Properties

Label 8036.2.a.t.1.15
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(1.53485\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.53485 q^{3}\) \(+1.74990 q^{5}\) \(-0.644239 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.53485 q^{3}\) \(+1.74990 q^{5}\) \(-0.644239 q^{9}\) \(+1.47075 q^{11}\) \(-0.836260 q^{13}\) \(+2.68583 q^{15}\) \(+4.36833 q^{17}\) \(-0.873796 q^{19}\) \(+3.62063 q^{23}\) \(-1.93785 q^{25}\) \(-5.59336 q^{27}\) \(+5.63878 q^{29}\) \(+9.19128 q^{31}\) \(+2.25737 q^{33}\) \(+2.15332 q^{37}\) \(-1.28353 q^{39}\) \(-1.00000 q^{41}\) \(-1.50136 q^{43}\) \(-1.12735 q^{45}\) \(+8.53276 q^{47}\) \(+6.70473 q^{51}\) \(+7.12226 q^{53}\) \(+2.57366 q^{55}\) \(-1.34115 q^{57}\) \(-12.9801 q^{59}\) \(-12.0540 q^{61}\) \(-1.46337 q^{65}\) \(-1.52821 q^{67}\) \(+5.55711 q^{69}\) \(-4.82901 q^{71}\) \(-0.0120510 q^{73}\) \(-2.97431 q^{75}\) \(+2.55280 q^{79}\) \(-6.65224 q^{81}\) \(+11.5377 q^{83}\) \(+7.64414 q^{85}\) \(+8.65467 q^{87}\) \(+3.91059 q^{89}\) \(+14.1072 q^{93}\) \(-1.52906 q^{95}\) \(-13.1173 q^{97}\) \(-0.947512 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.53485 0.886145 0.443073 0.896486i \(-0.353888\pi\)
0.443073 + 0.896486i \(0.353888\pi\)
\(4\) 0 0
\(5\) 1.74990 0.782579 0.391289 0.920268i \(-0.372029\pi\)
0.391289 + 0.920268i \(0.372029\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.644239 −0.214746
\(10\) 0 0
\(11\) 1.47075 0.443447 0.221723 0.975110i \(-0.428832\pi\)
0.221723 + 0.975110i \(0.428832\pi\)
\(12\) 0 0
\(13\) −0.836260 −0.231937 −0.115968 0.993253i \(-0.536997\pi\)
−0.115968 + 0.993253i \(0.536997\pi\)
\(14\) 0 0
\(15\) 2.68583 0.693479
\(16\) 0 0
\(17\) 4.36833 1.05948 0.529738 0.848161i \(-0.322290\pi\)
0.529738 + 0.848161i \(0.322290\pi\)
\(18\) 0 0
\(19\) −0.873796 −0.200463 −0.100231 0.994964i \(-0.531958\pi\)
−0.100231 + 0.994964i \(0.531958\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.62063 0.754953 0.377476 0.926019i \(-0.376792\pi\)
0.377476 + 0.926019i \(0.376792\pi\)
\(24\) 0 0
\(25\) −1.93785 −0.387570
\(26\) 0 0
\(27\) −5.59336 −1.07644
\(28\) 0 0
\(29\) 5.63878 1.04709 0.523547 0.851997i \(-0.324608\pi\)
0.523547 + 0.851997i \(0.324608\pi\)
\(30\) 0 0
\(31\) 9.19128 1.65080 0.825401 0.564547i \(-0.190949\pi\)
0.825401 + 0.564547i \(0.190949\pi\)
\(32\) 0 0
\(33\) 2.25737 0.392958
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.15332 0.354004 0.177002 0.984210i \(-0.443360\pi\)
0.177002 + 0.984210i \(0.443360\pi\)
\(38\) 0 0
\(39\) −1.28353 −0.205530
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −1.50136 −0.228955 −0.114477 0.993426i \(-0.536519\pi\)
−0.114477 + 0.993426i \(0.536519\pi\)
\(44\) 0 0
\(45\) −1.12735 −0.168056
\(46\) 0 0
\(47\) 8.53276 1.24463 0.622315 0.782767i \(-0.286192\pi\)
0.622315 + 0.782767i \(0.286192\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 6.70473 0.938850
\(52\) 0 0
\(53\) 7.12226 0.978318 0.489159 0.872195i \(-0.337304\pi\)
0.489159 + 0.872195i \(0.337304\pi\)
\(54\) 0 0
\(55\) 2.57366 0.347032
\(56\) 0 0
\(57\) −1.34115 −0.177639
\(58\) 0 0
\(59\) −12.9801 −1.68986 −0.844930 0.534878i \(-0.820358\pi\)
−0.844930 + 0.534878i \(0.820358\pi\)
\(60\) 0 0
\(61\) −12.0540 −1.54335 −0.771675 0.636017i \(-0.780581\pi\)
−0.771675 + 0.636017i \(0.780581\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.46337 −0.181509
\(66\) 0 0
\(67\) −1.52821 −0.186701 −0.0933506 0.995633i \(-0.529758\pi\)
−0.0933506 + 0.995633i \(0.529758\pi\)
\(68\) 0 0
\(69\) 5.55711 0.668998
\(70\) 0 0
\(71\) −4.82901 −0.573098 −0.286549 0.958066i \(-0.592508\pi\)
−0.286549 + 0.958066i \(0.592508\pi\)
\(72\) 0 0
\(73\) −0.0120510 −0.00141047 −0.000705233 1.00000i \(-0.500224\pi\)
−0.000705233 1.00000i \(0.500224\pi\)
\(74\) 0 0
\(75\) −2.97431 −0.343444
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.55280 0.287212 0.143606 0.989635i \(-0.454130\pi\)
0.143606 + 0.989635i \(0.454130\pi\)
\(80\) 0 0
\(81\) −6.65224 −0.739138
\(82\) 0 0
\(83\) 11.5377 1.26643 0.633215 0.773976i \(-0.281735\pi\)
