Properties

Label 6036.2.a.g.1.8
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.8
Root \(0.357651\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.642349 q^{5}\) \(-2.57693 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.642349 q^{5}\) \(-2.57693 q^{7}\) \(+1.00000 q^{9}\) \(-1.59395 q^{11}\) \(-3.01981 q^{13}\) \(-0.642349 q^{15}\) \(+5.85477 q^{17}\) \(+4.15803 q^{19}\) \(-2.57693 q^{21}\) \(+6.16672 q^{23}\) \(-4.58739 q^{25}\) \(+1.00000 q^{27}\) \(+0.244932 q^{29}\) \(-5.80673 q^{31}\) \(-1.59395 q^{33}\) \(+1.65529 q^{35}\) \(-2.35969 q^{37}\) \(-3.01981 q^{39}\) \(+3.00916 q^{41}\) \(-1.02072 q^{43}\) \(-0.642349 q^{45}\) \(-9.29799 q^{47}\) \(-0.359430 q^{49}\) \(+5.85477 q^{51}\) \(-8.77282 q^{53}\) \(+1.02388 q^{55}\) \(+4.15803 q^{57}\) \(+1.90637 q^{59}\) \(+3.09875 q^{61}\) \(-2.57693 q^{63}\) \(+1.93977 q^{65}\) \(+0.795114 q^{67}\) \(+6.16672 q^{69}\) \(+6.62085 q^{71}\) \(+5.75222 q^{73}\) \(-4.58739 q^{75}\) \(+4.10751 q^{77}\) \(-15.7483 q^{79}\) \(+1.00000 q^{81}\) \(+5.53292 q^{83}\) \(-3.76080 q^{85}\) \(+0.244932 q^{87}\) \(+6.54723 q^{89}\) \(+7.78184 q^{91}\) \(-5.80673 q^{93}\) \(-2.67091 q^{95}\) \(+12.6589 q^{97}\) \(-1.59395 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.642349 −0.287267 −0.143634 0.989631i \(-0.545879\pi\)
−0.143634 + 0.989631i \(0.545879\pi\)
\(6\) 0 0
\(7\) −2.57693 −0.973988 −0.486994 0.873405i \(-0.661907\pi\)
−0.486994 + 0.873405i \(0.661907\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.59395 −0.480595 −0.240298 0.970699i \(-0.577245\pi\)
−0.240298 + 0.970699i \(0.577245\pi\)
\(12\) 0 0
\(13\) −3.01981 −0.837545 −0.418772 0.908091i \(-0.637540\pi\)
−0.418772 + 0.908091i \(0.637540\pi\)
\(14\) 0 0
\(15\) −0.642349 −0.165854
\(16\) 0 0
\(17\) 5.85477 1.41999 0.709995 0.704207i \(-0.248697\pi\)
0.709995 + 0.704207i \(0.248697\pi\)
\(18\) 0 0
\(19\) 4.15803 0.953917 0.476958 0.878926i \(-0.341739\pi\)
0.476958 + 0.878926i \(0.341739\pi\)
\(20\) 0 0
\(21\) −2.57693 −0.562332
\(22\) 0 0
\(23\) 6.16672 1.28585 0.642925 0.765929i \(-0.277721\pi\)
0.642925 + 0.765929i \(0.277721\pi\)
\(24\) 0 0
\(25\) −4.58739 −0.917477
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.244932 0.0454827 0.0227414 0.999741i \(-0.492761\pi\)
0.0227414 + 0.999741i \(0.492761\pi\)
\(30\) 0 0
\(31\) −5.80673 −1.04292 −0.521460 0.853276i \(-0.674612\pi\)
−0.521460 + 0.853276i \(0.674612\pi\)
\(32\) 0 0
\(33\) −1.59395 −0.277472
\(34\) 0 0
\(35\) 1.65529 0.279795
\(36\) 0 0
\(37\) −2.35969 −0.387931 −0.193965 0.981008i \(-0.562135\pi\)
−0.193965 + 0.981008i \(0.562135\pi\)
\(38\) 0 0
\(39\) −3.01981 −0.483557
\(40\) 0 0
\(41\) 3.00916 0.469952 0.234976 0.972001i \(-0.424499\pi\)
0.234976 + 0.972001i \(0.424499\pi\)
\(42\) 0 0
\(43\) −1.02072 −0.155658 −0.0778290 0.996967i \(-0.524799\pi\)
−0.0778290 + 0.996967i \(0.524799\pi\)
\(44\) 0 0
\(45\) −0.642349 −0.0957558
\(46\) 0 0
\(47\) −9.29799 −1.35625 −0.678126 0.734946i \(-0.737207\pi\)
−0.678126 + 0.734946i \(0.737207\pi\)
\(48\) 0 0
\(49\) −0.359430 −0.0513471
\(50\) 0 0
\(51\) 5.85477 0.819831
\(52\) 0 0
\(53\) −8.77282 −1.20504 −0.602520 0.798104i \(-0.705836\pi\)
−0.602520 + 0.798104i \(0.705836\pi\)
\(54\) 0 0
\(55\) 1.02388 0.138059
\(56\) 0 0
\(57\) 4.15803 0.550744
\(58\) 0 0
\(59\) 1.90637 0.248188 0.124094 0.992270i \(-0.460398\pi\)
0.124094 + 0.992270i \(0.460398\pi\)
\(60\) 0 0
\(61\) 3.09875 0.396754 0.198377 0.980126i \(-0.436433\pi\)
0.198377 + 0.980126i \(0.436433\pi\)
\(62\) 0 0
\(63\) −2.57693 −0.324663
\(64\) 0 0
\(65\) 1.93977 0.240599
\(66\) 0 0
\(67\) 0.795114 0.0971386 0.0485693 0.998820i \(-0.484534\pi\)
0.0485693 + 0.998820i \(0.484534\pi\)
\(68\) 0 0
\(69\) 6.16672 0.742386
\(70\) 0 0
\(71\) 6.62085 0.785750 0.392875 0.919592i \(-0.371481\pi\)
0.392875 + 0.919592i \(0.371481\pi\)
\(72\) 0 0
\(73\) 5.75222 0.673247 0.336623 0.941639i \(-0.390715\pi\)
0.336623 + 0.941639i \(0.390715\pi\)
\(74\) 0 0
\(75\) −4.58739 −0.529706
\(76\) 0 0
\(77\) 4.10751 0.468094
\(78\) 0 0
\(79\) −15.7483 −1.77182 −0.885912 0.463854i \(-0.846466\pi\)
