Properties

Label 6040.2.a.p.1.19
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Root \(-3.37325\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.37325 q^{3}\) \(+1.00000 q^{5}\) \(-3.80572 q^{7}\) \(+8.37885 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.37325 q^{3}\) \(+1.00000 q^{5}\) \(-3.80572 q^{7}\) \(+8.37885 q^{9}\) \(-2.57642 q^{11}\) \(-4.49122 q^{13}\) \(+3.37325 q^{15}\) \(+4.43598 q^{17}\) \(-6.71504 q^{19}\) \(-12.8377 q^{21}\) \(-8.16971 q^{23}\) \(+1.00000 q^{25}\) \(+18.1442 q^{27}\) \(-8.65001 q^{29}\) \(-2.63378 q^{31}\) \(-8.69091 q^{33}\) \(-3.80572 q^{35}\) \(-2.00647 q^{37}\) \(-15.1500 q^{39}\) \(+0.367431 q^{41}\) \(-4.23046 q^{43}\) \(+8.37885 q^{45}\) \(-6.96940 q^{47}\) \(+7.48352 q^{49}\) \(+14.9637 q^{51}\) \(+12.5327 q^{53}\) \(-2.57642 q^{55}\) \(-22.6515 q^{57}\) \(-2.01138 q^{59}\) \(-6.13006 q^{61}\) \(-31.8876 q^{63}\) \(-4.49122 q^{65}\) \(-10.2416 q^{67}\) \(-27.5585 q^{69}\) \(+3.21081 q^{71}\) \(+0.138853 q^{73}\) \(+3.37325 q^{75}\) \(+9.80513 q^{77}\) \(+6.47365 q^{79}\) \(+36.0685 q^{81}\) \(-10.2321 q^{83}\) \(+4.43598 q^{85}\) \(-29.1787 q^{87}\) \(+16.5702 q^{89}\) \(+17.0923 q^{91}\) \(-8.88441 q^{93}\) \(-6.71504 q^{95}\) \(+7.03808 q^{97}\) \(-21.5874 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 3.37325 1.94755 0.973775 0.227515i \(-0.0730599\pi\)
0.973775 + 0.227515i \(0.0730599\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −3.80572 −1.43843 −0.719214 0.694789i \(-0.755498\pi\)
−0.719214 + 0.694789i \(0.755498\pi\)
\(8\) 0 0
\(9\) 8.37885 2.79295
\(10\) 0 0
\(11\) −2.57642 −0.776819 −0.388410 0.921487i \(-0.626975\pi\)
−0.388410 + 0.921487i \(0.626975\pi\)
\(12\) 0 0
\(13\) −4.49122 −1.24564 −0.622821 0.782365i \(-0.714013\pi\)
−0.622821 + 0.782365i \(0.714013\pi\)
\(14\) 0 0
\(15\) 3.37325 0.870971
\(16\) 0 0
\(17\) 4.43598 1.07588 0.537941 0.842982i \(-0.319202\pi\)
0.537941 + 0.842982i \(0.319202\pi\)
\(18\) 0 0
\(19\) −6.71504 −1.54054 −0.770268 0.637720i \(-0.779878\pi\)
−0.770268 + 0.637720i \(0.779878\pi\)
\(20\) 0 0
\(21\) −12.8377 −2.80141
\(22\) 0 0
\(23\) −8.16971 −1.70350 −0.851751 0.523947i \(-0.824459\pi\)
−0.851751 + 0.523947i \(0.824459\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 18.1442 3.49186
\(28\) 0 0
\(29\) −8.65001 −1.60627 −0.803133 0.595800i \(-0.796835\pi\)
−0.803133 + 0.595800i \(0.796835\pi\)
\(30\) 0 0
\(31\) −2.63378 −0.473041 −0.236520 0.971627i \(-0.576007\pi\)
−0.236520 + 0.971627i \(0.576007\pi\)
\(32\) 0 0
\(33\) −8.69091 −1.51289
\(34\) 0 0
\(35\) −3.80572 −0.643284
\(36\) 0 0
\(37\) −2.00647 −0.329862 −0.164931 0.986305i \(-0.552740\pi\)
−0.164931 + 0.986305i \(0.552740\pi\)
\(38\) 0 0
\(39\) −15.1500 −2.42595
\(40\) 0 0
\(41\) 0.367431 0.0573831 0.0286916 0.999588i \(-0.490866\pi\)
0.0286916 + 0.999588i \(0.490866\pi\)
\(42\) 0 0
\(43\) −4.23046 −0.645139 −0.322570 0.946546i \(-0.604547\pi\)
−0.322570 + 0.946546i \(0.604547\pi\)
\(44\) 0 0
\(45\) 8.37885 1.24904
\(46\) 0 0
\(47\) −6.96940 −1.01659 −0.508296 0.861183i \(-0.669724\pi\)
−0.508296 + 0.861183i \(0.669724\pi\)
\(48\) 0 0
\(49\) 7.48352 1.06907
\(50\) 0 0
\(51\) 14.9637 2.09533
\(52\) 0 0
\(53\) 12.5327 1.72150 0.860748 0.509031i \(-0.169996\pi\)
0.860748 + 0.509031i \(0.169996\pi\)
\(54\) 0 0
\(55\) −2.57642 −0.347404
\(56\) 0 0
\(57\) −22.6515 −3.00027
\(58\) 0 0
\(59\) −2.01138 −0.261860 −0.130930 0.991392i \(-0.541796\pi\)
−0.130930 + 0.991392i \(0.541796\pi\)
\(60\) 0 0
\(61\) −6.13006 −0.784874 −0.392437 0.919779i \(-0.628368\pi\)
−0.392437 + 0.919779i \(0.628368\pi\)
\(62\) 0 0
\(63\) −31.8876 −4.01745
\(64\) 0 0
\(65\) −4.49122 −0.557068
\(66\) 0 0
\(67\) −10.2416 −1.25121 −0.625606 0.780139i \(-0.715148\pi\)
−0.625606 + 0.780139i \(0.715148\pi\)
\(68\) 0 0
\(69\) −27.5585 −3.31765
\(70\) 0 0
\(71\) 3.21081 0.381053 0.190526 0.981682i \(-0.438981\pi\)
0.190526 + 0.981682i \(0.438981\pi\)
\(72\) 0 0
\(73\) 0.138853 0.0162515 0.00812573 0.999967i \(-0.497413\pi\)
0.00812573 + 0.999967i \(0.497413\pi\)
\(74\) 0 0
\(75\) 3.37325 0.389510
\(76\) 0 0
\(77\) 9.80513 1.11740
