Properties

Label 4008.2.a.l.1.7
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.53322\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+1.53322 q^{5}\) \(-0.915565 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+1.53322 q^{5}\) \(-0.915565 q^{7}\) \(+1.00000 q^{9}\) \(+3.09767 q^{11}\) \(+1.39795 q^{13}\) \(+1.53322 q^{15}\) \(-1.50046 q^{17}\) \(-4.21086 q^{19}\) \(-0.915565 q^{21}\) \(+4.95660 q^{23}\) \(-2.64923 q^{25}\) \(+1.00000 q^{27}\) \(+1.76793 q^{29}\) \(+3.79993 q^{31}\) \(+3.09767 q^{33}\) \(-1.40377 q^{35}\) \(+4.15442 q^{37}\) \(+1.39795 q^{39}\) \(+8.32859 q^{41}\) \(+8.45697 q^{43}\) \(+1.53322 q^{45}\) \(-6.81577 q^{47}\) \(-6.16174 q^{49}\) \(-1.50046 q^{51}\) \(+1.43276 q^{53}\) \(+4.74943 q^{55}\) \(-4.21086 q^{57}\) \(+12.9348 q^{59}\) \(-3.76679 q^{61}\) \(-0.915565 q^{63}\) \(+2.14337 q^{65}\) \(+7.30009 q^{67}\) \(+4.95660 q^{69}\) \(+0.883952 q^{71}\) \(-0.891880 q^{73}\) \(-2.64923 q^{75}\) \(-2.83612 q^{77}\) \(-1.12995 q^{79}\) \(+1.00000 q^{81}\) \(+4.26402 q^{83}\) \(-2.30053 q^{85}\) \(+1.76793 q^{87}\) \(+17.6794 q^{89}\) \(-1.27991 q^{91}\) \(+3.79993 q^{93}\) \(-6.45620 q^{95}\) \(-4.28751 q^{97}\) \(+3.09767 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.53322 0.685678 0.342839 0.939394i \(-0.388611\pi\)
0.342839 + 0.939394i \(0.388611\pi\)
\(6\) 0 0
\(7\) −0.915565 −0.346051 −0.173025 0.984917i \(-0.555354\pi\)
−0.173025 + 0.984917i \(0.555354\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.09767 0.933984 0.466992 0.884262i \(-0.345338\pi\)
0.466992 + 0.884262i \(0.345338\pi\)
\(12\) 0 0
\(13\) 1.39795 0.387721 0.193861 0.981029i \(-0.437899\pi\)
0.193861 + 0.981029i \(0.437899\pi\)
\(14\) 0 0
\(15\) 1.53322 0.395877
\(16\) 0 0
\(17\) −1.50046 −0.363914 −0.181957 0.983306i \(-0.558243\pi\)
−0.181957 + 0.983306i \(0.558243\pi\)
\(18\) 0 0
\(19\) −4.21086 −0.966038 −0.483019 0.875610i \(-0.660460\pi\)
−0.483019 + 0.875610i \(0.660460\pi\)
\(20\) 0 0
\(21\) −0.915565 −0.199793
\(22\) 0 0
\(23\) 4.95660 1.03352 0.516761 0.856129i \(-0.327137\pi\)
0.516761 + 0.856129i \(0.327137\pi\)
\(24\) 0 0
\(25\) −2.64923 −0.529845
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.76793 0.328297 0.164148 0.986436i \(-0.447512\pi\)
0.164148 + 0.986436i \(0.447512\pi\)
\(30\) 0 0
\(31\) 3.79993 0.682487 0.341244 0.939975i \(-0.389152\pi\)
0.341244 + 0.939975i \(0.389152\pi\)
\(32\) 0 0
\(33\) 3.09767 0.539236
\(34\) 0 0
\(35\) −1.40377 −0.237280
\(36\) 0 0
\(37\) 4.15442 0.682982 0.341491 0.939885i \(-0.389068\pi\)
0.341491 + 0.939885i \(0.389068\pi\)
\(38\) 0 0
\(39\) 1.39795 0.223851
\(40\) 0 0
\(41\) 8.32859 1.30071 0.650354 0.759631i \(-0.274621\pi\)
0.650354 + 0.759631i \(0.274621\pi\)
\(42\) 0 0
\(43\) 8.45697 1.28968 0.644838 0.764319i \(-0.276925\pi\)
0.644838 + 0.764319i \(0.276925\pi\)
\(44\) 0 0
\(45\) 1.53322 0.228559
\(46\) 0 0
\(47\) −6.81577 −0.994182 −0.497091 0.867699i \(-0.665598\pi\)
−0.497091 + 0.867699i \(0.665598\pi\)
\(48\) 0 0
\(49\) −6.16174 −0.880249
\(50\) 0 0
\(51\) −1.50046 −0.210106
\(52\) 0 0
\(53\) 1.43276 0.196804 0.0984021 0.995147i \(-0.468627\pi\)
0.0984021 + 0.995147i \(0.468627\pi\)
\(54\) 0 0
\(55\) 4.74943 0.640413
\(56\) 0 0
\(57\) −4.21086 −0.557742
\(58\) 0 0
\(59\) 12.9348 1.68397 0.841987 0.539499i \(-0.181386\pi\)
0.841987 + 0.539499i \(0.181386\pi\)
\(60\) 0 0
\(61\) −3.76679 −0.482288 −0.241144 0.970489i \(-0.577523\pi\)
−0.241144 + 0.970489i \(0.577523\pi\)
\(62\) 0 0
\(63\) −0.915565 −0.115350
\(64\) 0 0
\(65\) 2.14337 0.265852
\(66\) 0 0
\(67\) 7.30009 0.891848 0.445924 0.895071i \(-0.352875\pi\)
0.445924 + 0.895071i \(0.352875\pi\)
\(68\) 0 0
\(69\) 4.95660 0.596705
\(70\) 0 0
\(71\) 0.883952 0.104906 0.0524529 0.998623i \(-0.483296\pi\)
0.0524529 + 0.998623i \(0.483296\pi\)
\(72\) 0 0
\(73\) −0.891880 −0.104387 −0.0521933 0.998637i \(-0.516621\pi\)
−0.0521933 + 0.998637i \(0.516621\pi\)
\(74\) 0 0
\(75\) −2.64923 −0.305906
\(76\) 0 0
\(77\) −2.83612 −0.323206
\(78\) 0 0
\(79\) −1.12995 −0.127129 −0.0635645 0.997978i \(-0.520247\pi\)