0.633215 + 0.773976i \(0.281735\pi\)
\(84\) 0 0
\(85\) 7.64414 0.829124
\(86\) 0 0
\(87\) 8.65467 0.927878
\(88\) 0 0
\(89\) 3.91059 0.414522 0.207261 0.978286i \(-0.433545\pi\)
0.207261 + 0.978286i \(0.433545\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 14.1072 1.46285
\(94\) 0 0
\(95\) −1.52906 −0.156878
\(96\) 0 0
\(97\) −13.1173 −1.33186 −0.665931 0.746014i \(-0.731965\pi\)
−0.665931 + 0.746014i \(0.731965\pi\)
\(98\) 0 0
\(99\) −0.947512 −0.0952285
\(100\) 0 0
\(101\) 15.6521 1.55744 0.778720 0.627371i \(-0.215869\pi\)
0.778720 + 0.627371i \(0.215869\pi\)
\(102\) 0 0
\(103\) 1.93280 0.190445 0.0952225 0.995456i \(-0.469644\pi\)
0.0952225 + 0.995456i \(0.469644\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.99673 0.289705 0.144852 0.989453i \(-0.453729\pi\)
0.144852 + 0.989453i \(0.453729\pi\)
\(108\) 0 0
\(109\) 4.99040 0.477994 0.238997 0.971020i \(-0.423181\pi\)
0.238997 + 0.971020i \(0.423181\pi\)
\(110\) 0 0
\(111\) 3.30502 0.313699
\(112\) 0 0
\(113\) 11.7124 1.10181 0.550905 0.834568i \(-0.314283\pi\)
0.550905 + 0.834568i \(0.314283\pi\)
\(114\) 0 0
\(115\) 6.33573 0.590810
\(116\) 0 0
\(117\) 0.538751 0.0498076
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.83691 −0.803355
\(122\) 0 0
\(123\) −1.53485 −0.138393
\(124\) 0 0
\(125\) −12.1405 −1.08588
\(126\) 0 0
\(127\) 19.8201 1.75875 0.879376 0.476128i \(-0.157960\pi\)
0.879376 + 0.476128i \(0.157960\pi\)
\(128\) 0 0
\(129\) −2.30436 −0.202887
\(130\) 0 0
\(131\) −1.67196 −0.146080 −0.0730400 0.997329i \(-0.523270\pi\)
−0.0730400 + 0.997329i \(0.523270\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −9.78781 −0.842401
\(136\) 0 0
\(137\) 8.48383 0.724823 0.362411 0.932018i \(-0.381954\pi\)
0.362411 + 0.932018i \(0.381954\pi\)
\(138\) 0 0
\(139\) −7.87576 −0.668013 −0.334006 0.942571i \(-0.608401\pi\)
−0.334006 + 0.942571i \(0.608401\pi\)
\(140\) 0 0
\(141\) 13.0965 1.10292
\(142\) 0 0
\(143\) −1.22993 −0.102852
\(144\) 0 0
\(145\) 9.86729 0.819434
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.57393 0.784327 0.392163 0.919896i \(-0.371727\pi\)
0.392163 + 0.919896i \(0.371727\pi\)
\(150\) 0 0
\(151\) −9.19441 −0.748230 −0.374115 0.927382i \(-0.622054\pi\)
−0.374115 + 0.927382i \(0.622054\pi\)
\(152\) 0 0
\(153\) −2.81425 −0.227519
\(154\) 0 0
\(155\) 16.0838 1.29188
\(156\) 0 0
\(157\) 9.21209 0.735205 0.367603 0.929983i \(-0.380179\pi\)
0.367603 + 0.929983i \(0.380179\pi\)
\(158\) 0 0
\(159\) 10.9316 0.866932
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 20.0758 1.57246 0.786229 0.617935i \(-0.212031\pi\)
0.786229 + 0.617935i \(0.212031\pi\)
\(164\) 0 0
\(165\) 3.95018 0.307521
\(166\) 0 0
\(167\) 1.62426 0.125689 0.0628445 0.998023i \(-0.479983\pi\)
0.0628445 + 0.998023i \(0.479983\pi\)
\(168\) 0 0
\(169\) −12.3007 −0.946205
\(170\) 0 0
\(171\) 0.562934 0.0430486
\(172\) 0 0
\(173\) 23.7696 1.80717 0.903586 0.428407i \(-0.140925\pi\)
0.903586 + 0.428407i \(0.140925\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −19.9224 −1.49746
\(178\) 0 0
\(179\) −23.1111 −1.72741 −0.863704 0.504000i \(-0.831861\pi\)
−0.863704 + 0.504000i \(0.831861\pi\)
\(180\) 0 0
\(181\) −0.910960 −0.0677111 −0.0338556 0.999427i \(-0.510779\pi\)
−0.0338556 + 0.999427i \(0.510779\pi\)
\(182\) 0 0
\(183\) −18.5010 −1.36763
\(184\) 0 0
\(185\) 3.76810 0.277036
\(186\) 0 0
\(187\) 6.42471 0.469821
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.21085 0.159972 0.0799858 0.996796i \(-0.474513\pi\)
0.0799858 + 0.996796i \(0.474513\pi\)
\(192\) 0 0
\(193\) −14.2409 −1.02508 −0.512540 0.858664i \(-0.671295\pi\)
−0.512540 + 0.858664i \(0.671295\pi\)
\(194\) 0 0
\(195\) −2.24605 −0.160843
\(196\) 0 0
\(197\) −6.33659 −0.451463 −0.225732 0.974190i \(-0.572477\pi\)
−0.225732 + 0.974190i \(0.572477\pi\)
\(198\) 0 0
\(199\) −7.50825 −0.532246 −0.266123 0.963939i \(-0.585743\pi\)
−0.266123 + 0.963939i \(0.585743\pi\)
\(200\) 0 0
\(201\) −2.34558 −0.165444
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.74990 −0.122218
