Properties

Label 8016.2.a.bf.1.5
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(1\)
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 1.5
Root \(-0.716151\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-0.716151 q^{5}\) \(+3.33002 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-0.716151 q^{5}\) \(+3.33002 q^{7}\) \(+1.00000 q^{9}\) \(+1.47099 q^{11}\) \(-1.07152 q^{13}\) \(+0.716151 q^{15}\) \(+4.68991 q^{17}\) \(+1.60112 q^{19}\) \(-3.33002 q^{21}\) \(-5.96922 q^{23}\) \(-4.48713 q^{25}\) \(-1.00000 q^{27}\) \(+4.73151 q^{29}\) \(-8.82346 q^{31}\) \(-1.47099 q^{33}\) \(-2.38479 q^{35}\) \(-10.4028 q^{37}\) \(+1.07152 q^{39}\) \(-2.92019 q^{41}\) \(+8.38527 q^{43}\) \(-0.716151 q^{45}\) \(-6.24255 q^{47}\) \(+4.08900 q^{49}\) \(-4.68991 q^{51}\) \(-9.50501 q^{53}\) \(-1.05345 q^{55}\) \(-1.60112 q^{57}\) \(+4.74996 q^{59}\) \(+7.09947 q^{61}\) \(+3.33002 q^{63}\) \(+0.767367 q^{65}\) \(-13.6608 q^{67}\) \(+5.96922 q^{69}\) \(-13.6859 q^{71}\) \(+7.30688 q^{73}\) \(+4.48713 q^{75}\) \(+4.89844 q^{77}\) \(-12.8036 q^{79}\) \(+1.00000 q^{81}\) \(-1.24092 q^{83}\) \(-3.35869 q^{85}\) \(-4.73151 q^{87}\) \(-7.67545 q^{89}\) \(-3.56816 q^{91}\) \(+8.82346 q^{93}\) \(-1.14664 q^{95}\) \(+13.4461 q^{97}\) \(+1.47099 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut -\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.716151 −0.320272 −0.160136 0.987095i \(-0.551193\pi\)
−0.160136 + 0.987095i \(0.551193\pi\)
\(6\) 0 0
\(7\) 3.33002 1.25863 0.629314 0.777151i \(-0.283336\pi\)
0.629314 + 0.777151i \(0.283336\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.47099 0.443522 0.221761 0.975101i \(-0.428820\pi\)
0.221761 + 0.975101i \(0.428820\pi\)
\(12\) 0 0
\(13\) −1.07152 −0.297185 −0.148593 0.988899i \(-0.547474\pi\)
−0.148593 + 0.988899i \(0.547474\pi\)
\(14\) 0 0
\(15\) 0.716151 0.184909
\(16\) 0 0
\(17\) 4.68991 1.13747 0.568735 0.822520i \(-0.307433\pi\)
0.568735 + 0.822520i \(0.307433\pi\)
\(18\) 0 0
\(19\) 1.60112 0.367321 0.183661 0.982990i \(-0.441205\pi\)
0.183661 + 0.982990i \(0.441205\pi\)
\(20\) 0 0
\(21\) −3.33002 −0.726669
\(22\) 0 0
\(23\) −5.96922 −1.24467 −0.622334 0.782752i \(-0.713815\pi\)
−0.622334 + 0.782752i \(0.713815\pi\)
\(24\) 0 0
\(25\) −4.48713 −0.897426
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.73151 0.878620 0.439310 0.898336i \(-0.355223\pi\)
0.439310 + 0.898336i \(0.355223\pi\)
\(30\) 0 0
\(31\) −8.82346 −1.58474 −0.792370 0.610041i \(-0.791153\pi\)
−0.792370 + 0.610041i \(0.791153\pi\)
\(32\) 0 0
\(33\) −1.47099 −0.256067
\(34\) 0 0
\(35\) −2.38479 −0.403104
\(36\) 0 0
\(37\) −10.4028 −1.71021 −0.855106 0.518453i \(-0.826508\pi\)
−0.855106 + 0.518453i \(0.826508\pi\)
\(38\) 0 0
\(39\) 1.07152 0.171580
\(40\) 0 0
\(41\) −2.92019 −0.456058 −0.228029 0.973654i \(-0.573228\pi\)
−0.228029 + 0.973654i \(0.573228\pi\)
\(42\) 0 0
\(43\) 8.38527 1.27874 0.639371 0.768899i \(-0.279195\pi\)
0.639371 + 0.768899i \(0.279195\pi\)
\(44\) 0 0
\(45\) −0.716151 −0.106757
\(46\) 0 0
\(47\) −6.24255 −0.910569 −0.455285 0.890346i \(-0.650462\pi\)
−0.455285 + 0.890346i \(0.650462\pi\)
\(48\) 0 0
\(49\) 4.08900 0.584143
\(50\) 0 0
\(51\) −4.68991 −0.656719
\(52\) 0 0
\(53\) −9.50501 −1.30561 −0.652807 0.757524i \(-0.726409\pi\)
−0.652807 + 0.757524i \(0.726409\pi\)
\(54\) 0 0
\(55\) −1.05345 −0.142048
\(56\) 0 0
\(57\) −1.60112 −0.212073
\(58\) 0 0
\(59\) 4.74996 0.618393 0.309196 0.950998i \(-0.399940\pi\)
0.309196 + 0.950998i \(0.399940\pi\)
\(60\) 0 0
\(61\) 7.09947 0.908993 0.454497 0.890748i \(-0.349819\pi\)
0.454497 + 0.890748i \(0.349819\pi\)
\(62\) 0 0
\(63\) 3.33002 0.419543
\(64\) 0 0
\(65\) 0.767367 0.0951802
\(66\) 0 0
\(67\) −13.6608 −1.66893 −0.834466 0.551059i \(-0.814224\pi\)
−0.834466 + 0.551059i \(0.814224\pi\)
\(68\) 0 0
\(69\) 5.96922 0.718610
\(70\) 0 0
\(71\) −13.6859 −1.62422 −0.812109 0.583505i \(-0.801681\pi\)
−0.812109 + 0.583505i \(0.801681\pi\)
\(72\) 0 0
\(73\) 7.30688 0.855205 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(74\) 0 0
\(75\) 4.48713 0.518129
\(76\) 0 0
\(77\) 4.89844 0.558229