−0.885912 + 0.463854i \(0.846466\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.53292 0.607316 0.303658 0.952781i \(-0.401792\pi\)
0.303658 + 0.952781i \(0.401792\pi\)
\(84\) 0 0
\(85\) −3.76080 −0.407917
\(86\) 0 0
\(87\) 0.244932 0.0262595
\(88\) 0 0
\(89\) 6.54723 0.694005 0.347003 0.937864i \(-0.387200\pi\)
0.347003 + 0.937864i \(0.387200\pi\)
\(90\) 0 0
\(91\) 7.78184 0.815759
\(92\) 0 0
\(93\) −5.80673 −0.602130
\(94\) 0 0
\(95\) −2.67091 −0.274029
\(96\) 0 0
\(97\) 12.6589 1.28531 0.642657 0.766154i \(-0.277832\pi\)
0.642657 + 0.766154i \(0.277832\pi\)
\(98\) 0 0
\(99\) −1.59395 −0.160198
\(100\) 0 0
\(101\) −9.98911 −0.993953 −0.496977 0.867764i \(-0.665557\pi\)
−0.496977 + 0.867764i \(0.665557\pi\)
\(102\) 0 0
\(103\) −6.44516 −0.635060 −0.317530 0.948248i \(-0.602853\pi\)
−0.317530 + 0.948248i \(0.602853\pi\)
\(104\) 0 0
\(105\) 1.65529 0.161540
\(106\) 0 0
\(107\) −7.07502 −0.683968 −0.341984 0.939706i \(-0.611099\pi\)
−0.341984 + 0.939706i \(0.611099\pi\)
\(108\) 0 0
\(109\) −12.6482 −1.21148 −0.605741 0.795662i \(-0.707123\pi\)
−0.605741 + 0.795662i \(0.707123\pi\)
\(110\) 0 0
\(111\) −2.35969 −0.223972
\(112\) 0 0
\(113\) −12.7692 −1.20122 −0.600612 0.799541i \(-0.705076\pi\)
−0.600612 + 0.799541i \(0.705076\pi\)
\(114\) 0 0
\(115\) −3.96119 −0.369383
\(116\) 0 0
\(117\) −3.01981 −0.279182
\(118\) 0 0
\(119\) −15.0873 −1.38305
\(120\) 0 0
\(121\) −8.45931 −0.769028
\(122\) 0 0
\(123\) 3.00916 0.271327
\(124\) 0 0
\(125\) 6.15845 0.550829
\(126\) 0 0
\(127\) 1.98151 0.175831 0.0879155 0.996128i \(-0.471979\pi\)
0.0879155 + 0.996128i \(0.471979\pi\)
\(128\) 0 0
\(129\) −1.02072 −0.0898692
\(130\) 0 0
\(131\) 3.32004 0.290073 0.145037 0.989426i \(-0.453670\pi\)
0.145037 + 0.989426i \(0.453670\pi\)
\(132\) 0 0
\(133\) −10.7149 −0.929104
\(134\) 0 0
\(135\) −0.642349 −0.0552846
\(136\) 0 0
\(137\) −19.6930 −1.68249 −0.841243 0.540657i \(-0.818176\pi\)
−0.841243 + 0.540657i \(0.818176\pi\)
\(138\) 0 0
\(139\) −1.75068 −0.148491 −0.0742455 0.997240i \(-0.523655\pi\)
−0.0742455 + 0.997240i \(0.523655\pi\)
\(140\) 0 0
\(141\) −9.29799 −0.783032
\(142\) 0 0
\(143\) 4.81344 0.402520
\(144\) 0 0
\(145\) −0.157332 −0.0130657
\(146\) 0 0
\(147\) −0.359430 −0.0296453
\(148\) 0 0
\(149\) −19.8397 −1.62533 −0.812667 0.582729i \(-0.801985\pi\)
−0.812667 + 0.582729i \(0.801985\pi\)
\(150\) 0 0
\(151\) 13.2275 1.07644 0.538221 0.842804i \(-0.319097\pi\)
0.538221 + 0.842804i \(0.319097\pi\)
\(152\) 0 0
\(153\) 5.85477 0.473330
\(154\) 0 0
\(155\) 3.72995 0.299597
\(156\) 0 0
\(157\) −2.79464 −0.223037 −0.111518 0.993762i \(-0.535571\pi\)
−0.111518 + 0.993762i \(0.535571\pi\)
\(158\) 0 0
\(159\) −8.77282 −0.695730
\(160\) 0 0
\(161\) −15.8912 −1.25240
\(162\) 0 0
\(163\) 0.834639 0.0653740 0.0326870 0.999466i \(-0.489594\pi\)
0.0326870 + 0.999466i \(0.489594\pi\)
\(164\) 0 0
\(165\) 1.02388 0.0797086
\(166\) 0 0
\(167\) −18.2561 −1.41270 −0.706351 0.707861i \(-0.749660\pi\)
−0.706351 + 0.707861i \(0.749660\pi\)
\(168\) 0 0
\(169\) −3.88074 −0.298518
\(170\) 0 0
\(171\) 4.15803 0.317972
\(172\) 0 0
\(173\) −6.01260 −0.457130 −0.228565 0.973529i \(-0.573403\pi\)
−0.228565 + 0.973529i \(0.573403\pi\)
\(174\) 0 0
\(175\) 11.8214 0.893612
\(176\) 0 0
\(177\) 1.90637 0.143291
\(178\) 0 0
\(179\) 2.51258 0.187799 0.0938996 0.995582i \(-0.470067\pi\)
0.0938996 + 0.995582i \(0.470067\pi\)
\(180\) 0 0
\(181\) 2.59082 0.192574 0.0962872 0.995354i \(-0.469303\pi\)
0.0962872 + 0.995354i \(0.469303\pi\)
\(182\) 0 0
\(183\) 3.09875 0.229066
\(184\) 0 0
\(185\) 1.51575 0.111440
\(186\) 0 0
\(187\) −9.33223 −0.682440
\(188\) 0 0
\(189\) −2.57693 −0.187444
\(190\) 0 0
\(191\) −21.6020 −1.56307 −0.781533 0.623864i \(-0.785562\pi\)
−0.781533 + 0.623864i \(0.785562\pi\)
\(192\) 0 0
\(193\) −15.6272 −1.12487 −0.562434 0.826843i \(-0.690135\pi\)
−0.562434 + 0.826843i \(0.690135\pi\)
\(194\) 0 0
\(195\) 1.93977 0.138910
\(196\) 0 0
\(197\) −8.33545 −0.593876 −0.296938 0.954897i \(-0.595966\pi\)
−0.296938 + 0.954897i \(0.595966\pi\)
\(198\) 0 0
\(199\) 1.27093 0.0900942 0.0450471 0.998985i \(-0.485656\pi\)