\(206\) 0 0
\(207\) −2.33255 −0.162123
\(208\) 0 0
\(209\) −1.28513 −0.0888945
\(210\) 0 0
\(211\) 10.8136 0.744436 0.372218 0.928145i \(-0.378597\pi\)
0.372218 + 0.928145i \(0.378597\pi\)
\(212\) 0 0
\(213\) −7.41180 −0.507848
\(214\) 0 0
\(215\) −2.62723 −0.179175
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −0.0184965 −0.00124988
\(220\) 0 0
\(221\) −3.65306 −0.245732
\(222\) 0 0
\(223\) −5.08072 −0.340230 −0.170115 0.985424i \(-0.554414\pi\)
−0.170115 + 0.985424i \(0.554414\pi\)
\(224\) 0 0
\(225\) 1.24844 0.0832293
\(226\) 0 0
\(227\) 16.5185 1.09637 0.548186 0.836357i \(-0.315319\pi\)
0.548186 + 0.836357i \(0.315319\pi\)
\(228\) 0 0
\(229\) 15.0319 0.993335 0.496668 0.867941i \(-0.334557\pi\)
0.496668 + 0.867941i \(0.334557\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.6539 0.697960 0.348980 0.937130i \(-0.386528\pi\)
0.348980 + 0.937130i \(0.386528\pi\)
\(234\) 0 0
\(235\) 14.9315 0.974022
\(236\) 0 0
\(237\) 3.91816 0.254512
\(238\) 0 0
\(239\) 3.32385 0.215002 0.107501 0.994205i \(-0.465715\pi\)
0.107501 + 0.994205i \(0.465715\pi\)
\(240\) 0 0
\(241\) 4.59832 0.296204 0.148102 0.988972i \(-0.452684\pi\)
0.148102 + 0.988972i \(0.452684\pi\)
\(242\) 0 0
\(243\) 6.56989 0.421458
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.730721 0.0464947
\(248\) 0 0
\(249\) 17.7087 1.12224
\(250\) 0 0
\(251\) 24.7116 1.55978 0.779892 0.625914i \(-0.215274\pi\)
0.779892 + 0.625914i \(0.215274\pi\)
\(252\) 0 0
\(253\) 5.32502 0.334781
\(254\) 0 0
\(255\) 11.7326 0.734724
\(256\) 0 0
\(257\) 6.69307 0.417502 0.208751 0.977969i \(-0.433060\pi\)
0.208751 + 0.977969i \(0.433060\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3.63272 −0.224860
\(262\) 0 0
\(263\) −3.51374 −0.216667 −0.108333 0.994115i \(-0.534551\pi\)
−0.108333 + 0.994115i \(0.534551\pi\)
\(264\) 0 0
\(265\) 12.4632 0.765611
\(266\) 0 0
\(267\) 6.00217 0.367327
\(268\) 0 0
\(269\) 13.9825 0.852527 0.426264 0.904599i \(-0.359830\pi\)
0.426264 + 0.904599i \(0.359830\pi\)
\(270\) 0 0
\(271\) 18.9801 1.15296 0.576478 0.817113i \(-0.304427\pi\)
0.576478 + 0.817113i \(0.304427\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.85009 −0.171867
\(276\) 0 0
\(277\) −24.6215 −1.47936 −0.739682 0.672956i \(-0.765024\pi\)
−0.739682 + 0.672956i \(0.765024\pi\)
\(278\) 0 0
\(279\) −5.92138 −0.354504
\(280\) 0 0
\(281\) 23.6723 1.41217 0.706086 0.708126i \(-0.250459\pi\)
0.706086 + 0.708126i \(0.250459\pi\)
\(282\) 0 0
\(283\) 2.70659 0.160890 0.0804452 0.996759i \(-0.474366\pi\)
0.0804452 + 0.996759i \(0.474366\pi\)
\(284\) 0 0
\(285\) −2.34687 −0.139017
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.08233 0.122490
\(290\) 0 0
\(291\) −20.1331 −1.18022
\(292\) 0 0
\(293\) −16.9056 −0.987636 −0.493818 0.869565i \(-0.664399\pi\)
−0.493818 + 0.869565i \(0.664399\pi\)
\(294\) 0 0
\(295\) −22.7138 −1.32245
\(296\) 0 0
\(297\) −8.22640 −0.477344
\(298\) 0 0
\(299\) −3.02778 −0.175101
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 24.0236 1.38012
\(304\) 0 0
\(305\) −21.0932 −1.20779
\(306\) 0 0
\(307\) −22.6447 −1.29240 −0.646200 0.763168i \(-0.723643\pi\)
−0.646200 + 0.763168i \(0.723643\pi\)
\(308\) 0 0
\(309\) 2.96656 0.168762
\(310\) 0 0
\(311\) −26.2813 −1.49028 −0.745138 0.666910i \(-0.767617\pi\)
−0.745138 + 0.666910i \(0.767617\pi\)
\(312\) 0 0
\(313\) 14.2905 0.807744 0.403872 0.914815i \(-0.367664\pi\)
0.403872 + 0.914815i \(0.367664\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 15.3808 0.863872 0.431936 0.901904i \(-0.357831\pi\)
0.431936 + 0.901904i \(0.357831\pi\)
\(318\) 0 0
\(319\) 8.29321 0.464330
\(320\) 0 0
\(321\) 4.59952 0.256720
\(322\) 0 0
\(323\) −3.81703 −0.212385
\(324\) 0 0
\(325\) 1.62055 0.0898918
\(326\) 0 0
\(327\) 7.65952 0.423572
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.41289 0.407449 0.203725 0.979028i \(-0.434695\pi\)
0.203725 + 0.979028i \(0.434695\pi\)
\(332\) 0 0
\(333\) −1.38725 −0.0760211
\(334\) 0 0
\(335\) −2.67422 −0.146108
\(336\) 0 0
