 0.931039
\(251\) −1.96591 −0.124087 −0.0620436 0.998073i \(-0.519762\pi\)
−0.0620436 + 0.998073i \(0.519762\pi\)
\(252\) 0 0
\(253\) 17.4549 1.09738
\(254\) 4.34198 0.272440
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 22.3723 1.39554 0.697772 0.716320i \(-0.254175\pi\)
0.697772 + 0.716320i \(0.254175\pi\)
\(258\) 0 0
\(259\) −1.40004 −0.0869943
\(260\) 3.68594 0.228592
\(261\) 0 0
\(262\) −3.82187 −0.236116
\(263\) 22.1729 1.36724 0.683619 0.729839i \(-0.260405\pi\)
0.683619 + 0.729839i \(0.260405\pi\)
\(264\) 0 0
\(265\) −9.41119 −0.578125
\(266\) −11.1376 −0.682892
\(267\) 0 0
\(268\) 0.811742 0.0495850
\(269\) −18.7564 −1.14360 −0.571800 0.820393i \(-0.693755\pi\)
−0.571800 + 0.820393i \(0.693755\pi\)
\(270\) 0 0
\(271\) 19.4281 1.18017 0.590086 0.807341i \(-0.299094\pi\)
0.590086 + 0.807341i \(0.299094\pi\)
\(272\) 5.24725 0.318161
\(273\) 0 0
\(274\) 11.0978 0.670442
\(275\) 19.1599 1.15538
\(276\) 0 0
\(277\) −8.65289 −0.519902 −0.259951 0.965622i \(-0.583706\pi\)
−0.259951 + 0.965622i \(0.583706\pi\)
\(278\) −2.47689 −0.148554
\(279\) 0 0
\(280\) −9.79733 −0.585502
\(281\) 6.09541 0.363622 0.181811 0.983334i \(-0.441804\pi\)
0.181811 + 0.983334i \(0.441804\pi\)
\(282\) 0 0
\(283\) −13.5780 −0.807130 −0.403565 0.914951i \(-0.632229\pi\)
−0.403565 + 0.914951i \(0.632229\pi\)
\(284\) −3.95778 −0.234851
\(285\) 0 0
\(286\) 2.11502 0.125064
\(287\) 10.1940 0.601734
\(288\) 0 0
\(289\) 10.5337 0.619627
\(290\) −31.5035 −1.84995
\(291\) 0 0
\(292\) −8.88304 −0.519841
\(293\) −0.488415 −0.0285335 −0.0142668 0.999898i \(-0.504541\pi\)
−0.0142668 + 0.999898i \(0.504541\pi\)
\(294\) 0 0
\(295\) −12.0421 −0.701115
\(296\) −0.533584 −0.0310139
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −8.04195 −0.465078
\(300\) 0 0
\(301\) −6.66745 −0.384305
\(302\) 15.4626 0.889773
\(303\) 0 0
\(304\) −4.24478 −0.243455
\(305\) 29.9532 1.71512
\(306\) 0 0
\(307\) 21.7695 1.24245 0.621224 0.783633i \(-0.286636\pi\)
0.621224 + 0.783633i \(0.286636\pi\)
\(308\) −5.62177 −0.320330
\(309\) 0 0
\(310\) −19.4846 −1.10665
\(311\) −21.0144 −1.19162 −0.595809 0.803126i \(-0.703169\pi\)
−0.595809 + 0.803126i \(0.703169\pi\)
\(312\) 0 0
\(313\) 32.2306 1.82178 0.910890 0.412649i \(-0.135396\pi\)
0.910890 + 0.412649i \(0.135396\pi\)
\(314\) 20.0843 1.13342
\(315\) 0 0
\(316\) −14.7166 −0.827873
\(317\) −21.5139 −1.20834 −0.604171 0.796855i \(-0.706496\pi\)
−0.604171 + 0.796855i \(0.706496\pi\)
\(318\) 0 0
\(319\) −18.0769 −1.01211
\(320\) −3.73396 −0.208735
\(321\) 0 0
\(322\) 21.3757 1.19122
\(323\) −22.2734 −1.23933
\(324\) 0 0
\(325\) −8.82746 −0.489659
\(326\) 6.48075 0.358936
\(327\) 0 0
\(328\) 3.88515 0.214521
\(329\) 8.80139 0.485236
\(330\) 0 0
\(331\) −3.00592 −0.165221 −0.0826103 0.996582i \(-0.526326\pi\)
−0.0826103 + 0.996582i \(0.526326\pi\)
\(332\) −6.87510 −0.377320
\(333\) 0 0
\(334\) −2.40489 −0.131590
\(335\) −3.03101 −0.165602
\(336\) 0 0
\(337\) 27.2897 1.48657 0.743283 0.668977i \(-0.233268\pi\)
0.743283 + 0.668977i \(0.233268\pi\)
\(338\) 12.0256 0.654104
\(339\) 0 0
\(340\) −19.5930 −1.06258