−0.0635645 + 0.997978i \(0.520247\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.26402 0.468037 0.234018 0.972232i \(-0.424812\pi\)
0.234018 + 0.972232i \(0.424812\pi\)
\(84\) 0 0
\(85\) −2.30053 −0.249528
\(86\) 0 0
\(87\) 1.76793 0.189542
\(88\) 0 0
\(89\) 17.6794 1.87401 0.937007 0.349311i \(-0.113584\pi\)
0.937007 + 0.349311i \(0.113584\pi\)
\(90\) 0 0
\(91\) −1.27991 −0.134171
\(92\) 0 0
\(93\) 3.79993 0.394034
\(94\) 0 0
\(95\) −6.45620 −0.662392
\(96\) 0 0
\(97\) −4.28751 −0.435331 −0.217666 0.976023i \(-0.569844\pi\)
−0.217666 + 0.976023i \(0.569844\pi\)
\(98\) 0 0
\(99\) 3.09767 0.311328
\(100\) 0 0
\(101\) −15.5844 −1.55071 −0.775355 0.631526i \(-0.782429\pi\)
−0.775355 + 0.631526i \(0.782429\pi\)
\(102\) 0 0
\(103\) −5.71458 −0.563075 −0.281537 0.959550i \(-0.590844\pi\)
−0.281537 + 0.959550i \(0.590844\pi\)
\(104\) 0 0
\(105\) −1.40377 −0.136993
\(106\) 0 0
\(107\) −3.17924 −0.307349 −0.153675 0.988122i \(-0.549111\pi\)
−0.153675 + 0.988122i \(0.549111\pi\)
\(108\) 0 0
\(109\) −12.5475 −1.20184 −0.600919 0.799310i \(-0.705198\pi\)
−0.600919 + 0.799310i \(0.705198\pi\)
\(110\) 0 0
\(111\) 4.15442 0.394320
\(112\) 0 0
\(113\) 2.50783 0.235916 0.117958 0.993019i \(-0.462365\pi\)
0.117958 + 0.993019i \(0.462365\pi\)
\(114\) 0 0
\(115\) 7.59958 0.708664
\(116\) 0 0
\(117\) 1.39795 0.129240
\(118\) 0 0
\(119\) 1.37376 0.125933
\(120\) 0 0
\(121\) −1.40441 −0.127674
\(122\) 0 0
\(123\) 8.32859 0.750964
\(124\) 0 0
\(125\) −11.7280 −1.04898
\(126\) 0 0
\(127\) 17.3437 1.53900 0.769501 0.638646i \(-0.220505\pi\)
0.769501 + 0.638646i \(0.220505\pi\)
\(128\) 0 0
\(129\) 8.45697 0.744595
\(130\) 0 0
\(131\) −16.3850 −1.43156 −0.715782 0.698324i \(-0.753929\pi\)
−0.715782 + 0.698324i \(0.753929\pi\)
\(132\) 0 0
\(133\) 3.85532 0.334298
\(134\) 0 0
\(135\) 1.53322 0.131959
\(136\) 0 0
\(137\) −18.5673 −1.58631 −0.793154 0.609021i \(-0.791563\pi\)
−0.793154 + 0.609021i \(0.791563\pi\)
\(138\) 0 0
\(139\) 15.0137 1.27345 0.636724 0.771092i \(-0.280289\pi\)
0.636724 + 0.771092i \(0.280289\pi\)
\(140\) 0 0
\(141\) −6.81577 −0.573991
\(142\) 0 0
\(143\) 4.33039 0.362125
\(144\) 0 0
\(145\) 2.71064 0.225106
\(146\) 0 0
\(147\) −6.16174 −0.508212
\(148\) 0 0
\(149\) 22.6712 1.85729 0.928647 0.370965i \(-0.120973\pi\)
0.928647 + 0.370965i \(0.120973\pi\)
\(150\) 0 0
\(151\) 19.2737 1.56847 0.784237 0.620462i \(-0.213055\pi\)
0.784237 + 0.620462i \(0.213055\pi\)
\(152\) 0 0
\(153\) −1.50046 −0.121305
\(154\) 0 0
\(155\) 5.82614 0.467967
\(156\) 0 0
\(157\) 15.3895 1.22821 0.614107 0.789222i \(-0.289516\pi\)
0.614107 + 0.789222i \(0.289516\pi\)
\(158\) 0 0
\(159\) 1.43276 0.113625
\(160\) 0 0
\(161\) −4.53809 −0.357651
\(162\) 0 0
\(163\) −2.65971 −0.208325 −0.104162 0.994560i \(-0.533216\pi\)
−0.104162 + 0.994560i \(0.533216\pi\)
\(164\) 0 0
\(165\) 4.74943 0.369742
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −11.0457 −0.849672
\(170\) 0 0
\(171\) −4.21086 −0.322013
\(172\) 0 0
\(173\) 16.5038 1.25476 0.627382 0.778712i \(-0.284126\pi\)
0.627382 + 0.778712i \(0.284126\pi\)
\(174\) 0 0
\(175\) 2.42554 0.183353
\(176\) 0 0
\(177\) 12.9348 0.972242
\(178\) 0 0
\(179\) 0.202161 0.0151102 0.00755512 0.999971i \(-0.497595\pi\)
0.00755512 + 0.999971i \(0.497595\pi\)
\(180\) 0 0
\(181\) −2.91030 −0.216321 −0.108160 0.994133i \(-0.534496\pi\)
−0.108160 + 0.994133i \(0.534496\pi\)
\(182\) 0 0
\(183\) −3.76679 −0.278449
\(184\) 0 0
\(185\) 6.36965 0.468306
\(186\) 0 0
\(187\) −4.64792 −0.339890
\(188\) 0 0
\(189\) −0.915565 −0.0665975
\(190\) 0 0
\(191\) −15.2680 −1.10475 −0.552377 0.833594i \(-0.686279\pi\)
−0.552377 + 0.833594i \(0.686279\pi\)
\(192\) 0 0
\(193\) 8.99644 0.647578 0.323789 0.946129i \(-0.395043\pi\)
0.323789 + 0.946129i \(0.395043\pi\)
\(194\) 0 0
\(195\) 2.14337 0.153490
\(196\) 0 0
\(197\) 11.6292 0.828547 0.414273 0.910152i \(-0.364036\pi\)
0.414273 + 0.910152i \(0.364036\pi\)
\(198\) 0 0
\(199\) 12.6305 0.895350 0.447675 0.894196i \(-0.352252\pi\)
0.447675 + 0.894196i \(0.352252\pi\)
\(200\) 0 0
\(201\) 7.30009 0.514909
\(202\) 0 0
\(203\) −1.61866 −0.113607
\(204\) 0 0