\(337\) −19.1830 −1.04497 −0.522484 0.852649i \(-0.674994\pi\)
−0.522484 + 0.852649i \(0.674994\pi\)
\(338\) 0 0
\(339\) 17.9768 0.976364
\(340\) 0 0
\(341\) 13.5180 0.732043
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 9.72439 0.523544
\(346\) 0 0
\(347\) 12.0308 0.645848 0.322924 0.946425i \(-0.395334\pi\)
0.322924 + 0.946425i \(0.395334\pi\)
\(348\) 0 0
\(349\) 14.4115 0.771429 0.385714 0.922618i \(-0.373955\pi\)
0.385714 + 0.922618i \(0.373955\pi\)
\(350\) 0 0
\(351\) 4.67750 0.249667
\(352\) 0 0
\(353\) 12.2429 0.651622 0.325811 0.945435i \(-0.394363\pi\)
0.325811 + 0.945435i \(0.394363\pi\)
\(354\) 0 0
\(355\) −8.45028 −0.448494
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.58537 0.242007 0.121003 0.992652i \(-0.461389\pi\)
0.121003 + 0.992652i \(0.461389\pi\)
\(360\) 0 0
\(361\) −18.2365 −0.959815
\(362\) 0 0
\(363\) −13.5633 −0.711889
\(364\) 0 0
\(365\) −0.0210881 −0.00110380
\(366\) 0 0
\(367\) −29.7496 −1.55292 −0.776459 0.630168i \(-0.782986\pi\)
−0.776459 + 0.630168i \(0.782986\pi\)
\(368\) 0 0
\(369\) 0.644239 0.0335377
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −28.6714 −1.48455 −0.742274 0.670097i \(-0.766252\pi\)
−0.742274 + 0.670097i \(0.766252\pi\)
\(374\) 0 0
\(375\) −18.6339 −0.962250
\(376\) 0 0
\(377\) −4.71548 −0.242860
\(378\) 0 0
\(379\) −12.6935 −0.652022 −0.326011 0.945366i \(-0.605705\pi\)
−0.326011 + 0.945366i \(0.605705\pi\)
\(380\) 0 0
\(381\) 30.4209 1.55851
\(382\) 0 0
\(383\) 15.7683 0.805724 0.402862 0.915261i \(-0.368015\pi\)
0.402862 + 0.915261i \(0.368015\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.967233 0.0491672
\(388\) 0 0
\(389\) −23.6678 −1.20000 −0.600002 0.799999i \(-0.704833\pi\)
−0.600002 + 0.799999i \(0.704833\pi\)
\(390\) 0 0
\(391\) 15.8161 0.799854
\(392\) 0 0
\(393\) −2.56621 −0.129448
\(394\) 0 0
\(395\) 4.46714 0.224766
\(396\) 0 0
\(397\) 25.3815 1.27386 0.636931 0.770921i \(-0.280204\pi\)
0.636931 + 0.770921i \(0.280204\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −22.3440 −1.11581 −0.557903 0.829906i \(-0.688394\pi\)
−0.557903 + 0.829906i \(0.688394\pi\)
\(402\) 0 0
\(403\) −7.68630 −0.382882
\(404\) 0 0
\(405\) −11.6408 −0.578434
\(406\) 0 0
\(407\) 3.16699 0.156982
\(408\) 0 0
\(409\) 17.5318 0.866893 0.433447 0.901179i \(-0.357297\pi\)
0.433447 + 0.901179i \(0.357297\pi\)
\(410\) 0 0
\(411\) 13.0214 0.642298
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 20.1899 0.991081
\(416\) 0 0
\(417\) −12.0881 −0.591957
\(418\) 0 0
\(419\) 12.1476 0.593448 0.296724 0.954963i \(-0.404106\pi\)
0.296724 + 0.954963i \(0.404106\pi\)
\(420\) 0 0
\(421\) −35.1116 −1.71123 −0.855617 0.517609i \(-0.826822\pi\)
−0.855617 + 0.517609i \(0.826822\pi\)
\(422\) 0 0
\(423\) −5.49714 −0.267280
\(424\) 0 0
\(425\) −8.46518 −0.410622
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.88775 −0.0911415
\(430\) 0 0
\(431\) −10.7760 −0.519063 −0.259532 0.965735i \(-0.583568\pi\)
−0.259532 + 0.965735i \(0.583568\pi\)
\(432\) 0 0
\(433\) 27.9881 1.34502 0.672511 0.740087i \(-0.265216\pi\)
0.672511 + 0.740087i \(0.265216\pi\)
\(434\) 0 0
\(435\) 15.1448 0.726138
\(436\) 0 0
\(437\) −3.16369 −0.151340
\(438\) 0 0
\(439\) 9.33745 0.445652 0.222826 0.974858i \(-0.428472\pi\)
0.222826 + 0.974858i \(0.428472\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.3580 0.682170 0.341085 0.940033i \(-0.389206\pi\)
0.341085 + 0.940033i \(0.389206\pi\)
\(444\) 0 0
\(445\) 6.84314 0.324396
\(446\) 0 0
\(447\) 14.6945 0.695027
\(448\) 0 0
\(449\) 27.7795 1.31100 0.655498 0.755197i \(-0.272459\pi\)
0.655498 + 0.755197i \(0.272459\pi\)
\(450\) 0 0
\(451\) −1.47075 −0.0692547
\(452\) 0 0
\(453\) −14.1120 −0.663041
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12.8732 −0.602182 −0.301091 0.953595i \(-0.597351\pi\)
−0.301091 + 0.953595i \(0.597351\pi\)
\(458\) 0 0
\(459\) −24.4336 −1.14046
\(460\) 0 0
\(461\) −13.0210 −0.606447 −0.303224 0.952919i \(-0.598063\pi\)
−0.303224 + 0.952919i \(0.598063\pi\)
\(462\) 0 0