\(341\) −11.1804 −0.605452
\(342\) 0 0
\(343\) 18.6698 1.00808
\(344\) −2.54110 −0.137007
\(345\) 0 0
\(346\) 15.9773 0.858943
\(347\) −19.5990 −1.05213 −0.526064 0.850445i \(-0.676333\pi\)
−0.526064 + 0.850445i \(0.676333\pi\)
\(348\) 0 0
\(349\) −21.6076 −1.15663 −0.578313 0.815815i \(-0.696289\pi\)
−0.578313 + 0.815815i \(0.696289\pi\)
\(350\) 23.4636 1.25418
\(351\) 0 0
\(352\) −2.14257 −0.114199
\(353\) 22.9587 1.22197 0.610985 0.791642i \(-0.290774\pi\)
0.610985 + 0.791642i \(0.290774\pi\)
\(354\) 0 0
\(355\) 14.7782 0.784345
\(356\) 6.07130 0.321778
\(357\) 0 0
\(358\) 3.98077 0.210390
\(359\) −8.06534 −0.425673 −0.212836 0.977088i \(-0.568270\pi\)
−0.212836 + 0.977088i \(0.568270\pi\)
\(360\) 0 0
\(361\) −0.981830 −0.0516752
\(362\) −19.7064 −1.03574
\(363\) 0 0
\(364\) 2.59010 0.135758
\(365\) 33.1689 1.73614
\(366\) 0 0
\(367\) −13.5555 −0.707590 −0.353795 0.935323i \(-0.615109\pi\)
−0.353795 + 0.935323i \(0.615109\pi\)
\(368\) 8.14672 0.424677
\(369\) 0 0
\(370\) 1.99238 0.103579
\(371\) −6.61321 −0.343341
\(372\) 0 0
\(373\) 31.1012 1.61036 0.805180 0.593031i \(-0.202069\pi\)
0.805180 + 0.593031i \(0.202069\pi\)
\(374\) −11.2426 −0.581342
\(375\) 0 0
\(376\) 3.35439 0.172989
\(377\) 8.32850 0.428940
\(378\) 0 0
\(379\) 31.2257 1.60396 0.801979 0.597352i \(-0.203781\pi\)
0.801979 + 0.597352i \(0.203781\pi\)
\(380\) 15.8499 0.813080
\(381\) 0 0
\(382\) −19.7320 −1.00957
\(383\) −2.00824 −0.102616 −0.0513082 0.998683i \(-0.516339\pi\)
−0.0513082 + 0.998683i \(0.516339\pi\)
\(384\) 0 0
\(385\) 20.9915 1.06982
\(386\) −8.55331 −0.435352
\(387\) 0 0
\(388\) −1.67775 −0.0851750
\(389\) −11.1882 −0.567263 −0.283632 0.958933i \(-0.591539\pi\)
−0.283632 + 0.958933i \(0.591539\pi\)
\(390\) 0 0
\(391\) 42.7479 2.16185
\(392\) 0.115449 0.00583106
\(393\) 0 0
\(394\) −2.35388 −0.118587
\(395\) 54.9512 2.76489
\(396\) 0 0
\(397\) 15.7271 0.789320 0.394660 0.918827i \(-0.370862\pi\)
0.394660 + 0.918827i \(0.370862\pi\)
\(398\) −13.9149 −0.697490
\(399\) 0 0
\(400\) 8.94247 0.447123
\(401\) 18.6378 0.930729 0.465365 0.885119i \(-0.345923\pi\)
0.465365 + 0.885119i \(0.345923\pi\)
\(402\) 0 0
\(403\) 5.15110 0.256594
\(404\) 17.2529 0.858364
\(405\) 0 0
\(406\) −22.1374 −1.09866
\(407\) 1.14324 0.0566684
\(408\) 0 0
\(409\) −10.7222 −0.530177 −0.265088 0.964224i \(-0.585401\pi\)
−0.265088 + 0.964224i \(0.585401\pi\)
\(410\) −14.5070 −0.716449
\(411\) 0 0
\(412\) −0.973885 −0.0479799
\(413\) −8.46191 −0.416383
\(414\) 0 0
\(415\) 25.6714 1.26016
\(416\) 0.987139 0.0483985
\(417\) 0 0
\(418\) 9.09475 0.444839
\(419\) 21.0470 1.02821 0.514107 0.857726i \(-0.328123\pi\)
0.514107 + 0.857726i \(0.328123\pi\)
\(420\) 0 0
\(421\) −22.1796 −1.08097 −0.540483 0.841355i \(-0.681758\pi\)
−0.540483 + 0.841355i \(0.681758\pi\)
\(422\) −1.13848 −0.0554206
\(423\) 0 0
\(424\) −2.52043 −0.122403
\(425\) 46.9234 2.27612
\(426\) 0 0
\(427\) 21.0480 1.01859
\(428\) 13.1499 0.635626
\(429\) 0 0
\(430\) 9.48837 0.457570
\(431\) 32.4982 1.56538 0.782691 0.622411i \(-0.213847\pi\)
0.782691 + 0.622411i \(0.213847\pi\)
\(432\) 0 0