\(78\) 0 0
\(79\) −12.8036 −1.44052 −0.720259 0.693705i \(-0.755977\pi\)
−0.720259 + 0.693705i \(0.755977\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.24092 −0.136209 −0.0681045 0.997678i \(-0.521695\pi\)
−0.0681045 + 0.997678i \(0.521695\pi\)
\(84\) 0 0
\(85\) −3.35869 −0.364301
\(86\) 0 0
\(87\) −4.73151 −0.507271
\(88\) 0 0
\(89\) −7.67545 −0.813596 −0.406798 0.913518i \(-0.633355\pi\)
−0.406798 + 0.913518i \(0.633355\pi\)
\(90\) 0 0
\(91\) −3.56816 −0.374045
\(92\) 0 0
\(93\) 8.82346 0.914950
\(94\) 0 0
\(95\) −1.14664 −0.117643
\(96\) 0 0
\(97\) 13.4461 1.36525 0.682623 0.730771i \(-0.260839\pi\)
0.682623 + 0.730771i \(0.260839\pi\)
\(98\) 0 0
\(99\) 1.47099 0.147841
\(100\) 0 0
\(101\) −0.372387 −0.0370539 −0.0185269 0.999828i \(-0.505898\pi\)
−0.0185269 + 0.999828i \(0.505898\pi\)
\(102\) 0 0
\(103\) −7.26876 −0.716213 −0.358106 0.933681i \(-0.616577\pi\)
−0.358106 + 0.933681i \(0.616577\pi\)
\(104\) 0 0
\(105\) 2.38479 0.232732
\(106\) 0 0
\(107\) −7.75739 −0.749935 −0.374968 0.927038i \(-0.622346\pi\)
−0.374968 + 0.927038i \(0.622346\pi\)
\(108\) 0 0
\(109\) 9.49121 0.909094 0.454547 0.890723i \(-0.349801\pi\)
0.454547 + 0.890723i \(0.349801\pi\)
\(110\) 0 0
\(111\) 10.4028 0.987392
\(112\) 0 0
\(113\) 2.74341 0.258078 0.129039 0.991639i \(-0.458811\pi\)
0.129039 + 0.991639i \(0.458811\pi\)
\(114\) 0 0
\(115\) 4.27486 0.398633
\(116\) 0 0
\(117\) −1.07152 −0.0990617
\(118\) 0 0
\(119\) 15.6175 1.43165
\(120\) 0 0
\(121\) −8.83617 −0.803289
\(122\) 0 0
\(123\) 2.92019 0.263305
\(124\) 0 0
\(125\) 6.79422 0.607693
\(126\) 0 0
\(127\) −15.0695 −1.33720 −0.668600 0.743622i \(-0.733106\pi\)
−0.668600 + 0.743622i \(0.733106\pi\)
\(128\) 0 0
\(129\) −8.38527 −0.738282
\(130\) 0 0
\(131\) 8.64719 0.755508 0.377754 0.925906i \(-0.376696\pi\)
0.377754 + 0.925906i \(0.376696\pi\)
\(132\) 0 0
\(133\) 5.33174 0.462321
\(134\) 0 0
\(135\) 0.716151 0.0616365
\(136\) 0 0
\(137\) 13.9735 1.19383 0.596917 0.802303i \(-0.296392\pi\)
0.596917 + 0.802303i \(0.296392\pi\)
\(138\) 0 0
\(139\) −9.76531 −0.828283 −0.414141 0.910213i \(-0.635918\pi\)
−0.414141 + 0.910213i \(0.635918\pi\)
\(140\) 0 0
\(141\) 6.24255 0.525717
\(142\) 0 0
\(143\) −1.57619 −0.131808
\(144\) 0 0
\(145\) −3.38848 −0.281398
\(146\) 0 0
\(147\) −4.08900 −0.337255
\(148\) 0 0
\(149\) 12.6591 1.03708 0.518538 0.855054i \(-0.326476\pi\)
0.518538 + 0.855054i \(0.326476\pi\)
\(150\) 0 0
\(151\) 10.2773 0.836352 0.418176 0.908366i \(-0.362669\pi\)
0.418176 + 0.908366i \(0.362669\pi\)
\(152\) 0 0
\(153\) 4.68991 0.379157
\(154\) 0 0
\(155\) 6.31893 0.507549
\(156\) 0 0
\(157\) 17.3312 1.38318 0.691590 0.722291i \(-0.256911\pi\)
0.691590 + 0.722291i \(0.256911\pi\)
\(158\) 0 0
\(159\) 9.50501 0.753797
\(160\) 0 0
\(161\) −19.8776 −1.56657
\(162\) 0 0
\(163\) −6.39092 −0.500576 −0.250288 0.968171i \(-0.580525\pi\)
−0.250288 + 0.968171i \(0.580525\pi\)
\(164\) 0 0
\(165\) 1.05345 0.0820113
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −11.8519 −0.911681
\(170\) 0 0
\(171\) 1.60112 0.122440
\(172\) 0 0
\(173\) 23.0601 1.75323 0.876614 0.481195i \(-0.159797\pi\)
0.876614 + 0.481195i \(0.159797\pi\)
\(174\) 0 0
\(175\) −14.9422 −1.12952
\(176\) 0 0
\(177\) −4.74996 −0.357029
\(178\) 0 0
\(179\) 1.56721 0.117139 0.0585693 0.998283i \(-0.481346\pi\)
0.0585693 + 0.998283i \(0.481346\pi\)
\(180\) 0 0
\(181\) −9.66369 −0.718297 −0.359148 0.933281i \(-0.616933\pi\)
−0.359148 + 0.933281i \(0.616933\pi\)
\(182\) 0 0
\(183\) −7.09947 −0.524808
\(184\) 0 0
\(185\) 7.44999 0.547734
\(186\) 0 0
\(187\) 6.89884 0.504493
\(188\) 0 0
\(189\) −3.33002 −0.242223
\(190\) 0 0
\(191\) −15.1174 −1.09386 −0.546930 0.837179i \(-0.684204\pi\)
−0.546930 + 0.837179i \(0.684204\pi\)
\(192\) 0 0
\(193\) 14.9243 1.07427 0.537137 0.843495i \(-0.319506\pi\)
0.537137 + 0.843495i \(0.319506\pi\)
\(194\) 0 0
\(195\) −0.767367 −0.0549523
\(196\) 0 0
\(197\) −13.7458 −0.979350 −0.489675 0.871905i \(-0.662885\pi\)
−0.489675 + 0.871905i \(0.662885\pi\)
\(198\) 0 0
\(199\) −9.45882 −0.670518 −0.335259 0.942126i \(-0.608824\pi\)