\(463\) −31.6222 −1.46961 −0.734805 0.678278i \(-0.762726\pi\)
−0.734805 + 0.678278i \(0.762726\pi\)
\(464\) 0 0
\(465\) 24.6862 1.14480
\(466\) 0 0
\(467\) −25.3972 −1.17524 −0.587621 0.809136i \(-0.699935\pi\)
−0.587621 + 0.809136i \(0.699935\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 14.1392 0.651499
\(472\) 0 0
\(473\) −2.20812 −0.101529
\(474\) 0 0
\(475\) 1.69329 0.0776934
\(476\) 0 0
\(477\) −4.58844 −0.210090
\(478\) 0 0
\(479\) −38.1819 −1.74457 −0.872287 0.488994i \(-0.837364\pi\)
−0.872287 + 0.488994i \(0.837364\pi\)
\(480\) 0 0
\(481\) −1.80074 −0.0821066
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −22.9540 −1.04229
\(486\) 0 0
\(487\) −27.5359 −1.24777 −0.623886 0.781516i \(-0.714447\pi\)
−0.623886 + 0.781516i \(0.714447\pi\)
\(488\) 0 0
\(489\) 30.8133 1.39343
\(490\) 0 0
\(491\) −10.7959 −0.487211 −0.243606 0.969874i \(-0.578330\pi\)
−0.243606 + 0.969874i \(0.578330\pi\)
\(492\) 0 0
\(493\) 24.6320 1.10937
\(494\) 0 0
\(495\) −1.65805 −0.0745238
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.62488 0.162272 0.0811360 0.996703i \(-0.474145\pi\)
0.0811360 + 0.996703i \(0.474145\pi\)
\(500\) 0 0
\(501\) 2.49299 0.111379
\(502\) 0 0
\(503\) 3.23617 0.144294 0.0721469 0.997394i \(-0.477015\pi\)
0.0721469 + 0.997394i \(0.477015\pi\)
\(504\) 0 0
\(505\) 27.3896 1.21882
\(506\) 0 0
\(507\) −18.8797 −0.838475
\(508\) 0 0
\(509\) 26.9095 1.19274 0.596372 0.802708i \(-0.296608\pi\)
0.596372 + 0.802708i \(0.296608\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 4.88745 0.215786
\(514\) 0 0
\(515\) 3.38221 0.149038
\(516\) 0 0
\(517\) 12.5495 0.551927
\(518\) 0 0
\(519\) 36.4828 1.60142
\(520\) 0 0
\(521\) −14.1349 −0.619262 −0.309631 0.950857i \(-0.600206\pi\)
−0.309631 + 0.950857i \(0.600206\pi\)
\(522\) 0 0
\(523\) 10.7558 0.470318 0.235159 0.971957i \(-0.424439\pi\)
0.235159 + 0.971957i \(0.424439\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 40.1506 1.74899
\(528\) 0 0
\(529\) −9.89107 −0.430047
\(530\) 0 0
\(531\) 8.36226 0.362891
\(532\) 0 0
\(533\) 0.836260 0.0362224
\(534\) 0 0
\(535\) 5.24397 0.226717
\(536\) 0 0
\(537\) −35.4721 −1.53073
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −28.6645 −1.23238 −0.616191 0.787597i \(-0.711325\pi\)
−0.616191 + 0.787597i \(0.711325\pi\)
\(542\) 0 0
\(543\) −1.39819 −0.0600019
\(544\) 0 0
\(545\) 8.73271 0.374068
\(546\) 0 0
\(547\) −41.8343 −1.78870 −0.894352 0.447363i \(-0.852363\pi\)
−0.894352 + 0.447363i \(0.852363\pi\)
\(548\) 0 0
\(549\) 7.76563 0.331429
\(550\) 0 0
\(551\) −4.92714 −0.209903
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 5.78346 0.245494
\(556\) 0 0
\(557\) 12.8237 0.543357 0.271678 0.962388i \(-0.412421\pi\)
0.271678 + 0.962388i \(0.412421\pi\)
\(558\) 0 0
\(559\) 1.25553 0.0531031
\(560\) 0 0
\(561\) 9.86095 0.416330
\(562\) 0 0
\(563\) −38.7389 −1.63265 −0.816325 0.577593i \(-0.803992\pi\)
−0.816325 + 0.577593i \(0.803992\pi\)
\(564\) 0 0
\(565\) 20.4955 0.862254
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −25.1097 −1.05266 −0.526328 0.850282i \(-0.676431\pi\)
−0.526328 + 0.850282i \(0.676431\pi\)
\(570\) 0 0
\(571\) 2.81230 0.117691 0.0588456 0.998267i \(-0.481258\pi\)
0.0588456 + 0.998267i \(0.481258\pi\)
\(572\) 0 0
\(573\) 3.39332 0.141758
\(574\) 0 0
\(575\) −7.01623 −0.292597
\(576\) 0 0
\(577\) −1.58233 −0.0658732 −0.0329366 0.999457i \(-0.510486\pi\)
−0.0329366 + 0.999457i \(0.510486\pi\)
\(578\) 0 0
\(579\) −21.8576 −0.908369
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 10.4750 0.433832
\(584\) 0 0
\(585\) 0.942761 0.0389784
\(586\) 0 0
\(587\) 9.92623 0.409699 0.204850 0.978793i \(-0.434329\pi\)
0.204850 + 0.978793i \(0.434329\pi\)
\(588\) 0 0
\(589\) −8.03131 −0.330924
\(590\) 0 0
\(591\) −9.72571 −0.400062
\(592\) 0 0
\(593\) 1.35477 0.0556337 0.0278168 0.999613i \(-0.491144\pi\)
0.0278168 + 0.999613i \(0.491144\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −11.5240 −0.471647
\(598\) 0 0
\(599\) −24.0465 −0.982511 −0.491256 0.871015i \(-0.663462\pi\)