\(433\) −2.82924 −0.135965 −0.0679824 0.997687i \(-0.521656\pi\)
−0.0679824 + 0.997687i \(0.521656\pi\)
\(434\) −13.6918 −0.657226
\(435\) 0 0
\(436\) 6.48190 0.310427
\(437\) −34.5811 −1.65424
\(438\) 0 0
\(439\) −11.3455 −0.541489 −0.270744 0.962651i \(-0.587270\pi\)
−0.270744 + 0.962651i \(0.587270\pi\)
\(440\) 8.00028 0.381398
\(441\) 0 0
\(442\) 5.17977 0.246376
\(443\) 23.7537 1.12857 0.564287 0.825578i \(-0.309151\pi\)
0.564287 + 0.825578i \(0.309151\pi\)
\(444\) 0 0
\(445\) −22.6700 −1.07466
\(446\) 6.72193 0.318293
\(447\) 0 0
\(448\) −2.62384 −0.123965
\(449\) 31.7903 1.50028 0.750138 0.661281i \(-0.229987\pi\)
0.750138 + 0.661281i \(0.229987\pi\)
\(450\) 0 0
\(451\) −8.32421 −0.391972
\(452\) −9.79815 −0.460866
\(453\) 0 0
\(454\) 8.37087 0.392864
\(455\) −9.67132 −0.453399
\(456\) 0 0
\(457\) 2.44674 0.114453 0.0572267 0.998361i \(-0.481774\pi\)
0.0572267 + 0.998361i \(0.481774\pi\)
\(458\) −9.32680 −0.435813
\(459\) 0 0
\(460\) −30.4195 −1.41832
\(461\) 6.34903 0.295704 0.147852 0.989009i \(-0.452764\pi\)
0.147852 + 0.989009i \(0.452764\pi\)
\(462\) 0 0
\(463\) 0.408336 0.0189770 0.00948848 0.999955i \(-0.496980\pi\)
0.00948848 + 0.999955i \(0.496980\pi\)
\(464\) −8.43701 −0.391678
\(465\) 0 0
\(466\) −10.2941 −0.476867
\(467\) −4.73896 −0.219293 −0.109646 0.993971i \(-0.534972\pi\)
−0.109646 + 0.993971i \(0.534972\pi\)
\(468\) 0 0
\(469\) −2.12988 −0.0983488
\(470\) −12.5252 −0.577742
\(471\) 0 0
\(472\) −3.22501 −0.148443
\(473\) 5.44449 0.250338
\(474\) 0 0
\(475\) −37.9588 −1.74167
\(476\) −13.7680 −0.631054
\(477\) 0 0
\(478\) −12.0117 −0.549402
\(479\) 13.6810 0.625102 0.312551 0.949901i \(-0.398816\pi\)
0.312551 + 0.949901i \(0.398816\pi\)
\(480\) 0 0
\(481\) −0.526721 −0.0240164
\(482\) −24.9677 −1.13725
\(483\) 0 0
\(484\) −6.40939 −0.291336
\(485\) 6.26467 0.284464
\(486\) 0 0
\(487\) 8.54623 0.387267 0.193633 0.981074i \(-0.437973\pi\)
0.193633 + 0.981074i \(0.437973\pi\)
\(488\) 8.02184 0.363131
\(489\) 0 0
\(490\) −0.431082 −0.0194743
\(491\) −13.4171 −0.605504 −0.302752 0.953069i \(-0.597905\pi\)
−0.302752 + 0.953069i \(0.597905\pi\)
\(492\) 0 0
\(493\) −44.2711 −1.99387
\(494\) −4.19019 −0.188526
\(495\) 0 0
\(496\) −5.21821 −0.234305
\(497\) 10.3846 0.465813
\(498\) 0 0
\(499\) −9.21700 −0.412609 −0.206305 0.978488i \(-0.566144\pi\)
−0.206305 + 0.978488i \(0.566144\pi\)
\(500\) −14.7210 −0.658344
\(501\) 0 0
\(502\) 1.96591 0.0877428
\(503\) −26.3513 −1.17495 −0.587473 0.809244i \(-0.699877\pi\)
−0.587473 + 0.809244i \(0.699877\pi\)
\(504\) 0 0
\(505\) −64.4217 −2.86673
\(506\) −17.4549 −0.775966
\(507\) 0 0
\(508\) −4.34198 −0.192644
\(509\) −44.1347 −1.95623 −0.978117 0.208055i \(-0.933287\pi\)
−0.978117 + 0.208055i \(0.933287\pi\)
\(510\) 0 0
\(511\) 23.3077 1.03107
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −22.3723 −0.986799
\(515\) 3.63645 0.160241
\(516\) 0 0
\(517\) −7.18702 −0.316085
\(518\) 1.40004 0.0615142
\(519\) 0 0
\(520\) −3.68594 −0.161639
\(521\) 28.2207 1.23637 0.618185 0.786033i \(-0.287868\pi\)
0.618185 + 0.786033i \(0.287868\pi\)
\(522\) 0 0
\(523\) 33.9334 1.48380 0.741901 0.670509i \(-0.233924\pi\)