0.0450471 + 0.998985i \(0.485656\pi\)
\(200\) 0 0
\(201\) 0.795114 0.0560830
\(202\) 0 0
\(203\) −0.631173 −0.0442996
\(204\) 0 0
\(205\) −1.93293 −0.135002
\(206\) 0 0
\(207\) 6.16672 0.428617
\(208\) 0 0
\(209\) −6.62771 −0.458448
\(210\) 0 0
\(211\) −25.9437 −1.78604 −0.893019 0.450019i \(-0.851417\pi\)
−0.893019 + 0.450019i \(0.851417\pi\)
\(212\) 0 0
\(213\) 6.62085 0.453653
\(214\) 0 0
\(215\) 0.655657 0.0447155
\(216\) 0 0
\(217\) 14.9635 1.01579
\(218\) 0 0
\(219\) 5.75222 0.388699
\(220\) 0 0
\(221\) −17.6803 −1.18930
\(222\) 0 0
\(223\) 26.9487 1.80462 0.902308 0.431091i \(-0.141871\pi\)
0.902308 + 0.431091i \(0.141871\pi\)
\(224\) 0 0
\(225\) −4.58739 −0.305826
\(226\) 0 0
\(227\) −6.41503 −0.425781 −0.212890 0.977076i \(-0.568288\pi\)
−0.212890 + 0.977076i \(0.568288\pi\)
\(228\) 0 0
\(229\) 21.6447 1.43032 0.715162 0.698959i \(-0.246353\pi\)
0.715162 + 0.698959i \(0.246353\pi\)
\(230\) 0 0
\(231\) 4.10751 0.270254
\(232\) 0 0
\(233\) −7.27488 −0.476593 −0.238297 0.971192i \(-0.576589\pi\)
−0.238297 + 0.971192i \(0.576589\pi\)
\(234\) 0 0
\(235\) 5.97256 0.389607
\(236\) 0 0
\(237\) −15.7483 −1.02296
\(238\) 0 0
\(239\) −5.35849 −0.346612 −0.173306 0.984868i \(-0.555445\pi\)
−0.173306 + 0.984868i \(0.555445\pi\)
\(240\) 0 0
\(241\) −14.9547 −0.963314 −0.481657 0.876360i \(-0.659965\pi\)
−0.481657 + 0.876360i \(0.659965\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.230880 0.0147504
\(246\) 0 0
\(247\) −12.5565 −0.798948
\(248\) 0 0
\(249\) 5.53292 0.350634
\(250\) 0 0
\(251\) 16.8397 1.06292 0.531458 0.847085i \(-0.321644\pi\)
0.531458 + 0.847085i \(0.321644\pi\)
\(252\) 0 0
\(253\) −9.82948 −0.617974
\(254\) 0 0
\(255\) −3.76080 −0.235511
\(256\) 0 0
\(257\) 2.48952 0.155292 0.0776461 0.996981i \(-0.475260\pi\)
0.0776461 + 0.996981i \(0.475260\pi\)
\(258\) 0 0
\(259\) 6.08076 0.377840
\(260\) 0 0
\(261\) 0.244932 0.0151609
\(262\) 0 0
\(263\) 18.4315 1.13653 0.568267 0.822844i \(-0.307614\pi\)
0.568267 + 0.822844i \(0.307614\pi\)
\(264\) 0 0
\(265\) 5.63521 0.346168
\(266\) 0 0
\(267\) 6.54723 0.400684
\(268\) 0 0
\(269\) −7.78988 −0.474957 −0.237479 0.971393i \(-0.576321\pi\)
−0.237479 + 0.971393i \(0.576321\pi\)
\(270\) 0 0
\(271\) −15.3470 −0.932262 −0.466131 0.884716i \(-0.654352\pi\)
−0.466131 + 0.884716i \(0.654352\pi\)
\(272\) 0 0
\(273\) 7.78184 0.470979
\(274\) 0 0
\(275\) 7.31209 0.440936
\(276\) 0 0
\(277\) 18.7422 1.12611 0.563055 0.826419i \(-0.309626\pi\)
0.563055 + 0.826419i \(0.309626\pi\)
\(278\) 0 0
\(279\) −5.80673 −0.347640
\(280\) 0 0
\(281\) −18.9025 −1.12763 −0.563813 0.825903i \(-0.690666\pi\)
−0.563813 + 0.825903i \(0.690666\pi\)
\(282\) 0 0
\(283\) −9.54838 −0.567592 −0.283796 0.958885i \(-0.591594\pi\)
−0.283796 + 0.958885i \(0.591594\pi\)
\(284\) 0 0
\(285\) −2.67091 −0.158211
\(286\) 0 0
\(287\) −7.75440 −0.457728
\(288\) 0 0
\(289\) 17.2783 1.01637
\(290\) 0 0
\(291\) 12.6589 0.742077
\(292\) 0 0
\(293\) 30.6885 1.79284 0.896420 0.443205i \(-0.146159\pi\)
0.896420 + 0.443205i \(0.146159\pi\)
\(294\) 0 0
\(295\) −1.22455 −0.0712963
\(296\) 0 0
\(297\) −1.59395 −0.0924906
\(298\) 0 0
\(299\) −18.6223 −1.07696
\(300\) 0 0
\(301\) 2.63032 0.151609
\(302\) 0 0
\(303\) −9.98911 −0.573859
\(304\) 0 0
\(305\) −1.99048 −0.113974
\(306\) 0 0
\(307\) −9.47032 −0.540500 −0.270250 0.962790i \(-0.587106\pi\)
−0.270250 + 0.962790i \(0.587106\pi\)
\(308\) 0 0
\(309\) −6.44516 −0.366652
\(310\) 0 0
\(311\) −15.7391 −0.892483 −0.446242 0.894913i \(-0.647238\pi\)
−0.446242 + 0.894913i \(0.647238\pi\)
\(312\) 0 0
\(313\) −10.6972 −0.604643 −0.302321 0.953206i \(-0.597762\pi\)
−0.302321 + 0.953206i \(0.597762\pi\)
\(314\) 0 0
\(315\) 1.65529 0.0932650
\(316\) 0 0
\(317\) 7.00074 0.393201 0.196600 0.980484i \(-0.437010\pi\)
0.196600 + 0.980484i \(0.437010\pi\)
\(318\) 0 0
\(319\) −0.390411 −0.0218588
\(320\) 0 0
\(321\) −7.07502 −0.394889
\(322\) 0 0
\(323\) 24.3443 1.35455
\(324\) 0 0
\(325\) 13.8530 0.768429
\(326\) 0 0
\(327\) −12.6482 −0.699449
\(328\) 0 0
\(329\) 23.9603 1.32097
\(330\) 0 0
\(331\) 20.7091 1.13827 0.569137 0.822242i \(-0.307277\pi\)