−0.491256 + 0.871015i \(0.663462\pi\)
\(600\) 0 0
\(601\) −14.8462 −0.605587 −0.302794 0.953056i \(-0.597919\pi\)
−0.302794 + 0.953056i \(0.597919\pi\)
\(602\) 0 0
\(603\) 0.984535 0.0400934
\(604\) 0 0
\(605\) −15.4637 −0.628689
\(606\) 0 0
\(607\) −15.7007 −0.637271 −0.318635 0.947877i \(-0.603225\pi\)
−0.318635 + 0.947877i \(0.603225\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.13561 −0.288676
\(612\) 0 0
\(613\) −26.1916 −1.05787 −0.528935 0.848662i \(-0.677408\pi\)
−0.528935 + 0.848662i \(0.677408\pi\)
\(614\) 0 0
\(615\) −2.68583 −0.108303
\(616\) 0 0
\(617\) 3.85660 0.155261 0.0776304 0.996982i \(-0.475265\pi\)
0.0776304 + 0.996982i \(0.475265\pi\)
\(618\) 0 0
\(619\) 11.6126 0.466751 0.233376 0.972387i \(-0.425023\pi\)
0.233376 + 0.972387i \(0.425023\pi\)
\(620\) 0 0
\(621\) −20.2514 −0.812663
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −11.5555 −0.462219
\(626\) 0 0
\(627\) −1.97248 −0.0787734
\(628\) 0 0
\(629\) 9.40643 0.375059
\(630\) 0 0
\(631\) −13.3241 −0.530425 −0.265212 0.964190i \(-0.585442\pi\)
−0.265212 + 0.964190i \(0.585442\pi\)
\(632\) 0 0
\(633\) 16.5972 0.659678
\(634\) 0 0
\(635\) 34.6832 1.37636
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3.11104 0.123071
\(640\) 0 0
\(641\) 30.9769 1.22352 0.611758 0.791045i \(-0.290463\pi\)
0.611758 + 0.791045i \(0.290463\pi\)
\(642\) 0 0
\(643\) −11.8317 −0.466598 −0.233299 0.972405i \(-0.574952\pi\)
−0.233299 + 0.972405i \(0.574952\pi\)
\(644\) 0 0
\(645\) −4.03240 −0.158775
\(646\) 0 0
\(647\) −45.1197 −1.77384 −0.886919 0.461924i \(-0.847159\pi\)
−0.886919 + 0.461924i \(0.847159\pi\)
\(648\) 0 0
\(649\) −19.0904 −0.749362
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.8017 0.461838 0.230919 0.972973i \(-0.425827\pi\)
0.230919 + 0.972973i \(0.425827\pi\)
\(654\) 0 0
\(655\) −2.92576 −0.114319
\(656\) 0 0
\(657\) 0.00776374 0.000302892 0
\(658\) 0 0
\(659\) −15.6377 −0.609158 −0.304579 0.952487i \(-0.598516\pi\)
−0.304579 + 0.952487i \(0.598516\pi\)
\(660\) 0 0
\(661\) 21.5749 0.839168 0.419584 0.907717i \(-0.362176\pi\)
0.419584 + 0.907717i \(0.362176\pi\)
\(662\) 0 0
\(663\) −5.60690 −0.217754
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 20.4159 0.790507
\(668\) 0 0
\(669\) −7.79814 −0.301494
\(670\) 0 0
\(671\) −17.7283 −0.684393
\(672\) 0 0
\(673\) 37.3954 1.44149 0.720743 0.693202i \(-0.243801\pi\)
0.720743 + 0.693202i \(0.243801\pi\)
\(674\) 0 0
\(675\) 10.8391 0.417197
\(676\) 0 0
\(677\) 21.3496 0.820532 0.410266 0.911966i \(-0.365436\pi\)
0.410266 + 0.911966i \(0.365436\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 25.3534 0.971545
\(682\) 0 0
\(683\) −25.4024 −0.971998 −0.485999 0.873959i \(-0.661544\pi\)
−0.485999 + 0.873959i \(0.661544\pi\)
\(684\) 0 0
\(685\) 14.8459 0.567231
\(686\) 0 0
\(687\) 23.0717 0.880239
\(688\) 0 0
\(689\) −5.95606 −0.226908
\(690\) 0 0
\(691\) 18.1327 0.689802 0.344901 0.938639i \(-0.387913\pi\)
0.344901 + 0.938639i \(0.387913\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −13.7818 −0.522773
\(696\) 0 0
\(697\) −4.36833 −0.165462
\(698\) 0 0
\(699\) 16.3521 0.618494
\(700\) 0 0
\(701\) −20.3965 −0.770364 −0.385182 0.922841i \(-0.625861\pi\)
−0.385182 + 0.922841i \(0.625861\pi\)
\(702\) 0 0
\(703\) −1.88157 −0.0709646
\(704\) 0 0
\(705\) 22.9176 0.863125
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 14.6785 0.551264 0.275632 0.961263i \(-0.411113\pi\)
0.275632 + 0.961263i \(0.411113\pi\)
\(710\) 0 0
\(711\) −1.64461 −0.0616777
\(712\) 0 0
\(713\) 33.2782 1.24628
\(714\) 0 0
\(715\) −2.15225 −0.0804895
\(716\) 0 0
\(717\) 5.10161 0.190523
\(718\) 0 0
\(719\) 38.3806 1.43135 0.715677 0.698431i \(-0.246118\pi\)
0.715677 + 0.698431i \(0.246118\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 7.05772 0.262480
\(724\) 0 0
\(725\) −10.9271 −0.405823
\(726\) 0 0
\(727\) 11.6526 0.432172 0.216086 0.976374i \(-0.430671\pi\)
0.216086 + 0.976374i \(0.430671\pi\)
\(728\) 0 0
\(729\) 30.0405 1.11261
\(730\) 0 0
\(731\) −6.55843 −0.242572