0.741901 + 0.670509i \(0.233924\pi\)
\(524\) 3.82187 0.166959
\(525\) 0 0
\(526\) −22.1729 −0.966784
\(527\) −27.3813 −1.19275
\(528\) 0 0
\(529\) 43.3691 1.88561
\(530\) 9.41119 0.408796
\(531\) 0 0
\(532\) 11.1376 0.482878
\(533\) 3.83518 0.166120
\(534\) 0 0
\(535\) −49.1013 −2.12283
\(536\) −0.811742 −0.0350619
\(537\) 0 0
\(538\) 18.7564 0.808647
\(539\) −0.247358 −0.0106545
\(540\) 0 0
\(541\) 16.7627 0.720686 0.360343 0.932820i \(-0.382660\pi\)
0.360343 + 0.932820i \(0.382660\pi\)
\(542\) −19.4281 −0.834507
\(543\) 0 0
\(544\) −5.24725 −0.224974
\(545\) −24.2032 −1.03675
\(546\) 0 0
\(547\) −14.4259 −0.616809 −0.308404 0.951255i \(-0.599795\pi\)
−0.308404 + 0.951255i \(0.599795\pi\)
\(548\) −11.0978 −0.474074
\(549\) 0 0
\(550\) −19.1599 −0.816980
\(551\) 35.8133 1.52570
\(552\) 0 0
\(553\) 38.6140 1.64203
\(554\) 8.65289 0.367626
\(555\) 0 0
\(556\) 2.47689 0.105043
\(557\) 13.1292 0.556301 0.278150 0.960538i \(-0.410279\pi\)
0.278150 + 0.960538i \(0.410279\pi\)
\(558\) 0 0
\(559\) −2.50842 −0.106095
\(560\) 9.79733 0.414013
\(561\) 0 0
\(562\) −6.09541 −0.257119
\(563\) −45.2408 −1.90667 −0.953336 0.301911i \(-0.902375\pi\)
−0.953336 + 0.301911i \(0.902375\pi\)
\(564\) 0 0
\(565\) 36.5859 1.53918
\(566\) 13.5780 0.570727
\(567\) 0 0
\(568\) 3.95778 0.166065
\(569\) 27.4976 1.15276 0.576379 0.817183i \(-0.304465\pi\)
0.576379 + 0.817183i \(0.304465\pi\)
\(570\) 0 0
\(571\) 21.1168 0.883710 0.441855 0.897086i \(-0.354321\pi\)
0.441855 + 0.897086i \(0.354321\pi\)
\(572\) −2.11502 −0.0884333
\(573\) 0 0
\(574\) −10.1940 −0.425490
\(575\) 72.8518 3.03813
\(576\) 0 0
\(577\) −35.3110 −1.47001 −0.735007 0.678059i \(-0.762821\pi\)
−0.735007 + 0.678059i \(0.762821\pi\)
\(578\) −10.5337 −0.438142
\(579\) 0 0
\(580\) 31.5035 1.30811
\(581\) 18.0392 0.748392
\(582\) 0 0
\(583\) 5.40020 0.223653
\(584\) 8.88304 0.367583
\(585\) 0 0
\(586\) 0.488415 0.0201762
\(587\) −17.4372 −0.719711 −0.359856 0.933008i \(-0.617174\pi\)
−0.359856 + 0.933008i \(0.617174\pi\)
\(588\) 0 0
\(589\) 22.1502 0.912681
\(590\) 12.0421 0.495763
\(591\) 0 0
\(592\) 0.533584 0.0219302
\(593\) 3.88793 0.159658 0.0798291 0.996809i \(-0.474563\pi\)
0.0798291 + 0.996809i \(0.474563\pi\)
\(594\) 0 0
\(595\) 51.4090 2.10757
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) 8.04195 0.328860
\(599\) 47.4089 1.93707 0.968537 0.248868i \(-0.0800587\pi\)
0.968537 + 0.248868i \(0.0800587\pi\)
\(600\) 0 0
\(601\) 35.7611 1.45873 0.729364 0.684126i \(-0.239816\pi\)
0.729364 + 0.684126i \(0.239816\pi\)
\(602\) 6.66745 0.271745
\(603\) 0 0
\(604\) −15.4626 −0.629165
\(605\) 23.9324 0.972991
\(606\) 0 0
\(607\) 17.2471 0.700040 0.350020 0.936742i \(-0.386175\pi\)
0.350020 + 0.936742i \(0.386175\pi\)
\(608\) 4.24478 0.172149
\(609\) 0 0
\(610\) −29.9532 −1.21277
\(611\) 3.31125 0.133959
\(612\) 0 0
\(613\) 2.45411 0.0991206 0.0495603 0.998771i \(-0.484218\pi\)
0.0495603 + 0.998771i \(0.484218\pi\)
\(614\) −21.7695 −0.878544
\(615\) 0 0
\(616\) 5.62177 0.226508
\(617\) −29.8860 −1.20317 −0.601583 0.798811i \(-0.705463\pi\)