\(78\) 0 0
\(79\) 6.47365 0.728342 0.364171 0.931332i \(-0.381352\pi\)
0.364171 + 0.931332i \(0.381352\pi\)
\(80\) 0 0
\(81\) 36.0685 4.00761
\(82\) 0 0
\(83\) −10.2321 −1.12312 −0.561558 0.827437i \(-0.689798\pi\)
−0.561558 + 0.827437i \(0.689798\pi\)
\(84\) 0 0
\(85\) 4.43598 0.481149
\(86\) 0 0
\(87\) −29.1787 −3.12828
\(88\) 0 0
\(89\) 16.5702 1.75644 0.878218 0.478260i \(-0.158732\pi\)
0.878218 + 0.478260i \(0.158732\pi\)
\(90\) 0 0
\(91\) 17.0923 1.79176
\(92\) 0 0
\(93\) −8.88441 −0.921270
\(94\) 0 0
\(95\) −6.71504 −0.688949
\(96\) 0 0
\(97\) 7.03808 0.714609 0.357305 0.933988i \(-0.383696\pi\)
0.357305 + 0.933988i \(0.383696\pi\)
\(98\) 0 0
\(99\) −21.5874 −2.16962
\(100\) 0 0
\(101\) 2.70142 0.268802 0.134401 0.990927i \(-0.457089\pi\)
0.134401 + 0.990927i \(0.457089\pi\)
\(102\) 0 0
\(103\) 2.37032 0.233554 0.116777 0.993158i \(-0.462744\pi\)
0.116777 + 0.993158i \(0.462744\pi\)
\(104\) 0 0
\(105\) −12.8377 −1.25283
\(106\) 0 0
\(107\) −0.385224 −0.0372411 −0.0186205 0.999827i \(-0.505927\pi\)
−0.0186205 + 0.999827i \(0.505927\pi\)
\(108\) 0 0
\(109\) −5.71939 −0.547818 −0.273909 0.961756i \(-0.588317\pi\)
−0.273909 + 0.961756i \(0.588317\pi\)
\(110\) 0 0
\(111\) −6.76834 −0.642423
\(112\) 0 0
\(113\) 15.3078 1.44004 0.720018 0.693955i \(-0.244134\pi\)
0.720018 + 0.693955i \(0.244134\pi\)
\(114\) 0 0
\(115\) −8.16971 −0.761829
\(116\) 0 0
\(117\) −37.6313 −3.47901
\(118\) 0 0
\(119\) −16.8821 −1.54758
\(120\) 0 0
\(121\) −4.36207 −0.396552
\(122\) 0 0
\(123\) 1.23944 0.111756
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 7.03938 0.624644 0.312322 0.949976i \(-0.398893\pi\)
0.312322 + 0.949976i \(0.398893\pi\)
\(128\) 0 0
\(129\) −14.2704 −1.25644
\(130\) 0 0
\(131\) 11.9148 1.04100 0.520500 0.853862i \(-0.325746\pi\)
0.520500 + 0.853862i \(0.325746\pi\)
\(132\) 0 0
\(133\) 25.5556 2.21595
\(134\) 0 0
\(135\) 18.1442 1.56161
\(136\) 0 0
\(137\) −8.94271 −0.764027 −0.382014 0.924157i \(-0.624769\pi\)
−0.382014 + 0.924157i \(0.624769\pi\)
\(138\) 0 0
\(139\) −4.72445 −0.400723 −0.200361 0.979722i \(-0.564212\pi\)
−0.200361 + 0.979722i \(0.564212\pi\)
\(140\) 0 0
\(141\) −23.5096 −1.97986
\(142\) 0 0
\(143\) 11.5713 0.967638
\(144\) 0 0
\(145\) −8.65001 −0.718344
\(146\) 0 0
\(147\) 25.2438 2.08207
\(148\) 0 0
\(149\) 10.1001 0.827430 0.413715 0.910406i \(-0.364231\pi\)
0.413715 + 0.910406i \(0.364231\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) 37.1684 3.00488
\(154\) 0 0
\(155\) −2.63378 −0.211550
\(156\) 0 0
\(157\) 9.52854 0.760460 0.380230 0.924892i \(-0.375845\pi\)
0.380230 + 0.924892i \(0.375845\pi\)
\(158\) 0 0
\(159\) 42.2759 3.35270
\(160\) 0 0
\(161\) 31.0916 2.45036
\(162\) 0 0
\(163\) −16.7786 −1.31420 −0.657100 0.753804i \(-0.728217\pi\)
−0.657100 + 0.753804i \(0.728217\pi\)
\(164\) 0 0
\(165\) −8.69091 −0.676587
\(166\) 0 0
\(167\) 21.4191 1.65746 0.828730 0.559648i \(-0.189064\pi\)
0.828730 + 0.559648i \(0.189064\pi\)
\(168\) 0 0
\(169\) 7.17108 0.551622
\(170\) 0 0
\(171\) −56.2643 −4.30264
\(172\) 0 0
\(173\) 1.47999 0.112521 0.0562606 0.998416i \(-0.482082\pi\)
0.0562606 + 0.998416i \(0.482082\pi\)
\(174\) 0 0
\(175\) −3.80572 −0.287686
\(176\) 0 0
\(177\) −6.78490 −0.509984
\(178\) 0 0
\(179\) 6.08516 0.454826 0.227413 0.973798i \(-0.426973\pi\)
0.227413 + 0.973798i \(0.426973\pi\)
\(180\) 0 0
\(181\) −25.4550 −1.89205 −0.946026 0.324091i \(-0.894942\pi\)
−0.946026 + 0.324091i \(0.894942\pi\)
\(182\) 0 0
\(183\) −20.6783 −1.52858
\(184\) 0 0
\(185\) −2.00647 −0.147519
\(186\) 0 0
\(187\) −11.4289 −0.835766
\(188\) 0 0
\(189\) −69.0518 −5.02278
\(190\) 0 0
\(191\) −5.50059 −0.398009 −0.199004 0.979999i \(-0.563771\pi\)
−0.199004 + 0.979999i \(0.563771\pi\)
\(192\) 0 0
\(193\) 9.73741 0.700914 0.350457 0.936579i \(-0.386026\pi\)
0.350457 + 0.936579i \(0.386026\pi\)
\(194\) 0 0
\(195\) −15.1500 −1.08492
\(196\) 0 0
\(197\) −8.13384 −0.579512 −0.289756 0.957101i \(-0.593574\pi\)
−0.289756 + 0.957101i \(0.593574\pi\)
\(198\) 0 0
\(199\) 11.8288 0.838525 0.419262 0.907865i \(-0.362289\pi\)