\(205\) 12.7696 0.891867
\(206\) 0 0
\(207\) 4.95660 0.344508
\(208\) 0 0
\(209\) −13.0439 −0.902264
\(210\) 0 0
\(211\) −11.2769 −0.776331 −0.388166 0.921590i \(-0.626891\pi\)
−0.388166 + 0.921590i \(0.626891\pi\)
\(212\) 0 0
\(213\) 0.883952 0.0605674
\(214\) 0 0
\(215\) 12.9664 0.884303
\(216\) 0 0
\(217\) −3.47908 −0.236175
\(218\) 0 0
\(219\) −0.891880 −0.0602677
\(220\) 0 0
\(221\) −2.09756 −0.141097
\(222\) 0 0
\(223\) −11.4567 −0.767196 −0.383598 0.923500i \(-0.625315\pi\)
−0.383598 + 0.923500i \(0.625315\pi\)
\(224\) 0 0
\(225\) −2.64923 −0.176615
\(226\) 0 0
\(227\) 6.99214 0.464085 0.232042 0.972706i \(-0.425459\pi\)
0.232042 + 0.972706i \(0.425459\pi\)
\(228\) 0 0
\(229\) 4.84467 0.320145 0.160073 0.987105i \(-0.448827\pi\)
0.160073 + 0.987105i \(0.448827\pi\)
\(230\) 0 0
\(231\) −2.83612 −0.186603
\(232\) 0 0
\(233\) −26.4019 −1.72965 −0.864824 0.502075i \(-0.832570\pi\)
−0.864824 + 0.502075i \(0.832570\pi\)
\(234\) 0 0
\(235\) −10.4501 −0.681689
\(236\) 0 0
\(237\) −1.12995 −0.0733979
\(238\) 0 0
\(239\) 23.9728 1.55067 0.775335 0.631550i \(-0.217581\pi\)
0.775335 + 0.631550i \(0.217581\pi\)
\(240\) 0 0
\(241\) 6.33066 0.407794 0.203897 0.978992i \(-0.434639\pi\)
0.203897 + 0.978992i \(0.434639\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −9.44733 −0.603568
\(246\) 0 0
\(247\) −5.88657 −0.374553
\(248\) 0 0
\(249\) 4.26402 0.270221
\(250\) 0 0
\(251\) 10.5048 0.663059 0.331529 0.943445i \(-0.392435\pi\)
0.331529 + 0.943445i \(0.392435\pi\)
\(252\) 0 0
\(253\) 15.3539 0.965294
\(254\) 0 0
\(255\) −2.30053 −0.144065
\(256\) 0 0
\(257\) −25.5749 −1.59532 −0.797661 0.603107i \(-0.793929\pi\)
−0.797661 + 0.603107i \(0.793929\pi\)
\(258\) 0 0
\(259\) −3.80364 −0.236346
\(260\) 0 0
\(261\) 1.76793 0.109432
\(262\) 0 0
\(263\) −20.5255 −1.26566 −0.632828 0.774292i \(-0.718106\pi\)
−0.632828 + 0.774292i \(0.718106\pi\)
\(264\) 0 0
\(265\) 2.19674 0.134944
\(266\) 0 0
\(267\) 17.6794 1.08196
\(268\) 0 0
\(269\) 11.2640 0.686781 0.343390 0.939193i \(-0.388425\pi\)
0.343390 + 0.939193i \(0.388425\pi\)
\(270\) 0 0
\(271\) −5.25659 −0.319315 −0.159658 0.987172i \(-0.551039\pi\)
−0.159658 + 0.987172i \(0.551039\pi\)
\(272\) 0 0
\(273\) −1.27991 −0.0774638
\(274\) 0 0
\(275\) −8.20644 −0.494867
\(276\) 0 0
\(277\) −10.4026 −0.625034 −0.312517 0.949912i \(-0.601172\pi\)
−0.312517 + 0.949912i \(0.601172\pi\)
\(278\) 0 0
\(279\) 3.79993 0.227496
\(280\) 0 0
\(281\) −21.6130 −1.28932 −0.644661 0.764469i \(-0.723001\pi\)
−0.644661 + 0.764469i \(0.723001\pi\)
\(282\) 0 0
\(283\) 24.2913 1.44397 0.721983 0.691911i \(-0.243231\pi\)
0.721983 + 0.691911i \(0.243231\pi\)
\(284\) 0 0
\(285\) −6.45620 −0.382432
\(286\) 0 0
\(287\) −7.62537 −0.450111
\(288\) 0 0
\(289\) −14.7486 −0.867567
\(290\) 0 0
\(291\) −4.28751 −0.251339
\(292\) 0 0
\(293\) 15.1490 0.885014 0.442507 0.896765i \(-0.354089\pi\)
0.442507 + 0.896765i \(0.354089\pi\)
\(294\) 0 0
\(295\) 19.8320 1.15466
\(296\) 0 0
\(297\) 3.09767 0.179745
\(298\) 0 0
\(299\) 6.92907 0.400718
\(300\) 0 0
\(301\) −7.74290 −0.446293
\(302\) 0 0
\(303\) −15.5844 −0.895303
\(304\) 0 0
\(305\) −5.77533 −0.330694
\(306\) 0 0
\(307\) 8.37234 0.477835 0.238917 0.971040i \(-0.423208\pi\)
0.238917 + 0.971040i \(0.423208\pi\)
\(308\) 0 0
\(309\) −5.71458 −0.325091
\(310\) 0 0
\(311\) 4.65962 0.264223 0.132111 0.991235i \(-0.457824\pi\)
0.132111 + 0.991235i \(0.457824\pi\)
\(312\) 0 0
\(313\) −8.10404 −0.458067 −0.229034 0.973419i \(-0.573557\pi\)
−0.229034 + 0.973419i \(0.573557\pi\)
\(314\) 0 0
\(315\) −1.40377 −0.0790932
\(316\) 0 0
\(317\) −12.1018 −0.679706 −0.339853 0.940479i \(-0.610377\pi\)
−0.339853 + 0.940479i \(0.610377\pi\)
\(318\) 0 0
\(319\) 5.47648 0.306624
\(320\) 0 0
\(321\) −3.17924 −0.177448
\(322\) 0 0
\(323\) 6.31822 0.351555
\(324\) 0 0
\(325\) −3.70348 −0.205432
\(326\) 0 0
\(327\) −12.5475 −0.693881
\(328\) 0 0
\(329\) 6.24027 0.344037
\(330\) 0 0
\(331\) −11.5342 −0.633979 −0.316989 0.948429i \(-0.602672\pi\)
−0.316989 + 0.948429i \(0.602672\pi\)
\(332\) 0 0
\(333\) 4.15442 0.227661
\(334\) 0 0
\(335\) 11.1927 0.611521