−0.601583 + 0.798811i \(0.705463\pi\)
\(618\) 0 0
\(619\) 34.7323 1.39601 0.698005 0.716093i \(-0.254071\pi\)
0.698005 + 0.716093i \(0.254071\pi\)
\(620\) 19.4846 0.782520
\(621\) 0 0
\(622\) 21.0144 0.842601
\(623\) −15.9301 −0.638227
\(624\) 0 0
\(625\) 10.2554 0.410216
\(626\) −32.2306 −1.28819
\(627\) 0 0
\(628\) −20.0843 −0.801452
\(629\) 2.79985 0.111637
\(630\) 0 0
\(631\) −13.6310 −0.542641 −0.271320 0.962489i \(-0.587460\pi\)
−0.271320 + 0.962489i \(0.587460\pi\)
\(632\) 14.7166 0.585394
\(633\) 0 0
\(634\) 21.5139 0.854427
\(635\) 16.2128 0.643385
\(636\) 0 0
\(637\) 0.113964 0.00451543
\(638\) 18.0769 0.715671
\(639\) 0 0
\(640\) 3.73396 0.147598
\(641\) −28.7075 −1.13388 −0.566940 0.823759i \(-0.691873\pi\)
−0.566940 + 0.823759i \(0.691873\pi\)
\(642\) 0 0
\(643\) −12.6062 −0.497142 −0.248571 0.968614i \(-0.579961\pi\)
−0.248571 + 0.968614i \(0.579961\pi\)
\(644\) −21.3757 −0.842321
\(645\) 0 0
\(646\) 22.2734 0.876337
\(647\) −35.2613 −1.38627 −0.693133 0.720809i \(-0.743770\pi\)
−0.693133 + 0.720809i \(0.743770\pi\)
\(648\) 0 0
\(649\) 6.90981 0.271234
\(650\) 8.82746 0.346241
\(651\) 0 0
\(652\) −6.48075 −0.253806
\(653\) −16.8789 −0.660523 −0.330262 0.943889i \(-0.607137\pi\)
−0.330262 + 0.943889i \(0.607137\pi\)
\(654\) 0 0
\(655\) −14.2707 −0.557603
\(656\) −3.88515 −0.151690
\(657\) 0 0
\(658\) −8.80139 −0.343114
\(659\) −0.200950 −0.00782792 −0.00391396 0.999992i \(-0.501246\pi\)
−0.00391396 + 0.999992i \(0.501246\pi\)
\(660\) 0 0
\(661\) −40.1475 −1.56156 −0.780779 0.624808i \(-0.785177\pi\)
−0.780779 + 0.624808i \(0.785177\pi\)
\(662\) 3.00592 0.116829
\(663\) 0 0
\(664\) 6.87510 0.266806
\(665\) −41.5875 −1.61269
\(666\) 0 0
\(667\) −68.7340 −2.66139
\(668\) 2.40489 0.0930479
\(669\) 0 0
\(670\) 3.03101 0.117098
\(671\) −17.1874 −0.663511
\(672\) 0 0
\(673\) 9.22679 0.355667 0.177833 0.984061i \(-0.443091\pi\)
0.177833 + 0.984061i \(0.443091\pi\)
\(674\) −27.2897 −1.05116
\(675\) 0 0
\(676\) −12.0256 −0.462521
\(677\) 20.2690 0.779003 0.389501 0.921026i \(-0.372647\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(678\) 0 0
\(679\) 4.40216 0.168939
\(680\) 19.5930 0.751359
\(681\) 0 0
\(682\) 11.1804 0.428119
\(683\) 8.57482 0.328106 0.164053 0.986451i \(-0.447543\pi\)
0.164053 + 0.986451i \(0.447543\pi\)
\(684\) 0 0
\(685\) 41.4387 1.58329
\(686\) −18.6698 −0.712817
\(687\) 0 0
\(688\) 2.54110 0.0968786
\(689\) −2.48801 −0.0947858
\(690\) 0 0
\(691\) −8.37770 −0.318703 −0.159351 0.987222i \(-0.550940\pi\)
−0.159351 + 0.987222i \(0.550940\pi\)
\(692\) −15.9773 −0.607365
\(693\) 0 0
\(694\) 19.5990 0.743967
\(695\) −9.24860 −0.350820
\(696\) 0 0
\(697\) −20.3864 −0.772188
\(698\) 21.6076 0.817858
\(699\) 0 0
\(700\) −23.4636 −0.886842
\(701\) 7.14154 0.269732 0.134866 0.990864i \(-0.456940\pi\)
0.134866 + 0.990864i \(0.456940\pi\)
\(702\) 0 0
\(703\) −2.26495 −0.0854241
\(704\) 2.14257 0.0807512
\(705\) 0 0
\(706\) −22.9587 −0.864063
\(707\) −45.2689 −1.70251
\(708\) 0 0
\(709\) −0.367596 −0.0138053 −0.00690267 0.999976i \(-0.502197\pi\)
−0.00690267 + 0.999976i \(0.502197\pi\)
\(710\) −14.7782 −0.554616