\(732\) 0 0
\(733\) −9.35519 −0.345542 −0.172771 0.984962i \(-0.555272\pi\)
−0.172771 + 0.984962i \(0.555272\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.24762 −0.0827920
\(738\) 0 0
\(739\) 7.70686 0.283501 0.141751 0.989902i \(-0.454727\pi\)
0.141751 + 0.989902i \(0.454727\pi\)
\(740\) 0 0
\(741\) 1.12155 0.0412010
\(742\) 0 0
\(743\) −6.50488 −0.238641 −0.119320 0.992856i \(-0.538072\pi\)
−0.119320 + 0.992856i \(0.538072\pi\)
\(744\) 0 0
\(745\) 16.7534 0.613797
\(746\) 0 0
\(747\) −7.43305 −0.271961
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 32.2720 1.17762 0.588811 0.808270i \(-0.299596\pi\)
0.588811 + 0.808270i \(0.299596\pi\)
\(752\) 0 0
\(753\) 37.9286 1.38220
\(754\) 0 0
\(755\) −16.0893 −0.585549
\(756\) 0 0
\(757\) 13.6668 0.496730 0.248365 0.968667i \(-0.420107\pi\)
0.248365 + 0.968667i \(0.420107\pi\)
\(758\) 0 0
\(759\) 8.17310 0.296665
\(760\) 0 0
\(761\) −13.7686 −0.499113 −0.249556 0.968360i \(-0.580285\pi\)
−0.249556 + 0.968360i \(0.580285\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −4.92465 −0.178051
\(766\) 0 0
\(767\) 10.8547 0.391941
\(768\) 0 0
\(769\) −27.2814 −0.983793 −0.491897 0.870654i \(-0.663696\pi\)
−0.491897 + 0.870654i \(0.663696\pi\)
\(770\) 0 0
\(771\) 10.2728 0.369968
\(772\) 0 0
\(773\) −10.5768 −0.380421 −0.190210 0.981743i \(-0.560917\pi\)
−0.190210 + 0.981743i \(0.560917\pi\)
\(774\) 0 0
\(775\) −17.8113 −0.639802
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.873796 0.0313070
\(780\) 0 0
\(781\) −7.10224 −0.254138
\(782\) 0 0
\(783\) −31.5397 −1.12714
\(784\) 0 0
\(785\) 16.1202 0.575356
\(786\) 0 0
\(787\) 53.0929 1.89256 0.946280 0.323349i \(-0.104809\pi\)
0.946280 + 0.323349i \(0.104809\pi\)
\(788\) 0 0
\(789\) −5.39307 −0.191998
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 10.0802 0.357960
\(794\) 0 0
\(795\) 19.1292 0.678443
\(796\) 0 0
\(797\) 20.6355 0.730946 0.365473 0.930822i \(-0.380907\pi\)
0.365473 + 0.930822i \(0.380907\pi\)
\(798\) 0 0
\(799\) 37.2739 1.31866
\(800\) 0 0
\(801\) −2.51936 −0.0890171
\(802\) 0 0
\(803\) −0.0177240 −0.000625466 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 21.4610 0.755463
\(808\) 0 0
\(809\) −12.5891 −0.442609 −0.221304 0.975205i \(-0.571031\pi\)
−0.221304 + 0.975205i \(0.571031\pi\)
\(810\) 0 0
\(811\) −3.08769 −0.108423 −0.0542117 0.998529i \(-0.517265\pi\)
−0.0542117 + 0.998529i \(0.517265\pi\)
\(812\) 0 0
\(813\) 29.1315 1.02169
\(814\) 0 0
\(815\) 35.1306 1.23057
\(816\) 0 0
\(817\) 1.31188 0.0458969
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 11.0668 0.386235 0.193117 0.981176i \(-0.438140\pi\)
0.193117 + 0.981176i \(0.438140\pi\)
\(822\) 0 0
\(823\) 11.4780 0.400100 0.200050 0.979786i \(-0.435890\pi\)
0.200050 + 0.979786i \(0.435890\pi\)
\(824\) 0 0
\(825\) −4.37445 −0.152299
\(826\) 0 0
\(827\) −37.8562 −1.31639 −0.658195 0.752848i \(-0.728680\pi\)
−0.658195 + 0.752848i \(0.728680\pi\)
\(828\) 0 0
\(829\) −4.82053 −0.167424 −0.0837120 0.996490i \(-0.526678\pi\)
−0.0837120 + 0.996490i \(0.526678\pi\)
\(830\) 0 0
\(831\) −37.7903 −1.31093
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 2.84229 0.0983616
\(836\) 0 0
\(837\) −51.4101 −1.77699
\(838\) 0 0
\(839\) −12.4951 −0.431379 −0.215690 0.976462i \(-0.569200\pi\)
−0.215690 + 0.976462i \(0.569200\pi\)
\(840\) 0 0
\(841\) 2.79579 0.0964065
\(842\) 0 0
\(843\) 36.3334 1.25139
\(844\) 0 0
\(845\) −21.5249 −0.740480
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 4.15421 0.142572
\(850\) 0 0
\(851\) 7.79637 0.267256
\(852\) 0 0
\(853\) 40.7247 1.39439 0.697194 0.716882i \(-0.254432\pi\)
0.697194 + 0.716882i \(0.254432\pi\)
\(854\) 0 0
\(855\) 0.985077 0.0336889
\(856\) 0 0
\(857\) −10.9278 −0.373287 −0.186643 0.982428i \(-0.559761\pi\)
−0.186643 + 0.982428i \(0.559761\pi\)
\(858\) 0 0
\(859\) −24.9462 −0.851154 −0.425577 0.904922i \(-0.639929\pi\)
−0.425577 + 0.904922i \(0.639929\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −38.5081 −1.31083 −0.655416 0.755268i \(-0.727507\pi\)