\(336\) 0 0
\(337\) 4.87706 0.265670 0.132835 0.991138i \(-0.457592\pi\)
0.132835 + 0.991138i \(0.457592\pi\)
\(338\) 0 0
\(339\) 2.50783 0.136206
\(340\) 0 0
\(341\) 11.7709 0.637432
\(342\) 0 0
\(343\) 12.0504 0.650662
\(344\) 0 0
\(345\) 7.59958 0.409148
\(346\) 0 0
\(347\) −5.41332 −0.290602 −0.145301 0.989387i \(-0.546415\pi\)
−0.145301 + 0.989387i \(0.546415\pi\)
\(348\) 0 0
\(349\) 16.3896 0.877313 0.438656 0.898655i \(-0.355455\pi\)
0.438656 + 0.898655i \(0.355455\pi\)
\(350\) 0 0
\(351\) 1.39795 0.0746169
\(352\) 0 0
\(353\) −33.9228 −1.80553 −0.902765 0.430133i \(-0.858467\pi\)
−0.902765 + 0.430133i \(0.858467\pi\)
\(354\) 0 0
\(355\) 1.35530 0.0719316
\(356\) 0 0
\(357\) 1.37376 0.0727073
\(358\) 0 0
\(359\) 30.9733 1.63471 0.817354 0.576135i \(-0.195440\pi\)
0.817354 + 0.576135i \(0.195440\pi\)
\(360\) 0 0
\(361\) −1.26863 −0.0667699
\(362\) 0 0
\(363\) −1.40441 −0.0737126
\(364\) 0 0
\(365\) −1.36745 −0.0715757
\(366\) 0 0
\(367\) −19.7551 −1.03121 −0.515603 0.856827i \(-0.672432\pi\)
−0.515603 + 0.856827i \(0.672432\pi\)
\(368\) 0 0
\(369\) 8.32859 0.433569
\(370\) 0 0
\(371\) −1.31178 −0.0681043
\(372\) 0 0
\(373\) 9.12807 0.472634 0.236317 0.971676i \(-0.424060\pi\)
0.236317 + 0.971676i \(0.424060\pi\)
\(374\) 0 0
\(375\) −11.7280 −0.605630
\(376\) 0 0
\(377\) 2.47148 0.127288
\(378\) 0 0
\(379\) −13.9800 −0.718103 −0.359052 0.933318i \(-0.616900\pi\)
−0.359052 + 0.933318i \(0.616900\pi\)
\(380\) 0 0
\(381\) 17.3437 0.888543
\(382\) 0 0
\(383\) −34.7750 −1.77692 −0.888459 0.458956i \(-0.848224\pi\)
−0.888459 + 0.458956i \(0.848224\pi\)
\(384\) 0 0
\(385\) −4.34841 −0.221615
\(386\) 0 0
\(387\) 8.45697 0.429892
\(388\) 0 0
\(389\) −16.7127 −0.847369 −0.423684 0.905810i \(-0.639263\pi\)
−0.423684 + 0.905810i \(0.639263\pi\)
\(390\) 0 0
\(391\) −7.43716 −0.376113
\(392\) 0 0
\(393\) −16.3850 −0.826513
\(394\) 0 0
\(395\) −1.73246 −0.0871696
\(396\) 0 0
\(397\) −3.95221 −0.198356 −0.0991780 0.995070i \(-0.531621\pi\)
−0.0991780 + 0.995070i \(0.531621\pi\)
\(398\) 0 0
\(399\) 3.85532 0.193007
\(400\) 0 0
\(401\) −19.9460 −0.996055 −0.498028 0.867161i \(-0.665942\pi\)
−0.498028 + 0.867161i \(0.665942\pi\)
\(402\) 0 0
\(403\) 5.31210 0.264615
\(404\) 0 0
\(405\) 1.53322 0.0761865
\(406\) 0 0
\(407\) 12.8690 0.637894
\(408\) 0 0
\(409\) −4.18390 −0.206881 −0.103440 0.994636i \(-0.532985\pi\)
−0.103440 + 0.994636i \(0.532985\pi\)
\(410\) 0 0
\(411\) −18.5673 −0.915856
\(412\) 0 0
\(413\) −11.8427 −0.582740
\(414\) 0 0
\(415\) 6.53769 0.320923
\(416\) 0 0
\(417\) 15.0137 0.735225
\(418\) 0 0
\(419\) −39.5510 −1.93219 −0.966097 0.258179i \(-0.916877\pi\)
−0.966097 + 0.258179i \(0.916877\pi\)
\(420\) 0 0
\(421\) −15.4917 −0.755019 −0.377510 0.926006i \(-0.623220\pi\)
−0.377510 + 0.926006i \(0.623220\pi\)
\(422\) 0 0
\(423\) −6.81577 −0.331394
\(424\) 0 0
\(425\) 3.97505 0.192818
\(426\) 0 0
\(427\) 3.44874 0.166896
\(428\) 0 0
\(429\) 4.33039 0.209073
\(430\) 0 0
\(431\) 16.0476 0.772984 0.386492 0.922293i \(-0.373687\pi\)
0.386492 + 0.922293i \(0.373687\pi\)
\(432\) 0 0
\(433\) 21.5403 1.03516 0.517580 0.855635i \(-0.326833\pi\)
0.517580 + 0.855635i \(0.326833\pi\)
\(434\) 0 0
\(435\) 2.71064 0.129965
\(436\) 0 0
\(437\) −20.8716 −0.998423
\(438\) 0 0
\(439\) 20.1392 0.961191 0.480595 0.876942i \(-0.340421\pi\)
0.480595 + 0.876942i \(0.340421\pi\)
\(440\) 0 0
\(441\) −6.16174 −0.293416
\(442\) 0 0
\(443\) 17.2013 0.817257 0.408629 0.912701i \(-0.366007\pi\)
0.408629 + 0.912701i \(0.366007\pi\)
\(444\) 0 0
\(445\) 27.1065 1.28497
\(446\) 0 0
\(447\) 22.6712 1.07231
\(448\) 0 0
\(449\) −28.7950 −1.35892 −0.679461 0.733712i \(-0.737786\pi\)
−0.679461 + 0.733712i \(0.737786\pi\)
\(450\) 0 0
\(451\) 25.7993 1.21484
\(452\) 0 0
\(453\) 19.2737 0.905559
\(454\) 0 0
\(455\) −1.96239 −0.0919983
\(456\) 0 0
\(457\) 31.8010 1.48759 0.743794 0.668409i \(-0.233024\pi\)
0.743794 + 0.668409i \(0.233024\pi\)
\(458\) 0 0
\(459\) −1.50046 −0.0700353
\(460\) 0 0
\(461\) 23.3828 1.08905 0.544524 0.838745i \(-0.316710\pi\)
0.544524 + 0.838745i \(0.316710\pi\)
\(462\) 0 0