0.419262 + 0.907865i \(0.362289\pi\)
\(200\) 0 0
\(201\) −34.5476 −2.43680
\(202\) 0 0
\(203\) 32.9195 2.31050
\(204\) 0 0
\(205\) 0.367431 0.0256625
\(206\) 0 0
\(207\) −68.4527 −4.75779
\(208\) 0 0
\(209\) 17.3007 1.19672
\(210\) 0 0
\(211\) −20.3740 −1.40261 −0.701304 0.712863i \(-0.747398\pi\)
−0.701304 + 0.712863i \(0.747398\pi\)
\(212\) 0 0
\(213\) 10.8309 0.742119
\(214\) 0 0
\(215\) −4.23046 −0.288515
\(216\) 0 0
\(217\) 10.0234 0.680435
\(218\) 0 0
\(219\) 0.468385 0.0316505
\(220\) 0 0
\(221\) −19.9230 −1.34016
\(222\) 0 0
\(223\) 18.3631 1.22968 0.614842 0.788650i \(-0.289220\pi\)
0.614842 + 0.788650i \(0.289220\pi\)
\(224\) 0 0
\(225\) 8.37885 0.558590
\(226\) 0 0
\(227\) −21.6600 −1.43762 −0.718812 0.695204i \(-0.755314\pi\)
−0.718812 + 0.695204i \(0.755314\pi\)
\(228\) 0 0
\(229\) −30.1033 −1.98928 −0.994642 0.103381i \(-0.967034\pi\)
−0.994642 + 0.103381i \(0.967034\pi\)
\(230\) 0 0
\(231\) 33.0752 2.17619
\(232\) 0 0
\(233\) −4.16170 −0.272642 −0.136321 0.990665i \(-0.543528\pi\)
−0.136321 + 0.990665i \(0.543528\pi\)
\(234\) 0 0
\(235\) −6.96940 −0.454634
\(236\) 0 0
\(237\) 21.8373 1.41848
\(238\) 0 0
\(239\) 11.4316 0.739448 0.369724 0.929142i \(-0.379452\pi\)
0.369724 + 0.929142i \(0.379452\pi\)
\(240\) 0 0
\(241\) 10.4462 0.672900 0.336450 0.941701i \(-0.390774\pi\)
0.336450 + 0.941701i \(0.390774\pi\)
\(242\) 0 0
\(243\) 67.2356 4.31317
\(244\) 0 0
\(245\) 7.48352 0.478104
\(246\) 0 0
\(247\) 30.1587 1.91895
\(248\) 0 0
\(249\) −34.5154 −2.18733
\(250\) 0 0
\(251\) 24.3107 1.53448 0.767239 0.641361i \(-0.221630\pi\)
0.767239 + 0.641361i \(0.221630\pi\)
\(252\) 0 0
\(253\) 21.0486 1.32331
\(254\) 0 0
\(255\) 14.9637 0.937062
\(256\) 0 0
\(257\) −25.2368 −1.57423 −0.787115 0.616806i \(-0.788426\pi\)
−0.787115 + 0.616806i \(0.788426\pi\)
\(258\) 0 0
\(259\) 7.63608 0.474483
\(260\) 0 0
\(261\) −72.4771 −4.48622
\(262\) 0 0
\(263\) 10.6038 0.653857 0.326928 0.945049i \(-0.393986\pi\)
0.326928 + 0.945049i \(0.393986\pi\)
\(264\) 0 0
\(265\) 12.5327 0.769877
\(266\) 0 0
\(267\) 55.8955 3.42075
\(268\) 0 0
\(269\) −15.7916 −0.962828 −0.481414 0.876493i \(-0.659877\pi\)
−0.481414 + 0.876493i \(0.659877\pi\)
\(270\) 0 0
\(271\) −31.6036 −1.91978 −0.959892 0.280369i \(-0.909543\pi\)
−0.959892 + 0.280369i \(0.909543\pi\)
\(272\) 0 0
\(273\) 57.6568 3.48955
\(274\) 0 0
\(275\) −2.57642 −0.155364
\(276\) 0 0
\(277\) 0.318427 0.0191324 0.00956621 0.999954i \(-0.496955\pi\)
0.00956621 + 0.999954i \(0.496955\pi\)
\(278\) 0 0
\(279\) −22.0680 −1.32118
\(280\) 0 0
\(281\) −19.2708 −1.14960 −0.574801 0.818294i \(-0.694920\pi\)
−0.574801 + 0.818294i \(0.694920\pi\)
\(282\) 0 0
\(283\) −24.2315 −1.44041 −0.720207 0.693759i \(-0.755953\pi\)
−0.720207 + 0.693759i \(0.755953\pi\)
\(284\) 0 0
\(285\) −22.6515 −1.34176
\(286\) 0 0
\(287\) −1.39834 −0.0825414
\(288\) 0 0
\(289\) 2.67789 0.157523
\(290\) 0 0
\(291\) 23.7412 1.39174
\(292\) 0 0
\(293\) 25.3003 1.47806 0.739031 0.673671i \(-0.235284\pi\)
0.739031 + 0.673671i \(0.235284\pi\)
\(294\) 0 0
\(295\) −2.01138 −0.117107
\(296\) 0 0
\(297\) −46.7471 −2.71254
\(298\) 0 0
\(299\) 36.6920 2.12195
\(300\) 0 0
\(301\) 16.1000 0.927986
\(302\) 0 0
\(303\) 9.11259 0.523505
\(304\) 0 0
\(305\) −6.13006 −0.351006
\(306\) 0 0
\(307\) 18.3536 1.04750 0.523748 0.851873i \(-0.324533\pi\)
0.523748 + 0.851873i \(0.324533\pi\)
\(308\) 0 0
\(309\) 7.99568 0.454859
\(310\) 0 0
\(311\) 14.7087 0.834053 0.417026 0.908894i \(-0.363072\pi\)
0.417026 + 0.908894i \(0.363072\pi\)
\(312\) 0 0
\(313\) 0.877216 0.0495832 0.0247916 0.999693i \(-0.492108\pi\)
0.0247916 + 0.999693i \(0.492108\pi\)
\(314\) 0 0
\(315\) −31.8876 −1.79666
\(316\) 0 0
\(317\) −22.9407 −1.28848 −0.644240 0.764823i \(-0.722826\pi\)
−0.644240 + 0.764823i \(0.722826\pi\)
\(318\) 0 0
\(319\) 22.2860 1.24778
\(320\) 0 0
\(321\) −1.29946 −0.0725288
\(322\) 0 0
\(323\) −29.7878 −1.65744
\(324\) 0 0
\(325\) −4.49122 −0.249128
\(326\) 0 0
\(327\) −19.2930 −1.06690
\(328\) 0 0
\(329\) 26.5236 1.46229
\(330\) 0 0
\(331\) 4.67009 0.256692 0.128346 0.991729i \(-0.459033\pi\)