−0.335259 + 0.942126i \(0.608824\pi\)
\(200\) 0 0
\(201\) 13.6608 0.963558
\(202\) 0 0
\(203\) 15.7560 1.10586
\(204\) 0 0
\(205\) 2.09130 0.146063
\(206\) 0 0
\(207\) −5.96922 −0.414889
\(208\) 0 0
\(209\) 2.35523 0.162915
\(210\) 0 0
\(211\) −19.5293 −1.34445 −0.672227 0.740345i \(-0.734662\pi\)
−0.672227 + 0.740345i \(0.734662\pi\)
\(212\) 0 0
\(213\) 13.6859 0.937743
\(214\) 0 0
\(215\) −6.00512 −0.409546
\(216\) 0 0
\(217\) −29.3822 −1.99460
\(218\) 0 0
\(219\) −7.30688 −0.493753
\(220\) 0 0
\(221\) −5.02532 −0.338039
\(222\) 0 0
\(223\) −5.37221 −0.359750 −0.179875 0.983690i \(-0.557569\pi\)
−0.179875 + 0.983690i \(0.557569\pi\)
\(224\) 0 0
\(225\) −4.48713 −0.299142
\(226\) 0 0
\(227\) 27.0420 1.79484 0.897421 0.441174i \(-0.145438\pi\)
0.897421 + 0.441174i \(0.145438\pi\)
\(228\) 0 0
\(229\) −12.6136 −0.833527 −0.416764 0.909015i \(-0.636836\pi\)
−0.416764 + 0.909015i \(0.636836\pi\)
\(230\) 0 0
\(231\) −4.89844 −0.322293
\(232\) 0 0
\(233\) 25.6565 1.68082 0.840408 0.541954i \(-0.182315\pi\)
0.840408 + 0.541954i \(0.182315\pi\)
\(234\) 0 0
\(235\) 4.47061 0.291630
\(236\) 0 0
\(237\) 12.8036 0.831684
\(238\) 0 0
\(239\) −2.74058 −0.177273 −0.0886367 0.996064i \(-0.528251\pi\)
−0.0886367 + 0.996064i \(0.528251\pi\)
\(240\) 0 0
\(241\) −19.6085 −1.26310 −0.631548 0.775337i \(-0.717580\pi\)
−0.631548 + 0.775337i \(0.717580\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −2.92834 −0.187085
\(246\) 0 0
\(247\) −1.71562 −0.109162
\(248\) 0 0
\(249\) 1.24092 0.0786403
\(250\) 0 0
\(251\) 15.4602 0.975842 0.487921 0.872888i \(-0.337755\pi\)
0.487921 + 0.872888i \(0.337755\pi\)
\(252\) 0 0
\(253\) −8.78069 −0.552037
\(254\) 0 0
\(255\) 3.35869 0.210329
\(256\) 0 0
\(257\) −28.2550 −1.76250 −0.881250 0.472650i \(-0.843298\pi\)
−0.881250 + 0.472650i \(0.843298\pi\)
\(258\) 0 0
\(259\) −34.6415 −2.15252
\(260\) 0 0
\(261\) 4.73151 0.292873
\(262\) 0 0
\(263\) 0.0685960 0.00422981 0.00211490 0.999998i \(-0.499327\pi\)
0.00211490 + 0.999998i \(0.499327\pi\)
\(264\) 0 0
\(265\) 6.80702 0.418152
\(266\) 0 0
\(267\) 7.67545 0.469730
\(268\) 0 0
\(269\) −16.3857 −0.999053 −0.499526 0.866299i \(-0.666493\pi\)
−0.499526 + 0.866299i \(0.666493\pi\)
\(270\) 0 0
\(271\) 8.90565 0.540980 0.270490 0.962723i \(-0.412814\pi\)
0.270490 + 0.962723i \(0.412814\pi\)
\(272\) 0 0
\(273\) 3.56816 0.215955
\(274\) 0 0
\(275\) −6.60054 −0.398028
\(276\) 0 0
\(277\) −10.7421 −0.645430 −0.322715 0.946496i \(-0.604596\pi\)
−0.322715 + 0.946496i \(0.604596\pi\)
\(278\) 0 0
\(279\) −8.82346 −0.528247
\(280\) 0 0
\(281\) −20.4669 −1.22095 −0.610475 0.792035i \(-0.709022\pi\)
−0.610475 + 0.792035i \(0.709022\pi\)
\(282\) 0 0
\(283\) −0.746921 −0.0443998 −0.0221999 0.999754i \(-0.507067\pi\)
−0.0221999 + 0.999754i \(0.507067\pi\)
\(284\) 0 0
\(285\) 1.14664 0.0679212
\(286\) 0 0
\(287\) −9.72429 −0.574007
\(288\) 0 0
\(289\) 4.99528 0.293840
\(290\) 0 0
\(291\) −13.4461 −0.788225
\(292\) 0 0
\(293\) 23.0541 1.34683 0.673417 0.739263i \(-0.264826\pi\)
0.673417 + 0.739263i \(0.264826\pi\)
\(294\) 0 0
\(295\) −3.40169 −0.198054
\(296\) 0 0
\(297\) −1.47099 −0.0853558
\(298\) 0 0
\(299\) 6.39611 0.369897
\(300\) 0 0
\(301\) 27.9231 1.60946
\(302\) 0 0
\(303\) 0.372387 0.0213931
\(304\) 0 0
\(305\) −5.08429 −0.291126
\(306\) 0 0
\(307\) 20.1854 1.15204 0.576021 0.817435i \(-0.304605\pi\)
0.576021 + 0.817435i \(0.304605\pi\)
\(308\) 0 0
\(309\) 7.26876 0.413506
\(310\) 0 0
\(311\) 18.6993 1.06034 0.530171 0.847891i \(-0.322128\pi\)
0.530171 + 0.847891i \(0.322128\pi\)
\(312\) 0 0
\(313\) −33.3300 −1.88392 −0.941962 0.335719i \(-0.891021\pi\)
−0.941962 + 0.335719i \(0.891021\pi\)
\(314\) 0 0
\(315\) −2.38479 −0.134368
\(316\) 0 0
\(317\) −13.7905 −0.774553 −0.387277 0.921964i \(-0.626584\pi\)
−0.387277 + 0.921964i \(0.626584\pi\)
\(318\) 0 0
\(319\) 6.96003 0.389687
\(320\) 0 0
\(321\) 7.75739 0.432975
\(322\) 0 0
\(323\) 7.50910 0.417817
\(324\) 0 0
\(325\) 4.80803 0.266701
\(326\) 0 0
\(327\) −9.49121 −0.524865
\(328\) 0 0
\(329\) −20.7878 −1.14607
\(330\) 0 0
\(331\) −7.26826 −0.399500 −0.199750 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(332\) 0 0