\(463\) 39.4475 1.83328 0.916640 0.399714i \(-0.130891\pi\)
0.916640 + 0.399714i \(0.130891\pi\)
\(464\) 0 0
\(465\) 5.82614 0.270181
\(466\) 0 0
\(467\) −31.6227 −1.46332 −0.731661 0.681668i \(-0.761255\pi\)
−0.731661 + 0.681668i \(0.761255\pi\)
\(468\) 0 0
\(469\) −6.68370 −0.308625
\(470\) 0 0
\(471\) 15.3895 0.709110
\(472\) 0 0
\(473\) 26.1969 1.20454
\(474\) 0 0
\(475\) 11.1555 0.511851
\(476\) 0 0
\(477\) 1.43276 0.0656014
\(478\) 0 0
\(479\) −13.4628 −0.615129 −0.307565 0.951527i \(-0.599514\pi\)
−0.307565 + 0.951527i \(0.599514\pi\)
\(480\) 0 0
\(481\) 5.80766 0.264806
\(482\) 0 0
\(483\) −4.53809 −0.206490
\(484\) 0 0
\(485\) −6.57372 −0.298497
\(486\) 0 0
\(487\) 34.2506 1.55204 0.776022 0.630706i \(-0.217235\pi\)
0.776022 + 0.630706i \(0.217235\pi\)
\(488\) 0 0
\(489\) −2.65971 −0.120276
\(490\) 0 0
\(491\) −16.2041 −0.731279 −0.365639 0.930757i \(-0.619150\pi\)
−0.365639 + 0.930757i \(0.619150\pi\)
\(492\) 0 0
\(493\) −2.65271 −0.119472
\(494\) 0 0
\(495\) 4.74943 0.213471
\(496\) 0 0
\(497\) −0.809315 −0.0363027
\(498\) 0 0
\(499\) 19.1460 0.857091 0.428545 0.903520i \(-0.359026\pi\)
0.428545 + 0.903520i \(0.359026\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 8.19733 0.365501 0.182750 0.983159i \(-0.441500\pi\)
0.182750 + 0.983159i \(0.441500\pi\)
\(504\) 0 0
\(505\) −23.8944 −1.06329
\(506\) 0 0
\(507\) −11.0457 −0.490559
\(508\) 0 0
\(509\) 15.4558 0.685065 0.342533 0.939506i \(-0.388715\pi\)
0.342533 + 0.939506i \(0.388715\pi\)
\(510\) 0 0
\(511\) 0.816574 0.0361231
\(512\) 0 0
\(513\) −4.21086 −0.185914
\(514\) 0 0
\(515\) −8.76173 −0.386088
\(516\) 0 0
\(517\) −21.1130 −0.928550
\(518\) 0 0
\(519\) 16.5038 0.724438
\(520\) 0 0
\(521\) 22.9773 1.00666 0.503328 0.864096i \(-0.332109\pi\)
0.503328 + 0.864096i \(0.332109\pi\)
\(522\) 0 0
\(523\) −1.86529 −0.0815636 −0.0407818 0.999168i \(-0.512985\pi\)
−0.0407818 + 0.999168i \(0.512985\pi\)
\(524\) 0 0
\(525\) 2.42554 0.105859
\(526\) 0 0
\(527\) −5.70163 −0.248367
\(528\) 0 0
\(529\) 1.56789 0.0681692
\(530\) 0 0
\(531\) 12.9348 0.561324
\(532\) 0 0
\(533\) 11.6429 0.504312
\(534\) 0 0
\(535\) −4.87449 −0.210743
\(536\) 0 0
\(537\) 0.202161 0.00872390
\(538\) 0 0
\(539\) −19.0871 −0.822138
\(540\) 0 0
\(541\) −35.4871 −1.52571 −0.762854 0.646570i \(-0.776203\pi\)
−0.762854 + 0.646570i \(0.776203\pi\)
\(542\) 0 0
\(543\) −2.91030 −0.124893
\(544\) 0 0
\(545\) −19.2382 −0.824074
\(546\) 0 0
\(547\) 1.16371 0.0497568 0.0248784 0.999690i \(-0.492080\pi\)
0.0248784 + 0.999690i \(0.492080\pi\)
\(548\) 0 0
\(549\) −3.76679 −0.160763
\(550\) 0 0
\(551\) −7.44452 −0.317147
\(552\) 0 0
\(553\) 1.03454 0.0439931
\(554\) 0 0
\(555\) 6.36965 0.270377
\(556\) 0 0
\(557\) −27.6032 −1.16958 −0.584792 0.811183i \(-0.698824\pi\)
−0.584792 + 0.811183i \(0.698824\pi\)
\(558\) 0 0
\(559\) 11.8224 0.500034
\(560\) 0 0
\(561\) −4.64792 −0.196235
\(562\) 0 0
\(563\) 26.7132 1.12583 0.562913 0.826516i \(-0.309681\pi\)
0.562913 + 0.826516i \(0.309681\pi\)
\(564\) 0 0
\(565\) 3.84506 0.161763
\(566\) 0 0
\(567\) −0.915565 −0.0384501
\(568\) 0 0
\(569\) −24.6239 −1.03229 −0.516143 0.856502i \(-0.672633\pi\)
−0.516143 + 0.856502i \(0.672633\pi\)
\(570\) 0 0
\(571\) −16.6623 −0.697294 −0.348647 0.937254i \(-0.613359\pi\)
−0.348647 + 0.937254i \(0.613359\pi\)
\(572\) 0 0
\(573\) −15.2680 −0.637830
\(574\) 0 0
\(575\) −13.1312 −0.547607
\(576\) 0 0
\(577\) −10.9442 −0.455612 −0.227806 0.973707i \(-0.573155\pi\)
−0.227806 + 0.973707i \(0.573155\pi\)
\(578\) 0 0
\(579\) 8.99644 0.373879
\(580\) 0 0
\(581\) −3.90398 −0.161965
\(582\) 0 0
\(583\) 4.43821 0.183812
\(584\) 0 0
\(585\) 2.14337 0.0886173
\(586\) 0 0
\(587\) 1.12881 0.0465908 0.0232954 0.999729i \(-0.492584\pi\)
0.0232954 + 0.999729i \(0.492584\pi\)
\(588\) 0 0
\(589\) −16.0010 −0.659309
\(590\) 0 0
\(591\) 11.6292 0.478362
\(592\) 0 0
\(593\) 21.3857 0.878205 0.439102 0.898437i \(-0.355297\pi\)
0.439102 + 0.898437i \(0.355297\pi\)
\(594\) 0 0
\(595\) 2.10629 0.0863494
\(596\) 0 0
\(597\) 12.6305 0.516930
\(598\) 0 0
\(599\) −13.0654 −0.533837 −0.266919 0.963719i \(-0.586006\pi\)