0.569137 + 0.822242i \(0.307277\pi\)
\(332\) 0 0
\(333\) −2.35969 −0.129310
\(334\) 0 0
\(335\) −0.510741 −0.0279048
\(336\) 0 0
\(337\) −11.7529 −0.640223 −0.320112 0.947380i \(-0.603720\pi\)
−0.320112 + 0.947380i \(0.603720\pi\)
\(338\) 0 0
\(339\) −12.7692 −0.693527
\(340\) 0 0
\(341\) 9.25567 0.501223
\(342\) 0 0
\(343\) 18.9647 1.02400
\(344\) 0 0
\(345\) −3.96119 −0.213263
\(346\) 0 0
\(347\) 5.39993 0.289883 0.144942 0.989440i \(-0.453701\pi\)
0.144942 + 0.989440i \(0.453701\pi\)
\(348\) 0 0
\(349\) −6.03522 −0.323058 −0.161529 0.986868i \(-0.551643\pi\)
−0.161529 + 0.986868i \(0.551643\pi\)
\(350\) 0 0
\(351\) −3.01981 −0.161186
\(352\) 0 0
\(353\) −20.6927 −1.10136 −0.550679 0.834717i \(-0.685631\pi\)
−0.550679 + 0.834717i \(0.685631\pi\)
\(354\) 0 0
\(355\) −4.25290 −0.225720
\(356\) 0 0
\(357\) −15.0873 −0.798506
\(358\) 0 0
\(359\) 29.2602 1.54429 0.772147 0.635445i \(-0.219183\pi\)
0.772147 + 0.635445i \(0.219183\pi\)
\(360\) 0 0
\(361\) −1.71081 −0.0900428
\(362\) 0 0
\(363\) −8.45931 −0.443999
\(364\) 0 0
\(365\) −3.69494 −0.193402
\(366\) 0 0
\(367\) −14.9913 −0.782539 −0.391269 0.920276i \(-0.627964\pi\)
−0.391269 + 0.920276i \(0.627964\pi\)
\(368\) 0 0
\(369\) 3.00916 0.156651
\(370\) 0 0
\(371\) 22.6069 1.17369
\(372\) 0 0
\(373\) −13.6212 −0.705277 −0.352638 0.935760i \(-0.614715\pi\)
−0.352638 + 0.935760i \(0.614715\pi\)
\(374\) 0 0
\(375\) 6.15845 0.318021
\(376\) 0 0
\(377\) −0.739649 −0.0380938
\(378\) 0 0
\(379\) 20.5946 1.05788 0.528938 0.848661i \(-0.322591\pi\)
0.528938 + 0.848661i \(0.322591\pi\)
\(380\) 0 0
\(381\) 1.98151 0.101516
\(382\) 0 0
\(383\) −35.7833 −1.82844 −0.914222 0.405214i \(-0.867197\pi\)
−0.914222 + 0.405214i \(0.867197\pi\)
\(384\) 0 0
\(385\) −2.63846 −0.134468
\(386\) 0 0
\(387\) −1.02072 −0.0518860
\(388\) 0 0
\(389\) 11.3770 0.576836 0.288418 0.957505i \(-0.406871\pi\)
0.288418 + 0.957505i \(0.406871\pi\)
\(390\) 0 0
\(391\) 36.1047 1.82589
\(392\) 0 0
\(393\) 3.32004 0.167474
\(394\) 0 0
\(395\) 10.1159 0.508987
\(396\) 0 0
\(397\) −22.0959 −1.10896 −0.554482 0.832196i \(-0.687083\pi\)
−0.554482 + 0.832196i \(0.687083\pi\)
\(398\) 0 0
\(399\) −10.7149 −0.536418
\(400\) 0 0
\(401\) 13.6270 0.680502 0.340251 0.940335i \(-0.389488\pi\)
0.340251 + 0.940335i \(0.389488\pi\)
\(402\) 0 0
\(403\) 17.5352 0.873492
\(404\) 0 0
\(405\) −0.642349 −0.0319186
\(406\) 0 0
\(407\) 3.76124 0.186438
\(408\) 0 0
\(409\) 19.9098 0.984474 0.492237 0.870461i \(-0.336179\pi\)
0.492237 + 0.870461i \(0.336179\pi\)
\(410\) 0 0
\(411\) −19.6930 −0.971384
\(412\) 0 0
\(413\) −4.91258 −0.241732
\(414\) 0 0
\(415\) −3.55406 −0.174462
\(416\) 0 0
\(417\) −1.75068 −0.0857313
\(418\) 0 0
\(419\) 7.86876 0.384414 0.192207 0.981354i \(-0.438435\pi\)
0.192207 + 0.981354i \(0.438435\pi\)
\(420\) 0 0
\(421\) −28.4676 −1.38743 −0.693713 0.720252i \(-0.744026\pi\)
−0.693713 + 0.720252i \(0.744026\pi\)
\(422\) 0 0
\(423\) −9.29799 −0.452084
\(424\) 0 0
\(425\) −26.8581 −1.30281
\(426\) 0 0
\(427\) −7.98525 −0.386434
\(428\) 0 0
\(429\) 4.81344 0.232395
\(430\) 0 0
\(431\) −32.9459 −1.58695 −0.793475 0.608603i \(-0.791730\pi\)
−0.793475 + 0.608603i \(0.791730\pi\)
\(432\) 0 0
\(433\) 17.8087 0.855830 0.427915 0.903819i \(-0.359248\pi\)
0.427915 + 0.903819i \(0.359248\pi\)
\(434\) 0 0
\(435\) −0.157332 −0.00754349
\(436\) 0 0
\(437\) 25.6414 1.22659
\(438\) 0 0
\(439\) 30.6041 1.46066 0.730328 0.683096i \(-0.239367\pi\)
0.730328 + 0.683096i \(0.239367\pi\)
\(440\) 0 0
\(441\) −0.359430 −0.0171157
\(442\) 0 0
\(443\) −4.91149 −0.233352 −0.116676 0.993170i \(-0.537224\pi\)
−0.116676 + 0.993170i \(0.537224\pi\)
\(444\) 0 0
\(445\) −4.20561 −0.199365
\(446\) 0 0
\(447\) −19.8397 −0.938387
\(448\) 0 0
\(449\) 9.07590 0.428318 0.214159 0.976799i \(-0.431299\pi\)
0.214159 + 0.976799i \(0.431299\pi\)
\(450\) 0 0
\(451\) −4.79647 −0.225857
\(452\) 0 0
\(453\) 13.2275 0.621484
\(454\) 0 0
\(455\) −4.99866 −0.234341
\(456\) 0 0
\(457\) −15.6041 −0.729929 −0.364964 0.931021i \(-0.618919\pi\)
−0.364964 + 0.931021i \(0.618919\pi\)
\(458\) 0 0
\(459\) 5.85477 0.273277