0.128346 + 0.991729i \(0.459033\pi\)
\(332\) 0 0
\(333\) −16.8119 −0.921288
\(334\) 0 0
\(335\) −10.2416 −0.559559
\(336\) 0 0
\(337\) −20.0182 −1.09046 −0.545229 0.838287i \(-0.683557\pi\)
−0.545229 + 0.838287i \(0.683557\pi\)
\(338\) 0 0
\(339\) 51.6371 2.80454
\(340\) 0 0
\(341\) 6.78571 0.367467
\(342\) 0 0
\(343\) −1.84013 −0.0993579
\(344\) 0 0
\(345\) −27.5585 −1.48370
\(346\) 0 0
\(347\) −31.9949 −1.71758 −0.858788 0.512332i \(-0.828782\pi\)
−0.858788 + 0.512332i \(0.828782\pi\)
\(348\) 0 0
\(349\) −29.9764 −1.60460 −0.802300 0.596921i \(-0.796391\pi\)
−0.802300 + 0.596921i \(0.796391\pi\)
\(350\) 0 0
\(351\) −81.4897 −4.34960
\(352\) 0 0
\(353\) −17.4732 −0.930005 −0.465002 0.885309i \(-0.653947\pi\)
−0.465002 + 0.885309i \(0.653947\pi\)
\(354\) 0 0
\(355\) 3.21081 0.170412
\(356\) 0 0
\(357\) −56.9476 −3.01399
\(358\) 0 0
\(359\) 23.8229 1.25732 0.628662 0.777678i \(-0.283603\pi\)
0.628662 + 0.777678i \(0.283603\pi\)
\(360\) 0 0
\(361\) 26.0918 1.37325
\(362\) 0 0
\(363\) −14.7144 −0.772305
\(364\) 0 0
\(365\) 0.138853 0.00726787
\(366\) 0 0
\(367\) −18.9346 −0.988380 −0.494190 0.869354i \(-0.664535\pi\)
−0.494190 + 0.869354i \(0.664535\pi\)
\(368\) 0 0
\(369\) 3.07865 0.160268
\(370\) 0 0
\(371\) −47.6959 −2.47625
\(372\) 0 0
\(373\) 33.3904 1.72889 0.864445 0.502727i \(-0.167670\pi\)
0.864445 + 0.502727i \(0.167670\pi\)
\(374\) 0 0
\(375\) 3.37325 0.174194
\(376\) 0 0
\(377\) 38.8491 2.00083
\(378\) 0 0
\(379\) −25.2769 −1.29839 −0.649194 0.760623i \(-0.724894\pi\)
−0.649194 + 0.760623i \(0.724894\pi\)
\(380\) 0 0
\(381\) 23.7456 1.21652
\(382\) 0 0
\(383\) 15.2268 0.778052 0.389026 0.921227i \(-0.372812\pi\)
0.389026 + 0.921227i \(0.372812\pi\)
\(384\) 0 0
\(385\) 9.80513 0.499716
\(386\) 0 0
\(387\) −35.4464 −1.80184
\(388\) 0 0
\(389\) 2.61685 0.132680 0.0663398 0.997797i \(-0.478868\pi\)
0.0663398 + 0.997797i \(0.478868\pi\)
\(390\) 0 0
\(391\) −36.2406 −1.83277
\(392\) 0 0
\(393\) 40.1916 2.02740
\(394\) 0 0
\(395\) 6.47365 0.325724
\(396\) 0 0
\(397\) −36.2365 −1.81866 −0.909330 0.416076i \(-0.863405\pi\)
−0.909330 + 0.416076i \(0.863405\pi\)
\(398\) 0 0
\(399\) 86.2055 4.31567
\(400\) 0 0
\(401\) 0.212066 0.0105901 0.00529503 0.999986i \(-0.498315\pi\)
0.00529503 + 0.999986i \(0.498315\pi\)
\(402\) 0 0
\(403\) 11.8289 0.589239
\(404\) 0 0
\(405\) 36.0685 1.79226
\(406\) 0 0
\(407\) 5.16951 0.256243
\(408\) 0 0
\(409\) −27.0874 −1.33939 −0.669693 0.742638i \(-0.733574\pi\)
−0.669693 + 0.742638i \(0.733574\pi\)
\(410\) 0 0
\(411\) −30.1660 −1.48798
\(412\) 0 0
\(413\) 7.65476 0.376666
\(414\) 0 0
\(415\) −10.2321 −0.502273
\(416\) 0 0
\(417\) −15.9368 −0.780427
\(418\) 0 0
\(419\) 26.0027 1.27032 0.635158 0.772382i \(-0.280935\pi\)
0.635158 + 0.772382i \(0.280935\pi\)
\(420\) 0 0
\(421\) −13.5473 −0.660256 −0.330128 0.943936i \(-0.607092\pi\)
−0.330128 + 0.943936i \(0.607092\pi\)
\(422\) 0 0
\(423\) −58.3955 −2.83929
\(424\) 0 0
\(425\) 4.43598 0.215176
\(426\) 0 0
\(427\) 23.3293 1.12898
\(428\) 0 0
\(429\) 39.0328 1.88452
\(430\) 0 0
\(431\) −26.0281 −1.25373 −0.626864 0.779129i \(-0.715662\pi\)
−0.626864 + 0.779129i \(0.715662\pi\)
\(432\) 0 0
\(433\) 16.9097 0.812626 0.406313 0.913734i \(-0.366814\pi\)
0.406313 + 0.913734i \(0.366814\pi\)
\(434\) 0 0
\(435\) −29.1787 −1.39901
\(436\) 0 0
\(437\) 54.8599 2.62431
\(438\) 0 0
\(439\) −17.2413 −0.822882 −0.411441 0.911436i \(-0.634974\pi\)
−0.411441 + 0.911436i \(0.634974\pi\)
\(440\) 0 0
\(441\) 62.7032 2.98587
\(442\) 0 0
\(443\) 24.9806 1.18687 0.593433 0.804883i \(-0.297772\pi\)
0.593433 + 0.804883i \(0.297772\pi\)
\(444\) 0 0
\(445\) 16.5702 0.785502
\(446\) 0 0
\(447\) 34.0701 1.61146
\(448\) 0 0
\(449\) 39.3840 1.85864 0.929322 0.369269i \(-0.120392\pi\)
0.929322 + 0.369269i \(0.120392\pi\)
\(450\) 0 0
\(451\) −0.946656 −0.0445763
\(452\) 0 0
\(453\) 3.37325 0.158489
\(454\) 0 0
\(455\) 17.0923 0.801301
\(456\) 0 0
\(457\) −26.9955 −1.26280 −0.631399 0.775458i \(-0.717519\pi\)
−0.631399 + 0.775458i \(0.717519\pi\)
\(458\) 0 0
\(459\) 80.4873 3.75683
\(460\) 0 0
\(461\) 17.2448 0.803170 0.401585 0.915822i \(-0.368459\pi\)