−0.266919 + 0.963719i \(0.586006\pi\)
\(600\) 0 0
\(601\) −7.93394 −0.323632 −0.161816 0.986821i \(-0.551735\pi\)
−0.161816 + 0.986821i \(0.551735\pi\)
\(602\) 0 0
\(603\) 7.30009 0.297283
\(604\) 0 0
\(605\) −2.15328 −0.0875433
\(606\) 0 0
\(607\) 35.6021 1.44504 0.722522 0.691348i \(-0.242983\pi\)
0.722522 + 0.691348i \(0.242983\pi\)
\(608\) 0 0
\(609\) −1.61866 −0.0655913
\(610\) 0 0
\(611\) −9.52809 −0.385465
\(612\) 0 0
\(613\) 9.26461 0.374194 0.187097 0.982341i \(-0.440092\pi\)
0.187097 + 0.982341i \(0.440092\pi\)
\(614\) 0 0
\(615\) 12.7696 0.514920
\(616\) 0 0
\(617\) −18.9004 −0.760902 −0.380451 0.924801i \(-0.624231\pi\)
−0.380451 + 0.924801i \(0.624231\pi\)
\(618\) 0 0
\(619\) −1.98374 −0.0797333 −0.0398666 0.999205i \(-0.512693\pi\)
−0.0398666 + 0.999205i \(0.512693\pi\)
\(620\) 0 0
\(621\) 4.95660 0.198902
\(622\) 0 0
\(623\) −16.1866 −0.648504
\(624\) 0 0
\(625\) −4.73548 −0.189419
\(626\) 0 0
\(627\) −13.0439 −0.520923
\(628\) 0 0
\(629\) −6.23352 −0.248547
\(630\) 0 0
\(631\) −28.1079 −1.11896 −0.559480 0.828844i \(-0.688999\pi\)
−0.559480 + 0.828844i \(0.688999\pi\)
\(632\) 0 0
\(633\) −11.2769 −0.448215
\(634\) 0 0
\(635\) 26.5917 1.05526
\(636\) 0 0
\(637\) −8.61379 −0.341291
\(638\) 0 0
\(639\) 0.883952 0.0349686
\(640\) 0 0
\(641\) −13.6872 −0.540611 −0.270306 0.962775i \(-0.587125\pi\)
−0.270306 + 0.962775i \(0.587125\pi\)
\(642\) 0 0
\(643\) 11.8120 0.465820 0.232910 0.972498i \(-0.425175\pi\)
0.232910 + 0.972498i \(0.425175\pi\)
\(644\) 0 0
\(645\) 12.9664 0.510553
\(646\) 0 0
\(647\) 12.9647 0.509696 0.254848 0.966981i \(-0.417975\pi\)
0.254848 + 0.966981i \(0.417975\pi\)
\(648\) 0 0
\(649\) 40.0679 1.57280
\(650\) 0 0
\(651\) −3.47908 −0.136356
\(652\) 0 0
\(653\) −47.8071 −1.87084 −0.935419 0.353541i \(-0.884978\pi\)
−0.935419 + 0.353541i \(0.884978\pi\)
\(654\) 0 0
\(655\) −25.1219 −0.981592
\(656\) 0 0
\(657\) −0.891880 −0.0347956
\(658\) 0 0
\(659\) 16.2125 0.631550 0.315775 0.948834i \(-0.397735\pi\)
0.315775 + 0.948834i \(0.397735\pi\)
\(660\) 0 0
\(661\) −41.9378 −1.63119 −0.815595 0.578623i \(-0.803590\pi\)
−0.815595 + 0.578623i \(0.803590\pi\)
\(662\) 0 0
\(663\) −2.09756 −0.0814625
\(664\) 0 0
\(665\) 5.91106 0.229221
\(666\) 0 0
\(667\) 8.76294 0.339302
\(668\) 0 0
\(669\) −11.4567 −0.442941
\(670\) 0 0
\(671\) −11.6683 −0.450449
\(672\) 0 0
\(673\) −17.9537 −0.692064 −0.346032 0.938223i \(-0.612471\pi\)
−0.346032 + 0.938223i \(0.612471\pi\)
\(674\) 0 0
\(675\) −2.64923 −0.101969
\(676\) 0 0
\(677\) −9.80016 −0.376651 −0.188325 0.982107i \(-0.560306\pi\)
−0.188325 + 0.982107i \(0.560306\pi\)
\(678\) 0 0
\(679\) 3.92550 0.150647
\(680\) 0 0
\(681\) 6.99214 0.267939
\(682\) 0 0
\(683\) −42.7950 −1.63751 −0.818753 0.574145i \(-0.805334\pi\)
−0.818753 + 0.574145i \(0.805334\pi\)
\(684\) 0 0
\(685\) −28.4678 −1.08770
\(686\) 0 0
\(687\) 4.84467 0.184836
\(688\) 0 0
\(689\) 2.00292 0.0763051
\(690\) 0 0
\(691\) 47.2115 1.79601 0.898005 0.439985i \(-0.145016\pi\)
0.898005 + 0.439985i \(0.145016\pi\)
\(692\) 0 0
\(693\) −2.83612 −0.107735
\(694\) 0 0
\(695\) 23.0194 0.873176
\(696\) 0 0
\(697\) −12.4967 −0.473346
\(698\) 0 0
\(699\) −26.4019 −0.998613
\(700\) 0 0
\(701\) −0.0922506 −0.00348426 −0.00174213 0.999998i \(-0.500555\pi\)
−0.00174213 + 0.999998i \(0.500555\pi\)
\(702\) 0 0
\(703\) −17.4937 −0.659787
\(704\) 0 0
\(705\) −10.4501 −0.393573
\(706\) 0 0
\(707\) 14.2686 0.536624
\(708\) 0 0
\(709\) −33.0225 −1.24019 −0.620093 0.784528i \(-0.712905\pi\)
−0.620093 + 0.784528i \(0.712905\pi\)
\(710\) 0 0
\(711\) −1.12995 −0.0423763
\(712\) 0 0
\(713\) 18.8347 0.705366
\(714\) 0 0
\(715\) 6.63945 0.248301
\(716\) 0 0
\(717\) 23.9728 0.895279
\(718\) 0 0
\(719\) −2.96188 −0.110459 −0.0552297 0.998474i \(-0.517589\pi\)
−0.0552297 + 0.998474i \(0.517589\pi\)
\(720\) 0 0
\(721\) 5.23207 0.194852
\(722\) 0 0
\(723\) 6.33066 0.235440
\(724\) 0 0
\(725\) −4.68365 −0.173946
\(726\) 0 0
\(727\) 14.9351 0.553914 0.276957 0.960882i \(-0.410674\pi\)
0.276957 + 0.960882i \(0.410674\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.6893 −0.469331