\(711\) 0 0
\(712\) −6.07130 −0.227531
\(713\) −42.5113 −1.59206
\(714\) 0 0
\(715\) 7.89739 0.295346
\(716\) −3.98077 −0.148768
\(717\) 0 0
\(718\) 8.06534 0.300996
\(719\) −16.1535 −0.602422 −0.301211 0.953557i \(-0.597391\pi\)
−0.301211 + 0.953557i \(0.597391\pi\)
\(720\) 0 0
\(721\) 2.55532 0.0951651
\(722\) 0.981830 0.0365399
\(723\) 0 0
\(724\) 19.7064 0.732381
\(725\) −75.4477 −2.80206
\(726\) 0 0
\(727\) 4.68129 0.173620 0.0868098 0.996225i \(-0.472333\pi\)
0.0868098 + 0.996225i \(0.472333\pi\)
\(728\) −2.59010 −0.0959954
\(729\) 0 0
\(730\) −33.1689 −1.22764
\(731\) 13.3338 0.493168
\(732\) 0 0
\(733\) −18.5648 −0.685706 −0.342853 0.939389i \(-0.611393\pi\)
−0.342853 + 0.939389i \(0.611393\pi\)
\(734\) 13.5555 0.500342
\(735\) 0 0
\(736\) −8.14672 −0.300292
\(737\) 1.73921 0.0640648
\(738\) 0 0
\(739\) 18.1395 0.667273 0.333636 0.942702i \(-0.391724\pi\)
0.333636 + 0.942702i \(0.391724\pi\)
\(740\) −1.99238 −0.0732414
\(741\) 0 0
\(742\) 6.61321 0.242779
\(743\) 46.4016 1.70231 0.851155 0.524915i \(-0.175903\pi\)
0.851155 + 0.524915i \(0.175903\pi\)
\(744\) 0 0
\(745\) −3.73396 −0.136802
\(746\) −31.1012 −1.13870
\(747\) 0 0
\(748\) 11.2426 0.411071
\(749\) −34.5033 −1.26072
\(750\) 0 0
\(751\) 9.41823 0.343676 0.171838 0.985125i \(-0.445029\pi\)
0.171838 + 0.985125i \(0.445029\pi\)
\(752\) −3.35439 −0.122322
\(753\) 0 0
\(754\) −8.32850 −0.303306
\(755\) 57.7368 2.10126
\(756\) 0 0
\(757\) 7.57303 0.275246 0.137623 0.990485i \(-0.456054\pi\)
0.137623 + 0.990485i \(0.456054\pi\)
\(758\) −31.2257 −1.13417
\(759\) 0 0
\(760\) −15.8499 −0.574935
\(761\) 11.4404 0.414715 0.207357 0.978265i \(-0.433514\pi\)
0.207357 + 0.978265i \(0.433514\pi\)
\(762\) 0 0
\(763\) −17.0075 −0.615712
\(764\) 19.7320 0.713877
\(765\) 0 0
\(766\) 2.00824 0.0725608
\(767\) −3.18353 −0.114951
\(768\) 0 0
\(769\) −29.2382 −1.05435 −0.527177 0.849755i \(-0.676750\pi\)
−0.527177 + 0.849755i \(0.676750\pi\)
\(770\) −20.9915 −0.756480
\(771\) 0 0
\(772\) 8.55331 0.307840
\(773\) −34.8920 −1.25498 −0.627489 0.778626i \(-0.715917\pi\)
−0.627489 + 0.778626i \(0.715917\pi\)
\(774\) 0 0
\(775\) −46.6637 −1.67621
\(776\) 1.67775 0.0602278
\(777\) 0 0
\(778\) 11.1882 0.401116
\(779\) 16.4916 0.590873
\(780\) 0 0
\(781\) −8.47983 −0.303432
\(782\) −42.7479 −1.52866
\(783\) 0 0
\(784\) −0.115449 −0.00412318
\(785\) 74.9941 2.67665
\(786\) 0 0
\(787\) −6.66569 −0.237606 −0.118803 0.992918i \(-0.537906\pi\)
−0.118803 + 0.992918i \(0.537906\pi\)
\(788\) 2.35388 0.0838533
\(789\) 0 0
\(790\) −54.9512 −1.95508
\(791\) 25.7088 0.914100
\(792\) 0 0
\(793\) 7.91867 0.281200
\(794\) −15.7271 −0.558134
\(795\) 0 0
\(796\) 13.9149 0.493200
\(797\) −49.8679 −1.76641 −0.883205 0.468987i \(-0.844619\pi\)
−0.883205 + 0.468987i \(0.844619\pi\)
\(798\) 0 0
\(799\) −17.6013 −0.622690
\(800\) −8.94247 −0.316164
\(801\) 0 0
\(802\) −18.6378 −0.658125
\(803\) −19.0326 −0.671644
\(804\) 0 0
\(805\) 79.8161 2.81315
\(806\) −5.15110 −0.181440
\(807\) 0 0
\(808\) −17.2529 −0.606955
\(809\) 35.2546 1.23949 0.619743 0.784805i \(-0.287237\pi\)
0.619743 + 0.784805i \(0.287237\pi\)