\(460\) 0 0
\(461\) −19.1431 −0.891585 −0.445792 0.895136i \(-0.647078\pi\)
−0.445792 + 0.895136i \(0.647078\pi\)
\(462\) 0 0
\(463\) 9.87484 0.458923 0.229461 0.973318i \(-0.426304\pi\)
0.229461 + 0.973318i \(0.426304\pi\)
\(464\) 0 0
\(465\) 3.72995 0.172972
\(466\) 0 0
\(467\) −13.8413 −0.640498 −0.320249 0.947333i \(-0.603767\pi\)
−0.320249 + 0.947333i \(0.603767\pi\)
\(468\) 0 0
\(469\) −2.04895 −0.0946119
\(470\) 0 0
\(471\) −2.79464 −0.128770
\(472\) 0 0
\(473\) 1.62698 0.0748085
\(474\) 0 0
\(475\) −19.0745 −0.875197
\(476\) 0 0
\(477\) −8.77282 −0.401680
\(478\) 0 0
\(479\) −22.1039 −1.00995 −0.504977 0.863133i \(-0.668499\pi\)
−0.504977 + 0.863133i \(0.668499\pi\)
\(480\) 0 0
\(481\) 7.12582 0.324909
\(482\) 0 0
\(483\) −15.8912 −0.723075
\(484\) 0 0
\(485\) −8.13142 −0.369229
\(486\) 0 0
\(487\) 8.92524 0.404441 0.202221 0.979340i \(-0.435184\pi\)
0.202221 + 0.979340i \(0.435184\pi\)
\(488\) 0 0
\(489\) 0.834639 0.0377437
\(490\) 0 0
\(491\) −25.3096 −1.14221 −0.571103 0.820878i \(-0.693484\pi\)
−0.571103 + 0.820878i \(0.693484\pi\)
\(492\) 0 0
\(493\) 1.43402 0.0645850
\(494\) 0 0
\(495\) 1.02388 0.0460198
\(496\) 0 0
\(497\) −17.0615 −0.765311
\(498\) 0 0
\(499\) −5.26088 −0.235509 −0.117755 0.993043i \(-0.537570\pi\)
−0.117755 + 0.993043i \(0.537570\pi\)
\(500\) 0 0
\(501\) −18.2561 −0.815624
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 6.41650 0.285530
\(506\) 0 0
\(507\) −3.88074 −0.172350
\(508\) 0 0
\(509\) −17.3636 −0.769628 −0.384814 0.922994i \(-0.625734\pi\)
−0.384814 + 0.922994i \(0.625734\pi\)
\(510\) 0 0
\(511\) −14.8231 −0.655734
\(512\) 0 0
\(513\) 4.15803 0.183581
\(514\) 0 0
\(515\) 4.14004 0.182432
\(516\) 0 0
\(517\) 14.8206 0.651808
\(518\) 0 0
\(519\) −6.01260 −0.263924
\(520\) 0 0
\(521\) 32.6821 1.43183 0.715913 0.698189i \(-0.246011\pi\)
0.715913 + 0.698189i \(0.246011\pi\)
\(522\) 0 0
\(523\) 2.25399 0.0985602 0.0492801 0.998785i \(-0.484307\pi\)
0.0492801 + 0.998785i \(0.484307\pi\)
\(524\) 0 0
\(525\) 11.8214 0.515927
\(526\) 0 0
\(527\) −33.9971 −1.48094
\(528\) 0 0
\(529\) 15.0285 0.653412
\(530\) 0 0
\(531\) 1.90637 0.0827293
\(532\) 0 0
\(533\) −9.08710 −0.393606
\(534\) 0 0
\(535\) 4.54463 0.196482
\(536\) 0 0
\(537\) 2.51258 0.108426
\(538\) 0 0
\(539\) 0.572915 0.0246772
\(540\) 0 0
\(541\) 26.8934 1.15624 0.578118 0.815953i \(-0.303787\pi\)
0.578118 + 0.815953i \(0.303787\pi\)
\(542\) 0 0
\(543\) 2.59082 0.111183
\(544\) 0 0
\(545\) 8.12458 0.348019
\(546\) 0 0
\(547\) 40.2434 1.72068 0.860342 0.509718i \(-0.170250\pi\)
0.860342 + 0.509718i \(0.170250\pi\)
\(548\) 0 0
\(549\) 3.09875 0.132251
\(550\) 0 0
\(551\) 1.01843 0.0433867
\(552\) 0 0
\(553\) 40.5823 1.72573
\(554\) 0 0
\(555\) 1.51575 0.0643398
\(556\) 0 0
\(557\) 39.4195 1.67026 0.835130 0.550053i \(-0.185393\pi\)
0.835130 + 0.550053i \(0.185393\pi\)
\(558\) 0 0
\(559\) 3.08238 0.130371
\(560\) 0 0
\(561\) −9.33223 −0.394007
\(562\) 0 0
\(563\) 21.8100 0.919181 0.459590 0.888131i \(-0.347996\pi\)
0.459590 + 0.888131i \(0.347996\pi\)
\(564\) 0 0
\(565\) 8.20227 0.345072
\(566\) 0 0
\(567\) −2.57693 −0.108221
\(568\) 0 0
\(569\) 2.32164 0.0973283 0.0486642 0.998815i \(-0.484504\pi\)
0.0486642 + 0.998815i \(0.484504\pi\)
\(570\) 0 0
\(571\) 22.7309 0.951259 0.475629 0.879646i \(-0.342220\pi\)
0.475629 + 0.879646i \(0.342220\pi\)
\(572\) 0 0
\(573\) −21.6020 −0.902436
\(574\) 0 0
\(575\) −28.2892 −1.17974
\(576\) 0 0
\(577\) 20.7828 0.865200 0.432600 0.901586i \(-0.357596\pi\)
0.432600 + 0.901586i \(0.357596\pi\)
\(578\) 0 0
\(579\) −15.6272 −0.649442
\(580\) 0 0
\(581\) −14.2579 −0.591519
\(582\) 0 0
\(583\) 13.9835 0.579136
\(584\) 0 0
\(585\) 1.93977 0.0801998
\(586\) 0 0
\(587\) 16.3314 0.674070 0.337035 0.941492i \(-0.390576\pi\)
0.337035 + 0.941492i \(0.390576\pi\)
\(588\) 0 0
\(589\) −24.1445 −0.994859
\(590\) 0 0
\(591\) −8.33545 −0.342875
\(592\) 0 0
\(593\) −22.4020 −0.919941 −0.459971 0.887934i \(-0.652140\pi\)
−0.459971 + 0.887934i \(0.652140\pi\)
\(594\) 0 0
\(595\) 9.69133 0.397306
\(596\) 0 0
\(597\) 1.27093 0.0520159
\(598\) 0 0