0.401585 + 0.915822i \(0.368459\pi\)
\(462\) 0 0
\(463\) 10.9009 0.506610 0.253305 0.967387i \(-0.418482\pi\)
0.253305 + 0.967387i \(0.418482\pi\)
\(464\) 0 0
\(465\) −8.88441 −0.412005
\(466\) 0 0
\(467\) 0.615217 0.0284688 0.0142344 0.999899i \(-0.495469\pi\)
0.0142344 + 0.999899i \(0.495469\pi\)
\(468\) 0 0
\(469\) 38.9767 1.79978
\(470\) 0 0
\(471\) 32.1422 1.48103
\(472\) 0 0
\(473\) 10.8994 0.501156
\(474\) 0 0
\(475\) −6.71504 −0.308107
\(476\) 0 0
\(477\) 105.009 4.80805
\(478\) 0 0
\(479\) −11.2848 −0.515617 −0.257808 0.966196i \(-0.583000\pi\)
−0.257808 + 0.966196i \(0.583000\pi\)
\(480\) 0 0
\(481\) 9.01151 0.410890
\(482\) 0 0
\(483\) 104.880 4.77220
\(484\) 0 0
\(485\) 7.03808 0.319583
\(486\) 0 0
\(487\) 41.0311 1.85930 0.929648 0.368450i \(-0.120111\pi\)
0.929648 + 0.368450i \(0.120111\pi\)
\(488\) 0 0
\(489\) −56.5984 −2.55947
\(490\) 0 0
\(491\) −19.4719 −0.878756 −0.439378 0.898302i \(-0.644801\pi\)
−0.439378 + 0.898302i \(0.644801\pi\)
\(492\) 0 0
\(493\) −38.3712 −1.72815
\(494\) 0 0
\(495\) −21.5874 −0.970282
\(496\) 0 0
\(497\) −12.2194 −0.548117
\(498\) 0 0
\(499\) −3.46073 −0.154924 −0.0774618 0.996995i \(-0.524682\pi\)
−0.0774618 + 0.996995i \(0.524682\pi\)
\(500\) 0 0
\(501\) 72.2521 3.22799
\(502\) 0 0
\(503\) −3.01552 −0.134455 −0.0672277 0.997738i \(-0.521415\pi\)
−0.0672277 + 0.997738i \(0.521415\pi\)
\(504\) 0 0
\(505\) 2.70142 0.120212
\(506\) 0 0
\(507\) 24.1899 1.07431
\(508\) 0 0
\(509\) 12.6552 0.560933 0.280467 0.959864i \(-0.409511\pi\)
0.280467 + 0.959864i \(0.409511\pi\)
\(510\) 0 0
\(511\) −0.528434 −0.0233765
\(512\) 0 0
\(513\) −121.839 −5.37933
\(514\) 0 0
\(515\) 2.37032 0.104449
\(516\) 0 0
\(517\) 17.9561 0.789708
\(518\) 0 0
\(519\) 4.99237 0.219141
\(520\) 0 0
\(521\) −25.3687 −1.11142 −0.555712 0.831375i \(-0.687554\pi\)
−0.555712 + 0.831375i \(0.687554\pi\)
\(522\) 0 0
\(523\) −9.03765 −0.395189 −0.197594 0.980284i \(-0.563313\pi\)
−0.197594 + 0.980284i \(0.563313\pi\)
\(524\) 0 0
\(525\) −12.8377 −0.560282
\(526\) 0 0
\(527\) −11.6834 −0.508936
\(528\) 0 0
\(529\) 43.7441 1.90192
\(530\) 0 0
\(531\) −16.8531 −0.731360
\(532\) 0 0
\(533\) −1.65022 −0.0714788
\(534\) 0 0
\(535\) −0.385224 −0.0166547
\(536\) 0 0
\(537\) 20.5268 0.885796
\(538\) 0 0
\(539\) −19.2807 −0.830477
\(540\) 0 0
\(541\) 16.8584 0.724798 0.362399 0.932023i \(-0.381958\pi\)
0.362399 + 0.932023i \(0.381958\pi\)
\(542\) 0 0
\(543\) −85.8661 −3.68486
\(544\) 0 0
\(545\) −5.71939 −0.244992
\(546\) 0 0
\(547\) 20.2498 0.865819 0.432910 0.901437i \(-0.357487\pi\)
0.432910 + 0.901437i \(0.357487\pi\)
\(548\) 0 0
\(549\) −51.3628 −2.19211
\(550\) 0 0
\(551\) 58.0851 2.47451
\(552\) 0 0
\(553\) −24.6369 −1.04767
\(554\) 0 0
\(555\) −6.76834 −0.287300
\(556\) 0 0
\(557\) 29.8544 1.26497 0.632485 0.774573i \(-0.282035\pi\)
0.632485 + 0.774573i \(0.282035\pi\)
\(558\) 0 0
\(559\) 18.9999 0.803612
\(560\) 0 0
\(561\) −38.5527 −1.62770
\(562\) 0 0
\(563\) 29.5901 1.24708 0.623538 0.781793i \(-0.285695\pi\)
0.623538 + 0.781793i \(0.285695\pi\)
\(564\) 0 0
\(565\) 15.3078 0.644004
\(566\) 0 0
\(567\) −137.267 −5.76466
\(568\) 0 0
\(569\) −29.6119 −1.24139 −0.620697 0.784051i \(-0.713150\pi\)
−0.620697 + 0.784051i \(0.713150\pi\)
\(570\) 0 0
\(571\) 11.7793 0.492946 0.246473 0.969150i \(-0.420728\pi\)
0.246473 + 0.969150i \(0.420728\pi\)
\(572\) 0 0
\(573\) −18.5549 −0.775142
\(574\) 0 0
\(575\) −8.16971 −0.340700
\(576\) 0 0
\(577\) −17.4017 −0.724440 −0.362220 0.932093i \(-0.617981\pi\)
−0.362220 + 0.932093i \(0.617981\pi\)
\(578\) 0 0
\(579\) 32.8468 1.36507
\(580\) 0 0
\(581\) 38.9405 1.61552
\(582\) 0 0
\(583\) −32.2894 −1.33729
\(584\) 0 0
\(585\) −37.6313 −1.55586
\(586\) 0 0
\(587\) −22.9410 −0.946877 −0.473438 0.880827i \(-0.656987\pi\)
−0.473438 + 0.880827i \(0.656987\pi\)
\(588\) 0 0
\(589\) 17.6859 0.728736
\(590\) 0 0
\(591\) −27.4375 −1.12863
\(592\) 0 0
\(593\) 3.93575 0.161622 0.0808110 0.996729i \(-0.474249\pi\)
0.0808110 + 0.996729i \(0.474249\pi\)
\(594\) 0 0
\(595\) −16.8821 −0.692098
\(596\) 0 0