\(810\) 0 0
\(811\) −37.1164 −1.30333 −0.651667 0.758506i \(-0.725930\pi\)
−0.651667 + 0.758506i \(0.725930\pi\)
\(812\) 22.1374 0.776870
\(813\) 0 0
\(814\) −1.14324 −0.0400706
\(815\) 24.1989 0.847650
\(816\) 0 0
\(817\) −10.7864 −0.377369
\(818\) 10.7222 0.374892
\(819\) 0 0
\(820\) 14.5070 0.506606
\(821\) 19.8270 0.691968 0.345984 0.938240i \(-0.387545\pi\)
0.345984 + 0.938240i \(0.387545\pi\)
\(822\) 0 0
\(823\) 14.1898 0.494625 0.247312 0.968936i \(-0.420453\pi\)
0.247312 + 0.968936i \(0.420453\pi\)
\(824\) 0.973885 0.0339269
\(825\) 0 0
\(826\) 8.46191 0.294428
\(827\) 18.9668 0.659541 0.329770 0.944061i \(-0.393029\pi\)
0.329770 + 0.944061i \(0.393029\pi\)
\(828\) 0 0
\(829\) −38.6226 −1.34142 −0.670709 0.741721i \(-0.734010\pi\)
−0.670709 + 0.741721i \(0.734010\pi\)
\(830\) −25.6714 −0.891066
\(831\) 0 0
\(832\) −0.987139 −0.0342229
\(833\) −0.605790 −0.0209894
\(834\) 0 0
\(835\) −8.97976 −0.310757
\(836\) −9.09475 −0.314548
\(837\) 0 0
\(838\) −21.0470 −0.727057
\(839\) −38.8063 −1.33974 −0.669871 0.742478i \(-0.733650\pi\)
−0.669871 + 0.742478i \(0.733650\pi\)
\(840\) 0 0
\(841\) 42.1831 1.45459
\(842\) 22.1796 0.764358
\(843\) 0 0
\(844\) 1.13848 0.0391883
\(845\) 44.9030 1.54471
\(846\) 0 0
\(847\) 16.8172 0.577847
\(848\) 2.52043 0.0865519
\(849\) 0 0
\(850\) −46.9234 −1.60946
\(851\) 4.34696 0.149012
\(852\) 0 0
\(853\) −23.8861 −0.817846 −0.408923 0.912569i \(-0.634096\pi\)
−0.408923 + 0.912569i \(0.634096\pi\)
\(854\) −21.0480 −0.720249
\(855\) 0 0
\(856\) −13.1499 −0.449455
\(857\) −10.8617 −0.371028 −0.185514 0.982642i \(-0.559395\pi\)
−0.185514 + 0.982642i \(0.559395\pi\)
\(858\) 0 0
\(859\) −22.6126 −0.771532 −0.385766 0.922597i \(-0.626063\pi\)
−0.385766 + 0.922597i \(0.626063\pi\)
\(860\) −9.48837 −0.323551
\(861\) 0 0
\(862\) −32.4982 −1.10689
\(863\) −39.0059 −1.32777 −0.663887 0.747833i \(-0.731095\pi\)
−0.663887 + 0.747833i \(0.731095\pi\)
\(864\) 0 0
\(865\) 59.6585 2.02845
\(866\) 2.82924 0.0961416
\(867\) 0 0
\(868\) 13.6918 0.464729
\(869\) −31.5313 −1.06963
\(870\) 0 0
\(871\) −0.801302 −0.0271511
\(872\) −6.48190 −0.219505
\(873\) 0 0
\(874\) 34.5811 1.16972
\(875\) 38.6257 1.30579
\(876\) 0 0
\(877\) 13.3530 0.450899 0.225449 0.974255i \(-0.427615\pi\)
0.225449 + 0.974255i \(0.427615\pi\)
\(878\) 11.3455 0.382890
\(879\) 0 0
\(880\) −8.00028 −0.269689
\(881\) 46.1697 1.55550 0.777749 0.628575i \(-0.216362\pi\)
0.777749 + 0.628575i \(0.216362\pi\)
\(882\) 0 0
\(883\) 19.6600 0.661611 0.330806 0.943699i \(-0.392680\pi\)
0.330806 + 0.943699i \(0.392680\pi\)
\(884\) −5.17977 −0.174214
\(885\) 0 0
\(886\) −23.7537 −0.798023
\(887\) 30.8029 1.03426 0.517130 0.855907i \(-0.327000\pi\)
0.517130 + 0.855907i \(0.327000\pi\)
\(888\) 0 0
\(889\) 11.3927 0.382098
\(890\) 22.6700 0.759900
\(891\) 0 0
\(892\) −6.72193 −0.225067
\(893\) 14.2386 0.476478
\(894\) 0 0
\(895\) 14.8640 0.496850
\(896\) 2.62384 0.0876564
\(897\) 0 0
\(898\) −31.7903 −1.06086
\(899\) 44.0261 1.46835
\(900\) 0 0
\(901\) 13.2253 0.440600
\(902\) 8.32421 0.277166
\(903\) 0 0
\(904\) 9.79815 0.325882
\(905\) −73.5828 −2.44597