\(732\) 0 0
\(733\) −28.0289 −1.03527 −0.517635 0.855602i \(-0.673187\pi\)
−0.517635 + 0.855602i \(0.673187\pi\)
\(734\) 0 0
\(735\) −9.44733 −0.348470
\(736\) 0 0
\(737\) 22.6133 0.832971
\(738\) 0 0
\(739\) −34.2689 −1.26060 −0.630300 0.776351i \(-0.717068\pi\)
−0.630300 + 0.776351i \(0.717068\pi\)
\(740\) 0 0
\(741\) −5.88657 −0.216248
\(742\) 0 0
\(743\) −40.7965 −1.49668 −0.748340 0.663316i \(-0.769149\pi\)
−0.748340 + 0.663316i \(0.769149\pi\)
\(744\) 0 0
\(745\) 34.7600 1.27351
\(746\) 0 0
\(747\) 4.26402 0.156012
\(748\) 0 0
\(749\) 2.91080 0.106358
\(750\) 0 0
\(751\) 41.0708 1.49869 0.749347 0.662177i \(-0.230367\pi\)
0.749347 + 0.662177i \(0.230367\pi\)
\(752\) 0 0
\(753\) 10.5048 0.382817
\(754\) 0 0
\(755\) 29.5509 1.07547
\(756\) 0 0
\(757\) −33.5015 −1.21763 −0.608817 0.793311i \(-0.708356\pi\)
−0.608817 + 0.793311i \(0.708356\pi\)
\(758\) 0 0
\(759\) 15.3539 0.557313
\(760\) 0 0
\(761\) −15.9152 −0.576926 −0.288463 0.957491i \(-0.593144\pi\)
−0.288463 + 0.957491i \(0.593144\pi\)
\(762\) 0 0
\(763\) 11.4881 0.415897
\(764\) 0 0
\(765\) −2.30053 −0.0831760
\(766\) 0 0
\(767\) 18.0822 0.652912
\(768\) 0 0
\(769\) −24.5047 −0.883661 −0.441830 0.897099i \(-0.645671\pi\)
−0.441830 + 0.897099i \(0.645671\pi\)
\(770\) 0 0
\(771\) −25.5749 −0.921059
\(772\) 0 0
\(773\) 28.0247 1.00798 0.503990 0.863710i \(-0.331865\pi\)
0.503990 + 0.863710i \(0.331865\pi\)
\(774\) 0 0
\(775\) −10.0669 −0.361612
\(776\) 0 0
\(777\) −3.80364 −0.136455
\(778\) 0 0
\(779\) −35.0706 −1.25653
\(780\) 0 0
\(781\) 2.73819 0.0979803
\(782\) 0 0
\(783\) 1.76793 0.0631808
\(784\) 0 0
\(785\) 23.5955 0.842160
\(786\) 0 0
\(787\) −13.5173 −0.481840 −0.240920 0.970545i \(-0.577449\pi\)
−0.240920 + 0.970545i \(0.577449\pi\)
\(788\) 0 0
\(789\) −20.5255 −0.730727
\(790\) 0 0
\(791\) −2.29608 −0.0816391
\(792\) 0 0
\(793\) −5.26577 −0.186993
\(794\) 0 0
\(795\) 2.19674 0.0779102
\(796\) 0 0
\(797\) 12.3513 0.437504 0.218752 0.975780i \(-0.429801\pi\)
0.218752 + 0.975780i \(0.429801\pi\)
\(798\) 0 0
\(799\) 10.2268 0.361797
\(800\) 0 0
\(801\) 17.6794 0.624671
\(802\) 0 0
\(803\) −2.76275 −0.0974955
\(804\) 0 0
\(805\) −6.95790 −0.245234
\(806\) 0 0
\(807\) 11.2640 0.396513
\(808\) 0 0
\(809\) −49.9778 −1.75713 −0.878563 0.477626i \(-0.841497\pi\)
−0.878563 + 0.477626i \(0.841497\pi\)
\(810\) 0 0
\(811\) −41.8896 −1.47094 −0.735472 0.677556i \(-0.763039\pi\)
−0.735472 + 0.677556i \(0.763039\pi\)
\(812\) 0 0
\(813\) −5.25659 −0.184357
\(814\) 0 0
\(815\) −4.07793 −0.142844
\(816\) 0 0
\(817\) −35.6111 −1.24588
\(818\) 0 0
\(819\) −1.27991 −0.0447237
\(820\) 0 0
\(821\) −20.6369 −0.720232 −0.360116 0.932908i \(-0.617263\pi\)
−0.360116 + 0.932908i \(0.617263\pi\)
\(822\) 0 0
\(823\) 33.0136 1.15078 0.575390 0.817879i \(-0.304850\pi\)
0.575390 + 0.817879i \(0.304850\pi\)
\(824\) 0 0
\(825\) −8.20644 −0.285711
\(826\) 0 0
\(827\) −4.76225 −0.165600 −0.0827998 0.996566i \(-0.526386\pi\)
−0.0827998 + 0.996566i \(0.526386\pi\)
\(828\) 0 0
\(829\) 37.3978 1.29888 0.649439 0.760414i \(-0.275004\pi\)
0.649439 + 0.760414i \(0.275004\pi\)
\(830\) 0 0
\(831\) −10.4026 −0.360863
\(832\) 0 0
\(833\) 9.24542 0.320335
\(834\) 0 0
\(835\) 1.53322 0.0530594
\(836\) 0 0
\(837\) 3.79993 0.131345
\(838\) 0 0
\(839\) −29.8684 −1.03117 −0.515585 0.856838i \(-0.672425\pi\)
−0.515585 + 0.856838i \(0.672425\pi\)
\(840\) 0 0
\(841\) −25.8744 −0.892221
\(842\) 0 0
\(843\) −21.6130 −0.744390
\(844\) 0 0
\(845\) −16.9356 −0.582602
\(846\) 0 0
\(847\) 1.28583 0.0441817
\(848\) 0 0
\(849\) 24.2913 0.833674
\(850\) 0 0
\(851\) 20.5918 0.705877
\(852\) 0 0
\(853\) 21.5896 0.739214 0.369607 0.929188i \(-0.379492\pi\)
0.369607 + 0.929188i \(0.379492\pi\)
\(854\) 0 0
\(855\) −6.45620 −0.220797
\(856\) 0 0
\(857\) −30.7368 −1.04995 −0.524975 0.851118i \(-0.675925\pi\)
−0.524975 + 0.851118i \(0.675925\pi\)
\(858\) 0 0
\(859\) −0.952468 −0.0324978 −0.0162489 0.999868i \(-0.505172\pi\)
−0.0162489 + 0.999868i \(0.505172\pi\)
\(860\) 0 0
\(861\) −7.62537 −0.259872
\(862\) 0 0
\(863\) −14.7115 −0.500786 −0.250393 0.968144i \(-0.580560\pi\)