\(599\) 1.92173 0.0785197 0.0392599 0.999229i \(-0.487500\pi\)
0.0392599 + 0.999229i \(0.487500\pi\)
\(600\) 0 0
\(601\) −47.1530 −1.92341 −0.961705 0.274087i \(-0.911624\pi\)
−0.961705 + 0.274087i \(0.911624\pi\)
\(602\) 0 0
\(603\) 0.795114 0.0323795
\(604\) 0 0
\(605\) 5.43383 0.220917
\(606\) 0 0
\(607\) 11.4372 0.464221 0.232110 0.972689i \(-0.425437\pi\)
0.232110 + 0.972689i \(0.425437\pi\)
\(608\) 0 0
\(609\) −0.631173 −0.0255764
\(610\) 0 0
\(611\) 28.0782 1.13592
\(612\) 0 0
\(613\) 42.2523 1.70656 0.853278 0.521457i \(-0.174611\pi\)
0.853278 + 0.521457i \(0.174611\pi\)
\(614\) 0 0
\(615\) −1.93293 −0.0779434
\(616\) 0 0
\(617\) −26.8177 −1.07964 −0.539819 0.841781i \(-0.681507\pi\)
−0.539819 + 0.841781i \(0.681507\pi\)
\(618\) 0 0
\(619\) 12.1200 0.487144 0.243572 0.969883i \(-0.421681\pi\)
0.243572 + 0.969883i \(0.421681\pi\)
\(620\) 0 0
\(621\) 6.16672 0.247462
\(622\) 0 0
\(623\) −16.8718 −0.675953
\(624\) 0 0
\(625\) 18.9811 0.759242
\(626\) 0 0
\(627\) −6.62771 −0.264685
\(628\) 0 0
\(629\) −13.8154 −0.550857
\(630\) 0 0
\(631\) 20.5485 0.818021 0.409011 0.912530i \(-0.365874\pi\)
0.409011 + 0.912530i \(0.365874\pi\)
\(632\) 0 0
\(633\) −25.9437 −1.03117
\(634\) 0 0
\(635\) −1.27282 −0.0505105
\(636\) 0 0
\(637\) 1.08541 0.0430055
\(638\) 0 0
\(639\) 6.62085 0.261917
\(640\) 0 0
\(641\) 25.7509 1.01710 0.508550 0.861033i \(-0.330182\pi\)
0.508550 + 0.861033i \(0.330182\pi\)
\(642\) 0 0
\(643\) 29.6055 1.16753 0.583763 0.811924i \(-0.301580\pi\)
0.583763 + 0.811924i \(0.301580\pi\)
\(644\) 0 0
\(645\) 0.655657 0.0258165
\(646\) 0 0
\(647\) −1.43032 −0.0562319 −0.0281159 0.999605i \(-0.508951\pi\)
−0.0281159 + 0.999605i \(0.508951\pi\)
\(648\) 0 0
\(649\) −3.03867 −0.119278
\(650\) 0 0
\(651\) 14.9635 0.586468
\(652\) 0 0
\(653\) 24.4989 0.958714 0.479357 0.877620i \(-0.340870\pi\)
0.479357 + 0.877620i \(0.340870\pi\)
\(654\) 0 0
\(655\) −2.13263 −0.0833286
\(656\) 0 0
\(657\) 5.75222 0.224416
\(658\) 0 0
\(659\) −17.2369 −0.671456 −0.335728 0.941959i \(-0.608982\pi\)
−0.335728 + 0.941959i \(0.608982\pi\)
\(660\) 0 0
\(661\) −42.6049 −1.65714 −0.828569 0.559888i \(-0.810844\pi\)
−0.828569 + 0.559888i \(0.810844\pi\)
\(662\) 0 0
\(663\) −17.6803 −0.686646
\(664\) 0 0
\(665\) 6.88274 0.266901
\(666\) 0 0
\(667\) 1.51043 0.0584840
\(668\) 0 0
\(669\) 26.9487 1.04190
\(670\) 0 0
\(671\) −4.93926 −0.190678
\(672\) 0 0
\(673\) −16.8197 −0.648354 −0.324177 0.945996i \(-0.605087\pi\)
−0.324177 + 0.945996i \(0.605087\pi\)
\(674\) 0 0
\(675\) −4.58739 −0.176569
\(676\) 0 0
\(677\) 16.1519 0.620769 0.310385 0.950611i \(-0.399542\pi\)
0.310385 + 0.950611i \(0.399542\pi\)
\(678\) 0 0
\(679\) −32.6211 −1.25188
\(680\) 0 0
\(681\) −6.41503 −0.245825
\(682\) 0 0
\(683\) −10.2592 −0.392557 −0.196279 0.980548i \(-0.562886\pi\)
−0.196279 + 0.980548i \(0.562886\pi\)
\(684\) 0 0
\(685\) 12.6498 0.483323
\(686\) 0 0
\(687\) 21.6447 0.825798
\(688\) 0 0
\(689\) 26.4923 1.00927
\(690\) 0 0
\(691\) −11.9842 −0.455901 −0.227951 0.973673i \(-0.573202\pi\)
−0.227951 + 0.973673i \(0.573202\pi\)
\(692\) 0 0
\(693\) 4.10751 0.156031
\(694\) 0 0
\(695\) 1.12455 0.0426566
\(696\) 0 0
\(697\) 17.6179 0.667327
\(698\) 0 0
\(699\) −7.27488 −0.275161
\(700\) 0 0
\(701\) 43.9885 1.66142 0.830712 0.556703i \(-0.187934\pi\)
0.830712 + 0.556703i \(0.187934\pi\)
\(702\) 0 0
\(703\) −9.81166 −0.370054
\(704\) 0 0
\(705\) 5.97256 0.224940
\(706\) 0 0
\(707\) 25.7412 0.968099
\(708\) 0 0
\(709\) −14.7967 −0.555701 −0.277850 0.960624i \(-0.589622\pi\)
−0.277850 + 0.960624i \(0.589622\pi\)
\(710\) 0 0
\(711\) −15.7483 −0.590608
\(712\) 0 0
\(713\) −35.8085 −1.34104
\(714\) 0 0
\(715\) −3.09191 −0.115631
\(716\) 0 0
\(717\) −5.35849 −0.200117
\(718\) 0 0
\(719\) 37.9691 1.41601 0.708004 0.706208i \(-0.249596\pi\)
0.708004 + 0.706208i \(0.249596\pi\)
\(720\) 0 0
\(721\) 16.6087 0.618541
\(722\) 0 0
\(723\) −14.9547 −0.556170
\(724\) 0 0
\(725\) −1.12360 −0.0417294
\(726\) 0 0
\(727\) −18.1719 −0.673957 −0.336979 0.941512i \(-0.609405\pi\)
−0.336979 + 0.941512i \(0.609405\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.97606 −0.221033