\(906\) 0 0
\(907\) 9.99579 0.331905 0.165952 0.986134i \(-0.446930\pi\)
0.165952 + 0.986134i \(0.446930\pi\)
\(908\) −8.37087 −0.277797
\(909\) 0 0
\(910\) 9.67132 0.320601
\(911\) 11.8384 0.392223 0.196111 0.980582i \(-0.437169\pi\)
0.196111 + 0.980582i \(0.437169\pi\)
\(912\) 0 0
\(913\) −14.7304 −0.487505
\(914\) −2.44674 −0.0809308
\(915\) 0 0
\(916\) 9.32680 0.308166
\(917\) −10.0280 −0.331153
\(918\) 0 0
\(919\) 49.1503 1.62132 0.810660 0.585517i \(-0.199108\pi\)
0.810660 + 0.585517i \(0.199108\pi\)
\(920\) 30.4195 1.00290
\(921\) 0 0
\(922\) −6.34903 −0.209094
\(923\) 3.90688 0.128596
\(924\) 0 0
\(925\) 4.77156 0.156888
\(926\) −0.408336 −0.0134187
\(927\) 0 0
\(928\) 8.43701 0.276958
\(929\) 10.1963 0.334531 0.167266 0.985912i \(-0.446506\pi\)
0.167266 + 0.985912i \(0.446506\pi\)
\(930\) 0 0
\(931\) 0.490056 0.0160609
\(932\) 10.2941 0.337196
\(933\) 0 0
\(934\) 4.73896 0.155064
\(935\) −41.9795 −1.37288
\(936\) 0 0
\(937\) 36.3197 1.18651 0.593257 0.805013i \(-0.297842\pi\)
0.593257 + 0.805013i \(0.297842\pi\)
\(938\) 2.12988 0.0695431
\(939\) 0 0
\(940\) 12.5252 0.408526
\(941\) 41.5470 1.35439 0.677197 0.735802i \(-0.263194\pi\)
0.677197 + 0.735802i \(0.263194\pi\)
\(942\) 0 0
\(943\) −31.6512 −1.03071
\(944\) 3.22501 0.104965
\(945\) 0 0
\(946\) −5.44449 −0.177016
\(947\) 43.4552 1.41210 0.706052 0.708160i \(-0.250474\pi\)
0.706052 + 0.708160i \(0.250474\pi\)
\(948\) 0 0
\(949\) 8.76880 0.284647
\(950\) 37.9588 1.23155
\(951\) 0 0
\(952\) 13.7680 0.446222
\(953\) 25.6035 0.829377 0.414689 0.909963i \(-0.363890\pi\)
0.414689 + 0.909963i \(0.363890\pi\)
\(954\) 0 0
\(955\) −73.6784 −2.38418
\(956\) 12.0117 0.388486
\(957\) 0 0
\(958\) −13.6810 −0.442014
\(959\) 29.1189 0.940297
\(960\) 0 0
\(961\) −3.77029 −0.121622
\(962\) 0.526721 0.0169822
\(963\) 0 0
\(964\) 24.9677 0.804155
\(965\) −31.9377 −1.02811
\(966\) 0 0
\(967\) 19.2132 0.617855 0.308928 0.951086i \(-0.400030\pi\)
0.308928 + 0.951086i \(0.400030\pi\)
\(968\) 6.40939 0.206005
\(969\) 0 0
\(970\) −6.26467 −0.201146
\(971\) −18.6235 −0.597656 −0.298828 0.954307i \(-0.596596\pi\)
−0.298828 + 0.954307i \(0.596596\pi\)
\(972\) 0 0
\(973\) −6.49896 −0.208347
\(974\) −8.54623 −0.273839
\(975\) 0 0
\(976\) −8.02184 −0.256773
\(977\) −29.5674 −0.945946 −0.472973 0.881077i \(-0.656819\pi\)
−0.472973 + 0.881077i \(0.656819\pi\)
\(978\) 0 0
\(979\) 13.0082 0.415743
\(980\) 0.431082 0.0137704
\(981\) 0 0
\(982\) 13.4171 0.428156
\(983\) −12.1120 −0.386313 −0.193156 0.981168i \(-0.561872\pi\)
−0.193156 + 0.981168i \(0.561872\pi\)
\(984\) 0 0
\(985\) −8.78928 −0.280050
\(986\) 44.2711 1.40988
\(987\) 0 0
\(988\) 4.19019 0.133308
\(989\) 20.7016 0.658274
\(990\) 0 0
\(991\) 26.2842 0.834946 0.417473 0.908689i \(-0.362916\pi\)
0.417473 + 0.908689i \(0.362916\pi\)
\(992\) 5.21821 0.165678
\(993\) 0 0
\(994\) −10.3846 −0.329379
\(995\) −51.9576 −1.64717
\(996\) 0 0
\(997\) 27.5456 0.872377 0.436189 0.899855i \(-0.356328\pi\)
0.436189 + 0.899855i \(0.356328\pi\)
\(998\) 9.21700 0.291759
\(999\) 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 \(a_p\))