\(333\) −10.4028 −0.570071
\(334\) 0 0
\(335\) 9.78319 0.534513
\(336\) 0 0
\(337\) −6.75359 −0.367891 −0.183946 0.982936i \(-0.558887\pi\)
−0.183946 + 0.982936i \(0.558887\pi\)
\(338\) 0 0
\(339\) −2.74341 −0.149002
\(340\) 0 0
\(341\) −12.9793 −0.702866
\(342\) 0 0
\(343\) −9.69367 −0.523409
\(344\) 0 0
\(345\) −4.27486 −0.230151
\(346\) 0 0
\(347\) −1.61353 −0.0866191 −0.0433095 0.999062i \(-0.513790\pi\)
−0.0433095 + 0.999062i \(0.513790\pi\)
\(348\) 0 0
\(349\) 5.36893 0.287392 0.143696 0.989622i \(-0.454101\pi\)
0.143696 + 0.989622i \(0.454101\pi\)
\(350\) 0 0
\(351\) 1.07152 0.0571933
\(352\) 0 0
\(353\) −4.70610 −0.250480 −0.125240 0.992126i \(-0.539970\pi\)
−0.125240 + 0.992126i \(0.539970\pi\)
\(354\) 0 0
\(355\) 9.80118 0.520192
\(356\) 0 0
\(357\) −15.6175 −0.826565
\(358\) 0 0
\(359\) 21.9268 1.15725 0.578625 0.815594i \(-0.303590\pi\)
0.578625 + 0.815594i \(0.303590\pi\)
\(360\) 0 0
\(361\) −16.4364 −0.865075
\(362\) 0 0
\(363\) 8.83617 0.463779
\(364\) 0 0
\(365\) −5.23283 −0.273899
\(366\) 0 0
\(367\) −23.5650 −1.23008 −0.615040 0.788496i \(-0.710860\pi\)
−0.615040 + 0.788496i \(0.710860\pi\)
\(368\) 0 0
\(369\) −2.92019 −0.152019
\(370\) 0 0
\(371\) −31.6518 −1.64328
\(372\) 0 0
\(373\) 0.522216 0.0270393 0.0135197 0.999909i \(-0.495696\pi\)
0.0135197 + 0.999909i \(0.495696\pi\)
\(374\) 0 0
\(375\) −6.79422 −0.350852
\(376\) 0 0
\(377\) −5.06989 −0.261113
\(378\) 0 0
\(379\) −30.0093 −1.54147 −0.770737 0.637153i \(-0.780112\pi\)
−0.770737 + 0.637153i \(0.780112\pi\)
\(380\) 0 0
\(381\) 15.0695 0.772033
\(382\) 0 0
\(383\) −11.1272 −0.568572 −0.284286 0.958740i \(-0.591756\pi\)
−0.284286 + 0.958740i \(0.591756\pi\)
\(384\) 0 0
\(385\) −3.50802 −0.178785
\(386\) 0 0
\(387\) 8.38527 0.426247
\(388\) 0 0
\(389\) 25.8762 1.31198 0.655989 0.754771i \(-0.272252\pi\)
0.655989 + 0.754771i \(0.272252\pi\)
\(390\) 0 0
\(391\) −27.9951 −1.41577
\(392\) 0 0
\(393\) −8.64719 −0.436193
\(394\) 0 0
\(395\) 9.16932 0.461358
\(396\) 0 0
\(397\) −16.1106 −0.808569 −0.404284 0.914633i \(-0.632479\pi\)
−0.404284 + 0.914633i \(0.632479\pi\)
\(398\) 0 0
\(399\) −5.33174 −0.266921
\(400\) 0 0
\(401\) 30.7106 1.53361 0.766807 0.641878i \(-0.221844\pi\)
0.766807 + 0.641878i \(0.221844\pi\)
\(402\) 0 0
\(403\) 9.45448 0.470961
\(404\) 0 0
\(405\) −0.716151 −0.0355858
\(406\) 0 0
\(407\) −15.3025 −0.758516
\(408\) 0 0
\(409\) 21.7712 1.07652 0.538259 0.842779i \(-0.319082\pi\)
0.538259 + 0.842779i \(0.319082\pi\)
\(410\) 0 0
\(411\) −13.9735 −0.689260
\(412\) 0 0
\(413\) 15.8175 0.778326
\(414\) 0 0
\(415\) 0.888688 0.0436240
\(416\) 0 0
\(417\) 9.76531 0.478209
\(418\) 0 0
\(419\) 1.38933 0.0678734 0.0339367 0.999424i \(-0.489196\pi\)
0.0339367 + 0.999424i \(0.489196\pi\)
\(420\) 0 0
\(421\) 29.4498 1.43530 0.717648 0.696406i \(-0.245219\pi\)
0.717648 + 0.696406i \(0.245219\pi\)
\(422\) 0 0
\(423\) −6.24255 −0.303523
\(424\) 0 0
\(425\) −21.0442 −1.02080
\(426\) 0 0
\(427\) 23.6413 1.14408
\(428\) 0 0
\(429\) 1.57619 0.0760994
\(430\) 0 0
\(431\) 14.1214 0.680202 0.340101 0.940389i \(-0.389539\pi\)
0.340101 + 0.940389i \(0.389539\pi\)
\(432\) 0 0
\(433\) −32.8372 −1.57806 −0.789028 0.614357i \(-0.789415\pi\)
−0.789028 + 0.614357i \(0.789415\pi\)
\(434\) 0 0
\(435\) 3.38848 0.162465
\(436\) 0 0
\(437\) −9.55742 −0.457193
\(438\) 0 0
\(439\) −37.4769 −1.78868 −0.894338 0.447392i \(-0.852353\pi\)
−0.894338 + 0.447392i \(0.852353\pi\)
\(440\) 0 0
\(441\) 4.08900 0.194714
\(442\) 0 0
\(443\) −8.76333 −0.416358 −0.208179 0.978091i \(-0.566754\pi\)
−0.208179 + 0.978091i \(0.566754\pi\)
\(444\) 0 0
\(445\) 5.49678 0.260572
\(446\) 0 0
\(447\) −12.6591 −0.598757
\(448\) 0 0
\(449\) −8.19198 −0.386603 −0.193302 0.981139i \(-0.561920\pi\)
−0.193302 + 0.981139i \(0.561920\pi\)
\(450\) 0 0
\(451\) −4.29559 −0.202271
\(452\) 0 0
\(453\) −10.2773 −0.482868
\(454\) 0 0
\(455\) 2.55534 0.119796
\(456\) 0 0
\(457\) 26.6671 1.24743 0.623717 0.781651i \(-0.285622\pi\)
0.623717 + 0.781651i \(0.285622\pi\)
\(458\) 0 0
\(459\) −4.68991 −0.218906
\(460\) 0 0