\(732\) 0 0
\(733\) −34.3399 −1.26837 −0.634187 0.773180i \(-0.718665\pi\)
−0.634187 + 0.773180i \(0.718665\pi\)
\(734\) 0 0
\(735\) 0.230880 0.00851612
\(736\) 0 0
\(737\) −1.26738 −0.0466844
\(738\) 0 0
\(739\) −22.4903 −0.827319 −0.413660 0.910432i \(-0.635750\pi\)
−0.413660 + 0.910432i \(0.635750\pi\)
\(740\) 0 0
\(741\) −12.5565 −0.461273
\(742\) 0 0
\(743\) −26.8751 −0.985950 −0.492975 0.870043i \(-0.664091\pi\)
−0.492975 + 0.870043i \(0.664091\pi\)
\(744\) 0 0
\(745\) 12.7440 0.466905
\(746\) 0 0
\(747\) 5.53292 0.202439
\(748\) 0 0
\(749\) 18.2318 0.666177
\(750\) 0 0
\(751\) 52.2289 1.90586 0.952930 0.303190i \(-0.0980515\pi\)
0.952930 + 0.303190i \(0.0980515\pi\)
\(752\) 0 0
\(753\) 16.8397 0.613674
\(754\) 0 0
\(755\) −8.49670 −0.309227
\(756\) 0 0
\(757\) −34.3553 −1.24867 −0.624333 0.781159i \(-0.714629\pi\)
−0.624333 + 0.781159i \(0.714629\pi\)
\(758\) 0 0
\(759\) −9.82948 −0.356788
\(760\) 0 0
\(761\) 36.8627 1.33627 0.668136 0.744039i \(-0.267092\pi\)
0.668136 + 0.744039i \(0.267092\pi\)
\(762\) 0 0
\(763\) 32.5936 1.17997
\(764\) 0 0
\(765\) −3.76080 −0.135972
\(766\) 0 0
\(767\) −5.75687 −0.207869
\(768\) 0 0
\(769\) 26.2610 0.946998 0.473499 0.880794i \(-0.342991\pi\)
0.473499 + 0.880794i \(0.342991\pi\)
\(770\) 0 0
\(771\) 2.48952 0.0896580
\(772\) 0 0
\(773\) 27.2625 0.980563 0.490282 0.871564i \(-0.336894\pi\)
0.490282 + 0.871564i \(0.336894\pi\)
\(774\) 0 0
\(775\) 26.6377 0.956856
\(776\) 0 0
\(777\) 6.08076 0.218146
\(778\) 0 0
\(779\) 12.5122 0.448295
\(780\) 0 0
\(781\) −10.5533 −0.377628
\(782\) 0 0
\(783\) 0.244932 0.00875316
\(784\) 0 0
\(785\) 1.79514 0.0640711
\(786\) 0 0
\(787\) 10.7898 0.384614 0.192307 0.981335i \(-0.438403\pi\)
0.192307 + 0.981335i \(0.438403\pi\)
\(788\) 0 0
\(789\) 18.4315 0.656178
\(790\) 0 0
\(791\) 32.9053 1.16998
\(792\) 0 0
\(793\) −9.35763 −0.332299
\(794\) 0 0
\(795\) 5.63521 0.199860
\(796\) 0 0
\(797\) −45.2526 −1.60293 −0.801465 0.598042i \(-0.795946\pi\)
−0.801465 + 0.598042i \(0.795946\pi\)
\(798\) 0 0
\(799\) −54.4376 −1.92586
\(800\) 0 0
\(801\) 6.54723 0.231335
\(802\) 0 0
\(803\) −9.16878 −0.323559
\(804\) 0 0
\(805\) 10.2077 0.359775
\(806\) 0 0
\(807\) −7.78988 −0.274217
\(808\) 0 0
\(809\) −49.7421 −1.74884 −0.874420 0.485170i \(-0.838758\pi\)
−0.874420 + 0.485170i \(0.838758\pi\)
\(810\) 0 0
\(811\) 40.6208 1.42639 0.713194 0.700967i \(-0.247248\pi\)
0.713194 + 0.700967i \(0.247248\pi\)
\(812\) 0 0
\(813\) −15.3470 −0.538242
\(814\) 0 0
\(815\) −0.536130 −0.0187798
\(816\) 0 0
\(817\) −4.24417 −0.148485
\(818\) 0 0
\(819\) 7.78184 0.271920
\(820\) 0 0
\(821\) −25.9803 −0.906720 −0.453360 0.891328i \(-0.649775\pi\)
−0.453360 + 0.891328i \(0.649775\pi\)
\(822\) 0 0
\(823\) 41.4735 1.44567 0.722837 0.691018i \(-0.242838\pi\)
0.722837 + 0.691018i \(0.242838\pi\)
\(824\) 0 0
\(825\) 7.31209 0.254574
\(826\) 0 0
\(827\) −1.17722 −0.0409358 −0.0204679 0.999791i \(-0.506516\pi\)
−0.0204679 + 0.999791i \(0.506516\pi\)
\(828\) 0 0
\(829\) 2.51815 0.0874590 0.0437295 0.999043i \(-0.486076\pi\)
0.0437295 + 0.999043i \(0.486076\pi\)
\(830\) 0 0
\(831\) 18.7422 0.650160
\(832\) 0 0
\(833\) −2.10438 −0.0729124
\(834\) 0 0
\(835\) 11.7268 0.405823
\(836\) 0 0
\(837\) −5.80673 −0.200710
\(838\) 0 0
\(839\) −25.4576 −0.878895 −0.439447 0.898268i \(-0.644826\pi\)
−0.439447 + 0.898268i \(0.644826\pi\)
\(840\) 0 0
\(841\) −28.9400 −0.997931
\(842\) 0 0
\(843\) −18.9025 −0.651035
\(844\) 0 0
\(845\) 2.49279 0.0857546
\(846\) 0 0
\(847\) 21.7990 0.749024
\(848\) 0 0
\(849\) −9.54838 −0.327699
\(850\) 0 0
\(851\) −14.5516 −0.498821
\(852\) 0 0
\(853\) 38.7461 1.32664 0.663320 0.748336i \(-0.269147\pi\)
0.663320 + 0.748336i \(0.269147\pi\)
\(854\) 0 0
\(855\) −2.67091 −0.0913430
\(856\) 0 0
\(857\) 4.95621 0.169301 0.0846505 0.996411i \(-0.473023\pi\)
0.0846505 + 0.996411i \(0.473023\pi\)
\(858\) 0 0
\(859\) 22.9446 0.782861 0.391430 0.920208i \(-0.371980\pi\)
0.391430 + 0.920208i \(0.371980\pi\)
\(860\) 0 0
\(861\) −7.75440 −0.264269
\(862\) 0 0
\(863\) −15.6756 −0.533605 −0.266802 0.963751i \(-0.585967\pi\)