\(597\) 39.9017 1.63307
\(598\) 0 0
\(599\) 31.4344 1.28437 0.642187 0.766548i \(-0.278027\pi\)
0.642187 + 0.766548i \(0.278027\pi\)
\(600\) 0 0
\(601\) 22.6787 0.925084 0.462542 0.886597i \(-0.346938\pi\)
0.462542 + 0.886597i \(0.346938\pi\)
\(602\) 0 0
\(603\) −85.8129 −3.49457
\(604\) 0 0
\(605\) −4.36207 −0.177344
\(606\) 0 0
\(607\) −5.71008 −0.231765 −0.115883 0.993263i \(-0.536970\pi\)
−0.115883 + 0.993263i \(0.536970\pi\)
\(608\) 0 0
\(609\) 111.046 4.49981
\(610\) 0 0
\(611\) 31.3011 1.26631
\(612\) 0 0
\(613\) 7.85985 0.317456 0.158728 0.987322i \(-0.449261\pi\)
0.158728 + 0.987322i \(0.449261\pi\)
\(614\) 0 0
\(615\) 1.23944 0.0499790
\(616\) 0 0
\(617\) −12.7505 −0.513317 −0.256658 0.966502i \(-0.582622\pi\)
−0.256658 + 0.966502i \(0.582622\pi\)
\(618\) 0 0
\(619\) −46.4014 −1.86503 −0.932515 0.361130i \(-0.882391\pi\)
−0.932515 + 0.361130i \(0.882391\pi\)
\(620\) 0 0
\(621\) −148.233 −5.94838
\(622\) 0 0
\(623\) −63.0615 −2.52651
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 58.3598 2.33067
\(628\) 0 0
\(629\) −8.90066 −0.354893
\(630\) 0 0
\(631\) 18.8448 0.750199 0.375099 0.926985i \(-0.377609\pi\)
0.375099 + 0.926985i \(0.377609\pi\)
\(632\) 0 0
\(633\) −68.7268 −2.73165
\(634\) 0 0
\(635\) 7.03938 0.279349
\(636\) 0 0
\(637\) −33.6101 −1.33168
\(638\) 0 0
\(639\) 26.9029 1.06426
\(640\) 0 0
\(641\) 5.20934 0.205757 0.102878 0.994694i \(-0.467195\pi\)
0.102878 + 0.994694i \(0.467195\pi\)
\(642\) 0 0
\(643\) 39.8396 1.57112 0.785560 0.618785i \(-0.212375\pi\)
0.785560 + 0.618785i \(0.212375\pi\)
\(644\) 0 0
\(645\) −14.2704 −0.561897
\(646\) 0 0
\(647\) 1.37749 0.0541547 0.0270773 0.999633i \(-0.491380\pi\)
0.0270773 + 0.999633i \(0.491380\pi\)
\(648\) 0 0
\(649\) 5.18216 0.203417
\(650\) 0 0
\(651\) 33.8116 1.32518
\(652\) 0 0
\(653\) −8.05089 −0.315056 −0.157528 0.987515i \(-0.550352\pi\)
−0.157528 + 0.987515i \(0.550352\pi\)
\(654\) 0 0
\(655\) 11.9148 0.465549
\(656\) 0 0
\(657\) 1.16342 0.0453895
\(658\) 0 0
\(659\) −18.1094 −0.705443 −0.352721 0.935728i \(-0.614744\pi\)
−0.352721 + 0.935728i \(0.614744\pi\)
\(660\) 0 0
\(661\) 7.59373 0.295362 0.147681 0.989035i \(-0.452819\pi\)
0.147681 + 0.989035i \(0.452819\pi\)
\(662\) 0 0
\(663\) −67.2052 −2.61003
\(664\) 0 0
\(665\) 25.5556 0.991003
\(666\) 0 0
\(667\) 70.6680 2.73628
\(668\) 0 0
\(669\) 61.9434 2.39487
\(670\) 0 0
\(671\) 15.7936 0.609705
\(672\) 0 0
\(673\) 24.3801 0.939785 0.469893 0.882724i \(-0.344293\pi\)
0.469893 + 0.882724i \(0.344293\pi\)
\(674\) 0 0
\(675\) 18.1442 0.698371
\(676\) 0 0
\(677\) 8.67232 0.333304 0.166652 0.986016i \(-0.446704\pi\)
0.166652 + 0.986016i \(0.446704\pi\)
\(678\) 0 0
\(679\) −26.7850 −1.02791
\(680\) 0 0
\(681\) −73.0647 −2.79985
\(682\) 0 0
\(683\) −24.8358 −0.950317 −0.475158 0.879900i \(-0.657609\pi\)
−0.475158 + 0.879900i \(0.657609\pi\)
\(684\) 0 0
\(685\) −8.94271 −0.341683
\(686\) 0 0
\(687\) −101.546 −3.87423
\(688\) 0 0
\(689\) −56.2871 −2.14437
\(690\) 0 0
\(691\) 4.34267 0.165203 0.0826014 0.996583i \(-0.473677\pi\)
0.0826014 + 0.996583i \(0.473677\pi\)
\(692\) 0 0
\(693\) 82.1556 3.12083
\(694\) 0 0
\(695\) −4.72445 −0.179209
\(696\) 0 0
\(697\) 1.62992 0.0617375
\(698\) 0 0
\(699\) −14.0385 −0.530983
\(700\) 0 0
\(701\) 3.56255 0.134556 0.0672779 0.997734i \(-0.478569\pi\)
0.0672779 + 0.997734i \(0.478569\pi\)
\(702\) 0 0
\(703\) 13.4735 0.508164
\(704\) 0 0
\(705\) −23.5096 −0.885421
\(706\) 0 0
\(707\) −10.2809 −0.386652
\(708\) 0 0
\(709\) 32.3494 1.21491 0.607454 0.794355i \(-0.292191\pi\)
0.607454 + 0.794355i \(0.292191\pi\)
\(710\) 0 0
\(711\) 54.2417 2.03422
\(712\) 0 0
\(713\) 21.5172 0.805826
\(714\) 0 0
\(715\) 11.5713 0.432741
\(716\) 0 0
\(717\) 38.5617 1.44011
\(718\) 0 0
\(719\) −19.1705 −0.714939 −0.357470 0.933925i \(-0.616360\pi\)
−0.357470 + 0.933925i \(0.616360\pi\)
\(720\) 0 0
\(721\) −9.02077 −0.335951
\(722\) 0 0
\(723\) 35.2377 1.31051
\(724\) 0 0
\(725\) −8.65001 −0.321253
\(726\) 0 0
\(727\) 16.3944 0.608035 0.304017 0.952666i \(-0.401672\pi\)
0.304017 + 0.952666i \(0.401672\pi\)
\(728\) 0 0
\(729\) 118.597 4.39250