\(461\) −27.6394 −1.28730 −0.643648 0.765322i \(-0.722580\pi\)
−0.643648 + 0.765322i \(0.722580\pi\)
\(462\) 0 0
\(463\) 39.7468 1.84719 0.923595 0.383371i \(-0.125237\pi\)
0.923595 + 0.383371i \(0.125237\pi\)
\(464\) 0 0
\(465\) −6.31893 −0.293033
\(466\) 0 0
\(467\) 3.99234 0.184743 0.0923717 0.995725i \(-0.470555\pi\)
0.0923717 + 0.995725i \(0.470555\pi\)
\(468\) 0 0
\(469\) −45.4907 −2.10056
\(470\) 0 0
\(471\) −17.3312 −0.798579
\(472\) 0 0
\(473\) 12.3347 0.567149
\(474\) 0 0
\(475\) −7.18442 −0.329644
\(476\) 0 0
\(477\) −9.50501 −0.435205
\(478\) 0 0
\(479\) 20.4282 0.933390 0.466695 0.884418i \(-0.345445\pi\)
0.466695 + 0.884418i \(0.345445\pi\)
\(480\) 0 0
\(481\) 11.1468 0.508250
\(482\) 0 0
\(483\) 19.8776 0.904462
\(484\) 0 0
\(485\) −9.62944 −0.437251
\(486\) 0 0
\(487\) 29.7212 1.34680 0.673399 0.739280i \(-0.264834\pi\)
0.673399 + 0.739280i \(0.264834\pi\)
\(488\) 0 0
\(489\) 6.39092 0.289007
\(490\) 0 0
\(491\) 28.6530 1.29309 0.646546 0.762875i \(-0.276213\pi\)
0.646546 + 0.762875i \(0.276213\pi\)
\(492\) 0 0
\(493\) 22.1904 0.999404
\(494\) 0 0
\(495\) −1.05345 −0.0473493
\(496\) 0 0
\(497\) −45.5743 −2.04429
\(498\) 0 0
\(499\) 15.6063 0.698636 0.349318 0.937004i \(-0.386413\pi\)
0.349318 + 0.937004i \(0.386413\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −21.5905 −0.962671 −0.481335 0.876536i \(-0.659848\pi\)
−0.481335 + 0.876536i \(0.659848\pi\)
\(504\) 0 0
\(505\) 0.266685 0.0118673
\(506\) 0 0
\(507\) 11.8519 0.526359
\(508\) 0 0
\(509\) −32.2493 −1.42942 −0.714712 0.699419i \(-0.753442\pi\)
−0.714712 + 0.699419i \(0.753442\pi\)
\(510\) 0 0
\(511\) 24.3320 1.07638
\(512\) 0 0
\(513\) −1.60112 −0.0706910
\(514\) 0 0
\(515\) 5.20553 0.229383
\(516\) 0 0
\(517\) −9.18276 −0.403857
\(518\) 0 0
\(519\) −23.0601 −1.01223
\(520\) 0 0
\(521\) −5.29471 −0.231965 −0.115983 0.993251i \(-0.537002\pi\)
−0.115983 + 0.993251i \(0.537002\pi\)
\(522\) 0 0
\(523\) −30.7766 −1.34577 −0.672884 0.739748i \(-0.734945\pi\)
−0.672884 + 0.739748i \(0.734945\pi\)
\(524\) 0 0
\(525\) 14.9422 0.652131
\(526\) 0 0
\(527\) −41.3812 −1.80260
\(528\) 0 0
\(529\) 12.6316 0.549199
\(530\) 0 0
\(531\) 4.74996 0.206131
\(532\) 0 0
\(533\) 3.12903 0.135534
\(534\) 0 0
\(535\) 5.55546 0.240184
\(536\) 0 0
\(537\) −1.56721 −0.0676300
\(538\) 0 0
\(539\) 6.01490 0.259080
\(540\) 0 0
\(541\) −4.15500 −0.178637 −0.0893187 0.996003i \(-0.528469\pi\)
−0.0893187 + 0.996003i \(0.528469\pi\)
\(542\) 0 0
\(543\) 9.66369 0.414709
\(544\) 0 0
\(545\) −6.79714 −0.291158
\(546\) 0 0
\(547\) −33.6839 −1.44022 −0.720110 0.693860i \(-0.755909\pi\)
−0.720110 + 0.693860i \(0.755909\pi\)
\(548\) 0 0
\(549\) 7.09947 0.302998
\(550\) 0 0
\(551\) 7.57570 0.322736
\(552\) 0 0
\(553\) −42.6362 −1.81308
\(554\) 0 0
\(555\) −7.44999 −0.316234
\(556\) 0 0
\(557\) −42.2475 −1.79008 −0.895042 0.445983i \(-0.852854\pi\)
−0.895042 + 0.445983i \(0.852854\pi\)
\(558\) 0 0
\(559\) −8.98495 −0.380023
\(560\) 0 0
\(561\) −6.89884 −0.291269
\(562\) 0 0
\(563\) 0.759500 0.0320091 0.0160046 0.999872i \(-0.494905\pi\)
0.0160046 + 0.999872i \(0.494905\pi\)
\(564\) 0 0
\(565\) −1.96470 −0.0826554
\(566\) 0 0
\(567\) 3.33002 0.139848
\(568\) 0 0
\(569\) 37.2088 1.55987 0.779937 0.625858i \(-0.215251\pi\)
0.779937 + 0.625858i \(0.215251\pi\)
\(570\) 0 0
\(571\) −21.3536 −0.893621 −0.446811 0.894629i \(-0.647440\pi\)
−0.446811 + 0.894629i \(0.647440\pi\)
\(572\) 0 0
\(573\) 15.1174 0.631540
\(574\) 0 0
\(575\) 26.7846 1.11700
\(576\) 0 0
\(577\) 0.837781 0.0348773 0.0174386 0.999848i \(-0.494449\pi\)
0.0174386 + 0.999848i \(0.494449\pi\)
\(578\) 0 0
\(579\) −14.9243 −0.620233
\(580\) 0 0
\(581\) −4.13229 −0.171436
\(582\) 0 0
\(583\) −13.9818 −0.579068
\(584\) 0 0
\(585\) 0.767367 0.0317267
\(586\) 0 0
\(587\) −9.10109 −0.375642 −0.187821 0.982203i \(-0.560143\pi\)
−0.187821 + 0.982203i \(0.560143\pi\)
\(588\) 0 0
\(589\) −14.1274 −0.582109
\(590\) 0 0
\(591\) 13.7458 0.565428
\(592\) 0 0
\(593\) −32.8995 −1.35102 −0.675510 0.737351i \(-0.736076\pi\)
−0.675510 + 0.737351i \(0.736076\pi\)
\(594\) 0 0
\(595\) −11.1845 −0.458519