−0.266802 + 0.963751i \(0.585967\pi\)
\(864\) 0 0
\(865\) 3.86219 0.131318
\(866\) 0 0
\(867\) 17.2783 0.586801
\(868\) 0 0
\(869\) 25.1021 0.851530
\(870\) 0 0
\(871\) −2.40109 −0.0813580
\(872\) 0 0
\(873\) 12.6589 0.428438
\(874\) 0 0
\(875\) −15.8699 −0.536501
\(876\) 0 0
\(877\) −18.5255 −0.625562 −0.312781 0.949825i \(-0.601261\pi\)
−0.312781 + 0.949825i \(0.601261\pi\)
\(878\) 0 0
\(879\) 30.6885 1.03510
\(880\) 0 0
\(881\) −26.9982 −0.909593 −0.454797 0.890595i \(-0.650288\pi\)
−0.454797 + 0.890595i \(0.650288\pi\)
\(882\) 0 0
\(883\) −29.7939 −1.00264 −0.501322 0.865261i \(-0.667153\pi\)
−0.501322 + 0.865261i \(0.667153\pi\)
\(884\) 0 0
\(885\) −1.22455 −0.0411629
\(886\) 0 0
\(887\) −19.0104 −0.638306 −0.319153 0.947703i \(-0.603398\pi\)
−0.319153 + 0.947703i \(0.603398\pi\)
\(888\) 0 0
\(889\) −5.10622 −0.171257
\(890\) 0 0
\(891\) −1.59395 −0.0533995
\(892\) 0 0
\(893\) −38.6613 −1.29375
\(894\) 0 0
\(895\) −1.61396 −0.0539486
\(896\) 0 0
\(897\) −18.6223 −0.621782
\(898\) 0 0
\(899\) −1.42225 −0.0474349
\(900\) 0 0
\(901\) −51.3628 −1.71114
\(902\) 0 0
\(903\) 2.63032 0.0875315
\(904\) 0 0
\(905\) −1.66421 −0.0553203
\(906\) 0 0
\(907\) 15.0562 0.499932 0.249966 0.968255i \(-0.419581\pi\)
0.249966 + 0.968255i \(0.419581\pi\)
\(908\) 0 0
\(909\) −9.98911 −0.331318
\(910\) 0 0
\(911\) −5.37110 −0.177953 −0.0889763 0.996034i \(-0.528360\pi\)
−0.0889763 + 0.996034i \(0.528360\pi\)
\(912\) 0 0
\(913\) −8.81922 −0.291873
\(914\) 0 0
\(915\) −1.99048 −0.0658032
\(916\) 0 0
\(917\) −8.55552 −0.282528
\(918\) 0 0
\(919\) 4.06392 0.134056 0.0670281 0.997751i \(-0.478648\pi\)
0.0670281 + 0.997751i \(0.478648\pi\)
\(920\) 0 0
\(921\) −9.47032 −0.312058
\(922\) 0 0
\(923\) −19.9937 −0.658101
\(924\) 0 0
\(925\) 10.8248 0.355918
\(926\) 0 0
\(927\) −6.44516 −0.211687
\(928\) 0 0
\(929\) 21.5814 0.708061 0.354031 0.935234i \(-0.384811\pi\)
0.354031 + 0.935234i \(0.384811\pi\)
\(930\) 0 0
\(931\) −1.49452 −0.0489809
\(932\) 0 0
\(933\) −15.7391 −0.515275
\(934\) 0 0
\(935\) 5.99455 0.196043
\(936\) 0 0
\(937\) 17.1321 0.559683 0.279841 0.960046i \(-0.409718\pi\)
0.279841 + 0.960046i \(0.409718\pi\)
\(938\) 0 0
\(939\) −10.6972 −0.349091
\(940\) 0 0
\(941\) −52.4335 −1.70928 −0.854642 0.519218i \(-0.826223\pi\)
−0.854642 + 0.519218i \(0.826223\pi\)
\(942\) 0 0
\(943\) 18.5567 0.604288
\(944\) 0 0
\(945\) 1.65529 0.0538466
\(946\) 0 0
\(947\) −26.4725 −0.860239 −0.430120 0.902772i \(-0.641529\pi\)
−0.430120 + 0.902772i \(0.641529\pi\)
\(948\) 0 0
\(949\) −17.3706 −0.563874
\(950\) 0 0
\(951\) 7.00074 0.227014
\(952\) 0 0
\(953\) −11.1278 −0.360465 −0.180232 0.983624i \(-0.557685\pi\)
−0.180232 + 0.983624i \(0.557685\pi\)
\(954\) 0 0
\(955\) 13.8760 0.449018
\(956\) 0 0
\(957\) −0.390411 −0.0126202
\(958\) 0 0
\(959\) 50.7475 1.63872
\(960\) 0 0
\(961\) 2.71814 0.0876820
\(962\) 0 0
\(963\) −7.07502 −0.227989
\(964\) 0 0
\(965\) 10.0381 0.323138
\(966\) 0 0
\(967\) −7.69509 −0.247458 −0.123729 0.992316i \(-0.539485\pi\)
−0.123729 + 0.992316i \(0.539485\pi\)
\(968\) 0 0
\(969\) 24.3443 0.782051
\(970\) 0 0
\(971\) 49.7998 1.59815 0.799076 0.601231i \(-0.205323\pi\)
0.799076 + 0.601231i \(0.205323\pi\)
\(972\) 0 0
\(973\) 4.51139 0.144628
\(974\) 0 0
\(975\) 13.8530 0.443652
\(976\) 0 0
\(977\) 42.2241 1.35087 0.675435 0.737420i \(-0.263956\pi\)
0.675435 + 0.737420i \(0.263956\pi\)
\(978\) 0 0
\(979\) −10.4360 −0.333536
\(980\) 0 0
\(981\) −12.6482 −0.403827
\(982\) 0 0
\(983\) 27.4950 0.876953 0.438476 0.898743i \(-0.355518\pi\)
0.438476 + 0.898743i \(0.355518\pi\)
\(984\) 0 0
\(985\) 5.35427 0.170601
\(986\) 0 0
\(987\) 23.9603 0.762664
\(988\) 0 0
\(989\) −6.29448 −0.200153
\(990\) 0 0
\(991\) 34.2405 1.08768 0.543842 0.839187i \(-0.316969\pi\)
0.543842 + 0.839187i \(0.316969\pi\)
\(992\) 0 0
\(993\) 20.7091 0.657183
\(994\) 0 0
\(995\) −0.816384 −0.0258811
\(996\) 0 0
\(997\) −56.8944 −1.80186 −0.900932 0.433959i \(-0.857116\pi\)
−0.900932 + 0.433959i \(0.857116\pi\)
\(998\) 0 0
\(999\) −2.35969 −0.0746573
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 \(a_p\))