\(730\) 0 0
\(731\) −18.7662 −0.694094
\(732\) 0 0
\(733\) 19.1591 0.707657 0.353828 0.935310i \(-0.384880\pi\)
0.353828 + 0.935310i \(0.384880\pi\)
\(734\) 0 0
\(735\) 25.2438 0.931132
\(736\) 0 0
\(737\) 26.3867 0.971966
\(738\) 0 0
\(739\) 17.8584 0.656932 0.328466 0.944516i \(-0.393468\pi\)
0.328466 + 0.944516i \(0.393468\pi\)
\(740\) 0 0
\(741\) 101.733 3.73726
\(742\) 0 0
\(743\) −30.0882 −1.10383 −0.551915 0.833901i \(-0.686103\pi\)
−0.551915 + 0.833901i \(0.686103\pi\)
\(744\) 0 0
\(745\) 10.1001 0.370038
\(746\) 0 0
\(747\) −85.7330 −3.13681
\(748\) 0 0
\(749\) 1.46606 0.0535686
\(750\) 0 0
\(751\) −38.0985 −1.39023 −0.695116 0.718897i \(-0.744647\pi\)
−0.695116 + 0.718897i \(0.744647\pi\)
\(752\) 0 0
\(753\) 82.0062 2.98847
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −8.54920 −0.310726 −0.155363 0.987857i \(-0.549655\pi\)
−0.155363 + 0.987857i \(0.549655\pi\)
\(758\) 0 0
\(759\) 71.0022 2.57722
\(760\) 0 0
\(761\) −13.3327 −0.483309 −0.241655 0.970362i \(-0.577690\pi\)
−0.241655 + 0.970362i \(0.577690\pi\)
\(762\) 0 0
\(763\) 21.7664 0.787997
\(764\) 0 0
\(765\) 37.1684 1.34382
\(766\) 0 0
\(767\) 9.03356 0.326183
\(768\) 0 0
\(769\) −3.18700 −0.114926 −0.0574632 0.998348i \(-0.518301\pi\)
−0.0574632 + 0.998348i \(0.518301\pi\)
\(770\) 0 0
\(771\) −85.1303 −3.06589
\(772\) 0 0
\(773\) 5.99035 0.215458 0.107729 0.994180i \(-0.465642\pi\)
0.107729 + 0.994180i \(0.465642\pi\)
\(774\) 0 0
\(775\) −2.63378 −0.0946081
\(776\) 0 0
\(777\) 25.7584 0.924078
\(778\) 0 0
\(779\) −2.46732 −0.0884007
\(780\) 0 0
\(781\) −8.27238 −0.296009
\(782\) 0 0
\(783\) −156.948 −5.60885
\(784\) 0 0
\(785\) 9.52854 0.340088
\(786\) 0 0
\(787\) −4.33648 −0.154579 −0.0772894 0.997009i \(-0.524627\pi\)
−0.0772894 + 0.997009i \(0.524627\pi\)
\(788\) 0 0
\(789\) 35.7692 1.27342
\(790\) 0 0
\(791\) −58.2572 −2.07139
\(792\) 0 0
\(793\) 27.5315 0.977671
\(794\) 0 0
\(795\) 42.2759 1.49937
\(796\) 0 0
\(797\) −48.3726 −1.71345 −0.856723 0.515777i \(-0.827503\pi\)
−0.856723 + 0.515777i \(0.827503\pi\)
\(798\) 0 0
\(799\) −30.9161 −1.09373
\(800\) 0 0
\(801\) 138.839 4.90564
\(802\) 0 0
\(803\) −0.357742 −0.0126244
\(804\) 0 0
\(805\) 31.0916 1.09584
\(806\) 0 0
\(807\) −53.2689 −1.87515
\(808\) 0 0
\(809\) −39.1516 −1.37650 −0.688248 0.725476i \(-0.741620\pi\)
−0.688248 + 0.725476i \(0.741620\pi\)
\(810\) 0 0
\(811\) −1.41593 −0.0497201 −0.0248601 0.999691i \(-0.507914\pi\)
−0.0248601 + 0.999691i \(0.507914\pi\)
\(812\) 0 0
\(813\) −106.607 −3.73887
\(814\) 0 0
\(815\) −16.7786 −0.587728
\(816\) 0 0
\(817\) 28.4077 0.993860
\(818\) 0 0
\(819\) 143.214 5.00431
\(820\) 0 0
\(821\) −8.35788 −0.291692 −0.145846 0.989307i \(-0.546590\pi\)
−0.145846 + 0.989307i \(0.546590\pi\)
\(822\) 0 0
\(823\) −10.1203 −0.352770 −0.176385 0.984321i \(-0.556440\pi\)
−0.176385 + 0.984321i \(0.556440\pi\)
\(824\) 0 0
\(825\) −8.69091 −0.302579
\(826\) 0 0
\(827\) −45.3023 −1.57531 −0.787657 0.616114i \(-0.788706\pi\)
−0.787657 + 0.616114i \(0.788706\pi\)
\(828\) 0 0
\(829\) −43.4382 −1.50867 −0.754336 0.656488i \(-0.772041\pi\)
−0.754336 + 0.656488i \(0.772041\pi\)
\(830\) 0 0
\(831\) 1.07413 0.0372613
\(832\) 0 0
\(833\) 33.1967 1.15020
\(834\) 0 0
\(835\) 21.4191 0.741239
\(836\) 0 0
\(837\) −47.7879 −1.65179
\(838\) 0 0
\(839\) −37.9516 −1.31023 −0.655117 0.755528i \(-0.727381\pi\)
−0.655117 + 0.755528i \(0.727381\pi\)
\(840\) 0 0
\(841\) 45.8226 1.58009
\(842\) 0 0
\(843\) −65.0054 −2.23890
\(844\) 0 0
\(845\) 7.17108 0.246693
\(846\) 0 0
\(847\) 16.6008 0.570412
\(848\) 0 0
\(849\) −81.7391 −2.80528
\(850\) 0 0
\(851\) 16.3923 0.561921
\(852\) 0 0
\(853\) −19.9158 −0.681903 −0.340952 0.940081i \(-0.610749\pi\)
−0.340952 + 0.940081i \(0.610749\pi\)
\(854\) 0 0
\(855\) −56.2643 −1.92420
\(856\) 0 0
\(857\) 10.1274 0.345944 0.172972 0.984927i \(-0.444663\pi\)
0.172972 + 0.984927i \(0.444663\pi\)
\(858\) 0 0
\(859\) 20.5785 0.702131 0.351065 0.936351i \(-0.385819\pi\)
0.351065 + 0.936351i \(0.385819\pi\)
\(860\) 0 0
\(861\) −4.71696 −0.160754
\(862\) 0 0