\(596\) 0 0
\(597\) 9.45882 0.387124
\(598\) 0 0
\(599\) −14.9054 −0.609018 −0.304509 0.952509i \(-0.598492\pi\)
−0.304509 + 0.952509i \(0.598492\pi\)
\(600\) 0 0
\(601\) 45.6503 1.86212 0.931058 0.364871i \(-0.118887\pi\)
0.931058 + 0.364871i \(0.118887\pi\)
\(602\) 0 0
\(603\) −13.6608 −0.556311
\(604\) 0 0
\(605\) 6.32803 0.257271
\(606\) 0 0
\(607\) 7.14482 0.289999 0.145000 0.989432i \(-0.453682\pi\)
0.145000 + 0.989432i \(0.453682\pi\)
\(608\) 0 0
\(609\) −15.7560 −0.638466
\(610\) 0 0
\(611\) 6.68899 0.270608
\(612\) 0 0
\(613\) 12.0707 0.487530 0.243765 0.969834i \(-0.421617\pi\)
0.243765 + 0.969834i \(0.421617\pi\)
\(614\) 0 0
\(615\) −2.09130 −0.0843294
\(616\) 0 0
\(617\) −18.6455 −0.750640 −0.375320 0.926895i \(-0.622467\pi\)
−0.375320 + 0.926895i \(0.622467\pi\)
\(618\) 0 0
\(619\) −46.6989 −1.87699 −0.938495 0.345294i \(-0.887779\pi\)
−0.938495 + 0.345294i \(0.887779\pi\)
\(620\) 0 0
\(621\) 5.96922 0.239537
\(622\) 0 0
\(623\) −25.5594 −1.02401
\(624\) 0 0
\(625\) 17.5700 0.702798
\(626\) 0 0
\(627\) −2.35523 −0.0940590
\(628\) 0 0
\(629\) −48.7883 −1.94532
\(630\) 0 0
\(631\) −37.4683 −1.49159 −0.745794 0.666177i \(-0.767930\pi\)
−0.745794 + 0.666177i \(0.767930\pi\)
\(632\) 0 0
\(633\) 19.5293 0.776221
\(634\) 0 0
\(635\) 10.7920 0.428269
\(636\) 0 0
\(637\) −4.38143 −0.173599
\(638\) 0 0
\(639\) −13.6859 −0.541406
\(640\) 0 0
\(641\) 19.3368 0.763757 0.381878 0.924213i \(-0.375277\pi\)
0.381878 + 0.924213i \(0.375277\pi\)
\(642\) 0 0
\(643\) −35.6061 −1.40417 −0.702083 0.712095i \(-0.747747\pi\)
−0.702083 + 0.712095i \(0.747747\pi\)
\(644\) 0 0
\(645\) 6.00512 0.236451
\(646\) 0 0
\(647\) 24.6666 0.969743 0.484872 0.874585i \(-0.338866\pi\)
0.484872 + 0.874585i \(0.338866\pi\)
\(648\) 0 0
\(649\) 6.98717 0.274271
\(650\) 0 0
\(651\) 29.3822 1.15158
\(652\) 0 0
\(653\) 37.6448 1.47315 0.736577 0.676353i \(-0.236441\pi\)
0.736577 + 0.676353i \(0.236441\pi\)
\(654\) 0 0
\(655\) −6.19269 −0.241968
\(656\) 0 0
\(657\) 7.30688 0.285068
\(658\) 0 0
\(659\) 15.0705 0.587063 0.293532 0.955949i \(-0.405169\pi\)
0.293532 + 0.955949i \(0.405169\pi\)
\(660\) 0 0
\(661\) −15.4489 −0.600892 −0.300446 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(662\) 0 0
\(663\) 5.02532 0.195167
\(664\) 0 0
\(665\) −3.81833 −0.148069
\(666\) 0 0
\(667\) −28.2434 −1.09359
\(668\) 0 0
\(669\) 5.37221 0.207702
\(670\) 0 0
\(671\) 10.4433 0.403158
\(672\) 0 0
\(673\) −19.7469 −0.761187 −0.380593 0.924743i \(-0.624280\pi\)
−0.380593 + 0.924743i \(0.624280\pi\)
\(674\) 0 0
\(675\) 4.48713 0.172710
\(676\) 0 0
\(677\) 45.4498 1.74678 0.873388 0.487025i \(-0.161918\pi\)
0.873388 + 0.487025i \(0.161918\pi\)
\(678\) 0 0
\(679\) 44.7757 1.71834
\(680\) 0 0
\(681\) −27.0420 −1.03625
\(682\) 0 0
\(683\) 13.5432 0.518217 0.259108 0.965848i \(-0.416571\pi\)
0.259108 + 0.965848i \(0.416571\pi\)
\(684\) 0 0
\(685\) −10.0071 −0.382352
\(686\) 0 0
\(687\) 12.6136 0.481237
\(688\) 0 0
\(689\) 10.1848 0.388009
\(690\) 0 0
\(691\) 10.4424 0.397250 0.198625 0.980076i \(-0.436352\pi\)
0.198625 + 0.980076i \(0.436352\pi\)
\(692\) 0 0
\(693\) 4.89844 0.186076
\(694\) 0 0
\(695\) 6.99344 0.265276
\(696\) 0 0
\(697\) −13.6955 −0.518752
\(698\) 0 0
\(699\) −25.6565 −0.970420
\(700\) 0 0
\(701\) −6.26217 −0.236519 −0.118259 0.992983i \(-0.537731\pi\)
−0.118259 + 0.992983i \(0.537731\pi\)
\(702\) 0 0
\(703\) −16.6561 −0.628198
\(704\) 0 0
\(705\) −4.47061 −0.168373
\(706\) 0 0
\(707\) −1.24005 −0.0466371
\(708\) 0 0
\(709\) −38.7936 −1.45692 −0.728462 0.685086i \(-0.759765\pi\)
−0.728462 + 0.685086i \(0.759765\pi\)
\(710\) 0 0
\(711\) −12.8036 −0.480173
\(712\) 0 0
\(713\) 52.6692 1.97248
\(714\) 0 0
\(715\) 1.12879 0.0422145
\(716\) 0 0
\(717\) 2.74058 0.102349
\(718\) 0 0
\(719\) −26.4655 −0.986997 −0.493498 0.869747i \(-0.664282\pi\)
−0.493498 + 0.869747i \(0.664282\pi\)
\(720\) 0 0
\(721\) −24.2051 −0.901445
\(722\) 0 0
\(723\) 19.6085 0.729249
\(724\) 0 0
\(725\) −21.2309 −0.788496
\(726\) 0 0
\(727\) −43.0571 −1.59690 −0.798450 0.602062i \(-0.794346\pi\)