−0.250393 + 0.968144i \(0.580560\pi\)
\(864\) 0 0
\(865\) 25.3041 0.860365
\(866\) 0 0
\(867\) −14.7486 −0.500890
\(868\) 0 0
\(869\) −3.50021 −0.118736
\(870\) 0 0
\(871\) 10.2051 0.345788
\(872\) 0 0
\(873\) −4.28751 −0.145110
\(874\) 0 0
\(875\) 10.7377 0.363001
\(876\) 0 0
\(877\) −19.3949 −0.654919 −0.327459 0.944865i \(-0.606192\pi\)
−0.327459 + 0.944865i \(0.606192\pi\)
\(878\) 0 0
\(879\) 15.1490 0.510963
\(880\) 0 0
\(881\) −40.8536 −1.37639 −0.688197 0.725524i \(-0.741597\pi\)
−0.688197 + 0.725524i \(0.741597\pi\)
\(882\) 0 0
\(883\) −51.0635 −1.71843 −0.859213 0.511619i \(-0.829046\pi\)
−0.859213 + 0.511619i \(0.829046\pi\)
\(884\) 0 0
\(885\) 19.8320 0.666646
\(886\) 0 0
\(887\) −0.844140 −0.0283434 −0.0141717 0.999900i \(-0.504511\pi\)
−0.0141717 + 0.999900i \(0.504511\pi\)
\(888\) 0 0
\(889\) −15.8792 −0.532573
\(890\) 0 0
\(891\) 3.09767 0.103776
\(892\) 0 0
\(893\) 28.7003 0.960418
\(894\) 0 0
\(895\) 0.309958 0.0103608
\(896\) 0 0
\(897\) 6.92907 0.231355
\(898\) 0 0
\(899\) 6.71802 0.224058
\(900\) 0 0
\(901\) −2.14979 −0.0716198
\(902\) 0 0
\(903\) −7.74290 −0.257668
\(904\) 0 0
\(905\) −4.46214 −0.148326
\(906\) 0 0
\(907\) 14.2678 0.473754 0.236877 0.971540i \(-0.423876\pi\)
0.236877 + 0.971540i \(0.423876\pi\)
\(908\) 0 0
\(909\) −15.5844 −0.516903
\(910\) 0 0
\(911\) 2.15685 0.0714598 0.0357299 0.999361i \(-0.488624\pi\)
0.0357299 + 0.999361i \(0.488624\pi\)
\(912\) 0 0
\(913\) 13.2085 0.437139
\(914\) 0 0
\(915\) −5.77533 −0.190926
\(916\) 0 0
\(917\) 15.0015 0.495394
\(918\) 0 0
\(919\) −50.7401 −1.67376 −0.836881 0.547386i \(-0.815623\pi\)
−0.836881 + 0.547386i \(0.815623\pi\)
\(920\) 0 0
\(921\) 8.37234 0.275878
\(922\) 0 0
\(923\) 1.23572 0.0406742
\(924\) 0 0
\(925\) −11.0060 −0.361874
\(926\) 0 0
\(927\) −5.71458 −0.187692
\(928\) 0 0
\(929\) −20.0006 −0.656199 −0.328100 0.944643i \(-0.606408\pi\)
−0.328100 + 0.944643i \(0.606408\pi\)
\(930\) 0 0
\(931\) 25.9463 0.850354
\(932\) 0 0
\(933\) 4.65962 0.152549
\(934\) 0 0
\(935\) −7.12631 −0.233055
\(936\) 0 0
\(937\) 8.79635 0.287364 0.143682 0.989624i \(-0.454106\pi\)
0.143682 + 0.989624i \(0.454106\pi\)
\(938\) 0 0
\(939\) −8.10404 −0.264465
\(940\) 0 0
\(941\) −15.3968 −0.501921 −0.250961 0.967997i \(-0.580746\pi\)
−0.250961 + 0.967997i \(0.580746\pi\)
\(942\) 0 0
\(943\) 41.2815 1.34431
\(944\) 0 0
\(945\) −1.40377 −0.0456645
\(946\) 0 0
\(947\) −33.6342 −1.09297 −0.546483 0.837470i \(-0.684034\pi\)
−0.546483 + 0.837470i \(0.684034\pi\)
\(948\) 0 0
\(949\) −1.24680 −0.0404729
\(950\) 0 0
\(951\) −12.1018 −0.392429
\(952\) 0 0
\(953\) 19.0383 0.616712 0.308356 0.951271i \(-0.400221\pi\)
0.308356 + 0.951271i \(0.400221\pi\)
\(954\) 0 0
\(955\) −23.4093 −0.757507
\(956\) 0 0
\(957\) 5.47648 0.177029
\(958\) 0 0
\(959\) 16.9995 0.548943
\(960\) 0 0
\(961\) −16.5605 −0.534211
\(962\) 0 0
\(963\) −3.17924 −0.102450
\(964\) 0 0
\(965\) 13.7935 0.444030
\(966\) 0 0
\(967\) −37.3295 −1.20044 −0.600218 0.799836i \(-0.704920\pi\)
−0.600218 + 0.799836i \(0.704920\pi\)
\(968\) 0 0
\(969\) 6.31822 0.202970
\(970\) 0 0
\(971\) −52.8286 −1.69535 −0.847675 0.530516i \(-0.821998\pi\)
−0.847675 + 0.530516i \(0.821998\pi\)
\(972\) 0 0
\(973\) −13.7460 −0.440678
\(974\) 0 0
\(975\) −3.70348 −0.118606
\(976\) 0 0
\(977\) 31.0861 0.994532 0.497266 0.867598i \(-0.334337\pi\)
0.497266 + 0.867598i \(0.334337\pi\)
\(978\) 0 0
\(979\) 54.7651 1.75030
\(980\) 0 0
\(981\) −12.5475 −0.400612
\(982\) 0 0
\(983\) −2.74694 −0.0876136 −0.0438068 0.999040i \(-0.513949\pi\)
−0.0438068 + 0.999040i \(0.513949\pi\)
\(984\) 0 0
\(985\) 17.8302 0.568117
\(986\) 0 0
\(987\) 6.24027 0.198630
\(988\) 0 0
\(989\) 41.9178 1.33291
\(990\) 0 0
\(991\) 36.1120 1.14713 0.573567 0.819158i \(-0.305559\pi\)
0.573567 + 0.819158i \(0.305559\pi\)
\(992\) 0 0
\(993\) −11.5342 −0.366028
\(994\) 0 0
\(995\) 19.3653 0.613922
\(996\) 0 0
\(997\) −52.4769 −1.66196 −0.830980 0.556302i \(-0.812220\pi\)
−0.830980 + 0.556302i \(0.812220\pi\)
\(998\) 0 0
\(999\) 4.15442 0.131440
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 \(a_p\))