−0.655416 + 0.755268i \(0.727507\pi\)
\(864\) 0 0
\(865\) 41.5945 1.41425
\(866\) 0 0
\(867\) 3.19606 0.108544
\(868\) 0 0
\(869\) 3.75451 0.127363
\(870\) 0 0
\(871\) 1.27799 0.0433029
\(872\) 0 0
\(873\) 8.45068 0.286012
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −18.9021 −0.638278 −0.319139 0.947708i \(-0.603394\pi\)
−0.319139 + 0.947708i \(0.603394\pi\)
\(878\) 0 0
\(879\) −25.9475 −0.875189
\(880\) 0 0
\(881\) 11.7741 0.396681 0.198340 0.980133i \(-0.436445\pi\)
0.198340 + 0.980133i \(0.436445\pi\)
\(882\) 0 0
\(883\) −23.9761 −0.806860 −0.403430 0.915010i \(-0.632182\pi\)
−0.403430 + 0.915010i \(0.632182\pi\)
\(884\) 0 0
\(885\) −34.8622 −1.17188
\(886\) 0 0
\(887\) 0.850580 0.0285597 0.0142798 0.999898i \(-0.495454\pi\)
0.0142798 + 0.999898i \(0.495454\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −9.78375 −0.327768
\(892\) 0 0
\(893\) −7.45590 −0.249502
\(894\) 0 0
\(895\) −40.4422 −1.35183
\(896\) 0 0
\(897\) −4.64719 −0.155165
\(898\) 0 0
\(899\) 51.8276 1.72855
\(900\) 0 0
\(901\) 31.1124 1.03650
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.59409 −0.0529893
\(906\) 0 0
\(907\) −0.892050 −0.0296200 −0.0148100 0.999890i \(-0.504714\pi\)
−0.0148100 + 0.999890i \(0.504714\pi\)
\(908\) 0 0
\(909\) −10.0837 −0.334455
\(910\) 0 0
\(911\) 31.4136 1.04078 0.520389 0.853929i \(-0.325787\pi\)
0.520389 + 0.853929i \(0.325787\pi\)
\(912\) 0 0
\(913\) 16.9691 0.561594
\(914\) 0 0
\(915\) −32.3749 −1.07028
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −30.9838 −1.02206 −0.511031 0.859562i \(-0.670736\pi\)
−0.511031 + 0.859562i \(0.670736\pi\)
\(920\) 0 0
\(921\) −34.7562 −1.14525
\(922\) 0 0
\(923\) 4.03831 0.132923
\(924\) 0 0
\(925\) −4.17282 −0.137201
\(926\) 0 0
\(927\) −1.24519 −0.0408973
\(928\) 0 0
\(929\) 7.29045 0.239192 0.119596 0.992823i \(-0.461840\pi\)
0.119596 + 0.992823i \(0.461840\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −40.3378 −1.32060
\(934\) 0 0
\(935\) 11.2426 0.367672
\(936\) 0 0
\(937\) 39.2582 1.28251 0.641255 0.767328i \(-0.278414\pi\)
0.641255 + 0.767328i \(0.278414\pi\)
\(938\) 0 0
\(939\) 21.9337 0.715779
\(940\) 0 0
\(941\) −39.7133 −1.29462 −0.647308 0.762229i \(-0.724105\pi\)
−0.647308 + 0.762229i \(0.724105\pi\)
\(942\) 0 0
\(943\) −3.62063 −0.117904
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 32.0389 1.04112 0.520562 0.853824i \(-0.325722\pi\)
0.520562 + 0.853824i \(0.325722\pi\)
\(948\) 0 0
\(949\) 0.0100778 0.000327139 0
\(950\) 0 0
\(951\) 23.6072 0.765516
\(952\) 0 0
\(953\) 24.7950 0.803190 0.401595 0.915817i \(-0.368456\pi\)
0.401595 + 0.915817i \(0.368456\pi\)
\(954\) 0 0
\(955\) 3.86877 0.125190
\(956\) 0 0
\(957\) 12.7288 0.411464
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 53.4796 1.72515
\(962\) 0 0
\(963\) −1.93061 −0.0622130
\(964\) 0 0
\(965\) −24.9201 −0.802205
\(966\) 0 0
\(967\) −33.1966 −1.06753 −0.533765 0.845633i \(-0.679223\pi\)
−0.533765 + 0.845633i \(0.679223\pi\)
\(968\) 0 0
\(969\) −5.85857 −0.188204
\(970\) 0 0
\(971\) −37.8578 −1.21492 −0.607458 0.794352i \(-0.707811\pi\)
−0.607458 + 0.794352i \(0.707811\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 2.48730 0.0796572
\(976\) 0 0
\(977\) −27.4977 −0.879729 −0.439864 0.898064i \(-0.644973\pi\)
−0.439864 + 0.898064i \(0.644973\pi\)
\(978\) 0 0
\(979\) 5.75149 0.183818
\(980\) 0 0
\(981\) −3.21501 −0.102647
\(982\) 0 0
\(983\) −42.9383 −1.36952 −0.684759 0.728770i \(-0.740092\pi\)
−0.684759 + 0.728770i \(0.740092\pi\)
\(984\) 0 0
\(985\) −11.0884 −0.353306
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.43586 −0.172850
\(990\) 0 0
\(991\) 8.57637 0.272437 0.136219 0.990679i \(-0.456505\pi\)
0.136219 + 0.990679i \(0.456505\pi\)
\(992\) 0 0
\(993\) 11.3777 0.361059
\(994\) 0 0
\(995\) −13.1387 −0.416524
\(996\) 0 0
\(997\) −40.4669 −1.28160 −0.640800 0.767708i \(-0.721397\pi\)
−0.640800 + 0.767708i \(0.721397\pi\)
\(998\) 0 0
\(999\) −12.0443 −0.381065
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 \(a_p\))