−0.798450 + 0.602062i \(0.794346\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 39.3262 1.45453
\(732\) 0 0
\(733\) −21.9645 −0.811276 −0.405638 0.914034i \(-0.632951\pi\)
−0.405638 + 0.914034i \(0.632951\pi\)
\(734\) 0 0
\(735\) 2.92834 0.108014
\(736\) 0 0
\(737\) −20.0950 −0.740208
\(738\) 0 0
\(739\) −16.2983 −0.599542 −0.299771 0.954011i \(-0.596910\pi\)
−0.299771 + 0.954011i \(0.596910\pi\)
\(740\) 0 0
\(741\) 1.71562 0.0630250
\(742\) 0 0
\(743\) −32.0904 −1.17728 −0.588642 0.808394i \(-0.700337\pi\)
−0.588642 + 0.808394i \(0.700337\pi\)
\(744\) 0 0
\(745\) −9.06585 −0.332147
\(746\) 0 0
\(747\) −1.24092 −0.0454030
\(748\) 0 0
\(749\) −25.8322 −0.943889
\(750\) 0 0
\(751\) 20.8716 0.761616 0.380808 0.924654i \(-0.375646\pi\)
0.380808 + 0.924654i \(0.375646\pi\)
\(752\) 0 0
\(753\) −15.4602 −0.563403
\(754\) 0 0
\(755\) −7.36008 −0.267861
\(756\) 0 0
\(757\) 4.00358 0.145512 0.0727562 0.997350i \(-0.476820\pi\)
0.0727562 + 0.997350i \(0.476820\pi\)
\(758\) 0 0
\(759\) 8.78069 0.318719
\(760\) 0 0
\(761\) −42.4521 −1.53889 −0.769443 0.638716i \(-0.779466\pi\)
−0.769443 + 0.638716i \(0.779466\pi\)
\(762\) 0 0
\(763\) 31.6059 1.14421
\(764\) 0 0
\(765\) −3.35869 −0.121434
\(766\) 0 0
\(767\) −5.08966 −0.183777
\(768\) 0 0
\(769\) 8.42722 0.303893 0.151947 0.988389i \(-0.451446\pi\)
0.151947 + 0.988389i \(0.451446\pi\)
\(770\) 0 0
\(771\) 28.2550 1.01758
\(772\) 0 0
\(773\) 37.4061 1.34540 0.672702 0.739914i \(-0.265134\pi\)
0.672702 + 0.739914i \(0.265134\pi\)
\(774\) 0 0
\(775\) 39.5920 1.42219
\(776\) 0 0
\(777\) 34.6415 1.24276
\(778\) 0 0
\(779\) −4.67557 −0.167520
\(780\) 0 0
\(781\) −20.1319 −0.720376
\(782\) 0 0
\(783\) −4.73151 −0.169090
\(784\) 0 0
\(785\) −12.4117 −0.442994
\(786\) 0 0
\(787\) −13.8673 −0.494316 −0.247158 0.968975i \(-0.579497\pi\)
−0.247158 + 0.968975i \(0.579497\pi\)
\(788\) 0 0
\(789\) −0.0685960 −0.00244208
\(790\) 0 0
\(791\) 9.13560 0.324825
\(792\) 0 0
\(793\) −7.60719 −0.270139
\(794\) 0 0
\(795\) −6.80702 −0.241420
\(796\) 0 0
\(797\) −28.2739 −1.00151 −0.500756 0.865588i \(-0.666945\pi\)
−0.500756 + 0.865588i \(0.666945\pi\)
\(798\) 0 0
\(799\) −29.2770 −1.03575
\(800\) 0 0
\(801\) −7.67545 −0.271199
\(802\) 0 0
\(803\) 10.7484 0.379302
\(804\) 0 0
\(805\) 14.2354 0.501730
\(806\) 0 0
\(807\) 16.3857 0.576803
\(808\) 0 0
\(809\) 45.5606 1.60183 0.800913 0.598781i \(-0.204348\pi\)
0.800913 + 0.598781i \(0.204348\pi\)
\(810\) 0 0
\(811\) 39.1207 1.37371 0.686856 0.726794i \(-0.258990\pi\)
0.686856 + 0.726794i \(0.258990\pi\)
\(812\) 0 0
\(813\) −8.90565 −0.312335
\(814\) 0 0
\(815\) 4.57686 0.160321
\(816\) 0 0
\(817\) 13.4258 0.469709
\(818\) 0 0
\(819\) −3.56816 −0.124682
\(820\) 0 0
\(821\) 9.50395 0.331690 0.165845 0.986152i \(-0.446965\pi\)
0.165845 + 0.986152i \(0.446965\pi\)
\(822\) 0 0
\(823\) 36.2413 1.26329 0.631646 0.775257i \(-0.282380\pi\)
0.631646 + 0.775257i \(0.282380\pi\)
\(824\) 0 0
\(825\) 6.60054 0.229801
\(826\) 0 0
\(827\) −28.0245 −0.974508 −0.487254 0.873260i \(-0.662001\pi\)
−0.487254 + 0.873260i \(0.662001\pi\)
\(828\) 0 0
\(829\) −37.6916 −1.30908 −0.654542 0.756026i \(-0.727138\pi\)
−0.654542 + 0.756026i \(0.727138\pi\)
\(830\) 0 0
\(831\) 10.7421 0.372639
\(832\) 0 0
\(833\) 19.1771 0.664446
\(834\) 0 0
\(835\) 0.716151 0.0247834
\(836\) 0 0
\(837\) 8.82346 0.304983
\(838\) 0 0
\(839\) 13.3962 0.462490 0.231245 0.972896i \(-0.425720\pi\)
0.231245 + 0.972896i \(0.425720\pi\)
\(840\) 0 0
\(841\) −6.61279 −0.228027
\(842\) 0 0
\(843\) 20.4669 0.704916
\(844\) 0 0
\(845\) 8.48772 0.291986
\(846\) 0 0
\(847\) −29.4246 −1.01104
\(848\) 0 0
\(849\) 0.746921 0.0256343
\(850\) 0 0
\(851\) 62.0967 2.12865
\(852\) 0 0
\(853\) 2.22324 0.0761223 0.0380611 0.999275i \(-0.487882\pi\)
0.0380611 + 0.999275i \(0.487882\pi\)
\(854\) 0 0
\(855\) −1.14664 −0.0392143
\(856\) 0 0
\(857\) −44.5709 −1.52251 −0.761257 0.648451i \(-0.775417\pi\)
−0.761257 + 0.648451i \(0.775417\pi\)
\(858\) 0 0
\(859\) −9.70998 −0.331300 −0.165650 0.986185i \(-0.552972\pi\)
−0.165650 + 0.986185i \(0.552972\pi\)
\(860\) 0 0
\(861\) 9.72429 0.331403
\(862\) 0 0