\(863\) −19.8318 −0.675083 −0.337542 0.941311i \(-0.609595\pi\)
−0.337542 + 0.941311i \(0.609595\pi\)
\(864\) 0 0
\(865\) 1.47999 0.0503210
\(866\) 0 0
\(867\) 9.03319 0.306783
\(868\) 0 0
\(869\) −16.6788 −0.565790
\(870\) 0 0
\(871\) 45.9974 1.55856
\(872\) 0 0
\(873\) 58.9710 1.99587
\(874\) 0 0
\(875\) −3.80572 −0.128657
\(876\) 0 0
\(877\) −6.14680 −0.207563 −0.103781 0.994600i \(-0.533094\pi\)
−0.103781 + 0.994600i \(0.533094\pi\)
\(878\) 0 0
\(879\) 85.3445 2.87860
\(880\) 0 0
\(881\) −44.3491 −1.49416 −0.747080 0.664734i \(-0.768545\pi\)
−0.747080 + 0.664734i \(0.768545\pi\)
\(882\) 0 0
\(883\) −27.9200 −0.939582 −0.469791 0.882778i \(-0.655671\pi\)
−0.469791 + 0.882778i \(0.655671\pi\)
\(884\) 0 0
\(885\) −6.78490 −0.228072
\(886\) 0 0
\(887\) 6.93478 0.232847 0.116424 0.993200i \(-0.462857\pi\)
0.116424 + 0.993200i \(0.462857\pi\)
\(888\) 0 0
\(889\) −26.7899 −0.898505
\(890\) 0 0
\(891\) −92.9276 −3.11319
\(892\) 0 0
\(893\) 46.7998 1.56610
\(894\) 0 0
\(895\) 6.08516 0.203404
\(896\) 0 0
\(897\) 123.771 4.13261
\(898\) 0 0
\(899\) 22.7822 0.759829
\(900\) 0 0
\(901\) 55.5947 1.85213
\(902\) 0 0
\(903\) 54.3092 1.80730
\(904\) 0 0
\(905\) −25.4550 −0.846151
\(906\) 0 0
\(907\) −22.3509 −0.742149 −0.371075 0.928603i \(-0.621011\pi\)
−0.371075 + 0.928603i \(0.621011\pi\)
\(908\) 0 0
\(909\) 22.6348 0.750749
\(910\) 0 0
\(911\) 35.4959 1.17603 0.588015 0.808850i \(-0.299909\pi\)
0.588015 + 0.808850i \(0.299909\pi\)
\(912\) 0 0
\(913\) 26.3621 0.872459
\(914\) 0 0
\(915\) −20.6783 −0.683602
\(916\) 0 0
\(917\) −45.3443 −1.49740
\(918\) 0 0
\(919\) −44.9349 −1.48226 −0.741132 0.671359i \(-0.765711\pi\)
−0.741132 + 0.671359i \(0.765711\pi\)
\(920\) 0 0
\(921\) 61.9114 2.04005
\(922\) 0 0
\(923\) −14.4205 −0.474655
\(924\) 0 0
\(925\) −2.00647 −0.0659724
\(926\) 0 0
\(927\) 19.8605 0.652305
\(928\) 0 0
\(929\) 21.6642 0.710779 0.355390 0.934718i \(-0.384348\pi\)
0.355390 + 0.934718i \(0.384348\pi\)
\(930\) 0 0
\(931\) −50.2521 −1.64695
\(932\) 0 0
\(933\) 49.6161 1.62436
\(934\) 0 0
\(935\) −11.4289 −0.373766
\(936\) 0 0
\(937\) 13.3315 0.435521 0.217761 0.976002i \(-0.430125\pi\)
0.217761 + 0.976002i \(0.430125\pi\)
\(938\) 0 0
\(939\) 2.95907 0.0965657
\(940\) 0 0
\(941\) −6.62779 −0.216060 −0.108030 0.994148i \(-0.534454\pi\)
−0.108030 + 0.994148i \(0.534454\pi\)
\(942\) 0 0
\(943\) −3.00181 −0.0977522
\(944\) 0 0
\(945\) −69.0518 −2.24626
\(946\) 0 0
\(947\) −20.0496 −0.651523 −0.325762 0.945452i \(-0.605621\pi\)
−0.325762 + 0.945452i \(0.605621\pi\)
\(948\) 0 0
\(949\) −0.623618 −0.0202435
\(950\) 0 0
\(951\) −77.3849 −2.50938
\(952\) 0 0
\(953\) −13.5161 −0.437831 −0.218915 0.975744i \(-0.570252\pi\)
−0.218915 + 0.975744i \(0.570252\pi\)
\(954\) 0 0
\(955\) −5.50059 −0.177995
\(956\) 0 0
\(957\) 75.1764 2.43011
\(958\) 0 0
\(959\) 34.0335 1.09900
\(960\) 0 0
\(961\) −24.0632 −0.776233
\(962\) 0 0
\(963\) −3.22774 −0.104012
\(964\) 0 0
\(965\) 9.73741 0.313458
\(966\) 0 0
\(967\) −26.7288 −0.859541 −0.429770 0.902938i \(-0.641406\pi\)
−0.429770 + 0.902938i \(0.641406\pi\)
\(968\) 0 0
\(969\) −100.482 −3.22794
\(970\) 0 0
\(971\) 50.9996 1.63665 0.818327 0.574753i \(-0.194902\pi\)
0.818327 + 0.574753i \(0.194902\pi\)
\(972\) 0 0
\(973\) 17.9799 0.576410
\(974\) 0 0
\(975\) −15.1500 −0.485189
\(976\) 0 0
\(977\) 38.8774 1.24380 0.621899 0.783098i \(-0.286362\pi\)
0.621899 + 0.783098i \(0.286362\pi\)
\(978\) 0 0
\(979\) −42.6917 −1.36443
\(980\) 0 0
\(981\) −47.9219 −1.53003
\(982\) 0 0
\(983\) 6.39114 0.203846 0.101923 0.994792i \(-0.467501\pi\)
0.101923 + 0.994792i \(0.467501\pi\)
\(984\) 0 0
\(985\) −8.13384 −0.259166
\(986\) 0 0
\(987\) 89.4709 2.84789
\(988\) 0 0
\(989\) 34.5616 1.09900
\(990\) 0 0
\(991\) −42.5343 −1.35115 −0.675573 0.737293i \(-0.736104\pi\)
−0.675573 + 0.737293i \(0.736104\pi\)
\(992\) 0 0
\(993\) 15.7534 0.499920
\(994\) 0 0
\(995\) 11.8288 0.375000
\(996\) 0 0
\(997\) 9.04748 0.286537 0.143268 0.989684i \(-0.454239\pi\)
0.143268 + 0.989684i \(0.454239\pi\)
\(998\) 0 0
\(999\) −36.4059 −1.15183
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 \(a_p\))