\(863\) −22.7865 −0.775662 −0.387831 0.921731i \(-0.626776\pi\)
−0.387831 + 0.921731i \(0.626776\pi\)
\(864\) 0 0
\(865\) −16.5145 −0.561511
\(866\) 0 0
\(867\) −4.99528 −0.169649
\(868\) 0 0
\(869\) −18.8340 −0.638901
\(870\) 0 0
\(871\) 14.6378 0.495982
\(872\) 0 0
\(873\) 13.4461 0.455082
\(874\) 0 0
\(875\) 22.6248 0.764859
\(876\) 0 0
\(877\) 18.2439 0.616051 0.308026 0.951378i \(-0.400332\pi\)
0.308026 + 0.951378i \(0.400332\pi\)
\(878\) 0 0
\(879\) −23.0541 −0.777595
\(880\) 0 0
\(881\) 38.2386 1.28829 0.644145 0.764904i \(-0.277213\pi\)
0.644145 + 0.764904i \(0.277213\pi\)
\(882\) 0 0
\(883\) 23.0956 0.777228 0.388614 0.921401i \(-0.372954\pi\)
0.388614 + 0.921401i \(0.372954\pi\)
\(884\) 0 0
\(885\) 3.40169 0.114347
\(886\) 0 0
\(887\) −13.8961 −0.466584 −0.233292 0.972407i \(-0.574950\pi\)
−0.233292 + 0.972407i \(0.574950\pi\)
\(888\) 0 0
\(889\) −50.1816 −1.68304
\(890\) 0 0
\(891\) 1.47099 0.0492802
\(892\) 0 0
\(893\) −9.99505 −0.334471
\(894\) 0 0
\(895\) −1.12236 −0.0375163
\(896\) 0 0
\(897\) −6.39611 −0.213560
\(898\) 0 0
\(899\) −41.7483 −1.39238
\(900\) 0 0
\(901\) −44.5777 −1.48510
\(902\) 0 0
\(903\) −27.9231 −0.929222
\(904\) 0 0
\(905\) 6.92066 0.230051
\(906\) 0 0
\(907\) 52.7844 1.75268 0.876339 0.481694i \(-0.159978\pi\)
0.876339 + 0.481694i \(0.159978\pi\)
\(908\) 0 0
\(909\) −0.372387 −0.0123513
\(910\) 0 0
\(911\) −57.2105 −1.89547 −0.947735 0.319059i \(-0.896633\pi\)
−0.947735 + 0.319059i \(0.896633\pi\)
\(912\) 0 0
\(913\) −1.82539 −0.0604116
\(914\) 0 0
\(915\) 5.08429 0.168081
\(916\) 0 0
\(917\) 28.7953 0.950903
\(918\) 0 0
\(919\) 28.2303 0.931230 0.465615 0.884987i \(-0.345833\pi\)
0.465615 + 0.884987i \(0.345833\pi\)
\(920\) 0 0
\(921\) −20.1854 −0.665131
\(922\) 0 0
\(923\) 14.6647 0.482693
\(924\) 0 0
\(925\) 46.6788 1.53479
\(926\) 0 0
\(927\) −7.26876 −0.238738
\(928\) 0 0
\(929\) −44.0655 −1.44574 −0.722871 0.690983i \(-0.757178\pi\)
−0.722871 + 0.690983i \(0.757178\pi\)
\(930\) 0 0
\(931\) 6.54697 0.214568
\(932\) 0 0
\(933\) −18.6993 −0.612189
\(934\) 0 0
\(935\) −4.94061 −0.161575
\(936\) 0 0
\(937\) 20.3892 0.666087 0.333043 0.942912i \(-0.391924\pi\)
0.333043 + 0.942912i \(0.391924\pi\)
\(938\) 0 0
\(939\) 33.3300 1.08768
\(940\) 0 0
\(941\) 30.8213 1.00475 0.502373 0.864651i \(-0.332460\pi\)
0.502373 + 0.864651i \(0.332460\pi\)
\(942\) 0 0
\(943\) 17.4313 0.567641
\(944\) 0 0
\(945\) 2.38479 0.0775773
\(946\) 0 0
\(947\) 38.8708 1.26313 0.631566 0.775322i \(-0.282413\pi\)
0.631566 + 0.775322i \(0.282413\pi\)
\(948\) 0 0
\(949\) −7.82943 −0.254154
\(950\) 0 0
\(951\) 13.7905 0.447188
\(952\) 0 0
\(953\) −19.3760 −0.627649 −0.313824 0.949481i \(-0.601610\pi\)
−0.313824 + 0.949481i \(0.601610\pi\)
\(954\) 0 0
\(955\) 10.8264 0.350333
\(956\) 0 0
\(957\) −6.96003 −0.224986
\(958\) 0 0
\(959\) 46.5318 1.50259
\(960\) 0 0
\(961\) 46.8534 1.51140
\(962\) 0 0
\(963\) −7.75739 −0.249978
\(964\) 0 0
\(965\) −10.6880 −0.344060
\(966\) 0 0
\(967\) 24.4967 0.787761 0.393880 0.919162i \(-0.371132\pi\)
0.393880 + 0.919162i \(0.371132\pi\)
\(968\) 0 0
\(969\) −7.50910 −0.241227
\(970\) 0 0
\(971\) 14.0223 0.449996 0.224998 0.974359i \(-0.427762\pi\)
0.224998 + 0.974359i \(0.427762\pi\)
\(972\) 0 0
\(973\) −32.5186 −1.04250
\(974\) 0 0
\(975\) −4.80803 −0.153980
\(976\) 0 0
\(977\) −20.1355 −0.644191 −0.322096 0.946707i \(-0.604387\pi\)
−0.322096 + 0.946707i \(0.604387\pi\)
\(978\) 0 0
\(979\) −11.2905 −0.360847
\(980\) 0 0
\(981\) 9.49121 0.303031
\(982\) 0 0
\(983\) −36.0705 −1.15047 −0.575235 0.817988i \(-0.695089\pi\)
−0.575235 + 0.817988i \(0.695089\pi\)
\(984\) 0 0
\(985\) 9.84409 0.313659
\(986\) 0 0
\(987\) 20.7878 0.661682
\(988\) 0 0
\(989\) −50.0535 −1.59161
\(990\) 0 0
\(991\) 28.6331 0.909561 0.454780 0.890604i \(-0.349718\pi\)
0.454780 + 0.890604i \(0.349718\pi\)
\(992\) 0 0
\(993\) 7.26826 0.230651
\(994\) 0 0
\(995\) 6.77395 0.214749
\(996\) 0 0
\(997\) 19.1826 0.607518 0.303759 0.952749i \(-0.401758\pi\)
0.303759 + 0.952749i \(0.401758\pi\)
\(998\) 0 0
\(999\) 10.4028 0.329131
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 \(a_p\))